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ALTERNATING EXCHANGE IN FERRIMAGNETIC
ISING CHAINS
F. Sapiña, E. Coronado, M. Drillon, Robert Georges, D. Beltrán
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Supplement au no 12, Tome 49, decembre 1988
ALTERNATING EXCHANGE IN FERRIMAGNETIC ISING CHAINS
F. SapGa ( I ) , E. Coronado (I), M. Drillon ('), R. Georges (3) and D. Beltr6n ( I ) ( I ) A t . Quimica Ino~~cinica, 46100 Bu jasot, Valencia, Spain(2) Dept. Science Materia-, EHICS, 67008 Strasbourg, France ( 3 ) Lab. Chimie du Solide, LP 8661, 33405 Talence, France
Abstract.
-
We propose a general treatment for solving J-alternating ferrimagnetic Ising chains, made up of two spin sublattices (s, S). Exact expressions of the susceptibility are derived for s = 112 spins alternating with arbitrary Squantum spins, including a local anisotropy on the second sublattice, Db. The magnetic properties of the ordered bimetallic chain MnCo (EDTA), 6 H 2 0 is discussed on the basis of the developed model.Stimulated by the discovery of new quasi-one di- mensional compounds MM' (EDTA). 6Hz0-in short (MM')), the structure of which may be viewed as or- dered bimetallic chains with alternating M
-
M' dis-tances, M
-
M'-
M-
M' [I], we have focused for a time on the general behavior of ferrimagnetic chains with Heisenberg or Ising exchange couplings [2-51. So far, all the models developed have assumed uniform chains, ignoring the alternation of the exchange pa- rameter, J.We present here a general treatment for solving J- alternating ferrimagnetic Ising chains, made up of two spin sublattices (s
-
S).
Exact expressions of the ther- modynamic quantities of interest can be derived for s = 1/2 spins alternating with arbitrary Squantum spins, including local anisotropies.Theoretical treatment of the J-alternating fer- rimagnetic Ising chains (1/2-S)
The full hamiltonian is written as
where the current spin operator Sk takes the values Sa = 1/2 and Sb = S for odd and even sites, respec- tively, g, and g b are the corresponding Land6 factors, and Db is the zero field splitting on site b.
A similar procedure to that reported for other ferri- magnetic chains [5, 61 allows us to deduce the transfer matrix:
where r = exp (gafi~HP)
,
s = exp (s~PBHP),
K =exp(DbP),P= 1 /kT
The summations are extended over j = 0 (1/2) t o S, for S integer (semi-integer).
Taking into account that the partition function per pair of sites corresponds to the largest eigenvalue of T, we obtain the following expression for the zero-field parallel susceptibility:
where So and Po are the values at zero field of the trace and determinant of T, respectively.
Using this expression we have calculated the mag- netic behavior of the (1/2
-
5/2) Ising system for t h e two limiting cases, namely the regular chain (J =J')
and dimer unit (solid lines of Fig. 1). In this figure, X ,represents the normalized susceptibility per spin pair defined as
These results can be compared with those obtained for J-alternating Heisenberg chains made up of s = 112 spins alternating with classical spins [7]. We observe that in the regular chain limit both models give a sim- ilar variation of the X,T product with a close coin- cidence in the height of the minimum and in the di- vergence at lower temperatures. On the contrary, the
C8 - 1424 JOURNAL DE PHYSIQUE
Fig. 1. - Theoretical variation of the normalyzed magnetic Fig. 2. - Magnetic behavior of the bimetallic chain susceptibility of a (112-5/2) Ising chain in the limiting cases (MnCo). Solid line corresponds to the best fit from the
J = J' (A) and J' = 0 (B). Dashed lines correspond to J-alternating Ising model. Comparison to uniform chain the calculated behaviors from the (112-classical) Heisenberg (- - -) and dimer (.---) limits are also given.
model.
curve of the Ising dimer is significantly above that of the Heisenberg dimer and further exhibits a narrow minimum around kT
/
1
JI = 1.This drastic difference may come from the fact that we are comparing an average susceptibility (in the Heisenberg case) with the parallel component of X (in the Ising case), thus neglecting the perpendicular con- tribution, which decreases toward zero upon cooling down. This assumption, that is justifiable in the chain limit owing to the divergence of XiI, is no longer valid in the dimer limit. Thus, the value of X,T at absolute zero (4.2) is divided by one third when X L is taken into account and hence, the difference with the corre- sponding Heisenberg value (2.1) is reduced.
The above remarks allow us to emphasize that, ex- cept near the dimer limit, the magnetic susceptibility of this kind of systems is little sensitive to the symme- try of the exchange Hamiltonian.
The MnCo(EDTA).6H20 ferrimagnetic chain
Its structure consists of i n h t e zigzag chains in- volving two alternating octahedral sites selectively oc- cupied by Mn(I1) and Co(I1) ions. Co(I1) can be described at low temperatures by a very anisotropic Kramers doublet (gI1 = 9, g l = 1.3) with an effec- tive spin 112 and hence, the anisotropic Ising model is expected to describe conveniently the magnetic prop- erties.
Accordingly, the low temperature data are reported in figure 2, along with the best fitted curves. A very close agreement with experiment has been obtained for J = -2.7 a i l J' = -0.6 K (solid line), which indicates a significant J-alternation. In order t o test the validity of this result we have fit the data to a regular chain ( J = J' = -1.6 K) and a dimer ( J = -3.4 K; J' = 0)
model. We observe that the uniform chain behavior gives a close agreement for tempera1;ures around and below the minimum, but is less satisfactory a t higher temperatures. Conversely, the dimeric behavior well reproduces the decrease of X T upon cooling down and the position of the minimum, but does not allow to explain the sharp divergence at lowel- temperature.
Acknowledgments
This work was supported by the European Economic Community (grant ST2/164), and Th,e Comision Inter- ministerial en Ciencia y Tecnologia (grant PB85-0106- c o 2 - 0 2 ) .
[I] Coronado, E., Drillon, M., Fuel-tes, A., Beltran, D., Mosset, A., Galy, J., J. Am. Chem. Soc. 108 (1986) 900 and references therein.
(21 Drillon, M., Coronado, E., Beltran, D., Curely, J., Georges, R., Nugteren, P. R., de Jongh, L. J., Genicon, J. L., J. Magn. Magn. Mater. 54-57
(1986) 1507.
[3] Coronado, E., Nugteren, P. R., Drillon, M., Bel- tran, D., de Jongh, L. J., Georges, R., Organic and Inorganic Low Dimensional Crystalline Mate- rials, Eds. P. Delhaes, M. Drill011 (Plenum: N.Y.)
NATO ASI Ser. B 168 (1987) 405.
[4] Curely, J., Georges, R., Drillon, M., Phys. Rev.
B 33 (1986) 6243.
[5] Georges, R., Curely, J., Drillca, M., J. Appl.
Phys. 58 (1985) 914.
[6] Kramers, H. A., Wannier, G . H., Phys. Rev. 60 (1941) 252.
[7] Pei, Y., Kahn, O., Sletten, J., %nard, J. P., Georges, R., Gianduzzo, J. C., Curely, J., Chu,
