Journal of Magnetism and Magnetic Materials 54-57 (1986) 1507-1509 1507

M A G N E T I C P R O P E R T I E S O F F E R R I M A G N E T I C C H A I N S

M. D R I L L O N ~, E. C O R O N A D O ~, D. B E L T R A N b, j . C U R E L Y ~, R. G E O R G E S c

P.R. N U G T E R E N d, L.J. D E J O N G H d and J .L. G E N I C O N ~

" Dbpartement Science des Matbriaux, - E.N.S.C.S. 1, rue Blaise Pascal, 67008 Strasbourg, France Departamento de Quimica Inorganica, Valencia, Spain

' Laboratoire de Chirnie du Solide, 33405 Talence, France a Karnerlingh Onnes Laboratorium, 2300 RA Leiden, The Netherlands '~ C.R.T.B. T 38042 Grenoble, France

The magnetic behaviors of complexes MnM' (EDTA).6H20 (M' = Ni, Co) are discussed in terms of so-called ferrimagnetic l-d systems. The data agree very well with theoretical predictions for Heisenberg ([MnNi] complex) or Ising ([MnCo] complex) models, yielding the respective values J = - 1,5 K and J = - 1,9 K for the exchange constants.

1. Introduction XT

One-dimensional ( l -d) exchange coupled systems 15 offer great challenges to physicists and chemists to

describe phenomena which cannot be explained in higher dimension. Thermodynamic quantities of interest have 12 been derived exactly in some specific cases such as the l -d lsing network [1] or the Heisenberg chain in the 9 classical spin limit [2]. Stimulated by the recent synthe- sis of new bimetallic quasi 1-d complexes, MM' (EDTA) 6 -6H20, the structure of which may be schematized as infinite chains M - M ' - M M' .. . [3], we have focused 3 attention on the general behavior of ferrimagnetic chains ($1, S2)N made of unequal spin sublattices [4-6]. Several attractive situations, related to some typical combina- tions of the metal ions, were solved in particular from the viewpoint of the spin dimensionality and nature of the coupling. As part of these studies, we report here on the thermodynamics of two complexes of the above series corresponding to [MnNi] and [MnCo] chains. These will be shown to be good candidates for discuss- ing the properties of ferrimagnetic 1-d systems, on basis of the symmetry of the exchange coupling.

2. Experiment

The complexes formulated as MnIIM'(EDTA)(H20)4 • 2 H 2 0 (with M ' = Ni It or Co ll) belong to a series of ferrimagnetic systems in which both the 1-d character and the cationic ordering are well-established. The structure may roughly be described as infinite zig-zag chains involving alternating metal ions. The one (Mn n) is surrounded by four water molecules and two oxygen atoms, belonging to bridging carboxylate groups, while the other (Ni II or Co II) exhibits an hexacoordination through the EDTA ligand. Due to the selective occupa- tion of both sites, distinct spin sublattices are expected to result in a so-called ferrimagnetic 1-d behavior. Let us now examine the magnetic behavior of the [MnNi] complex in the temperature range 0.1-150 K through a

+

.d" ÷

$ ÷+

4

3 . -

2

* 2 4 6 8 T/K

+*~.+ + ++ + ÷÷+

+#

+ ~ ' ~ . . . . . . . . . . . . . . . . . . . . . . . . .

0.1 1 10 T / g

Fig. ]. Magnetic behavior of the [MnNi] complex. The inset gives the result of the fit from the Heisenberg model(full line). The behavior of an isolated dimer (5/2, 1) is reported in dashed line.

plot of xT=f(T) on a semilogarithmic scale (fig. 1). The main features to be emphasized down are: (i) a regular decrease of the x T product from 5.8 emu at 150 K to 2.5 emu at 3 K, (ii) a rounded minimum located around T = 2.5 K that is a characteristic feature of 1-d ferrimagnets [4], (iii) a sharp maximum at 655mK that suggests a phase transition to a magnetically ordered state. At lower temperatures, the drop to zero of the data agrees with an antiferromagnetic three dimensional ordering.

Notice that zero-field splitting generally observed for the Ni II ion ground-term does not seem to prevent the magnetic ordering in the present case. A singlet-doublet splitting of the Ni n ion that is very large compared to the M n - N i exchange (and leaves the singlet lowest), would result in Mn xl moments feeling no exchange field to first order so that a constant x T value (close to 4.37 emu) would be expected at low temperatures. Heat capacity measurements performed in the range 0.07-30 K confirm the above assumptions (fig. 2). A transition to long range magnetic order is noted at T~ = 660 mK,

0 3 0 4 - 8 8 5 3 / 8 6 / $ 0 3 . 5 0 © Elsev ier Sc ience Publ i shers B.V.

1508 M. Drillon et aL / Properties qf ferrirnagnetic chains

CIR

O. I /t f:ff"

0.1 1 10 TIK

Fig. 2. Experimental specific heat data for the [MnNi] complex.

×T

0 5 10 15 rlK Fig. 3. Magnetic behavior of the [MnCo] complex. The full line is the result of the fit from the Ising model.

in very good agreement with susceptibility results. Then, a slight bump in the data, near 4.5 K, indicates the presence of a Schottky anomaly which is to be attri- buted, according to magnetic findings, to the l -d char- acter of the system. Finally, at higher temperatures, the increase of the specific heat corresponds to the expected lattice contribution fitted by a T 3 law. The main char- acteristics common to ferrimagnetic chains are equally present for the [MnCo] complex, whose magnetic behav- ior is plotted in the range 1.2-20 K in fig. 3. Specific heat measurements carried out at lower temperatures allow the location of the phase transition at T~. = 1.06 K, not very far from the minimum of xT.

the current spin vector S~ takes values S , - 5 / 2 or S b - 1 depending on the site parity. For finite strings of N pairs (S~,- Sb), the eigenvalue problem consists in solving a 18 '~' × 18 x energy matrix. As previously shown in similar studies, a very significant reduction of the computational work is obtained by taking fully into account the geometrical and spin space symmetries of a 2 N-site closed chain [4]. Then, the eigenfunctions of J{ transform according to the irreducible representations of the point group D x, instead of D, when assmning linear segments.

Let us now turn our attention towards the magnetic behavior. Let g~ and gb be the Land6 factors for the spins S~ and S b, respectively. The magnetic susceptibil- ity may be divided into two contributions, c~ and X2. related to first- and second-order Zeeman effects. As long as g~ =egb, only X1 is concerned so that the susceptibility is computed from the diagonal matrix elements of

M=:,~,,E s~, ,+g~Y~s~,, (2) t I t 1

within the states diagonalizing J r , For g, = gh, the X2 contribution arising from nondiagonal terms of M: needs in turn to be considered. The computations per- formed on rings of increasing size were limited to N - 3 because of the size of the matrices to be diagonalized and the required computing times. Theoretical data were then extrapolated to the thermodynamic limit (N --+ m) by means of relations of the type X.~(T)-- X x ( T ) + a(T)/N, previously tested on other ( S,, St,) ~. systems with larger N values.

Using these results, a very good agreement with experiment is obtained over the whole temperature range with the set of parameters J = - 1 . 5 0 K. gMn = 1.95 and gN, = 2.39. In particular, this model provides a very' satisfying description of the xT minimum (fig. 1 ) that is the characteristic feature of a ferrimagnetic chain. An analysis of the magnetic part of the specific heat may also be worked out from the above model. However. the possible influence of the Ni n zero-field splitting makes an attempt to fit the Schottky anomaly less relevant. Thus, the height of the latter is significantly lower than predicted by the model and also the position of the maximum disagrees. Indeed, from experiment on the isostructural [MgNi] complex we find evidence for large zero-field splitting of the Ni u ions.

3. ]MnNi] Ferrimagnetic Heisenberg chain

Owing to the ground state symmetry of the inter- acting ions, the [MnNi] chain is assumed to be de- scribed by the isotropic Hamiltonian

N

j~t9 _ j Z S 2 t ( S 2 i - i -~- S2I+ 1), ( 1 ) t I

where J < 0 refers to an antiferromagnetic coupling and

4. [MnCo] Ferrimagnetic king chain

In describing the properties of the [MnCo] complex, we have to bear in mind that in distorted Ot, symmetry the high spin Co n ion behaves as an effective spin S = 1 /2 at temperatures below 20 K. This results from the combina t ion of crystal-field distort ion and spin orbit coupling, which split up t he 4 T 1 ground-tern1 into six Kramers doublets that are well-separated in

M. Drillon et al. / Properties of ferrimagnetic chains 1509

energy. From EPR results indicating a high anisotropy of the Co n site (gll = 9.85, g~. = 1.42), it may be as- sumed that the [MnCo] complex is quite accurately described by the Ising model (the direction of the Mn n spins will also be fixed through the M n - C o exchange). Then, only S ~ components of the spins need to be considered in the exchange Hamiltonian.

Since we are dealing with large spins on one of the sublattices, the system may reduce to a ferrimagnetic chain in which quantum spins 1 / 2 alternate with classi- cal ones of amplitude S. Then, exact expressions of the principal susceptibility may be derived from the transfer matrix method. In a previous paper, we have shown that the size of the transfer matrix reduces to 2 × 2, thus allowing an easy determination of the largest eigenvalue and further thermodynamic quantities of interest [6]. For instance, the parallel susceptibility may be written:

2 2 N g b l ~ (

Xz = k T r 213a (a 2 + 2) sinh a

- 6 a ( a + sinh a ) cosh a + 3( a 2 + 1) sinh 2 a

+ a 2 ( a 2 + 3)] [q_a3(a + sinh a) ] - '

_ 2 r a cosh a - sinh a + sinh a (3) a 2 a )

where a = - J S / k T and r is the ratio between classical

and quantum moments. As shown in fig. 3 the data agree closely with the Ising model for J = -1 .91 K, gMn = 1.95 and r = 1.8. Clearly, the classical-quantum model provides a good description of the temperature dependence of x T up to about 20 K. Obviously, the quality of the fit becomes less at higher temperatures due to the increasing thermal occupation of the upper levels of the Co I1 ion.

Finally, it may be argued that the above treatments are based on negligible interchain ( J ' ) exchange cou- plings, which becomes questionable near to the phase transitions at low temperatures. In fact, the 1-d char- acter of the complexes studied can be checked by con- sidering that T~ is proportional to ( j j , ) l / 2 for Heisen- berg chains [7]. Taking into account that each chain is surrounded by four equivalent ones, we find for the [MnNi] complex J ' / J "= 10 -2, which justifies the use of 1-d models for the data analysis.

[1] M. Suzuki and S. Katsura, J. Math. Phys. 8 (1967) 124. [2] M.E. Fisher, Am. J. Phys. 32 (1974) 241. [3] D. Beltran, E. Escriva and M. Drillon, J. Chem. Soc. Far.

I178 (1982) 1773. [4] M. Drillon, J.C. Gianduzzo and R. Georges, Phys. Lett.

96A (1983) 41. [5] R. Georges, J. Curely and M. Drillon, J. Appl. Phys. 58

(1985) 914 and references therein. [6] J. Curely, R. Georges and M. Drillon submitted to Phys.

Rev. B. [7] P.M. Richards, Phys. Rev. B10 (1974) 4687.