SPIN-CROSSOVER IN THE PENTANUCLEAR BYPIRAMIDAL
Co2Fe3 AND Fe2Fe3 COMPOUNDS
Sophia Klokishner, Sergei Ostrovsky, Andrei Palii
Institute of Applied Physics, Academy of Sciences of Moldova,
Kishinev, Moldova
Kim Dunbar
Department of Chemistry, Texas A&M University,
College Station, TX, USA
Boris Tsukerblat
Chemistry Department, Ben-Gurion University of the Negev,
Beer-Sheva, Israel
In this article we report a model for a spin-crossover phenomenon
in pentanuclear bypiramidal {[M(III)(CN)6]2[M'(II)(tmphen)2]3} (M/
M'=Co/Fe, Fe/Fe) cluster compounds. The spin-crossover phenomenon
is considered as a phase transformation accompanied by a change of the
ground state spin. The model takes into account cooperative interactions
in the crystal network, local crystal fields and spin-orbit coupling acting
within the degenerate metal sites. Magnetic properties and Mössbauer
spectra are analyzed and compared to the experimental data.
1. Introduction
Spin-crossover compounds have been a subject of many
experimental and theoretical studies [1-6]. Till now only a few
experimental reports on spin crossover in cluster compounds [7-11] have
been reported. Recently FeII ions were introduced into the equatorial
metal sites of discrete cyano-bridged pentanuclear clusters
{[MIII(CN)6]2[M'II(tmphen)2]3 } (M/M' =Co/Fe(1), Fe/Fe(2) ) [12] with a
trigonal bipyramidal (TBP) structure. The octahedral nitrogen
surrounding of FeII ions facilitates the spin-crossover behavior. The
occurrence of the ls-hs transition in compounds 1 and 2 was proved by
the combination of Mössbauer spectroscopy, magnetic measurements
and single-crystal X-ray studies. For both types of clusters
[FeII(tmphen)2]3[MIII(CN)6]2(M=Fe,Co)7 the T product increases by
~9emu·K/mol between 150 K and 375 K thus indicating the ls –hs
transition at the FeII sites. The TBP FeII3CoIII2 cluster due to its electronic
65
structure represents an ideal system for studying the effects of
intracluster short-range and intercluster long-range interactions
facilitating spin-crossover. In the (FeIII)2 (FeII)3 cluster the hs-FeII and lsFeIII ions are coupled by exchange interaction. In spite of the fact that the
exchange interaction of the hs-FeII and ls-FeIII ions through the cyanide
bridge is sufficiently weak as compared with that in oxide clusters it is
interestingly to understand whether this interaction may affect the spin
transformation. The effects of orbital degeneracy on the spin-crossover
transformation in the [FeII(tmphen)2]3[FeIII(CN)6]2 crystal will be
examined as well. In the present article a microscopic approach to the
problem of spin crossover in crystals containing metal clusters is
developed.
2. The model
In the basic structural unit of compounds 1 and 2 two MIII ions
surrounded by six carbon atoms occupy the apical positions and three
FeII ions coordinated by the nitrogen atoms reside in the equatorial plane
[12]. In a strong crystal field of carbon atoms, the ground terms of the
CoIII and FeIII ions are the low-spin orbital singlet 1 A1 (t 26 ) ( S  0 ) and
the orbital triplet 3T1 (t 24 ) , respectively. The ground state of a FeII -ion in
the crystal field induced by the nitrogen atoms can be either low-spin
(ls)- term 1 A1 (t 26 ) or high spin (hs) –term 5T2 t 24 e 2 . Both magnetic
measurements and Mössbauer spectroscopy for water containing crystals
[12] demonstrate the presence of some amount of FeII ions in the hs
configuration even at very low temperatures. Further on we consider in
the model two types of FeII ions and denote by x the fraction of FeII ions which are in the hs –state at all temperatures, while the
concentration of those ions which undergo the ls-hs transition is (1-x).
The number pi of trigonal bypiramidal clusters in which i (i=0,1,2,3) of
three FeII ions are in the hs configuration in the whole temperature range


is estimated as pi  Ci3 xi 1  x  , where C lr  r! l!l  r !.
The Hamiltonian of intraion interactions can be written in the form
3 i
66
 
H 0    s k l k    (l Zk ) 2  2 / 3   B H  g 0 sk   lk







(1)
  B Hg1  ( 1   2 )   H 
k
k


where  numbers the hs  Fe ions in the k-th bypiramidal cluster, the
first term is the spin-orbit (SO) coupling in the cubic 5T2 (t24e2) - term of
II
the hs  FeII -ion, the second term describes the axial crystal field
splitting the 5T2 l  1 term into an orbital singlet ( ml  0 ) and an
orbital doublet ( ml  1 ), the third term refers to the Zeeman
interaction for hs-FeII ions and contains both the spin and orbital
contributions, B is the Bohr magneton and g0 is the spin Lande factor.
Finally, the fourth term represents the interaction of the ground Kramers
doublets of two ls-FeIII ions in the cluster with the external magnetic
field,  i is the matrix of the pseudo -spin ½ of the ls-FeIII ion, g1 =1.73
is the Lande factor. Up to room temperature the ls-FeIII can be regarded
as an ion with the pseudo-spin ½ because the ground Kramers doublet
and the excited quadruplet arising from the splitting of the 2T2 term by
the spin-orbital interaction are separated by the gap 3 / 2  730 cm 1
(   486 cm 1 [13] for a free ls-FeIII) that is large enough from the
thermal population of the excited quadruplet at room temperature.
The superexchange interaction (several cm-1, [14,15].) in the
[FeII(tmphen)2]3[FeIII(CN)6]2 through the cyanide bridges couples the hsFeII ions in equatorial and ls-FeIII –ions in axial positions. Further on we
will neglect the essentially anisotropic orbitally dependent terms and
retain only the isotropic part of the exchange interaction between the hs
–FeII and ls –FeIII ions in a cluster. The Hamiltonian of exchange
interaction for the k  th cluster looks as follows


k
H ex
 2 J ex  s k σ 1k  σ k2 ,

(2)
where s  2 is the spin of the hs-FeII ion, the summation in (2) takes
into account the hs-FeII ions appearing in the k  th cluster due to the
spin transition and those which are in the hs-state in the whole
67
temperature range. As in [16-18] we suppose that the mechanism
responsible for the ls-hs transition is the interaction of FeII ions with the
spontaneous all-round full symmetric lattice strain. Applying the
procedure suggested in [16-18] we obtain the Hamiltonian of electrondeformational interaction
H st   B  k 
k ,
where
B  A1 2 ,
J
2nm
    
k
k,
J  A12 , A 
'
k'
(3)
k ', '
c2
,
c1 c2  0  c1    0 
n
(n=1,2,3) is the number of FeII ions which undergo the ls-hs transition in
a complex, m is the number of TBP MIII2M’II3 complexes whose FeII ions
are involved in the spin conversion, =1,...,n , k=1,...,m, 0 is the
volume that falls at a Fe ion and its nearest surrounding and  is the unit
cell volume per one iron, respectively. In the basis of the states 5T2 and
1
A1 the 16  16 matrix  k is diagonal and has 15 eigenvalues equal to 1
and one eigenvalue equal to -1. Finally,
1  (hs  ls ) / 2 ,
2  (hs  ls ) / 2 ,  hs and ls are the constants of interaction of the
FeII ion with the full symmetric strain  A1 in the hs and ls states,
respectively. The first term in (3) acts as an additional field applied to
each spin-crossover ion and redefines the effective energy gap 0
between the hs and ls states of the FeII in the cubic crystal field. The
second term in (3) represents an infinite range interaction between the
FeII ions which undergo the spin conversion. This interaction arises from
the coupling to the strain. The model of the elastic continuum introduced
above satisfactorily describes only the long-wave acoustic vibrations of
the lattice. Therefore, the obtained intermolecular interaction
corresponds to the interaction via the field of long-wave acoustic
phonons.
Due to the proximity of the FeII ions in the clusters short-range
interactions between these ions inside the cluster are relevant. The
largest is the effect of the exchange arising from the optic phonons [19].
68
The Hamiltonian describing short-range interactions between FeII ions
within the trigonal bipyramid can be written as:
(4)
H sr   J 0
 k k ' .
 
k
  '
The Hamiltonian (4) takes into account the interaction between the FeII
ions participating in the spin transitions, the interaction of these ions
with those FeII ions which are in the hs-state in the whole temperature
range as well as the interaction between the latter. It should be
mentioned that eq. (3) as compared with eq.(4) only accounts for FeII
ions participating in spin conversion. The Hamiltonian for the whole
crystal can be written as
H  H 0  H sr  H st  H ex
where H ex 
 H exk .
0
 k ,

2 k 
(5)
In the molecular field approximation the full
k
Hamiltonian H can be written as a sum of one-cluster Hamiltonians

 
~
H k  ( J  B  0 ) k  J 0  k  k '    s k l k I 1k
2 
  '

 


(l Zk ) 2

k
 2 / 3 I1 
k
H ex


  B H  g 0 s   l  I 1 

k
k
k
, (6)
 B Hg1 ( 1k

k
2)
where in the basis of the states 5T2 and 1 A1 I 1k is a diagonal 16 16 -
matrix with 15 eigenvalues equal to 1 and one vanishing eigenvalue, 
~
is the order parameter. In fact the Hamiltonians H k describe clusters
with different numbers of spin-crossover FeII ions, and k as before
numbers the clusters in the crystal. For calculation of the temperature
dependence of the order parameter the self-consistent procedure was
applied. The calculations of the magnetic properties were based on the
Hamiltonian given in Eq.(6).
3. Results and discussion
The estimation of the parameters J and B was performed
according the procedure suggested in paper [16-18]. For characteristic
for compounds 1 and 2 parameters  =1026Å3, 0 =8Å3,
c2  (0.05÷0.1)c1, c2  1011dyne / cm 2 , 1  6.4 104 cm1, , 2  7.8  104 cm1 the
69
parameters J and B take on the values 20÷80 cm-1 and -95 ÷ -24 cm-1,
respectively.
Fig.1 shows the experimental data for compound 1 together with
the calculated T vs. T curves. The result of the best fit procedure in
the model above developed is presented by curve 1. The best fit
parameters are the part of the figure caption. One can see that a quite
good agreement with the experimental data is obtained. At temperatures
below 100 K the T values show that the FeII ions are mainly in the ls –
state. However, some small admixture of hs ions is present. In the
temperature range 150-300 K the T product gradually increases thus
indicating the ls - hs transition in the FeII ions.
9
3
T, cm K mol
-1
6
-1
1
0.8
3
3
7
1.0
T, cm K mol
8
2
0.6
1
0.4
5
0
2,3
5
10
15
20
25
30
35
Temperature, K
4
3
2
1
0
0
50
100
150
200
250
300
Temperature, K
Fig.1. Temperature dependence of the T product for 1. Circles-experimental
data [12]. The solid lines represent a theoretical fit with =-103 cm-1, x=10%
and (1) hs-ls =640 cm-1, J =35 cm-1, J0=45 cm-1, =180 cm-1, =1.0; (2) hs-1
-1
-1
-1
ls=620 cm , = -136 cm , J=0, J0=0,=0.6; (3) hs-ls=630 cm , =168 cm ,
J=0, J0=0, =0.6.
The parameter J of long -range cooperative electron-deformational
interaction obtained from the best fit procedure falls inside the limits
70
estimated above. Relatively small values of the parameters J and J0 as
compared with the gaps hs-ls= 0-2B and  are also in agreement with
the observed gradual temperature dependence of T and noticeable
increase of T at temperatures higher than 150K. Finally, the estimated
from the best fit procedure percentage of FeII ions (x=10%) which are in
the hs-state at any temperature is very close to that obtained from the
Mössbauer spectra [12]. For comparison in the same figure (curves 2,3)
the results of fitting of the T curve in neglect of long- and shortrange interactions are shown for the cases of   0 and   0 . It is
seen that in this approximation the calculated curves 2 and 3 differ
significantly from the experimental one both at low and high
temperatures, besides this the obtained value   0.6 is too small for
hs-FeII-ions.
For compound 2 the variation of the observed magnetic
susceptibility as a function of temperature is presented in Fig.2.
7
T, cm3 K mol-1
6
5
4
3
2
1
1
2
3
0
0
50
100
150
200
250
300
Temperature, K
Fig.2. Temperature dependence of the T product for 2. Circles experimental
data [12]. Curves 1- 3 were calculated with the following parameter values hs-1
-1
-1
-1
-1
ls =690 cm , J=30 cm , J0=40 cm , =100 cm , =-103 cm , =1.0, x=9%
-1
-1
and (1) Jex = 3 cm , (2) Jex = 0, (3) Jex = -3 cm .
71
First, the magnetic behavior of complex 2 was analyzed with
neglect of intracluster Heisenberg exchange interaction between Fe II and
FeIII ions. The result of the best fit procedure is presented by curve 2 in
Fig.2. The best fit parameters are the part of the figure caption. One can
see that the values of the key parameters are close to those for complex
1. However, the obtained energy gap hs-ls between the ls and hs
configurations for complex 2 is a bit larger than the corresponding gap
for compound 1 while the parameters of short-range and long-range
interactions are smaller. Namely, this difference in the characteristic
parameters leads to lower values of T for compound 2 as compared
with compound 1 at temperatures higher than 150K. The effect of
exchange interaction on the magnetic behavior is illustrated in Fig.2 by
curves 1 and 3. Since typical values of the exchange parameters in
cyanide bridged complexes are of several cm-1, we calculated the T
product with the set of the best fit parameters and Jex = -3 cm-1 and 3
cm-1. One can see that at temperatures higher than 50K the small
exchange interaction has no effect on the magnetic properties of
complex 2.
Mössbauer spectra provide direct information about the population
of the hs and ls states and serve a reliable test for the theoretical
background of the SCO phenomenon. The total Mössbauer spectrum
(i.e. the observable spectrum) was obtained by summing up the spectra
yielded by different cluster electronic states in the molecular field, with
due account for their equilibrium populations for a given (at a certain
temperature) value of the molecular field. In calculations the
experimental values for the parameters of the quadrupole splttings and
isomeric shifts were taken from [12]. The calculated and experimental
spectra are shown in Fig.3.
Quite good agreement between the experimental data and
theoretical calculations is obtained. It should be underlined that the
model takes into account the main effect inducing the temperature
dependence of the Mössbauer spectra , and this is the temperature
dependence of the cluster energies in the molecular field. Namely, this
effect is responsible for the transformations of the Mössbauer spectra
with temperature.
72
The proposed model gives a good fit to the observed temperature
dependence of the static magnetic susceptibility and the Mössbauer
spectra. The last clearly illustrates the cooperative nature of SCO
transformations in TBP compounds that leads to a crossing of the ls and
hs levels due structural phase transition induced by the ordering of the
local deformations through the field of the acoustic phonons.
Fig.3. Mössbauer spectra for compound 1 calculated at T=4.2, 220 and 300K
with the set of the best fit parameters (thick solid lines). Contributions from ls FeII and hs -FeII ions are shown in dash and dot lines, respectively. The halfwidth of the individual lines: Г=0.16 cm-1(4.2 К), Г=0.18 cm-1(220К),
Г=0.24cm-1(300К).
73
Acknowledgments
Financial support of
the STCU (project N5062) is highly
appreciated. B.T. and K.D. gratefully acknowledge financial support of
the Binational US-Israel Science Foundation (BSF grant no. 2006498).
B.T. thanks the Israel Science Foundation for the financial support (ISF
grant no. 168/09).
References
1. Gütlich, P.; Goodwin, H. A. Spin Crossover in Transition Metal
Compounds, Springer-Verlag, 2004;
2. Hauser, A. Light-Induced Spin Crossover and the High-Spin →LowSpin Relaxation; Springer-Verlag, 2004;
3. P. Gütlich, J. Jung, Nuovo Cimento D 1996, 18, 107;
4. P. Gütlich, A. Hauser, H. Spiering, Angew. Chem. Int. Ed. Engl.
1994, 33, 2024;
5. J. Zarembowitch, New. J. Chem. 1992, 16, 255;
6. A. B. Gaspar, V. Ksenofontov, M. Serdyuk, P. Gütlich, Coord.
Chem. Rev., 2005, 249, 2661;
7. J.A. Real, A.B. Gaspar, M.C. Munoz, P. Gütlich, V. Ksenofontov, H.
Spiering, Top.Curr.Chem.2004, 233,167;
8. G. Vos, R.A.G. De Graaff, J.G.Haasnoot, A.M. van der Kraan, De,
P.Vaal, J.Reedijk, Inorg.Chem. 1984, 23, 2905;
9. E.Breuning, M.Ruben, J.M.Lehn, F.Renz, Y.Garcia, V.Ksenofontov,
P. Gütlich, E. Wegelius, K.Rissanen, Angew.Chem.,Int.Ed. 2000, 39,
2504;
10. M. Nihei, M.Yi, M.Yokota, L.Han, A.Maeda, H.Kushida, H.
Okamoto, H.Oshio, Angew.Chem, Int.Ed. 2005, 44,6484;
11. D.-Y. Wu, O. Sato, Y. Einaga, C.-Y. Duan, Angew. Chem. Int. Ed.
2009, 48, 1475 –1478 2009;
12. M.Shatruk, A.Dragulescu-Andrasi, K.E.Chambers, S.A.Stoian,
E.L.Bominaar, C.Achim, K.R.Dunbar, J. Am. Chem.2007,129,6104;
13. A.Abragam, B.Bleaney, Electron Paramagnetic Resonance of
Transition Ions, Clarendon Press, Oxford, 1970;
14. A. V. Palii, S.M. Ostrovsky, S. I. Klokishner, B. S. Tsukerblat, C. P.
Berlinguette, K. R. Dunbar, J. R. Galán-Mascarós, J.Am.Chem.Soc.,
2004, 126, 16860;
15. H.Weihe, H. Gudel, H. , Comments Inorg. Chem. 2000, 22, 75;
74
16. S.I. Klokishner, F. Varret, J. Linares, Chem.Phys., 2000, 255, 317;
17. S.I. Klokishner, J.Linares, Phys.Chem.C, 2007, 111, 10644;
18. S.I. Klokishner, J. Linares, F. Varret, Journal of Physics:
Condensed Matter, 2001, 13, 595;
19. J.M. Baker, Rep. Prog. Phys. 1971, 341, 109.
75