~ Journal of magnetism

, ~ and magnetic materials

ELSEVIER Journal of Magnetism and Magnetic Materials 139 (1995) 102-108

Magnetic and structural properties of KCoxMg l_xF3 compounds

D. Skrzypek *, J. Heimann Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland

Received 2 May 1994; in revised form 6 July 1994

Abstract

The mixed crystals KCoxMg 1 _xF3 with 0.25 < x < 1 were studied by static susceptibility and X-ray diffraction methods, in the temperature range 4.2-350 K. From these measurements, the variations of several quantities, viz. T N, t = T N ( x ) / T N (1), 0 (Curie-Weiss temperature), /zef f (effective moment), and a, c (lattice parameters) with concentration or temperature were determined. The exchange constant was evaluated using theoretical results obtained for random, dilute magnetic systemg with magnetic ions having nonvanishing orbital momenta. From the temperature evolution of the cubic (400) Bragg line, the values of temperature for the structural phase transition and tetragonal deformation lattice with c /a < i were estimated. A strong correlation was found between the magnetic and structural phase transition, with the lattice deformation resulting from the magnetic properties of the crystals studied.

I. Introduction

In this paper we report the results of our study carried out using temperature-dependent magnetic susceptibility measurements and temperature-depen- dent measurements of lattice parameters. Five sam- ples were investigated in the composition range 0.25 < x < 1 and in the temperature range 4 .2 -350 K. From these studies, the variations of several quanti- ties, viz. Try, t = TN(x) /TN(1) , 0 (Cur ie -Weiss temperature), /zef f (effective magnetic moment) and a, c (lattice parameters) with x or temperature were determined.

The magnetic properties of K C o x M g l _ x F 3 are of particular interest because the orbital angular mo- mentum of the Co 2+ ion is not quenched by the

* Corresponding author.

octahedrally coordinated crystal field. The free CO 2+

ion has seven d electrons so that L = 3 and S = 3 / 2 . The octahedral crystal field produces, as the lowest state, a T 1 triplet within which the matrix elements of L may be described in terms of those of an effective orbital angular momentum l = 1. The pro- portionally constant L--* a l l is - - 3 / 2 when the mixing with an upper state is neglected. In the perovskite structure the sp in-orb i t interaction gives, as the lowest, a doublet state with s' = 1 /2 .

The crystal KCoF 3 is a G-type antiferromagnet with T N = 114 K [1]. In the antiferromagnetic region the spins are arranged along the z-axis. The ex- change interactions for cations having cubic-field ground state terms T2g of Tlg have been discussed by Eremin et al. [2]. It follows from the studies of the effective Hamiltonian, which contains an or- bitally dependent part expressed in terms of fictitious orbital moments, that in the case of KCoF 3 the anisotropic exchange is smaller by an order of mag-

0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD1 0304-8853(94)00457-9

D. Skrzypek, J. Heimann /Journal of Magnetism and Magnetic Materials 139 (1995) 102-108 103

Table 1

Measured lattice parameters for all samples at a room temperature

Compounds a (A)

KC00.88 Mg0.12 F3 4.0575 KCo0.75Mg0.25F3 4.0452 KCo0.67 Mg0.33F3 4.0385 KCo0.45 Mg0.55 F 3 4.0168 KC°0.25 Mg 0.75 F3 4.0035

nitude than the isotropic exchange. Consequently, for KCoF 3 the exchange interaction may assume the well-known Heisenberg form.

2. Experimental

2.1. Sample preparation

Single crystals of KCoxMgl_xF3 were grown from the melt by the horizontal Bridgman method. The starting stoichiometric mixtures KHF2, CoF 2 and MgF 2 were heated to maximum temperatures higher than their respective melting points by about 50 K. The low cooling rates were maintained by driving the melt through the temperature gradient of the furnace at a rate of 4 mm h- 1. The crystallization process was performed under an argon atmosphere. Since the ions Mg 2+ and Co 2÷ showed sufficient chemical singularity, solid solutions were formed over the whole range of concentrations 0 ~< x ~< 1. The crystals, 2 cm 3 in volume, were obtained with a concentration gradient along their length. Therefore, the compositions of the specimens studied were ex- amined by the X-'ray diffraction method. The lattice constant measurements made it possible to determine the sample composition parameter x, assuming that Vegard's law is valid over the range of x from 0.0 to 1.0. The results are shown in Table 1. At room temperature all samples show the perovskite cubic symmetry (Pm3m).

2.2. Magnetic measurements

The magnetic susceptibilities in the temperature range 4.2-350 K were measured by the Faraday method in a field of 0.125 T. The measurements were carried out without sample orientation. The

experimental values of susceptibility were corrected for a diamagnetic contribution.

2.3. X-ray measurements

The selected crystals of KCoxMgl_xF3 were studied by X-ray diffraction in the temperature range 10-300 K. The experiments were carried out on powdered samples from the line profile measure- ments in order to achieve high-precision estimates of the cell parameters and any possible cell distortions. An automated diffractometer of the DRON type, which employs Cu K,~ radiation, was used in the experiments. By scanning the line profiles with a step value set t o [ A 2 0 1 = 0 . 0 1 °, the number of counter pulses was measured at intervals of AT = 10 s. Next, the data were subjected to profile refinement using the Pearson VII function. This procedure al- lowed us to obtain certain fundamental characteris- tics of the lines, namely position, intensity and half- width value of the lines; in the case of any distor- tions connected with structural phase transitions we could also determine the number of overlapping lines [ 3 ] .

3. Results and discussion

3.1. Temperature dependence of the magnetic sus- ceptibility of KCoxMg I _ xF3

The temperature dependence of the magnetic sus- ceptibility for several compounds is shown in Fig. 1.

03 , 0100

E

0075

> 02 !

0050

0025

0 100 200 300 400

TEMPERATURE[K]

Fig. 1. Magnetic susceptibility versus temperature ~ r KCo x Mgl_x~ crystals.

104 D. Skrzypek, J. Heimann /Journal of Magnetism and Magnetic Materials 139 (1995) 102-108

Table 2 The Curie-Weiss temperature 0, the effective moment /.tar, the NOel temperature T N and structural phase transition Tic in KCo~ Mgl - x F3 for various concentrations

Compounds 0 /'/'eft TN Tlc ( - K) (/.t B) (K) (K)

KCo0.88Mg012F 3 300 5.82 95 KCoo.75 Mg0.25F 3 200 4.95 70 KCoo.67 Mgo.33 F 3 208 4.80 52 KCoo.45Mgo.ssF 3 118 3.70 MC°o.25 Mg 0.751:3 65 2.69

94 68

It is evident that the temperature corresponding to the peak in XM decrease with decreasing x. The NOel temperature was indentified based on the dis- continuity in the derivative of the curve for X versus temperature. A large value of X at low temperatures is due to the unquenched orbital magnetic moments.

In the paramagnetic region the measured values of the susceptibility were fitted by the formula:

CM )(M =,~VV q- T - 0 ' (1)

where Xvv is a Van Vleck susceptibility. The fitting procedure depends on Xvv. For KCoF 3 the value of Xvv = 5 × 10 -3 e m u / m o l [4] can be estimated from the experimental results obtained by NMR torque measurements. This value is close to Xvv = 3.5 × 10 -3 emu/mol , found for KECoF 4 by Breed [5]. Unfortunately, for KCoxMgl_xF 3 the experimental curves could not be satisfactorily described if the Van Vleck susceptibility was assumed to be equal to the values quoted.

The values of the parameters 0 and ~L~ef f pre- sented in Table 2 were estimated from the Curie- Weiss law without the Xvv term and for T > 200 K. In case of KCoxMgl_xF 3, the values of 0 and /Zef f depend upon the temperature region over which they were determined. In the paper of Hirakawa et al. [1] the values of 0 and /Xef f for KCoF 3 were obtained in the region 500-700 K and are - 125 K and 4.95/* B, respectively.

Twardowski et al. [6] have derived a theoretical expression for the static magnetic susceptibility in the high-temperature regime of random, diluted mag- netic systems containing ions having not only a spin momentum but also a nonvanishing orbital momen-

tum. The Hamiltonian for a random, dilute system was expressed as follows:

H = - 1 /2~2Ji jSiSj~i l~j i ,j

+ #BB~ ~ (Lzi + gSzi) ~i i

-}- E n c f i ~ i - } - ~ A L i S i ~ i, ( 2 ) i i

where the sums over i and j are calculated over all the lattice sites (i =~j) and ~i is 0 or 1, depending on whether the cation site is occupied by a nonmagnetic or a magnetic ion; and S i and L i are the atomic spin and orbital momentum operators, respectively. The first term in the Hamiltonian (2) describes the ex- change interaction, the second term the influence of the magnetic field, the third term the crystal field splitting, and the last term the spin-orbit interaction.

In the high-temperature limit the magnetic suscep- tibility was expressed by means of the Curie-Weiss law:

C(x) x(r) T- 0(x) ' (3)

with the Curie constant

#~ N( M [ )~ C ( x ) x = Cox, (3a)

kBV

and the Curie-Weiss temperature

(M2)~(E)~ - (M2E)~

O( x) = (M2)~k u

2(MzSz)~ + (M2) ~ ~ Z p ( J p / k , ) , (38)

p

where ( . . . ) :~ denotes a statistical average of the operator considered in the limit T--+ ~; Jp is the d - d exchange integral between pth neighbours; Zp is the number of cations in the pth coordination sphere; E is the energy of an isolated ion submitted to the crystal field and the spin-orbit interaction.

Fig. 2 shows O(x) as a function of x. For x < 0.8 this quantity is proportional to the concentration x, in agreement with Eq. (3b). At higher concentrations a deviation of O(x) from a straight line can be observed. However, for x > 0.8 the value of O(x) =

D. Skrzypek, J. Heimann /Journal of Magnetism and Magnetic Materials 139 (1995) 102-108 105

- 3 0 0 K is comparable in magnitude with the maxi- mum temperature at which the measurement were made. Strictly speaking, it cannot be assumed that the magnetic moments on different sites (i :~j) are independent. Furthermore, it can be seen from Fig. 2 that for x ~ O, O(x) -~ O. This is in agreement with the susceptibility analysis for the compounds con- taining magnetic ions of nonvanishing orbital mo- mentum (see Eq. (3)).

The value of 00 was determined from the slope of O(x) versus x. Upon combining the experimental Curie-Weiss temperature 00 with Eq. (3b), we ob- tain

E = 202 K. P

Hence the nearest-neighbour interaction is

I J ~ / k B ] = 16.8 K.

The variation of J with lattice parameter has been estimated by de Jongh and Block [7] according to the rule J ~ a -n, where n = 12 for perovskites of the cubic structure. For the compounds analyzed in the present work, a varies from 4.069 A for KCoF 3 to 4.0035 ,~ for KCo0.25Mg0.75F3. The change in the mean value of JNN/kB may reach about + 3 K. Therefore, if we take into account the change in the C o - F - C o mean bond length following the dilution of the KCoF 3 host with the Mg 2+ ions, the value of the exchange constant [JNN/kB [ = (16.8 + 3) K is obtained. This value is consistent with those deduced

1.0

300 P w EL

2o0-

I

u 100 % o

4-00

0 0.0 O J2 O J4 O J6 O J8 1.0

CONCENTRATION x

Fig. 2. Curie-Weiss temperatures of KCoxMg 1 xF3 as function of concentration.

0.8

G

KMn Mg

0 . 6 .~,

-~0.4

0.2

0.0 0.0 0 J2 0 J4 0 J6 0.18 1.0

CONCENTRATION x

Fig. 3. Reduced N6el temperatures of some magnetically diluted systems. The values in the K M n x M g l _ x F 3 curve were obtained from Ref. [10].

from: (i) susceptibility measurements of pairs of Co 2÷ in KMgF 3 by Sakamoto et al. [8], where [J/kB I = 18.2 K within about 10% error; and (ii)

the theoretical model of the exchange interaction in KCoF 3 presented by Buyers et al. [9], where ] J / k ~ l = 20 K.

3.2. Critical properties of mixed crystals KCo x Mgz ~F3

The studies of randomly diluted magnetic systems focus upon two problems: (i) the way the transition temperature is reduced when the concentration of magnetic atoms is decreased, and (ii) determination of a critical concentration at which the magnetic order begins to manifest itself.

The shape of the critical curve depends upon the lattice structure and the symmetry of the interaction Hamiltonian. Fig. 3 shows the critical curve for KCoxMgl_xF s. For comparison, the values of TN(x)/TN(1) in KMnxMgl~_xF 3 obtained by Breed et al. [10] are also presented. As the concentration of magnetic ions is reduced, the N~el temperature de- creases faster for KCoxMg 1 xF3 than that for KMnxMgl_~F 3. To explain such differences in KNixMgl_xF%, de Aguiar et al. [11] proposed a dilution model that is quite different from the usual site-dilution percolation scheme. In this model, the coupling between two nearest-neighbour magnetic

106 D. Skrzypek, J. Heimann /Journal of Magnetism and Magnetic Materials 139 (1995) 102-108

atoms is assumed to be dependent upon the occu- pancy of the other nearest-neighbour sites.

In Mn 2+, with a 3d 5 electron configuration, all five of the one-electron orbitals are half-filled (L = 0), having the unpaired spins available to form both ~r and -rr bonds with the fluorine ligands. However, in Co 2+ with a 3d 7 configuration, two of the orbitals dxy , dxz , dr z are completely filled and one is half- filled, while the d~ y: and dz: orbitals are half- filled; these unpaired electrons can only form o- bonds. It might therefore be assumed that the direc- tionality of the cr bonds suggests that the substitution of a Co 2÷ ion by a nonmagnetic ion has a stronger effect on the exchange coupling of a nearest- neighbour magnetic pair situated along line joining the three atoms. For Mn 2+ the directionality of this effect should be less and the overall perturbation of the coupling weaker. In other words, we may assume that for the Co 2÷ ions the strength of the exchange interaction between two nearest-neighbour sites is also dependent upon the magnetic occupancy of their own nearest-neighbours along the line joining the two atoms.

3.3. Crystal structure and correlation between struc- tural and magnetic phase transitions for KCo~

M g I _ xF3

Fig. 4 shows temperature dependence of the lat- tice parameters in the mixed crystals, and the appear- ance of tetragonal distortion for the KCo0.ssMg0.12F 3 and KCo0.75Mg0.25F 3 samples. For KCo0.25Mg0.75F 3 crystal no structural phase transition can be observed over the temperature range 10-300 K. The values of the transition temperatures Tic were determined as the temperatures at which the phase of a lower symmetry is well formed. The phase transition tem- peratures obtained in such a way are presented in Table 2. It may be seen that a strong correlation exists between the structural (Tic) and magnetic (T N) phase transitions.

In the KCoF 3 crystal, antiferromagnetic ordering is accompanied by tetragonal distortion with c / a < 1 [12]. It follows from the data obtained in the present study that in the KCoxMg~_xF 3 mixed crystals, for x > Xc, the presence of tetragonal distortion may be seen with c /a < 1; x c is the critical concentration of

4 0 6 5

4 . 0 5 5

o<<.. 4.045

C/9

L J

B 4.055 < < m 4 . 0 2 5

5 4.o~5

4.005

5 . 9 9 5

TIc=g4K a p 1 u u lU u u u n u u

n a a l ~ ~ u ~ u a u ~ o ~ # l U a n u u u u u u a ap

uu

%' 0 u ~a ~ Tic =68K , , * * * op

u u u u u c o o l i n g K(Ooo,88Mgon2)F5

• * * * * cooling - A A ~ h e a t i n g K ( C Oo.7~Mgo,25) F~

+*+++ cooling K(Coo2sMgo75)F~

D OQ D

0 ' 510

+ +

+

+

a f + + +

÷ ÷

' 160 ' 150 ~ 200 ' 250 ' 300 TEMPERATURE (K)

Fig. 4. Changes in the lattice parameters with temperature for KCoxMg]_xF 3 systems (the subscript p refers to relative pseudo-cubic parameters).

D. Skrzypek, J. Heimann /Journal of Magnetism and Magnetic Materials 139 (1995) 102-108 107

~=0

Lz= ,. 1 (d,z,dyz)

t29 . . . . i - t2g _ ~ ~ i i -

~ ] i L,=O(d~, ) (a) (b)

Fig. 5. Energy level diagram of t2g ions showing the effects of the Jahn-Teller and spin-orbit interactions.

ously with the magnetic ordering. This conclusion follows from the analysis of the Hamiltonian, which depends on both the spin and the orbital variables [13]. These variables, due to the exchange interaction and the spin-orbit interaction, are markedly interre- lated. Consequently, we deal not only with the mag- netic ordering, but also with the orbital ordering which, in turn, produces the distortion of the crystal lattice.

It may therefore be concluded that the lattice distortion occurs at the N6el point, and that it is the result of the magnetic properties of the system stud- ied.

the magnetic ions below which no ordering can occur at a finite temperature, and c / a = 0.998 for T = Tic - 10 K. The observed effect of the lowering of the crystal lattice symmetry is due to the presence of the Co 2+ cations, which in the cubic field possess a threefold orbitally degenerate ground state. For such ions, the degeneracy can be removed in either of two ways: (i) due to the spin-orbit interaction; or (ii) by means of the Jahn-Teller effect. In KCoF 3 the spins are ordered along the z-axis. An ion of Co 2+ can be analyzed as a single hole in the t2g level. For such a case, the splitting of the t2g level can be expected, as shown in Fig. 5. During tetragonal deformation with c /a > 1 (Fig. 5a), the Jahn-Teller effect stabilizes the hole-orbital Idxy)= I / z - 0 ) . Since the ground state has a zero orbital moment, the spin-orbit interaction is ineffective. For tetragonal deformation whose sign is opposite to that of c / a < 1 (Fig. 5b), the level inversion takes place. The dou- blet I I z = 1) appears to be lower, but the lowering of the level is less pronounced than in case (a). However, for case (b) we have a ground state charac- terized by an unquenched orbital momentum, and the spin-orbit interaction leads to the splitting of this level. It may thus be seen that in the case discussed the Jahn-Teller effect and the spin-orbit interaction stabilize opposite types of deformation (with c /a > 1 and c / a < 1, respectively). The final outcome de- pends on the relative magnitudes of the energies Ej_ T and ALS. For the 3d ions these quantities are of the same order of magnitude. Usually, however, the transition leading to the disappearance of degen- eracy by the spin-orbit effect takes place simultane-

4. Conclusions

The main results obtained in this paper may be summarized as follows:

(1) The behaviour of the high-temperature sus- ceptibility was analyzed within the crystal field model, using the theoretical results obtained for ran- dom, dilute magnetic systens with magnetic ions having unquenched orbital momentum. The ex- change constant deduced from the Curie-Weiss tem- perature was found to be in agreement with the values obtained from previous experiments carried out using different techniques by the various authors.

(2) Based on the studies of the static susceptibil- ity, the N6el temperature T N was determined, and the variation of T~(x)/TN(1) with x was given for KCoxMg l_xF3 . The results of our measurements are compared with earlier data obtained for another sys- tem, namely KMnxMg I_xF3 . The two sets of results are different in that the KCo~Mga_xF3 compounds exhibit a larger initial slope of the critical curve. It seems that the model representing the randomly di- luted Heisenberg magnets and assuming that the coupling between two nearest-neighbour magnetic atoms is dependent upon the occupancy of the other nearest-neighbour sites as well as upon the electron configuration of magnetic ions, better describes the experimental results compared with the usual site-di- lution scheme.

(3) The temperature dependences of the crystal lattice parameters were analyzed using the cubic (400) Bragg line. The evolution of the (400) line from the cubic to tetragonal phase with c /a < 1,

108 D. Skrzypek, Jr. Heimann /Journal of Magnetism and Magnetic Materials 139 (1995) 102-108

was found for high concentrations of magnetic ions. In the present study a strong correlation was ob- served between the structural (Tic) and magnetic (T N) phase transitions. The interrelationship between the magnetic and the crystal structure in KCo x Mgl_xF 3 is due to the presence of the Co 2÷ cations, which in the cubic crystal field possess a threefold, orbitally degenerate ground state. The spin-orbit interaction cancels out this degeneracy and stabilizes the tetragonal deformation with c / a < 1. The analy- sis of the Hamiltonian, which depends on both the spin and the orbital variables markedly coupled to- gether, leads to the conclusion that we are dealing with simultaneous magnetic and orbital ordering, which subsequently produces the above-mentioned distortion of the crystal lattice.

In summary, the deformation of the crystal lattice in KCoxMgl_xF 3 for x > x c occurs at the N6el temperature and results from the magnetic properties of the crystal analyzed.

Acknowledgements

We wish to thank Dr A. Ratuszna and Miss J. Kapusta for the X-ray measurements and computer calculations.

References

[1] K. Hirakawa, K. Hirakawa and T. Hashimoto, J. Phys. Soc. Jpn. 15 (1960) 2063.

[2] M.B. Eremin, B.H. Kalinenkov and Yu.V. Rakitin, Phys. Star. Solidi (b) 90 (1978) 123.

[3] A. Ratuszna and K. Majewska, Powder Diffraction 5 (1990) 41.

[4] N. Suzuki, T. Isu and K. Motizuki, Solid. State Commun. 23 (1977) 319.

[5] D.J. Breed, K. Gilijamse and A.R. Miedema, Physica 45 (1969) 205.

[6] A. Twardowski, A. Lewicki, M. Arciszewska, W.J.M. de Jonge, H.J.M. Swagten and M. Demianiuk, Phys. Rev. B 38 (1988-II) 10749.

[7] LJ. de Jongh and R. Block, Physica B 79 (1975) 568. [8] N. Sakamoto and Y. Yamaguchi, J. Phys. Soc. Jpn. 22

(1967) 885. [9] W.J.L Buyers, T.M. Holden, E.C. Svesson, R.A. Cowley

and M.T. Hutchings, J. Phys. C 4 (1971) 2139. [10] D.J. Breed, K. Gilijamse, J.W.E. Sterkemburg and R.A.

Miedema, J. Appl. Phys. 41 (1970) 1267. [11] J. Albino O. de Aguiar, F.G. Brady Moreira and M. Engels-

berg, Phys. Rev. B 33 (1986) 652. [12] V. Scatturin, L. Corliss, N. Elliott and J. Hastings, Acta

Crystallogr. 14 (1961) 19; A. Okazaki and Y. Suemune, J. Phys. Soc. Jpn. 16 (1961) 671.

[13] M.B. Eremin and B.H. Kalinenkov, Fiz. Tver. Tela 23 (1981) 1422; K.U. Kugel and D.U. Homski, Usp. Fiz. Nauk 136 (1982) 621.