Inorg. Chem. 2006, 45, 529−546
Fast Magnetization Tunneling in Tetranickel(II) Single-Molecule Magnets
En-Che Yang,† Wolfgang Wernsdorfer,‡ Lev N. Zakharov,† Yoshitomo Karaki,§ Akira Yamaguchi,§
Rose M. Isidro,† Guo-Di Lu,† Samuel A. Wilson,† Arnold L. Rheingold,† Hidehiko Ishimoto,§ and
David N. Hendrickson*,†
Department of Chemistry and Biochemistry, UniVersity of California at San Diego,
La Jolla, California 92093-0358, Laboratoire Louis Néel-CNRS, 25 AVenue des Martyrs,
38042 Grenoble Cedex 9, France, and Institute of Solid State Physics, The UniVersity of Tokyo,
Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581, Japan
Received January 20, 2005
A series of Ni4 cubane complexes with the composition [Ni(hmp)(ROH)Cl]4 complexes 1−4 where R) −CH3 (complex
1), −CH2CH3 (complex 2), −CH2CH2(C4H9) (complex 3), −CH2CH2CH2(C6H11) (complex 4), hmp- is the anion of
2-hydroxymethylpyridine, t-Buhmp- is the anion of 4-tert-butyl-2-hydroxymethylpyridine, and dmb is 3,3-dimethyl1-butanol] and [Ni(hmp)(dmb)Br]4 (complex 5) and [Ni(t-Buhmp)(dmb)Cl]4 (complex 6) were prepared. All six complexes
were characterized by dc magnetic susceptibility data to be ferromagnetically coupled to give an S ) 4 ground
state with significant magnetoanisotropy (D ≈ −0.6 cm-1). Magnetization hysteresis measurements carried out on
single crystals of complexes 1−6 establish the single-molecule magnet (SMM) behavior of these complexes. The
exchange bias observed in the magnetization hysteresis loops of complexes 1 and 2 is dramatically decreased to
zero in complex 3, where the bulky dmb ligand is employed. Fast tunneling of magnetization is observed for the
high-symmetry (S4 site symmetry) Ni4 complexes in the crystal of complex 3, and the tunneling rate can even be
enhanced by destroying the S4 site symmetry, as is the case for complex 4, where there are two crystallographically
different Ni4 molecules, one with C2 and the other with C1 site symmetry. Magnetic ordering temperatures due to
intermolecular dipolar and magnetic exchange interactions were determined by means of very low-temperature ac
susceptibility measurements; complex 1 orders at 1100 mK, complex 3 at 290 mK, complex 4 at ∼80 mK, and
complex 6 at <50 mK. This confirms that bulkier ligands correspond to more isolated molecules, and therefore,
magnetic ordering occurs at lower temperatures for those complexes with the bulkiest ligands.
Introduction
There is a growing interest in single-molecule magnets
(SMMs), molecules that function as nanomagnets.1-4 The
three requirements for a molecule to be an SMM are (1)
a high-spin S ground state, (2) appreciable negative magnetoanisotropy, and (3) a weak tunnel splitting that leads
* To whom correspondence should be addressed. Fax: 1-858-534-5383.
E-mail: dhendrickson@ucsd.edu.
† University of California at San Diego.
‡ Laboratoire Louis Néel-CNRS.
§ The University of Tokyo.
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10.1021/ic050093r CCC: $33.50
Published on Web 12/16/2005
© 2006 American Chemical Society
to quantum tunneling of the direction of magnetization.
Because all of the molecules in a crystal of an SMM have
the same size, spin, shape, and magnetoanisotropy, it has
been possible for the first time to characterize the quantum
effects associated with the magnetization dynamics of nanomagnets. The quantum effects that have been studied for
SMMs include tunneling of the direction of magnetization,5,6 quantum phase interference,7,8 and spin parity
effects.9-11
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Inorganic Chemistry, Vol. 45, No. 2, 2006
529
Yang et al.
Many different directions are being pursued in the study
of SMMs, including attaching SMMs to surfaces.12-14 SMMs
that have the largest spin ground state are one focus. In 2000,
Goodwin et al.15,16 reported an Fe19 SMM with S ) 33/2
and axial zero-field splitting of D ) -0.56 K that exhibits
magnetization hysteresis at temperatures below 1 K. Two
years later, Andres et al.17 reported a Ni12 complex that is
an SMM with S ) 12 and D ) -0.067 K that shows
magnetization hysteresis below 0.40 K. A [Mn18]2+ SMM
with S ) 13 and D ) -0.13 cm-1 was also reported in 2002
by Brechin et al.18 Finally, in 2004, Murugesu et al.19 reported
an SMM with the highest spin of S ) 51/2. This S ) 51/2
complex has a Mn25 composition with D ) -0.032 K, which
gives an upper limit to the magnetization relaxation barrier
of (S2 - 1/4)|D| ) 21 K. Magnetization hysteresis was
observed for a single crystal below ∼0.6 K. Increasing the
molecular size is another goal in the research on SMMs.
However, it has been found that simply increasing the
number of metal ions in a given molecule does not lead to
an increase in S. For example, a Mn30 SMM has been
reported to have only S ) 5 in the ground state (D ) -0.73
K) with a blocking temperature of ∼1.4 K.20 The largest
SMM was recently reported as a 4-nm-diameter torus-shaped
Mn84 SMM.21 Magnetic susceptibility studies down to 0.04
K indicate that the ground state has S ) 6, and magnetization
hysteresis was observed below 1.5 K. Below 0.2 K, the rate
of magnetization relaxation is temperature-independent for
this Mn84 SMM, which clearly establishes the presence of
quantum tunneling of magnetization (QTM) in this large
SMM.
Another direction in SMM research involves detailed
studies of the mechanism of magnetization tunneling. It has
been found that Kramers degeneracy affects the tunnel
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530 Inorganic Chemistry, Vol. 45, No. 2, 2006
splitting in half-integer-spin SMMs such as the S ) 9/2 Mn4
cubane complexes.10 The small internal magnetic field
associated with nuclear spins was also found to have an
appreciable effect.10,22,23 Very recently, the nature of the
transverse interactions responsible for QTM in the first SMM,
[Mn12O12(O2CCH3)16(H2O)4]‚2(CH3CO2H)‚4(H2O), called
Mn12-Ac, has been established.24-26 The site symmetry for
the Mn12 SMM in a crystal of Mn12-Ac is S4, and for 10
years, the origin of QTM in this complex was an open
question. Although Mn12-Ac has an apparent high symmetry, QTM does not reflect this symmetry, which leads to
selection rules in QTM that are not observed. QTM was
established by detailed high-field electron paramagnetic
resonance (HFEPR) spectroscopy and micro-Hall magnetometry to be due to discrete solvate molecule disorder in
the crystal. The water and acetic acid solvate molecules are
disordered and provide for Mn12 molecules with different
environments, so-called microenvironments.
In other studies of the mechanism of QTM in SMMs, it
has been found that intermolecular magnetic exchange
interactions are important.27-29 Detailed magnetization data
were presented for [Mn4O3Cl4(O2CEt)3(py)3]2 (py is pyridine), a supramolecular dimer of two S ) 9/2 Mn4 SMMs
held together in a head-to-head fashion by a Cl‚‚‚Cl contact
and six weak C-H‚‚‚Cl hydrogen bonds. These intermolecular contacts result in an antiferromagnetic exchange
interaction (J ) -0.05 K) between the two S ) 9/2 Mn4
molecules. This interaction leads to an “exchange bias” in
the magnetic field at which QTM occurs. When one S ) 9/2
complex is undergoing a QTM event, flipping its magnetization vector from “spin up” to “spin down”, it does so under
the influence of the weak antiferromagnetic interaction with
its neighboring molecule.
The above observations about the effects of intermolecular
magnetic exchange interactions upon QTM led us to prepare
a series of SMMs where we could use chemistry to modify
the intermolecular interactions. A series of SMMs was sought
where the ground-state spin S was not too large and would
facilitate the application of HFEPR to determine the spin
Hamiltonian parameters characterizing SMMs. Preliminary
data have been reported30 for a few complexes of the
composition [Ni(hmp)(ROH)X]4, where hmp- is the anion
(22) Wernsdorfer, W.; Sessoli, R.; Gatteschi, D. Europhys. Lett. 1999, 47
(2), 254-259.
(23) Wernsdorfer, W.; Caneschi, A.; Sessoli, R.; Gatteschi, D.; Cornia, A.;
Villar, V.; Paulsen, C. Phys. ReV. Lett. 2000, 84 (13), 2965-2968.
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Rheingold, A. L.; Hendrickson, D. N.; Christou, G. Phys. ReV. B 2004,
69 (2), 020411(R). (b) Hill, S.; Macagnano, S.; Park, K.; Achey, R.
M.; North, J. M.; Dalal, N. S. Phys. ReV. B 2002, 65, 224410. (c)
Park, K.; Novotny, M. A.; Dalal, N. S.; Hill, S.; Rikvold, P. A. Phys.
ReV. B 2001, 65, 014426.
(25) Amigo, R.; del Barco, E.; Casas, L.; Molins, E.; Tejada, J.; Rutel, I.
B.; Mommouton, B.; Dalal, N.; Brooks, J. Phys. ReV. B 2002, 65 (17),
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(27) Wernsdorfer, W.; Ohm, T.; Sangregorio, C.; Sessoli, R.; Gatteschi,
D.; Paulsen, C. Physica B 2000, 284, 1229-1230.
(28) Wernsdorfer, W.; Bhaduri, S.; Tiron, R.; Hendrickson, D. N.; Christou,
G. Phys. ReV. Lett. 2002, 89 (19), 197201.
(29) Wernsdorfer, W.; Allaga-Alcalde, N.; Hendrickson, D. N.; Christou,
G. Nature 2002, 416 (6879), 406-409.
Tunneling in Ni4 Single-Molecule Magnets
of 2-hydroxymethylpyridine, R is some alkyl substituent, and
X- is either Cl- or Br-. In this article, we report on an
extensive series of these Ni4 SMMs, where the R substituent
and halide ligand are varied to modulate weak intermolecular
magnetic exchange interactions. Within each NiII4 molecule,
there are relatively strong ferromagnetic interactions between
neighboring NiII ions, giving an S ) 4 ground state. Several
goals have been set in our studies of these S ) 4 tetranickel
SMMs. First, it is interesting to see how changes in the R
substituent or a tert-butyl group added to the hmp- ligand
modulate intermolecular magnetic exchange interactions and
how this is manifested in the magnetization vs magnetic field
hysteresis loops for these SMMs. Second, the rate of groundstate QTM is relatively high in these Ni4 SMMs, and it is
important to understand the origin of the fast QTM. A longerrange goal is to study the decoherence rate of QTM in these
Ni4 SMMs.31 The preparation, X-ray structures, magnetization hysteresis, and dc and ac magnetization data are reported
in this paper for six Ni4 SMMs. Very low-temperature (from
∼50 mK to ∼1.5 K) ac/dc magnetization data were obtained
to characterize the magnetic ordering in these Ni4 SMMs.
In later articles, HFEPR data will be analyzed to characterize
magnetization reversal in individual molecules and spin
Hamiltonian parameters for an analogous Zn3Ni complex
crystal and for the crystals of nondoped Ni4 SMMs.
Experimental Section
Synthesis. All manipulations were performed under aerobic
conditions. The ligand 4-tert-butyl-2-hydroxymethylpyridine (tBuhmpH) was synthesized as reported in the literature.32
[Ni(hmp)(MeOH)Cl]4 (1). A mixture of NiCl2‚4H2O (4.75 g,
20 mmol), 2-hydroxymethylpyridine (hmpH) (2.18 g, 20 mmol),
and NaOMe (1.08 g, 20 mmol) in 100 mL of MeOH was refluxed
for 30 min. The resulting solution was filtered when it was still
hot. Green crystals suitable for X-ray analysis were then collected
after the solution cooled; the yield was 20%. Anal. Calcd (found)
for Ni4C28N4H42O9Cl4: C, 35.4 (35.4); H, 4.46 (4.37); N, 5.90
(5.80). Selected IR data (KBr, cm-1): 3340 (br, s), 2906 (w), 2841
(m), 1605 (s), 1480 (s), 1442 (s), 1360 (m), 1284 (s), 1219 (w),
1153 (m), 1071 (s), 821 (w), 761 (m), 722 (m), 646 (m).
[Ni(hmp)(EtOH)Cl]4 (2). A mixture of NiCl2‚4H2O (4.75 g, 20
mmol), 2-hydroxymethylpyridine (hmpH) (2.18 g, 20 mmol), and
NaOEt (1.36 g, 20 mmol) in 100 mL of EtOH was refluxed for 30
min. The resulting solution was filtered when it is still hot. Green
crystals suitable for X-ray analysis were then obtained after the
solution cooled; the yield was 30%. Anal. Calcd (found) for
Ni4C32N4H50O9Cl4: C, 38.2 (38.3); H, 5.01 (4.71); N, 5.57 (5.56).
Selected IR data (KBr, cm-1): 3337 (br, s), 2907 (w), 2842 (m),
1605 (s), 1480 (s), 1442 (s), 1366 (m), 1284 (s), 1219 (w), 1153
(m), 1071 (s), 815 (w), 761 (m), 727 (m), 646 (m).
[Ni(hmp)(dmb)Cl]4 (3). Complex 1 (3.9 g) was dissolved in a
solution of 50 g of 3,3-dimethyl-1-butanol (dmb) and 60 mL of
methylenechloride. After filtration, the solution was allowed to
evaporate slowly. Green-colored crystals suitable for X-ray structure
(30) Yang, E. C.; Wernsdorfer, W.; Hill, S.; Edwards, R. S.; Nakano, M.;
Maccagnano, S.; Zakharov, L. N.; Rheingold, A. L.; Christou, G.;
Hendrickson, D. N. Polyhedron 2003, 22 (14-17), 1727-1733.
(31) del Barco, E.; Kent, A. D.; Yang, E. C.; Hendrickson, D. N. Phys.
ReV. Lett. 2004, 93 (15), 157202/1-157202/4.
(32) Kuhler, T. C.; Swanson, M.; Shcherbuchin, V.; Larsson, H.; Mellgard,
B.; Sjostrom, J. E. J. Med. Chem. 1998, 41 (11), 1777-1788.
analysis were obtained; the yield was 80%. Anal. Calcd (found)
for Ni4C48N4H80O8Cl4: C, 47.5 (47.1); H, 6.65 (6.10); N, 4.62
(4.59). Selected IR data (KBr, cm-1): 3212 (s), 2956 (s), 2902 (s),
1606 (s), 1567 (s), 1480 (s), 1442 (s), 1398 (m), 1366 (s), 1284
(s), 1246 (m), 1153 (s), 1077 (s), 1044 (s), 995 (m), 968 (w), 815
(w), 750 (s), 729 (s), 646 (s).
[Ni(hmp)(chp)Cl]4 (4). Complex 1 (2.5 g) was dissolved in a
solution of 50 g of 3-cyclohexyl-1-propanol (chp) and 40 mL of
methylenechloride. After filtration, the solution was allowed to
evaporate slowly. Green-colored crystals suitable for X-ray structural analysis were obtained; the yield was 50%. Anal. Calcd (found)
for Ni4C60N4H96O8Cl4: C, 52.5 (52.65); H, 7.05 (6.64); N, 4.08
(3.89). Selected IR data (KBr, cm-1): 3218 (s), 2918 (s), 2842 (s),
1605 (s), 1570 (s), 1481 (s), 1443 (s), 1399 (s), 1360 (m), 1287
(s), 1233 (w), 1151 (s), 1071 (s), 1020 (s), 957 (m), 890 (m), 820
(m), 760 (s), 725 (s), 649 (s), 502 (s).
[Ni(hmp)(dmb)Br]4 (5). Complex 5 was prepared by a procedure
similar to that employed for complex 3, except that the metal salt
NiCl2‚4H2O was replaced with NiBr2‚4H2O. The yield was 20%.
Anal. Calcd (found) for Ni4C48N4H80O8Br4: C, 41.5 (41.22); H,
5.81 (5.79); N, 4.04 (3.97). Selected IR data (KBr, cm-1): 3245
(s), 2951 (s), 2895 (s), 1605 (s), 1570 (s), 1478 (s), 1443 (s), 1395
(s), 1364 (s), 1284 (s), 1243 (m), 1154 (s), 1075 (s), 1046 (s), 998
(s), 966 (m), 919 (w), 887 (w), 820 (m), 754 (s), 731 (s), 649 (s),
502 (s), 464 (s).
[Ni(t-Buhmp)(dmb)Cl]4 (6). Complex 6 was prepared by a
procedure similar to that employed for complex 3, except that the
ligand hmpH was replaced by t-BuhmpH. The yield was 25%. Anal.
Calcd (found) for Ni4C48N4H80O8Br4: C, 53.5 (53.5); H, 7.86 (8.16);
N, 3.90 (3.86). Selected IR data (KBr, cm-1): 3223 (s), 2962 (s),
1615 (s), 1551 (m), 1475 (s), 1405 (s), 1364 (s), 1344 (m), 1294
(m), 1249 (m), 1202 (m), 1170 (w), 1084 (s), 1043 (s), 992 (m),
894 (m), 836 (m), 728 (m), 677 (m), 604 (m), 544 (w), 518 (m).
X-ray Crystallography. Diffraction data were collected at low
temperatures with Bruker Smart Apex CCD (1-4) and Bruker P4/
CCC (5,6) diffractometers equipped with Mo KR radiation (λ )
0.71073 Å). Absorption corrections were applied by SADABS for
all data. The structures were solved by direct methods and refined
on F2 (SHELXTL, version 6.10, Bruker AXS, Inc., Madison, WI,
2000) by a full-matrix least-squares procedure. All non-hydrogen
atoms were refined anisotropically, except for the C atoms of
disordered CH2 groups in ROH ligands (4), which were refined
isotropically. All H atoms in 3 and 5 and H atoms at O atoms in
the ROH groups in 1 and 6 involved in the hydrogen bonds were
found on the residual density and refined with isotropic thermal
parameters. Other H atoms in 1 and 6 and all H atoms in 2 and 4
were treated in calculated idealized positions. The H atoms of
disordered CH2 groups in 4 were not taken into consideration. The
CH2 groups in 4 and some methyl groups in 6 are disordered over
two positions. In addition to the Ni4 molecules, solvent water
molecules were found in crystal structures of 1 (disordered over
two positions around a center of symmetry) and 2 (on a 2-fold
axis). Peaks on the F maps corresponding to these water molecules
in 1 and 2 are not strong and indicate that these water positions in
the crystal structures are not fully occupied. The Flack parameters
for noncentrosymmetric structures are 0.08(3) (1), 0.00(2) (2), and
0.06(2) (6). Crystallographic data and details of the X-ray study
are reported in Tables 1-3. All software and sources of scattering
factors are contained in the SHELXTL (6.10) program package
(G. Sheldrick, Bruker XRD, Madison, WI).
Other Physical Property Measurements. Orientated singlecrystal magnetization hysteresis loops were measured by employing
a micro-SQUID array that has been described elsewhere.33 A single
Inorganic Chemistry, Vol. 45, No. 2, 2006
531
Yang et al.
Table 1. Crystallographic Data for Complexes 1 and 2
Table 3. Crystallographic Data for Complexes 5 and 6
complex
1
2
complex
5
6
formula
fw, g/mol
temperature, K
space group
a, Å
b, Å
c, Å
R, deg
β, deg
γ, deg
volume, Å3
Z, Z′
F(000)
density (calcd) g/cm3
absorption coefficient, mm-1
absorption correction
transmission max/min
reflns, measured
reflns, independent
reflns, observed
data/restraints/params
goodness-of-fit on F2
R indices [I > 2σ(I)]a,b
C28H42Cl4N4Ni4O9
955.30
173(2)
I4h2d
16.1421(6)
16.1421(6)
29.4689(14)
90
90
90
7678.6(5)
8, 0.5
3920
1.653
2.262
SADABS
0.714/0.660
17832
4394 (Rint ) 0.0451)
3949
4394/1/231
1.120
R ) 0.0521
R(ωF2) ) 0.1055
R ) 0.0626
R(ωF2) ) 0.1124
C32H50Cl4N4Ni4O9
1011.40
150(2)
I4h2d
16.6017(5)
16.6017(5)
29.3656(17)
90
90
90
8093.6(6)
8, 0.5
4176
1.660
2.150
SADABS
0.739/0.565
25077
4845 (Rint ) 0.0330)
4668
4845/2/231
1.107
R ) 0.0382
R(ωF2) ) 0.1049
R ) 0.0400
R(ωF2) ) 0.1069
formula
fw, g/mol
temperature, K
space group
a, Å
b, Å
c, Å
R, deg
β, deg
γ, deg
volume, Å3
Z, Z′
F(000)
density (calcd), g/cm3
absorption coefficient, mm-1
absorption correction
transmission max/min
reflns, measured
reflns, independent
reflns, observed
data/restraints/params
goodness-of-fit on F2
R indices [I > 2σ(I)]a,b
C48H80Brl4N4Ni4O8
1395.64
213(2)
I41/a
12.8739(3)
12.8739(3)
36.3672(19)
90
90
90
6027.4(4)
4, 0.25
2848
1.538
3.930
SADABS
1.000/0.729
23208
3648 (Rint ) 0.0280)
2966
3648/0/234
1.027
R ) 0.0256
R(ωF2) ) 0.0646
R ) 0.0358
R(ωF2) ) 0.0686
C64H112Cl4N4Ni4O8
1442.22
213(2)
I4h2d
13.4080(4)
13.4080(4)
42.329(3)
90
90
90
7609.7(6)
4, 0.25
3072
1.259
1.164
SADABS
1.000/0.785
27031
4469 (Rint ) 0.0347)
3918
4469/18/183
1.148
R ) 0.0506
R(ωF2) ) 0.1343
R ) 0.0575
R(ωF2) ) 0.1395
R indices (all data)a,b
a R ) ∑||F | - |F ||/∑|F |. b R(ωF2) ) {∑[ω(F 2 - F 2)2]/∑[ω(F 2)2]}1/2;
o
c
o
c
o
o
ω ) 1/[σ2(Fo2) + (aP)2 + bP], where P ) [2Fc2 + max(Fo,0)]/3.
Table 2. Crystallographic Data for Complexes 3 and 4
complex
3
4
formula
fw, g/mol
temperature, K
space group
a, Å
b, Å
c, Å
R, deg
β, deg
γ, deg
volume, Å3
Z, Z′
F(000)
density (calcd), g/cm3
absorption coefficient, mm-1
absorption correction
transmission max/min
reflns, measured
reflns, independent
reflns, observed
data/restraints/params
goodness-of-fit on F2
R indices [I > 2σ(I)]a,b
C48H80Cl4N4Ni4O8
1217.80
173(2)
I41/a
12.8389(3)
12.8389(3)
35.047(2)
90
90
90
5777.1(4)
4, 0.25
2560
1.400
1.519
SADABS
1.000/0.827
18178
3323 (Rint ) 0.0310)
3043
3323/0/234
1.268
R ) 0.0329
R(ωF2) ) 0.0794
R ) 0.0370
R(ωF2) ) 0.0809
C60H96Cl4N4Ni4O8
1378.05
150(2)
C2/c
25.2519(16)
20.2768(13)
40.811(3)
90
106.9140(10)
90
19993(2)
12, 1.5
8736
1.373
1.325
SADABS
1.000/0.863
61994
22832 (Rint ) 0.0335)
16942
22832/0/1074
1.002
R ) 0.0539
R(ωF2) ) 0.1279
R ) 0.0773
R(ωF2) ) 0.1405
R indices (all data)a,b
a R ) ∑||F | - |F ||/∑|F |. b R(ωF2) ) {∑[ω(F 2 - F 2)2]/∑[ω(F 2)2]}1/2;
o
c
o
c
o
o
ω ) 1/[σ2(Fo2) + (aP)2 + bP], where P ) [2Fc2 + max(Fo,0)]/3.
crystal was placed onto the array, and the external magnetic field
was oriented to be parallel to the crystal easy axis.
Results and Discussion
Strategy. The goal of this work was to vary the electronic
insulation between the NiII4 complexes in the crystals of [Ni(hmp)(ROH)X]4 (X-) Cl- or Br-) in order to change the
(33) Wernsdorfer, W. AdV. Chem. Phys. 2001, 118, 99-190.
532 Inorganic Chemistry, Vol. 45, No. 2, 2006
R indices (all data)a,b
a R ) ∑||F | - |F ||/∑|F |. b R(ωF2) ) {∑[ω(F 2 - F 2)2]/∑[ω(F 2)2]}1/2;
o
c
o
c
o
o
ω ) 1/[σ2(Fo2) + (aP)2 + bP], where P ) [2Fc2 + max(Fo,0)]/3
magnitude of the weak intermolecular magnetic exchange
interactions. It was found that this could be achieved by
dissolving the parent MeOH complex 1 (R ) CH3) in a
solution of dichloromethane/ROH. After slow evaporation
of this solution, crystalline samples of the complexes 2
(EtOH), 3 (3,3-dimethyl-1-butanol), and 4 (3-cyclohexyl-1propanol) were isolated. The bromide complex 5 and the
tert-butyl-substituted hmp- complex 6 were also prepared
according to a similar procedure. In the series of complexes
1-3, the tert-butyl substituent on the alcohol ligand should
provide the greatest insulation between complexes. In
complex 6, there are tert-butyl substituents on both the
alcohol and the hmp- ligand, and this should provide the
maximum shielding in all six complexes.
Because the results of this article involve complicated
physical data, it is important to discuss the order of
presentation of the data at the outset. Magnetization hysteresis
data definitively establish that the six Ni4 complexes
presented in this paper are single-molecule magnets (SMMs).
The major goal in this work was to investigate how very
weak intermolecular magnetic exchange interactions between
Ni4 complexes affect the magnetization tunneling in individual Ni4 complexes. The order of presentation of this paper
is as follows: First, we describe the X-ray structures of the
six Ni4 complexes with an eye toward possible pathways
that propagate intermolecular magnetic exchange interactions.
Second, we present detailed magnetization versus magnetic
field data for single crystals that definitively establish these
six Ni4 complexes as SMMs. Third, we present dc magnetic
susceptibility used to evaluate the ground-state spin S and
axial zero-field splitting (DŜz2) for the six complexes. Fourth,
we present variable-temperature ac magnetic susceptibility
data. These Ni4 SMMs do not exhibit frequency-dependent
Tunneling in Ni4 Single-Molecule Magnets
out-of-phase ac signals as seen for many other SMMs. The
in-phase ac signal disappears, and an out-of-phase ac signal
is observed. The kinetics sensed by these ac signals is not
simply due to an isolated Ni4 SMM. The Ni4 complexes do
not magnetically order, as the Ni4 complexes continue to
exhibit magnetization tunneling at temperatures below the
temperatures at which the ac signals change. The in-phase
ac signal disappears at low temperatures because the same
numbers of Ni4 complexes always tunnel forward and
backward.
X-ray Structures of Complexes 1 and 2. The MeOH (1)
and EtOH (2) complexes are isostructural and crystallize in
the I4h2d space group. Table 1 gives the details of the
crystallography for these two complexes. All six of the
complexes with the composition [Ni(hmp)(ROH)X]4 have a
distorted metal-oxide cubane core with four Ni(II) ions and
four oxygen atoms of the four hmp- ligands occupying
alternating corners. Each Ni(II) ion is chelated by an hmpligand and is also coordinated by a halide ion, an oxygen
atom from the alcohol (ROH) ligand, and three oxygen atoms
from three other hmp- ligands. Thus, each Ni(II) ion is sixcoordinate, and except for complex 4, all Ni4 molecules have
S4 site symmetry.
Both complexes 1 and 2 contain two symmetrically
independent [Ni(hmp)(ROH)Cl]4 complexes: one in a general position and the other on an inversion axis. The
differences in the bond distances and angles for the two
different Ni4 complexes in both 1 and 2 are relatively small
(Table 4). It should be noted that the dimensions in all six
Ni4 complexes 1-6 reported in this work are quite similar.
The ethyl arms of the EtOH ligands in 2 are disordered over
two positions in a ratio of 7:2 (Figure 2 below).
In all six complexes 1-6, there are intramolecular
O-H‚‚‚Hal (Hal ) Cl, Br) hydrogen bonds. The protons
from the OH group of the alcoholic ligand in 1 and 2 interact
with the nearby chloride ligand to form relatively strong
intramolecular hydrogen bonds (Figure 1 shows complex 1;
a drawing of complex 2 is given in the Supporting Information). The distances for the two different Ni4 molecules in
complex 1 are 3.026(6) and 3.043(5) Å for O‚‚‚Cl contacts
and 2.2(1) and 2.22(7) Å for the H‚‚‚Cl contacts. The H
atoms were located by residual electron density. It has been
reported34 that a H‚‚‚Cl contact can be classified as “short”
for a distance of less than 2.52 Å, “intermediate” in the range
of 2.52-2.95 Å, and “long” in the range of 2.95-3.15 Å.
The intramolecular hydrogen bonds in complex 1 fall into
the short category and thus involve relatively strong intramolecular hydrogen bonds. The H atom involved in the
hydrogen bond was not found from the real F map for
complex 2, but the O‚‚‚Cl distances in 2, 3.038(3) and 3.024(3) Å, are close to those in 1 and also indicate the presence
of strong hydrogen bonds. These hydrogen bonds restrict
the freedom of the MeOH ligand from rotating about the
Ni-O bonds to some degree. The H atoms involved in the
O-H‚‚‚Cl hydrogen bonds are slightly out of the average
(34) Aullon, G.; Bellamy, D.; Brammer, L.; Bruton, E. A.; Orpen, A. G.
Chem. Commun. 1998, (6), 653-654.
Table 4. Metal-Ligand Bond Lengths (Å) and Angles (deg) in
Complexes 1 and 2
Ni(1)-O(1)
Ni(1)-O(1)#1
Ni(1)-N(1)
Ni(1)-O(1)#2
Ni(1)-O(2)
Ni(1)-Cl(1)
Ni(2)-O(3)
Ni(2)-O(3)#3
Ni(2)-N(2)
Ni(2)-O(3)#4
Ni(2)-O(4)
Ni(2)-Cl(2)
O(1)-Ni(1)-O(1)#1
O(1)-Ni(1)-N(1)
O(1)#1-Ni(1)-N(1)
O(1)-Ni(1)-O(1)#2
O(1)#1-Ni(1)-O(1)#2
N(1)-Ni(1)-O(1)#2
O(1)-Ni(1)-O(2)
O(1)#1-Ni(1)-O(2)
N(1)-Ni(1)-O(2)
O(1)#2-Ni(1)-O(2)
O(1)-Ni(1)-Cl(1)
O(1)#1-Ni(1)-Cl(1)
N(1)-Ni(1)-Cl(1)
O(1)#2-Ni(1)-Cl(1)
O(2)-Ni(1)-Cl(1)
O(3)-Ni(2)-O(3)#3
O(3)-Ni(2)-N(2)
Complex 1a
2.049(4)
O(3)#3-Ni(2)-N(2)
2.067(4)
O(3)-Ni(2)-O(3)#4
2.080(4)
O(3)#3-Ni(2)-O(3)#4
2.105(4)
N(2)-Ni(2)-O(3)#4
2.111(5)
O(3)-Ni(2)-O(4)
2.3677(17) O(3)#3-Ni(2)-O(4)
2.046(4)
N(2)-Ni(2)-O(4)
2.052(3)
O(3)#4-Ni(2)-O(4)
2.068(4)
O(3)-Ni(2)-Cl(2)
2.087(4)
O(3)#3-Ni(2)-Cl(2)
2.098(4)
N(2)-Ni(2)-Cl(2)
2.3716(16) O(3)#4-Ni(2)-Cl(2)
82.20(17) O(4)-Ni(2)-Cl(2)
79.79(17) C(12)-N(2)-Ni(2)
161.27(18) C(8)-N(2)-Ni(2)
79.69(17) C(6)-O(1)-Ni(1)
80.87(16) C(6)-O(1)-Ni(1)#5
100.82(18) Ni(1)-O(1)-Ni(1)#5
91.6(2)
C(6)-O(1)-Ni(1)#2
89.44(17) Ni(1)-O(1)-Ni(1)#2
85.97(19) Ni(1)#5-O(1)-Ni(1)#2
167.73(17) C(7)-O(2)-Ni(1)
173.87(13) C(13)-O(3)-Ni(2)
99.72(12) C(13)-O(3)-Ni(2)#6
98.72(14) Ni(2)-O(3)-Ni(2)#6
94.81(12) C(13)-O(3)-Ni(2)#4
94.23(16) Ni(2)-O(3)-Ni(2)#4
81.86(15) Ni(2)#6-O(3)-Ni(2)#4
79.64(17) C(14)-O(4)-Ni(2)
160.68(17)
80.76(15)
80.87(14)
101.51(18)
94.19(18)
86.19(16)
89.63(19)
166.64(15)
174.95(12)
99.22(11)
99.70(15)
94.51(11)
90.81(15)
128.6(4)
111.9(4)
110.4(3)
127.5(4)
98.43(17)
119.0(4)
100.00(17)
96.67(16)
132.6(10)
110.0(3)
126.5(3)
98.58(15)
120.6(3)
98.74(15)
97.25(15)
130.6(5)
Ni(1)-O(1)
Ni(1)-O(1)#1
Ni(1)-N(1)
Ni(1)-O(1)#2
Ni(1)-O(2)
Ni(1)-Cl(1)
Ni(1′)-O(1′)
Ni(1′)-O(1′)#4
Ni(1′)-N(1′)
Ni(1′)-O(1′)#5
Ni(1′)-O(2′)
Ni(1′)-Cl(1′)
O(1)-Ni(1)-O(1)#1
O(1)-Ni(1)-N(1)
O(1)#1-Ni(1)-N(1)
O(1)-Ni(1)-O(1)#2
O(1)#1-Ni(1)-O(1)#2
N(1)-Ni(1)-O(1)#2
O(1)-Ni(1)-O(2)
O(1)#1-Ni(1)-O(2)
N(1)-Ni(1)-O(2)
O(1)#2-Ni(1)-O(2)
O(1)-Ni(1)-Cl(1)
O(1)#1-Ni(1)-Cl(1)
N(1)-Ni(1)-Cl(1)
O(1)#2-Ni(1)-Cl(1)
O(2)-Ni(1)-Cl(1)
C(6)-O(1)-Ni(1)
C(6)-O(1)-Ni(1)#3
Ni(1)-O(1)-Ni(1)#3
C(6)-O(1)-Ni(1)#2
Ni(1)-O(1)-Ni(1)#2
Complex 2b
2.045(2) Ni(1)#3-O(1)-Ni(1)#2
2.052(2) C(7A)-O(2)-C(7)
2.057(3) C(7A)-O(2)-Ni(1)
2.093(3) C(7)-O(2)-Ni(1)
2.105(3) C(1)-N(1)-C(5)
2.3789(10) C(1)-N(1)-Ni(1)
2.044(3) C(5)-N(1)-Ni(1)
2.058(2) O(1′)-Ni(1′)-O(1′)#4
2.058(3) O(1′)-Ni(1′)-N(1′)
2.103(3) O(1′)#4-Ni(1′)-N(1′)
2.113(3) O(1′)-Ni(1′)-O(1′)#5
2.3740(10) O(1′)#4-Ni(1′)-O(1′)#5
81.95(10) N(1′)-Ni(1′)-O(1′)#5
79.96(11) O(1′)-Ni(1′)-O(2′)
161.11(12) O(1′)#4-Ni(1′)-O(2′)
80.38(10) N(1′)-Ni(1′)-O(2′)
80.81(10) O(1′)#5-Ni(1′)-O(2′)
101.37(11) O(1′)-Ni(1′)-Cl(1′)
93.20(12) O(1′)#4-Ni(1′)-Cl(1′)
86.82(10) N(1′)-Ni(1′)-Cl(1′)
88.80(12) O(1′)#5-Ni(1′)-Cl(1′)
166.73(10) O(2′)-Ni(1′)-Cl(1′)
175.31(8) C(6′)-O(1′)-Ni(1′)
99.26(8) C(6′)-O(1′)-Ni(1′)#6
99.21(10) Ni(1′)-O(1′)-Ni(1′)#6
95.30(7) C(6′)-O(1′)-Ni(1′)#5
91.40(9) Ni(1′)-O(1′)-Ni(1′)#5
110.1(2) Ni(1′)#6-O(1′)-Ni(1′)#5
127.3(2) C(7′)-O(2′)-Ni(1′)
98.59(10) C(5′)-N(1′)-C(1′)
119.6(2) C(5′)-N(1′)-Ni(1′)
99.19(10) C(1′)-N(1′)-Ni(1′)
97.07(10)
46.0(8)
133.9(7)
125.8(3)
118.7(3)
128.8(3)
112.2(2)
82.27(11)
80.44(12)
162.06(12)
79.27(11)
80.86(11)
100.47(11)
91.82(12)
89.74(11)
86.09(12)
167.79(11)
174.78(8)
99.20(8)
98.44(9)
95.98(8)
93.19(10)
109.8(2)
128.4(2)
98.37(11)
118.5(2)
100.48(11)
96.51(10)
134.7(13)
118.8(3)
112.3(2)
128.5(3)
a Symmetry transformations used to generate equivalent atoms for
complex 1: #1 y + 1/2, -x + 3/2, -z + 1/2; #2 -x + 2, -y + 1, z; #3 y,
-x + 1, -z; #4 -x + 1, -y + 1, z; #5 -y + 3/2, x - 1/2, -z + 1/2; #6 -y
+ 1, x, -z; #7 x + 0, -y + 3/2, -z + 1/4. b Symmetry transformations used
to generate equivalent atoms for complex 2: #1 y + 1/2, -x - 1/2, -z +
3/ ; #2 -x, -y - 1, z; #3 -y - 1/ , x - 1/ , -z + 3/ ; #4 -y + 1/ , x - 1/ ,
2
2
2
2
2
2
-z + 3/2; #5 -x + 1, -y, z; #6 y + 1/2, -x + 1/2, -z + 3/2; #7 x + 0, -y
1
5
- /2, -z + /4.
plane of the NiOClNi fragment. A disorder of the ROH
groups over two positions seems to be related to two possible
positions of the H atoms involved in such hydrogen bonds:
up and down relative to the average plane.
Inorganic Chemistry, Vol. 45, No. 2, 2006
533
Yang et al.
Figure 1. 30% ORTEP plot of complex 1, [Ni(hmp)(MeOH)Cl]4.
Because we are interested in the effects of intermolecular
interactions on the quantum tunneling of magnetization, it
is important to investigate the packing in the crystals of
complexes 1 and 2, looking closely at the intermolecular
contacts that could affect magnetic exchange interactions
between Ni4 molecules. For both complexes 1 and 2, there
are two symmetrically independent Ni4 molecules, one sitting
at the body center and the other at the C-face center. Each
[Ni(hmp)(ROH)Cl]4 molecule is surrounded tetrahedrally by
four other Ni4 molecules. Thus, the body-centered Ni4
molecule forms one diamond-like lattice, and the Ni4
molecule that is at the C-face center forms a second diamondlike lattice. These two interpenetrating diamond-like lattices
are illustrated in Figure 2 for complex 1. In the crystal lattices
of complexes 1 and 2, there is also a H2O solvate molecule
that is not fully occupied and also is disordered. The distances
from the oxygen atom of the solvate water molecule to the
Cl- ligand are in the range of 3.6-3.8 Å for complex 1 and
3.97 Å for complex 2. This could lead to weak hydrogenbonding interactions. Because the H2O solvate molecules are
disordered and because there are two crystallographically
different Ni4 molecules in complex 1 (also in complex 2),
this could lead to range of microenvironments, that is, Ni4
molecules that experience different crystal environments. The
explanation for the symmetry of QTM in Mn12-Ac involved
six different microenvironments present for Mn12 molecules
as a result of disordered solvate molecules in the crystal,
and this was confirmed by precise HFEPR spectroscopy and
micro-Hall magnetometry.24,26,35
In a recent report,29 it was shown that intermolecular
C-H‚‚‚Cl hydrogen bonds and Cl‚‚‚Cl contacts provide a
pathway for intermolecular magnetic exchange interactions
between two S ) 9/2 Mn4 SMMs. This type of hydrogen bond
is also observed in this Ni4 series of complexes. Chloride
ligands from one Ni4 molecule interact with certain hydrogen
atoms from the pyridine moiety of the hmp- ligand on a
neighboring Ni4 molecule. In the cases of complexes 1 and
(35) Cornia, A.; Sessoli, R.; Sorace, L.; Gatteschi, D.; Barra, A. L.;
Daiguebonne, C. Phys. ReV. Lett. 2002, 89 (25), 257201.
534 Inorganic Chemistry, Vol. 45, No. 2, 2006
2, chloride ions contact with the hydrogen atoms at the 5
and 6 positions of the hmp- pyridine ring. The Cl‚‚‚H
distances are 2.9 and 3.0 Å in complex 1 and 3.0 Å in
complex 2. These distances are only slightly longer than the
reported literature value of 2.8 Å.29 Hence, intermolecular
magnetic exchange interactions through this pathway could
lead to an exchange bias seen in magnetization hysteresis
loops.
Another possible pathway for intermolecular magnetic
exchange interactions involves the Cl‚‚‚Cl contacts between
Ni4 molecules. The shortest Cl‚‚‚Cl contacts are 4.867 and
4.862 Å in complex 1 and 4.951 and 4.884 Å in complex 2
for the molecules on the body and at the C-face centers,
respectively. In both complexes, the Cl‚‚‚Cl distances are
significantly longer than the sum of the van der Waals radii
of two chloride ions, 3.6 Å;29,36 thus, the intermolecular
Cl‚‚‚Cl contacts in both complexes 1 and 2 are long and
likely do not lead to intermolecular magnetic exchange
interactions. In summary, two different types of intermolecular contacts are present in complexes 1 and 2 that could
lead to magnetic exchange interactions between Ni4 molecules. One contact involves the H2O solvate molecule. The
other involves a Cl‚‚‚H-C (pyridine) contact. Although it
is not possible to anticipate whether the observed contacts
would lead to intermolecular antiferromagnetic or ferromagnetic exchange interactions, it is possible to predict that
complex 1 would exhibit a stronger interaction than complex
2.
X-ray Structure of Complex 3. Complex 3 crystallizes
in the tetragonal space group I41/a. As with complexes 1
and 2, complex 3 has a distorted cubane core with S4
symmetry; however, the alcohol ligands in the complex 3
have a longer aliphatic chain (figure available in Supporting
Information). There is only one symmetrically independent
molecule in the unit cell. An examination of the conformation
of the aliphatic chain in the dmb ligand by a Newman
projection viewed along the C7-C8 bond shows that the
substituents are in a staggered conformation with the tertbutyl substituent in a trans position relative to the OH group
as well as the main body of the complex. The molecule
adopts this conformation to avoid having the bulky tert-butyl
group approach the main body of the complex. On the other
hand, because there is less restriction for the tert-butyl
rotating about the C8-C9 bond, the thermal parameters for
the C10-C12 atoms are considerably larger than those for
all of the other carbon atoms. The coordinates and the thermal
parameters of complex 3 are listed in Table 5.
No packing solvate or water molecules are found in the
crystal lattice of complex 3. Hence, intermolecular interactions between the metal complex and lattice solvate molecules is not an issue in this compound. Recently, it was
reported that the lattice solvate molecule can have a profound
influence on the QTM in Mn12 SMMs.35,37 The absence of
(36) Freytag, M.; Jones, P. G.; Ahrens, B.; Fischer, A. K. New J. Chem.
1999, 23 (12), 1137-1139.
(37) Cornia, A.; Fabretti, A. C.; Sessoli, R.; Sorace, L.; Gatteschi, D.; Barra,
A. L.; Daiguebonne, C.; Roisnel, T. Acta Crystallogr. C 2002, 58,
m371-m373.
Tunneling in Ni4 Single-Molecule Magnets
Figure 2. Illustration of the interpenetrating diamond-like sublattices of complex 1, where green balls represent the chlorides. All carbon and hydrogen
atoms are omitted for clarity, and the two plots represent (a) the sublattice linked from the C-face center, (b) the sublattice linked from body center.
Table 5. Atomic Coordinates (× 104) and Equivalent Isotropic
Displacement Parameters (Å2 × 103) for Complex 3a
Ni(1)
Cl(1)
O(1)
O(2)
N(1)
C(1)
C(2)
C(3)
C(4)
C(5)
C(6)
C(7)
C(8)
C(9)
C(10)
C(11)
C(12)
x
y
z
U(eq)a
791(1)
634(1)
816(1)
2384(1)
1110(1)
1047(2)
1343(2)
1733(2)
1799(2)
1474(1)
1501(2)
3174(2)
4109(2)
4986(2)
4564(2)
5515(2)
5795(2)
3443(1)
5262(1)
1859(1)
3581(1)
3075(1)
3684(2)
3349(2)
2349(2)
1720(2)
2097(1)
1446(2)
3955(2)
4347(2)
4814(2)
5656(3)
3953(3)
5295(2)
943(1)
867(1)
976(1)
1053(1)
382(1)
71(1)
-289(1)
-327(1)
-9(1)
343(1)
701(1)
800(1)
1020(1)
774(1)
511(1)
545(1)
1040(1)
15(1)
22(1)
16(1)
22(1)
17(1)
21(1)
26(1)
26(1)
22(1)
18(1)
19(1)
24(1)
22(1)
31(1)
49(1)
48(1)
42(1)
a U(eq) is defined as one-third of the trace of the orthogonalized U
ij
tensor.
lattice solvate molecules in complex 3 makes it a relatively “clean” candidate for the study of QTM. The shortest
Cl‚‚‚Cl contacts between neighbor molecules in compound
3 are about 6.036 and 6.408 Å, which are far longer than
the 3.6 Å obtained for the sum of the van der Waals radii of
two chloride ions. Therefore, intermolecular magnetic exchange interactions propagated by this pathway should be
negligible. Although a bulky aliphatic group is incorporated
on the dbm alcohol ligand, intermolecular hydrogen bonds
between chloride ligands on one complex and a hydrogen
atom from the pyridine of hmp- ligands on a neighboring
complex are still observed in complex 3. In this case, the
chloride ligands approach two pyridines of the hmp- ligands
of a neighboring molecule with distances 3.031 Å to the
hydrogen at the 5 position on one hmp- and 3.045 Å to the
hydrogen at the 4 position of another hmp-. These H‚‚‚Cl
distances in complex 3 are in the same range as found for
complexes 1 and 2. Thus, this could also be a factor affecting
the magnitude of intermolecular magnetic exchange interactions in complex 3. As with complexes 1 and 2, it is not
possible to conclude from the nature of Cl‚‚‚H-C contacts
in complex 3 whether the intermolecular exchange interactions would be expected to be antiferromagnetic or ferromagnetic.
Intramolecular hydrogen bonds from the protons on OH
groups to the chloride ligands are also seen in complex 3
and can be classified as being in the short hydrogen-bond
category based on the found H‚‚‚Cl distance, 2.300 Å. This
interaction also could restrict the aliphatic chain on the 3,3dimethyl-1-butanol ligand from free rotation about the
metal-oxygen bond.
X-ray Structure of Complex 4. In contrast to complexes
1-3, complex 4 crystallizes in the monoclinic space group
C2/c. Although complex 4 also has a distorted cubane core,
it does not have S4 site symmetry in the crystal. There
are two crystallographically independent molecules in
the crystal of 4: one in a general position with C1 site
symmetry and the other in a special position with C2 site
symmetry. The fact that both of these molecules do not
have S4 site symmetry indicates that appreciable transverse zero-field interactions are likely to be present that
would lead to even faster QTM than observed in complexes
1-3.38 The disorder of the aliphatic chain in complex 4 is
more extensive than that in complex 3. An ORTEP plot for
(38) Aliaga-Alcalde, N.; Edwards, R. S.; Hill, S. O.; Wernsdorfer, W.;
Folting, K.; Christou, G. J. Am. Chem. Soc. 2004, 126 (39), 1250312516.
Inorganic Chemistry, Vol. 45, No. 2, 2006
535
Yang et al.
Table 6. Nonclassical Intermolecular Hydrogen-Bond Lengths (Å) in
the Crystal of Complex 4
C1-symmetry moleculea
C2-symmetry moleculea
mol type
(H on Py)b
Py f Clc
Cl f Pyd
mol type
b
Py f Clc
Cl f Pyd
C2 (3)
C2 (4)
C2 (3)
C2 (4)
C1 (3)
C1 (4)
C1 (3)
C1 (4)
3.201
3.037
2.863
3.732
2.755
3.267
2.906
2.998
3.457
3.232
2.889
3.583
2.755
3.267
2.906
2.998
C1 (3)
C1 (4)
C1 (3)
C1 (4)
C1 (3)
C1 (4)
C1 (3)
C1 (4)
3.457
3.232
2.889
3.583
3.457
3.232
2.889
3.583
3.201
3.037
2.863
3.732
3.201
3.037
2.863
3.732
a Type of object molecule. b Symbols in columns 1 and 4 indicate the
type of the neighboring molecule named by symmetry, with the position of
H on the pyridine ring of hmp ligand in parentheses, e.g., C2 (3) means the
neighboring molecule has C2 symmetry contact through the H atom on
position 3 of the hmp ring. c Py f Cl: the hmp ligand is on the object
molecule and chloride is on the neighboring molecule. d Cl f Py: the hmp
ligand is on the neighboring molecule, and chloride is on the object
molecule.
complex 4 given in the Supporting Information shows the
disorder of the 3-cyclohexyl-1-propanol ligand. Once again,
no crystal solvate molecule is found in the lattice of complex
4; thus, intermolecular magnetic exchange interactions are
not propagated by solvate molecules. Cl‚‚‚Cl contacts in this
complex are all in excess of 7 Å; therefore, magnetic
exchange interactions propagated through this pathway would
be much weaker than those in complex 3. Intermolecular
interactions between hydrogen atoms on the hmp- ligand
and chloride ligands on neighboring molecules are seen.
Because of the low symmetry of this crystal, these H‚‚‚Cl
contact distances vary over a wide range. Most of these
nonclassical hydrogen bonds are around 3 Å, some of them
run to 3.76 Å, and a few of them are extremely short at 2.755
Å. Table 6 summarizes the nonclassical hydrogen bonds
within the crystal lattice. Here, we classify the molecules
according to their symmetry as C1 and C2 molecules. Each
C1 molecule contacts with both C1 and C2 molecules through
the nonclassical hydrogen bonds but C2 molecules make
contact with C1 molecules only through these nonclassical
hydrogen bonds.
X-ray Structure of Complex 5. Complex 5 is an analogue
of complex 3 in which the chloride ligands have been
replaced by bromides (an ORTEP plot is available in the
Supporting Information). The two complexes not only have
the same packing and I41/a space group, but also have the
same S4 site symmetry. The aliphatic chain of the 3,3dimethyl-1-butanol ligand adopts the same conformation in
complex 5 as in complex 3, with the tert-butyl group directed
away from the main body of the complex. No crystal solvate
molecule is found in the lattice. The Br‚‚‚Br contacts in
complex 5 are 5.738 and 6.597 Å. One of them is longer
than the corresponding Cl‚‚‚Cl contact in complex 3, but
the shorter Br‚‚‚Br contact in complex 5 is shorter than the
Cl‚‚‚Cl contact in complex 3. These Br‚‚‚Br distances are
considerably larger than the sum of the van der Waals radii
of two bromides, which is equal to 3.7 Å. Intermolecular
H‚‚‚Br hydrogen bonds involving hydrogen atoms on the
hmp- ligands are the same as in complex 3, with H‚‚‚Br
536 Inorganic Chemistry, Vol. 45, No. 2, 2006
distances of 3.106 Å for the hydrogen atom on the 4 position
of one hmp- ligand and 3.191 Å for the hydrogen on the 5
position of another hmp-. Both are close to the sum of the
van der Waals radii of hydrogen and bromide of 3.05 Å.
Intramolecular hydrogen bonds in this complex are also seen
with H‚‚‚Br distances of 2.432 Å.
X-ray Structure of Complex 6. Complex 6 crystallizes
in the I4h2d space group, where each unit cell contains only
one kind of crystallographically independent molecule with
S4 site symmetry. Because of the added bulk of the tertbutyl group on the hmp- ligand, more free space is available
in the crystal of complex 6. As a consequence, the aliphatic
chain of the 3,3-dimethyl-1-butanol (dmb) ligand on complex
6 exhibits greater disorder than does the same ligand in
complex 3 (an ORTEP plot is available in the Supporting
Information). The aliphatic chains are disordered for complex
6 and reside in two possible positions. The tert-butyl groups
on both the t-Buhmp and 3,3-dimethyl-1-butanol ligands are
highly disordered, as indicated by their large thermal
parameters. The Cl‚‚‚Cl contact distances seen in complex
6 are characterized by distances of 6.377 Å for the molecules
on the same a-b plane and 7.868 Å for the molecules on
adjacent layers of the a-c plane. These values are larger
than those in complex 3 and are significantly larger than
the sum of van der Waals radii of two chloride ions.
Nonclassical intermolecular hydrogen bonds for chloride ions
interacting with the hydrogen atoms on the 5 position of the
hmp- ligands in complex 6 are significantly weaker than
those in all of the previous complexes, as evidenced by the
Cl‚‚‚H distance of 3.540 Å, which is significantly longer than
those in complexes 1-4, where 2.9-3.2 Å distances are
found as compared to the sum of van der Waals radii of
2.95 Å. Intramolecular hydrogen bonds between the chlorides
and the protons on alcohol ligand have H‚‚‚Cl distances of
2.448 Å. Although they still fall in the short contact category, this value is somewhat longer than those in complexes
1-3.
Some conclusions can be drawn from the above structural
information about intermolecular contacts observed for
complexes 1-6. First, the tert-butyl groups on the two
different ligands in complex 6 clearly lead to the greatest
insulation between Ni4 complexes of all six complexes.
Intermolecular magnetic exchange interactions would be
anticipated to be the weakest for complex 6. Second, for the
two isostructural complexes 1 and 2, intermolecular exchange
interactions should be greater for complex 1. Third, complex
3 would be expected to exhibit weaker intermolecular
magnetic exchange interactions than complexes 1 and 2.
Fourth, it is difficult to determine whether observed intermolecular contacts would lead to either net antiferromagnetic
or ferromagnetic ordering. Fifth, because of the Br- ligand
in complex 5 and the low site symmetries in complex 4, it
is difficult to anticipate the nature of the intermolecular
exchange interactions in these two complexes.
Magnetization versus Magnetic Field Hysteresis Loops.
To examine how the chemical tuning of the peripheral
ligands in the [Ni(hmp)(ROH)X]4 complexes affects the
magnetic properties of the complex, magnetization versus
Tunneling in Ni4 Single-Molecule Magnets
Figure 3. Magnetization hysteresis loops of a single crystal of [Ni(hmp)(MeOH)Cl]4 (1) at 0.04 K at various scan rates from 0.002 to 0.56 T/s.
The external magnetic field is oriented parallel to the easy axis of the crystal.
Magnetization is plotted as a fraction of the maximum value of Ms, the
saturation magnetization.
Figure 4. Hysteresis loops of a single-crystal sample of [Ni(hmp)(EtOH)Cl]4 (2) at 0.16 K at various scan rates from 0.008 to 0.07 T/s. The magnetic
field is oriented parallel to the easy axis of the crystal. Magnetization is
plotted as a fraction of the maximum value of Ms, the saturation
magnetization.
magnetic field hysteresis measurements were carried out for
single crystals of complexes 1-6. Magnetization hysteresis
data were obtained for each of the six complexes with a
micro-SQUID array in the range of 0.040-6.0 K at scan
rates of 0.002-0.56 T/s. The field was aligned parallel to
the mean easy axis of magnetization using the transverse
field method.39 Hysteresis is seen for all six complexes, and
it is concluded that complexes 1-6 are single-molecule
magnets (see Figures 3-8). For a single crystal of an SMM
that has negligible intermolecular exchange interactions, the
first step in the hysteresis loop due to quantum tunneling
occurs at zero field when the external field is oriented parallel
to the easy axis of the crystal. In a recent report,29 it has
been found that the presence of intermolecular exchange
interactions in the supramolecular dimer [Mn4O3Cl4(O2CEt)3(py)3]2 shifts the first step to a nonzero magnetic field. The
[Mn4] units in the dimer interact with each other through
six C-H‚‚‚Cl hydrogen bonds and one Cl‚‚‚Cl contact. These
contacts within the [Mn4]2 dimer lead to a weak intermolecular antiferromagnetic interaction (J ) -0.05 K for H )
-2JS1‚S2) between the two S ) 9/2 SMMs.29,40 This antiferromagnetic interaction shifts the first hysteresis step significantly from zero field to -0.33 T.
The hysteresis loops of complexes 1 and 2 are illustrated
in Figures 3 and 4. The first steps for both complexes are
shifted from zero field. Obviously, there are intermolecular
(39) Wernsdorfer, W.; Chakov, N. E.; Chirstou, G. Phys. ReV. B 2004, 70,
132413.
(40) Hill, S.; Edwards, R. S.; Aliaga-Alcalde, N.; Christou, G. Science 2003,
302 (5647), 1015-1018.
Figure 5. Magnetization hysteresis loops of a single crystal of [Ni(hmp)(dmb)Cl]4 (3) measured at scan rates ranging from 0.002 to 0.280 T/s at
0.04 K. Magnetization is plotted as a fraction of the maximum value of
Ms, the saturation magnetization.
antiferromagnetic exchange interactions between neighboring
molecules. The first step of the hysteresis loop is shifted to
-0.33 T for complex 1 and to -0.28 T for complex 2,
indicating that the intermolecular interactions are stronger
in complex 1 than in complex 2. This results from the fact
that complex 1 has shorter distances associated with the two
significant intermolecular contacts: (i) hydrogen bonding
between the crystal water molecules and chloride ligands
and (ii) nonclassical hydrogen bonding between hydrogen
atoms on the hmp- ligands of one Ni4 complex and the
chloride ligands of a neighboring Ni4 complex.
Figure 5 illustrates the hysteresis loops for [Ni(hmp)(dmb)Cl]4 (3). Because a bulky aliphatic chain on the dmb ligand
has been incorporated, the Ni4 molecules are more isolated
from each other, which should reduce the intermolecular
magnetic dipolar and magnetic exchange interactions. There
are also no solvate molecules in the crystal of complex 3.
Although the intermolecular nonclassical hydrogen bonds
present in complex 3 are of the same magnitude as those in
complexes 1 and 2, the intermolecular Cl‚‚‚Cl contact
distances are significantly longer in complex 3. With all of
the comparisons given above, the first step feature in the
hysteresis loop due to the ground-state QTM in complex 3
should be shifted closer to zero magnetic field. Indeed, in
Figure 5, it is observed that the ground-state QTM occurs
essentially at zero field. The fact that the first step is sharp
indicates that there is a relatively high rate of magnetization
quantum tunneling in complex 3. A detailed analysis of the
magnetization hysteresis loop for complex 3 is presented in
the next section.
Hysteresis loops for [Ni(hmp)(chp)Cl]4 (4) are shown in
Figure 6. As with complex 3, no solvate molecules are found
in the crystal of complex 4. Although some of the nonclassical H‚‚‚Cl contacts in complex 4 are even shorter than those
observed in complexes 1-3, the intermolecular Cl‚‚‚Cl
contact distances are larger than those in complex 3. As a
consequence of these observations, it is reasonable to
anticipate that the first step of the hysteresis loop for complex
4 will occur close to zero field. This is confirmed by the
experimental results, as shown in Figure 6. Detailed study
of the hysteresis loops also shows that the step around zero
field is actually split into two parts: one is above zero field,
and the other is below zero field. This feature provides a
clear indication of a small exchange bias caused by intermolecular antiferromagnetic interactions.
Inorganic Chemistry, Vol. 45, No. 2, 2006
537
Yang et al.
Figure 6. Magnetization hysteresis loops of a single crystal of [Ni(hmp)(chp)Cl]4 (4) at 0.04 K at various scan rates from 0.004 to 0.28 T/s. The
magnetic field is parallel to the easy axis. The magnetization is plotted as
a fraction of the maximum value of Ms, the saturation magnetization.
Figure 7. Magnetization hysteresis loops of a single crystal of [Ni(hmp)(dmb)Br]4 (5) at 0.04 K at various scan rates from 0.004 to 0.14 T/s. The
magnetic field is parallel to the easy axis. The magnetization is plotted as
a fraction of the maximum value of Ms, the saturation magnetization.
Figure 8. Magnetization hysteresis loops of a single crystal of [Ni(tBuhmp)(dmb)Cl]4 (6) at 0.04 K at various scan rates from 0.004 to 0.14
T/s. The magnetic field is parallel to the easy axis. The magnetization is
plotted as a fraction of the maximum value of Ms, the saturation
magnetization.
As shown in Figure 7, the antiferromagnetic exchange bias
is even more obvious in complex 5. The first step in the
hysteresis loops symmetrically splits to (0.1 T, which is
significantly larger than those observed for complexes 3 and
4. It is known that complex 5 is isostructural to complex 3
with Cl- replaced by Br-. The nonclassical H‚‚‚Br contacts
in complex 5 have about the same distance as H‚‚‚Cl in
complex 3, whereas the closest Br‚‚‚Br distances are even
shorter than the closest Cl‚‚‚Cl distances in complex 3. The
large exchange bias in complex 5 is attributable to the larger
polarity of bromide ions compared to chloride ions.
Among all of the complexes, complex 6 has the largest
aliphatic groups to protect its NiII4 cubane core, and therefore,
it is expected to have the smallest exchange bias. Indeed, as
shown in Figure 8, the tunneling step around zero field shows
smaller splitting than any other complex in this series of
complexes. A precise measurement of the exchange bias can
538 Inorganic Chemistry, Vol. 45, No. 2, 2006
Figure 9. Plot of the first derivative (dM/dH) of the magnetization versus
magnetic field for a single crystal of each 3-6 close to zero field. The
field was swept from -1 to +1 T at a field sweep rate of 0.035 T/s.
Complexes clearly 4-6 show an antiferomagnetic exchange bias of about
-20, -71, and -10 mT, respectively. Complex 3 presents a ferromagnetic
intermolecular coupling of about 12 mT.
Figure 10. Hysteresis loops of a single crystal of [Ni(hmp)(dmb)Cl]4 (3).
The magnetic field is oriented parallel to the easy axis of the crystal at a
scan rate 0.56 T/s at 0.004 K. The black line represents the major loop,
and the colored lines represent minor loops.
be obtained by examining the first derivative (dM/dH) of
the magnetization versus magnetic field close to zero field
for the single crystals of complexes 3-6 (see Figure 9). The
field was swept from -1 to +1 T at a field sweep rate of
0.035 T/s. Complexes 4-6 clearly show antiferromagnetic
exchange biases of about -20, -71, and -10 mT, respectively, whereas complex 3 presents a ferromagnetic intermolecular coupling of about 12 mT. Except for complex 5,
which has bromide ligands, the absolute value of the
exchange bias seems to parallel the order of nonclassical
hydrogen-bonding contact distances.
Detailed Study of the Magnetization Hysteresis for
Complex 3. Because [Ni(hmp)(dmb)Cl]4 (3) has negligible
intermolecular magnetic exchange interactions as evidenced
by the absence of an exchange bias in its hysteresis loop
(Figure 5) and because complex 3 has only one unique highsymmetry Ni4 complex in its crystal, it was decided to take
a closer look at the magnetization hysteresis loops for this
complex. Experiments were carried out on a single crystal
with a micro-SQUID energized such that the magnetic field
was oriented parallel to the easy axis of the crystal using
the transverse field method.39 Figure 10 illustrates some of
the hysteresis data collected for this interesting SMM. The
black curve describes the main loop that was obtained during
a 0.56 T/s scan at 0.04 K. The most striking features of this
hysteresis loop are the steep steps observed at zero field.
These precipitous steps result from fast ground-state quantum
tunneling (QTM) between the Ms ) (4 states. The occurrence of ground-state QTM at zero magnetic field means
Tunneling in Ni4 Single-Molecule Magnets
that intermolecular magnetic exchange interactions have been
largely turned off. Upon scanning the field to larger values,
two fast relaxation processes are observed at about 0.40 and
0.55 T; these two step features have been found to be
reproducible for different crystals.
To explore the nature of the step features occurring at 0.40
and 0.55 T, additional experiments were performed. Minor
hysteresis loops were traced out by starting with different
initial magnetization values. The colored lines in Figure 10
represent the results of this experiment. Two features
resulting from these experiments should be noted. First, when
we scan backward from 0.60 T to zero field, a slight decay
of magnetization away from its saturation value is observed.
It is also found that the higher the initial value of the
magnetization is, the smaller the decay is found to be.
Second,41 the fact that the step feature seen at 0.43 T is
reproducible with different initial magnetization values
suggests that this step is not due to a thermal avalanche
process. However, this step at 0.43 T is not a quantum
tunneling process from the ground state (Ms ) -4) to an
excited state (Ms ) +3). This point can be confirmed if we
substitute the value of 0.43 T into the expression for the
Zeeman energy E ) gβH with the value g ) 2.26 obtained
from the high-frequency EPR (HFEPR) data;42 a value of D
) -0.46 cm-1 was obtained. This value is smaller than the
D value obtained from reduced-magnetization and HFEPR
experiments. Also, the step at 0.43 T has less amplitude than
the step at zero field but does not reach the magnetization
saturation value. Because the rate of the second resonance
tunneling should be higher than the rate of the first resonant
tunneling at zero field, the lower magnetization relaxation
rate at 0.43 T indicates that the step in the range of 0.420.45 T does not result from a single-molecule tunneling
process. Judging from the above experiments, it is more
reasonable to suggest that the relaxation associated with the
0.43 T step is due to a spin-spin cross relaxation (SSCR)
process.28
As the magnetic field is swept to a larger value, a
reproducible small step is also observed around 0.55 T.
Because its initial value is very close to the saturation
magnetization, it is very difficult to estimate the relaxation
rate for this step feature. However, substituting the value of
the magnetic field (0.55 T) into the expression for the
Zeeman energy E ) gβH with g ) 2.26, the separation
between this step and the ground-state quantum tunneling
transition is calculated to be 0.58 cm-1. This fully agrees
with the D value obtained from HFEPR (average D ) -0.59
cm-1) and the reduced-magnetization (D ) -0.6 cm-1)
experiments (vide infra). Therefore, this step at 0.55 T can
be assigned as the second resonant quantum tunneling
transition from the Ms ) -4 to the Ms ) +3 state.
To see these fine structures in the hysteresis loops clearly,
the first derivative of the magnetization versus magnetic field
(41) del Barco, E.; Hernandez, J. M.; Sales, M.; Tejada, J.; Rakoto, H.;
Broto, J. M.; Chudnovsky, E. M. Phys. ReV. B 1999, 60 (17), 1189811901.
(42) Lawrence, J.; Yang, E.-C.; Edwards, R. S.; Olmstead, M. M.; Ramsey,
C.; Dalal, N.; Gantzel, P. K.; Hill, S.; Hendrickson, D. N., manuscript
in preparation.
Figure 11. Plot of the first derivative (dM/dH) of the magnetization versus
magnetic field for a single crystal of [Ni(hmp)(dmb)Cl]4 (3), where the
magnetic field is oriented parallel to the easy axis of the crystal.
Figure 12. Magnetization hysteresis loops of a single crystal of [Ni(hmp)(dmb)Cl]4 (3) measured in the temperature range of 0.04-1.1 K at a scan
rate 0.28 T/s. The external magnetic field is oriented parallel to the easy
axis of the crystal.
curve was taken. The results are shown in Figure 11, for
which a scan rate of 0.28 T/s was employed. Four important
features are observed in this plot. The most striking feature
is the large peak at zero field that corresponds to the groundstate QTM. The high intensity of this peak reflects the high
tunneling rate. The bandwidth of this peak reveals that there
are some residual dipolar and magnetic exchange interactions
within the crystal that have not yet been entirely turned off
by the bulky aliphatic chain on the alcohol ligand. The
remaining interaction estimated by the bandwidth (0.06 T)
is about 0.3-0.4 K. This is very close to the magnetic
ordering temperature of 0.28 K observed in the ac susceptibility experiment (vide infra).
The second largest peak observed in Figure 11 is the one
at 0.43 T. This peak was tentatively assigned above to be
an SSCR process. If the field is increased to 0.55 T, there is
a small but obvious peak. Judging from the D and g values
obtained from the HFEPR data, this peak is assigned to be
the second tunneling transition (from Ms ) -4 to Ms ) +3).
Similar results were obtained for experiments at different
temperatures and scanning rates. In Figure 12, we present
the hysteresis loops obtained at a 0.28 T/s scan rate in the
temperature range of 0.04-1.1 K. Above 0.7 K, the
hysteresis loop due to a phonon bottleneck process is seen.
As the temperature is decreased, the area enclosed in the
hysteresis loop increases. It can be seen that the fine
structures of hysteresis loops obtained at a scan rate of 0.28
T/s are essentially the same as those obtained at 0.56 T/s.
This reproducibility reveals that these fine-structure features
are not random events. Below 0.2 K, both ground-state and
second resonance quantum tunneling processes can be clearly
observed in both the 0.28 and 0.56 T/s scan rate runs.
Inorganic Chemistry, Vol. 45, No. 2, 2006
539
Yang et al.
Hysteresis loops were also investigated at constant temperature with different scan rates. Figure 5 illustrates the
results obtained at different scan rates ranging from 0.02 to
0.28 T/s at 0.04 K. Obviously, the greater the scan rate, the
larger the area enclosed in the hysteresis loop. A large
amplitude of magnetization change at zero field corresponding to the ground-state QTM process is observed for all of
the scan rates. However, the second resonant QTM transition
is not seen until the scan rates are above 0.14 T/s. As the
scan rate is decreased and the magnetic field is allowed to
reside for a longer time in the tunneling window, steeper
magnetization transitions are seen at zero field for lower scan
rates. Analogous to the frequency dependence seen in the
out-of-phase ac susceptibilities for SMMs, the fact that the
hysteresis loops are scan-rate-dependent also supports the
conclusion that complex 3 has the intrinsic properties of an
SMM.
As we show in this article, there are several reasons why
we are convinced that all six Ni4 complexes are SMMs: (1)
The complexes exhibit magnetization relaxation. (2) The
complexes exhibit hysteresis in their magnetization versus
magnetic field response, (3) The complexes show quantum
tunneling of the magnetization. This is evidenced both by
the steps observed in the hysteresis plots and by the
temperature-independent rate of magnetization reversal observed (vide infra) at the lowest temperatures. (4) As we
have shown, the magnetization hysteresis does not result from
a phonon bottleneck. (5) The magnetization hysteresis is not
due to a magnetic ordering, i.e., a phase transition to a
magnetically ordered phase. The Ni4 complexes continue to
tunnel rapidly down to the lowest temperature of 0.04 K.
Magnetic ordering would stop the magnetization tunneling.
Detailed Study of the Magnetization Hysteresis for
Complexes 4 and 6. If one compares the hysteresis loops
observed at 0.04 K, it is found that the first step in the
hysteresis loop is steeper in complex 4 than in complex 3.
In addition, the loops of complex 4 are more closed at zero
field than those of complex 3. This means that the QTM
process in complex 4 is faster than that in complex 3. From
the structural data, it is known that the two crystallographically independent molecules in the crystal of complex 4 have
a symmetry lower than S4. One Ni4 complex has C2
symmetry, and the other has only C1 site symmetry. A
reduction in crystal site symmetry leads to an increase in
transverse zero-field interactions and a higher rate of QTM
for complex 4 compared to complex 3.
Because fast tunneling blocks a detailed study of the fine
structure associated with the hysteresis loop for complex 4,
another experiment was designed to examine the SMM
behavior of this complex. In this experiment, a single crystal
of complex 4 was cooled from 5 to 0.04 K in zero field, and
then the external magnetic field was swept from 0 to 0.7 T
while the scan rate was varied from 0.002 to 1.120 T/s. The
results of these measurements are shown in Figure 13. Welldeveloped SMM-type hysteresis loops are seen in this
experiment. Significant area is enclosed in the hysteresis
loop, and the area increases as the scan rate is increased. It
can be seen that two steps repeatedly occur in the hysteresis
540 Inorganic Chemistry, Vol. 45, No. 2, 2006
Figure 13. Minor hysteresis loops of a single crystal of [Ni(hmp)(chp)Cl]4 (4) at 0.04 K observed at scan rates in the range of 0.002-1.120 T/s.
Loops are obtained by starting the scan from zero field.
Figure 14. Minor hysteresis loops of a single crystal of [Ni(t-Buhmp)(dmb)Cl]4 (6) at 0.04 K observed at scan rates in the range of 0.002-1.120
T/s. Loops are obtained by starting the scan from zero field.
loop: one is around 0.47 T, and the other is around 0.58 T.
It is reasonable to assign these two steps to the second
resonant QTM processes (ie., the Ms ) -4 to Ms ) +3
tunneling) for the two crystallographically different molecules
in the crystal of complex 4. However, other mechanisms such
as intermolecular spin-spin cross relaxation28 might also
cause similar steps in the hysteresis loop.
As with complex 4, the direct observation of the fine
structure in hysteresis loops for complex 6 was also blocked
by the fast QTM; therefore, a similar experiment was also
performed on 6. Figure 14 gives the result of this experiment,
and the SMM-type behavior such as scan-rate-dependent
phenomena are clearly seen. However, further step features
are not seen at scan rates up to 0.28 T/s.
Discussion of Ground-State Tunneling. It is clear that
[Ni(hmp)(dmb)Cl]4 (3) exhibits a relatively high rate of
ground-state quantum tunneling of magnetization (QTM).
The abrupt step observed at zero field for complex 3 in the
plot of magnetization versus magnetic field is a manifestation
of this rapid QTM. A more detailed kinetic study of
magnetization relaxation was conducted to gain insight into
the rapid QTM in complex 3. dc magnetization decay
measurements were carried out on a single crystal of complex
3. The experiment involved saturating the magnetization of
a crystal and then turning off the magnetic field and
measuring the magnetization remaining as a function of time.
To obtain a semiquantitative evaluation of the magnetization
relaxation rate, we first saturated the crystal sample and then
turned off the magnetic field and simply recorded the time
(τ) for 90% relaxation at each temperature. The 90%
relaxation value was selected so that we could make
measurements over a larger temperature range. Figure 15
Tunneling in Ni4 Single-Molecule Magnets
Table 7. Comparison of Temperature-Independent QTM Rates
Figure 15. Magnetization relaxation versus time for a single crystal of
[Ni(hmp)(dmb)Cl]4 (3) in the temperature range 0.04-0.60 K at zero field.
Relaxation times were taken as the time it took for the magnetization to
decay to 0.1Ms (where Ms represents the saturation magnetization).
Figure 16. Temperature dependence of the logarithm of the magnetization
relaxation time for a single crystal of [Ni(hmp)(dmb)Cl]4 based on the data
shown in Figure 12.
shows the results of dc magnetization decay experiments
carried out at 14 different temperatures in the range of 0.040.60 K. At each temperature, there is a plot of magnetization
versus time. The dashed line indicates the magnetization
corresponding to 90% relaxation. Figure 16 presents an
Arrhenius plot of the natural logarithm of the relaxation time
versus the inverse absolute temperature. It can be seen that
the relaxation time significantly increases as the temperature
is decreased in the range of 0.6-0.2 K. Below 0.1 K, the
relaxation rate gradually approaches a constant value. This
temperature-independent relaxation rate provides a clear
indication of QTM-dominant magnetization relaxation at low
temperatures. The temperature independence of the rate is
only explicable in terms of a ground-state QTM, where each
Ni4 SMM is tunneling between its Ms ) -4 and Ms ) 4
states. This further confirms the previous assignment of the
step feature observed at zero field in the magnetization versus
magnetic field hysteresis loops. As indicated in Figure 16,
the relaxation time-temperature relationship obtained in the
high-temperature limit (i.e., thermally assisted tunneling
region) is τ ) 6.3 × 10-3exp(2/T) s, where τ is the 90%
relaxation time and T is the absolute temperature. It is quite
amazing that the effective energy barrier, Ueff, is 2 K, which
is considerably smaller than the 13 K (= U) classical energy
barrier obtained from the formula U ) |D|Sz2. This extremely
low effective activation energy indicates that the quantum
tunneling is very fast in this molecule and makes a significant
contribution to the magnetization relaxation even at higher
temperatures.
It is important to compare the rate of ground-state QTM
in the Ni4 SMM complex 3 with the rates reported for other
SMMs. Table 7 provides such a comparison.10,18,20,43-47
complex
QTM rate
(s-1)
S
D
(cm-1)
|D|S2
(cm-1)
ref(s)
complex 3
Mn4 cubanea
Mn12-Acb
Fe8c
Mn4 dicubaned
Mn30e
Mn18f
Mn2g
2 × 10-1
3.2 × 10-2
<10-8
4.5 × 10-5
10-4
10-6
1.3 × 10-8
5 × 103
4
9/
2
10
10
8
5
13
4
-0.6
-0.53
-0.46
-0.19
-0.25
-0.51
-0.13
-2.3
9.6
10.6
46
19
16
12.8
22
36.7
this work
10
43
47
46
20
18, 44
45
a [Mn O Cl(O CCH ) (dbm)]. b [Mn O (O CCH ) (H O) ].
4 3
2
3 3
12 12
2
3 16
2
4
[(tacn) 6 Fe 8 O 2 (OH) 12 ] 8+ . d [Mn 4 (OAc) 2 (pdmH) 6 (H 2 O) 4 ](ClO 4 ) 2 .
e [Mn O (OH) (O CCH But) (H O) (MeNO ) ]; f [Mn O (O CMe) 30 24
8
2
2
32
2
2
2 4
18 14
2
18
(hep)4(hepH)2(H2O)2](ClO4)2. g [Mn2(Saltmen)2(ReO4)2].
c
Ground-state QTM is not measurable in the prototypical S
) 10 SMM, Mn12-Ac. This complex exhibits only thermally
assisted QTM, where each molecule is excited by phonons
to an excited state, from the Ms ) -10 to the Ms ) -3
state, for example, and then tunneling occurs between the
Ms ) -3 and Ms ) 3 excited states. Only a lower limit can
be given for the rate of ground-state QTM in Mn12-Ac as
<10-8 s-1. For the other SMMs listed in Table 7, Arrhenius
plots of the natural logarithm of the relaxation time versus
inverse temperature have been determined. In all cases, a
temperature-independent magnetization rate was observed at
low temperatures. This rate of ground-state QTM varies from
1.3 × 10-8 s-1 for the Mn18 SMM44 that has a ground state
with S ) 13 and D ) -0.18 K () 0.13 cm-1) to the highest
rate of 5 × 103 s-1 for a Mn2 complex45 that has an S ) 4
ground state with D ) -1.1 cm-1. The rate of ground-state
QTM depends on several factors. SMMs that have ground
states with large spin values will tend to exhibit the lowest
rates of QTM because they have large thermodynamic
barriers for magnetization reversal. A naı̈ve anticipation
would be that small-spin SMMs might be expected to exhibit
the fastest QTM. Examination of Table 7 shows that there
is a Mn30 SMM20 that has S ) 5 and D ) -0.51 cm-1 to
give a barrier of U ) |D|Sz2 ) 12.8 cm-1, which is
comparable to the barrier height expected for [Ni(hmp)(dmb)Cl]4. However, this Mn30 SMM exhibits a low tunneling rate
of 10-6 s-1, compared to the rate of 2 × 10-1 s-1 for the Ni4
SMM complex 3.
Obviously, it is not just the height of the thermodynamic
barrier that determines the rate of ground-state QTM.
Basically, magnetization tunneling occurs when two equienergy states on either side of the barrier experience an
interaction that mixes the two states. The magnitude of the
tunnel splitting (i.e., mixing) determines the rate of QTM.
(43) Quantum Tunneling of Magnetization: QTM ′94; Kluwer Academic
Publishers: Dordrecht, The Netherlands, 1995.
(44) Brechin, E. K.; Sanudo, E. C.; Wernsdorfer, W.; Boskovic, C.; Yoo,
J.; Hendrickson, D. N.; Yamaguchi, A.; Ishimoto, H.; Concolino, T.
E.; Rheingold, A. L.; Christou, G. Inorg. Chem., in press.
(45) Miyasaka, H.; Clerac, R.; Wernsdorfer, W.; Lecren, L.; Bonhomme,
C.; Sugiura, K.-i.; Yamashita, M. Angew. Chem., Int. Ed. 2004, 43,
2801-2805.
(46) Yoo, J.; Rumberger, E. M.; Hendrickson, D. N.; Yamaguchi, A.;
Ishimoto, H.; Brechin, E. K.; Christou, G. J. Appl. Phys. 2002, 91
(10), 7155-7157.
(47) Sangregorio, C.; Ohm, T.; Paulsen, C.; Sessoli, R.; Gatteschi, D. Phys.
ReV. Lett. 1997, 78 (24), 4645-4648.
Inorganic Chemistry, Vol. 45, No. 2, 2006
541
Yang et al.
Table 8. Spin Parameters Obtained from the One-J (Td-Symmetry)
Kambe Model
complex
g
J (cm-1)
S
1
2
3
4
5
6
2.07
2.17
2.02
2.01
2.05
1.93
+4.36
+3.65
+5.21
+5.38
+5.26
+6.55
4
4
4
4
4
4
dc Magnetic Susceptibility Measurements. Magnetic
susceptibility data were obtained for powdered samples of
complexes 1-6 with a 1 T magnetic field in the temperature
range of 2-300 K. The χMT data were interpreted employing
two different models, as has been reported48 for other Ni4
cubane complexes. The first approach employed a total
symmetric model assuming Td symmetry of the molecule
with all of the Ni‚‚‚Ni interactions being equivalent. This
gives the spin Hamiltonian
Ĥ ) -2J(Ŝ1‚Ŝ2 + Ŝ1‚Ŝ3 + Ŝ1‚Ŝ4 + Ŝ2‚Ŝ3 + Ŝ2‚Ŝ4 + Ŝ3‚Ŝ4)
(1)
The Kambe technique49 gives directly the energies in eq 2
for the 19 different spin states of a Ni4 molecule as
E(ST) ) -J[ST(ST + 1)]
(2)
where ŜT ) Ŝ1 + Ŝ2 + Ŝ3 + Ŝ4 to give ŜT values of 4, 3, 2,
1, and 0. Substituting the energies of these 19 spin states
into the van Vleck equation gives a theoretical expression
for the χMT values of a symmetric Ni4 molecule. The χMT
data for the above six complexes 1-6 were least-squares fit
to this expression to give a positive J value. The resulting J
and g values for these six complexes are listed in Table 8.
The positive J values indicate the presence of ferromagnetic
coupling between the four NiII ions and thus give an S ) 4
ground state for each of these six complexes.
As has been reported48 in the literature, to account for the
fact that the cubane complexes in this article actually have
S4 site symmetry, which is lower than Td, a lower-symmetry
two-J model was employed to fit the χMT data. The spin
Hamiltonian for this case is
Ĥ ) - 2J1(Ŝ1‚Ŝ2 + Ŝ3‚Ŝ4) 2J2(Ŝ1‚Ŝ3 + Ŝ1‚Ŝ4 + Ŝ2‚Ŝ3 + Ŝ2‚Ŝ4) (3)
With the definitions of ŜA ) Ŝ1 + Ŝ2, ŜB ) Ŝ3 + Ŝ4, and ŜT
) ŜA + ŜB, the spin Hamiltonian defined in eq 3 leads to
the energies of different ST, SA, and SB states given as
E(ST,SA,SB) ) - J1[SA(SA + 1) + SB(SB + 1)] J2[ST(ST + 1) - SA(SA + 1) - SB(SB + 1)] (4)
As in the simple exchange parameter model above, the
energies obtained from eq 4 were substituted into the van
Vleck magnetic susceptibility equation and then used to leastsquares fit the χMT versus temperature data for each complex.
(48) Halcrow, M. A.; Sun, J. S.; Huffman, J. C.; Christou, G. Inorg. Chem.
1995, 34 (16), 4167-4177.
(49) Kambe, K. J. Phys. Soc. Jpn. 1950, 5, 48.
542 Inorganic Chemistry, Vol. 45, No. 2, 2006
Figure 17. Plot of χMT vs temperature for a polycrystalline sample of
[Ni(hmp)(MeOH)Cl]4 (1) measured in a 10-kG field. The solid line
represents the least-squares fit of the data to a two-J Kambe model.
Table 9. Spin Parameters Obtained from the Two-J (S4-Symmetry)
Kambe Model
complex
g
J1 (cm-1)
J2 (cm-1)
S
1
2
3
4
5
6
2.06
2.16
2.02
2.01
2.05
1.93
+9.24
+8.27
+5.21
+5.38
+5.26
+6.55
+2.75
+2.26
+5.21
+5.38
+5.26
+6.55
4
4
4
4
4
4
Table 10. Energy Separation (cm-1) between the S ) 4 Ground State
and Lowest-Lying S ) 3 Excited State
complex
two-J model
one-J model
1
2
3
4
5
6
22.0
18.1
41.7
43.0
42.1
52.4
34.9
29.2
41.7
43.0
42.1
52.4
Figure 17 shows the fitting of the data for complex 1 as an
example. The fitting parameters from this lower-symmetry
model are listed in Table 9. Again, each complex is found
to have an S ) 4 ground state. As expected, the fits obtained
with the two-exchange-parameter model are better than those
obtained for the one-parameter model. Also, in both cases,
the data were fit to ∼15 K because neither model accounts
for the zero-field spltting (DŜz2) in the S ) 4 ground state.
HFEPR data will be presented in a forthcoming paper,42 and
these data allow a characterization of the spin Hamiltonian
parameters.
The analysis employing the Kambe model also allows the
energy separation between the ground state and the lowestlying excited state to be evaluated by substituting the
coupling constants J back into eqs 2 and 4. The results are
reported in Table 10, where it can be seen that the lowestenergy S ) 3 excited state for these Ni4 complexes is 1852 cm-1 above the S ) 4 ground state. Zipse et al.51 have
reported high-field EPR signals for the S ) 9 first excited
(50) Wang, S. Y.; Tsai, H. L.; Libby, E.; Folting, K.; Streib, W. E.;
Hendrickson, D. N.; Christou, G. Inorg. Chem. 1996, 35 (26), 75787589.
(51) Zipse, D.; North, J. M.; Dalal, N. S.; Hill, S.; Edwards, R. S. Phys.
ReV. B 2003, 68, 184408.
Tunneling in Ni4 Single-Molecule Magnets
Figure 18. Reduced magnetization of a polycrystalline sample of [Ni(hmp)(dmb)Cl]4 (3) measured with a dc magnetic field of 1-5 T in the
temperature range of 2-4 K.
Table 11. Spin Hamiltonian Parameters Obtained from Least-Square
Fitting of Reduced Magnetization
complex
1
2
3
4
5
6
g
2.09
2.12
2.02
2.11
2.18
2.13
D (cm-1)
-0.60
-0.60
-0.61
-0.59
-0.56
-0.68
B4° (cm-1)
S
10-5
4
4
4
4
4
4
4.6 ×
4.6 × 10-5
3.4 × 10-5
6.4 × 10-5
6.1 × 10-5
1.9 × 10-5
state of an S ) 10 Mn12 SMM. They determined that the S
) 9 excited state is 24 ( 2 K above the S ) 10 ground
state.
To further confirm the spin of the ground state and the
spin Hamiltonian parameters such as the g value and the
axial zero-field splitting parameter, magnetization measurements were performed by applying a magnetic field of
magnitude 1-5 T in the temperature range of 2-4 K. Figure
18 presents the M/Nβ versus H/T plot for complex 3, where
M is the magnetization, N is Avogadro’s number, β is the
Bohr magneton, and H/T is ratio of the magnetic field to the
absolute temperature. The solid lines in Figure 18 illustrate
the full-matrix diagonalization fitting including a powder
average to the experimental data. The fitting parameters are
S ) 4, g ) 2.16, and D ) -0.6 cm-1. The results of the
fitting for all complexes 1-6 are reported in Table 11. It is
important to note that there are two crystallographically
independent molecules in the crystal of both complexes
1 and 2 with the same population; therefore, the D values
obtained in the reduced-magnetization fitting are actually
the averages for these two molecules. The D values obtained from the fitting of reduced-magnetization data are
similar to the values obtained from an analysis of HFEPR
data.42
ac Magnetic Susceptibility Data. For many SMMs, ac
magnetic susceptibility data can be employed to characterize
the magnetization dynamics of molecular nanomagnets. If
the frequency of the ac field encompasses a range including
the rate of magnetization reversal for an SMM, then
frequency-dependent in-phase and out-of-phase ac susceptibility signals are seen. However, ac susceptibility data can
also be employed to determine the presence of a magnetic
ordering phase transition, where, as a result of intermolecular
Figure 19. ac susceptibility measurements for a polycrystalline sample
of complex 3 measured to the milli-Kelvin range, given in arbitrary units.
The in-phase signals (χ′) are shown in the top plot, and the out-of-phase
signals (χ′′) are presented in the bottom plot.
magnetic exchange or dipolar interactions, there is a phase
transition involving a magnetic ordering of all of the SMM
complexes in the crystal. At temperatures above the phase
transition, the complexes are functioning independent of their
neighboring complexes, but below the phase transition
temperature, the intermolecular interactions become dominant, and there is a long-range magnetic ordering. Either the
spins on neighboring molecules are paired to give an
antiferromagnetic ordering, or the neighboring spins are
ferromagnetically coupled. ac magnetic data were collected
for complexes 1, 3, 4, and 6 to determine whether magnetization dynamics of individual SMMs could be seen or to
determine the temperatures at which magnetic ordering is
seen. Figure 19 presents the ac susceptibility data collected
for a polycrystalline sample of [Ni(hmp)(dmb)Cl]4 (3)
measured in an ac field oscillating in the frequency range of
16-761 Hz. As the temperature is decreased, it can be seen
that the in-phase susceptibility at each frequency increases
until 289 mK, below which χ′ decreases rapidly essentially
to zero. There is little frequency dependence, but the onset
of the abrupt decrease in χ′ occurs at 289 mK essentially
independent of the ac frequency. In concert with the changes
in the in-phase signal χ′, there is an increase in the out-ofphase χ′′ signal seen at the same critical temperature, and
below 289 mK, the values of χ′′ also collapse to zero. In the
crystal of complex 3, there must be intermolecular interactions such that, below 289 mK, there is a magnetic ordering
of the magnetic moments of the Ni4 molecules. This is further
substantiated by Figure 20, which shows plots of dc
magnetization versus temperature measured at different
values of external dc field in the range of 1.73-17.31 G. At
Inorganic Chemistry, Vol. 45, No. 2, 2006
543
Yang et al.
Figure 20. dc Magnetization measurements of a polycrystalline
sample of [Ni(hmp)(dmb)Cl]4 (3) given in arbitrary units. The measurements
were carried out by applying dc magnetic fields in the range of 1.7317.31 G.
each value of the external field, the dc susceptibility increases
with decreasing temperature until 280 mK, where the increase
in susceptibility abruptly stops.
To compare the relative strengths of intermolecular
interactions in the series of Ni4 complexes, ac magnetic
susceptibility data were also obtained for complexes 1, 4,
and 6. It was anticipated that the MeOH complex 1 should
have the strongest intermolecular magnetic exchange interactions and therefore would magnetically order at the highest
temperature. Plots of the temperature dependency of the outof-phase ac susceptibility (χ′′) for [Ni(hmp)(MeOH)Cl]4‚
xH2O (1) are shown in Figure 21. For this complex, the
abrupt fall off of the χ′ signal occurs at 1100 mK (i.e., 1.10
K). Again, there is little frequency dependence. Thus,
complex 1 magnetically orders at a temperature (1.1 K) that
is almost 4 times higher than the 0.289 K ordering temperature seen for complex 3.
For comparison purposes, an expanded view of the outof-phase ac data for complex 3 is also included in Figure
21. In both cases, there is some frequency dependence, but
it is not the simple frequency dependence seen for an isolated
SMM. It is important to emphasize that the out-of-phase ac
signals shown in Figure 21 are the only out-of-phase ac
signals that can be seen for these two Ni4 SMMs in the range
from 300 to 0.040 K. Frequently chemists measure ac
susceptibilities down to ∼1.8 K. Figure 22 illustrates the ac
data obtained with a Quantum Design ac SQUID in the 1.85.0 K range for a polycrystalline sample of complex 1.
Similar data were obtained for the other five complexes. As
can be seen in Figure 22, the onset of an out-of-phase (χM′′)
ac signal is seen as the temperature is decreased to 1.8 K.
This signal also seems to exhibit a frequency dependence.
In many studies, this type of onset of χM′′ signal, together
with its apparent simple frequency dependence, would be
taken as evidence for the presence of SMM behavior.
However, a comparison of the data in Figure 22 measured
to 1.8 K with the data measured to 0.040 K shows that there
is not a simple frequency dependence. This raises a caveat
about deciding, with ac data measured only to 1.8 K that
show an onset of a χM′′ signal, that a given complex is an
SMM.
544 Inorganic Chemistry, Vol. 45, No. 2, 2006
Figure 21. Out-of-phase (χ′′) ac susceptibility data for (top) [Ni(hmp)(MeOH)Cl]4‚x(H2O) (1) and (bottom) [Ni(hmp)(dmb)Cl]4 (3). Data from
scans with both increasing and decreasing temperature are included in the
plots.
Figure 23 illustrates the χM′′ ac data for samples of
complexes 4 and 6. Again, it is seen that the frequency
dependence is not simple. Although there is some small
frequency dependence, the line shape of the χM′′ data
measured at one frequency is not simple. In the case of [Ni(t-Buhmp)(dmb)Cl]4 (6), the tert-butyl substituents on both
the hmp- and the dmb ligands provide the greatest isolation
between Ni4 molecules in all six complexes. In keeping with
this, the ac data for complex 6 show a χM′′ peak at ∼50 mK
(Figure 23). Finally, the peak in χM′′ for [Ni(hmp)(chp)Cl]4
(4) is found to be ∼80 mK. The peaks in χM′′ ac data are
arranged in the order complex 1 > complex 3 > complex 4
> complex 6 (see Table 12). If these χM′′ peak temperatures
reflect, in some way, intermolecular magnetic exchange
interactions, then this ordering is in agreement with the
expectations for intermolecular interactions obtained from
the X-ray results. The order also agrees with the magnitudes
of exchange bias seen in the magnetization hysteresis plots.
Figure 24 provides definitive support for the suggestion
that the χM′′ versus temperature responses found for these
Ni4 SMMs is not simply that for an isolated SMM. If only
Tunneling in Ni4 Single-Molecule Magnets
Figure 22. ac susceptibility data between 50 and 1000 Hz from 5 to 1.8
K for [Ni(hmp)(MeOH)Cl]4 (1): (top) in-phase (χ′)and (bottom) out-ofphase (χ′′) ac signals.
Figure 23. Out-of-phase (χ′′) ac susceptibility data for polycrystalline
samples of (top) [Ni(hmp)(chp)Cl]4 (4) and (bottom) [Ni(t-Buhmp)(dmb)Cl]4 (6).
one relaxation process is present, a plot of χM′′ versus χM′
(called a Cole-Cole plot) should give a semicircle. Such a
behavior has been reported for several SMMs. However, as
can be seen in Figure 24, when the ac susceptibility data for
complex 3 is plotted in a Cole-Cole plot, the result that is
obtained is far from a semicircle. Clearly, at least two
different relaxation processes are contributing to these data.
Further research is needed to establish the origin of the two
or more relaxation processes that are contributing to the χM′′
and χM′ responses. It is our suggestion that there are two
processes. One involves the magnetization dynamics of
individual Ni4 nanomagnets, and the other involves some
magnetization relaxation of several (domains of?) Ni4 SMMs.
The magnetic ordering of regions of the crystal of a Ni4 SMM
is not static, as we observe a high rate of QTM even at 40
mK.
Concluding Comments. The four main findings in this
paper are as follows: (1) the six NiII4 complexes studied are
SMMs; (2) the rate of ground-state (Ms ) -4 to Ms ) +4)
quantum tunneling of magnetization (QTM) is quite high in
the six NiII4 SMMs; (3) intermolecular magnetic exchange
interactions are present in these NiII4 SMMs, and this affects
the magnetic field (exchange bias) at which QTM occurs;
Table 12. Magnetic Ordering Temperature of Ni4 Complexes Based on
ac Susceptibility Measurements
complex
ordering
temperature (mK
[Ni(hmp)(MeOH)Cl]4‚xH2O
[Ni(hmp)(dmb)Cl]4
[Ni(hmp)(chp)Cl]4
[Ni(t-Buhmp)(dmb)Cl]4
1100
290
∼80
∼50
Table 13. Strength of Intermolecular Dipolar Interactions in
Complexes 1, 3, 4, and 6
closest
closest
intermolecular Ni‚‚‚Ni
distance (Å) distance (Å)
complex formula
[Ni(hmp)(MeOH)Cl]4
[Ni(hmp)(dmb)Cl]4
[Ni(hmp)(chp)Cl]4
[Ni(tBuhmp)(dmb)Cl]4
7.2
8.0
9.0
9.4
11.4
10.9
9.9
12.5
dipolar interactions (mK)
based on
column 2
based on
column 3
130
96
67
59
33
38
50
25
and (4) changes in the steric bulk associated with the ligands
can be made to modulate the intermolecular magnetic
exchange interactions present in a given SMM.
In future work, we will determine the origin of the fast
ground-state QTM in these NiII4 SMMs by employing highfrequency EPR to determine the spin Hamiltonian parameters. The fact that there is fast QTM in these NiII4 SMMs
Inorganic Chemistry, Vol. 45, No. 2, 2006
545
Yang et al.
Figure 25. Magnetization hysteresis loops of [Mn4O3Cl(dbm)3(OAc)3]
cubane molecule with a transverse magnetic field 0.9 T (green curve) and
without a transverse magnetic field (red lines) at 0.04 K. The magnetization
M is plotted as a fraction of the maximum value of Ms, the saturation
magnetization.
Figure 24. Cole-Cole plot for [Ni(hmp)(dmb)Cl]4 (3). Data show four
noncircular ellipsoid shapes indicating the presence of multiple processes
at low temperatures.
can be further demonstrated by examining the magnetization
loop for the complex [Mn4O3Cl(dbm)3(OAc)3], an S ) 9/2
SMM with a thermodynamic magnetization reversal barrier
of U ) 10.6 cm-1, that is comparable to the U ) 9.6 cm-1
barrier found for [Ni(hmp)(dmb)Cl]4 (3). In Figure 25 is
shown the hysteresis loop of a single crystal of the S ) 9/2
SMM with the external magnetic field oriented parallel to
the easy axis of the crystal. A comparison with the loops
seen for complex 3 (Figures 5 and 10) shows that the S )
9/ Mn SMM exhibits a much larger coercive field (i.e.,
2
4
larger area in loop) than is seen for complex 3. This is
because the rate of QTM in the S ) 9/2 Mn4 SMM is an
order of magnitude lower. It is possible to “turn on” the QTM
for the S ) 9/2 Mn4 SMM by introducing a transverse
interaction that causes tunnel splitting (mixing) between the
Ms ) -9/2 and Ms ) +9/2 states of the S ) 9/2 SMM. In
Figure 25, the transverse interaction is added in the form of
a transverse magnetic field, which can be seen to affect
dramatically the appearance of the hysteresis loop. With such
a transverse magnetic field present, the coercive field is
collapsed, and the hysteresis loop for the S ) 9/2 Mn4 SMM
now looks very similar to that seen for complex 3.
546 Inorganic Chemistry, Vol. 45, No. 2, 2006
Transverse interactions present in the crystals of the NiII4
SMMs cause the high rate of QTM. These transverse
interactions either can be magnetic in origin or can arise from
zero-field interactions. The transverse magnetic field can
potentially arise from either external or an internal magnetic
field. The fast ground-state QTM occurs in the absence of
an external field (first steep hysteresis step). It is very likely
that the fast QTM in NiII4 SMMs arises from transverse zerofield interactions. Because high crystal site symmetry (S4)
is present in several of them, it is likely that it is higher(quartic-) order transverse zero-field interactions that are most
important. Furthermore, the zero-field interactions in the S
) 4 ground state arise from a tensor projection of the singleion zero-field interactions at each of the NiII ions in the
complex. In short, the spin-orbit interactions present at each
NiII ion project onto the S ) 4 ground state of the NiII4
complex and give fast QTM. Delineating this single-ion
effect will be focus of future work.
Acknowledgment. This work was supported by the
National Science Foundation.
Supporting Information Available: X-ray crystallographic
files in CIF format are available for complexes 1-6. This material is made available free of charge via the Internet at http://
pubs.acs.org.
IC050093R