# Magnetic excitations in two-dimensional antiferromagnets Rb2CocNi1cF4

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Physica 120B (1983) 193-196 North-Holland Publishing Company

MAGNETIC EXCITATIONS IN TWO-DIMENSIONAL ANTIFERROMAGNETS Rb2CocNil-cF4

H. IKEDA, Y. SOMEYA*, Y. ENDOH**, Y. NODA** t and F. SH IBATA Department of Physics, Ochanomizu University, Bunkyo-ku, Tokyo 112, Japan **Department of Physics, Tohoku University, Sendai 980, Japan.

Results of an investigation of the magnetic excitations in randomly mixed antiferromagnets Rb2CocNil oF4 by means of neutron scattering are presented. Two bands of excitations are observed over a whole Brillouin zone. In Rb2Coo.sNio.sF4, a simple Ising cluster model using pure crystal exchange and anisotropy constants is found to fail in predicting the measured zone-boundary excitations. A considerable reduction of the exchange parameters in the mixed system yields satisfactory agreement between experimental and calculated spin-wave dispersion relations. A discussion is also given on the calculation of concentration dependence of the N6el temperature.

1. Introduction

During the last decade, excitations in the ran- dom magnetic systems have received a con- siderable amount of attention [1]. As neutron scattering provides invaluable information on excitations in these systems throughout the Bril- louin zone, many experimental studies were focussed on the determination of spin-wave dis- persion relations in certain insulating magnetic systems, especially the transition-metal fluoride compounds such as KCocMnl-cF3 [2], Mn~Col_cF2 [2], KMncNil_cF3 [3], Rb2Mn0.sNi0.sF4 [4,5], RbzCo0.sMn0.sF4 [6] etc. In these com- pounds, two well-defined bands of excitations with large dispersion compared with the resolu- tion width are observed throughout the Brillouin zone. To date, it is believed that the response function at the zone boundary should exhibit structure originating from the multiple Ising cluster modes. In the two-dimensional mixed systems with the so-called K2NiF4-structure, zone-boundary magnon energies, in general, split into ten Ising energies which are determined by the exchange constants J~gA, J~CB and J~ and

spin values SA and SB where A and B are different kinds of magnetic species. Thus, the two bands of excitations observed result from a degeneracy of the Ising energies of each mag- netic atom. It should be noted that the cal- culations using essentially the same exchange constants as in the pure crystal from the A-A and B-B interactions and also a geometrical mean of JAB = (JAAJBB) m for the A-B inter- actions are in agreement with experiments.

On the other hand, in Rb2CocNil-cF4, whose magnetic excitations are reported below, a sim- ple Ising cluster calculation using pure-crystal parameters for the interactions suggests that the zone-boundary energy splits into ten energies and it will be possible to resolve the predicted fine structure. In the present paper, we report the results on Rb2Co0.sNi0.sF4 only; a full dis- cussion including the results on different con- centrations and a detailed analysis will be repor- ted elsewhere. The appropriate anisotropy and exchange constants for the pure crystals Rb2CoF4 and Rb2NiF4 are given in table 1 together with the lattice constants and N6el temperatures.

*Present address: Toshiba Research and Development Center, Saiwai-ku, Kawasaki 210, Japan.

t Permanent address: Sendai College of Radio Technology, Miyagi 939-31, Japan.

2. Experiments

The experiments were performed on a triple axis spectrometer of Tohoku University (TUNS) installed at JRR-2, Tokai Establishment JAERI .

0378-4363/83/0000-0000/$03.00 1983 North-Holland and Yamada Science Foundation

- 194 H. lkeda et al. / Magnetic excitations in Rb2C'o,.Ni~
H. lkeda et al. / Magnetic excitations in Rb2CocNi>cF4 195

40

> O E30

B

20

] I I I

Rb 2 Co0.5 Ni0.5 F 4

10

/

Rb2CoF 4 /

!

/

// Rb2NiF 4 /

/ /

[ I I 1 00 0.1 0.2 0.3 0.4 0.5

WAVE VECTOR qa

Fig. 2. Dispersion relations in the qa-direction for RbaCoF4, Rb2NiF4 and Rb2Coo.sNio.sF4. Solid lines are the results of spin-wave calculations, eq. (1), with the parameters given in table I.

J~2%-Ni satisfies an empir ical re lat ion JCo-Ni= (Jco_CoJNi_Ni) I/z. The results indicate that the in- teract ion constants J~{,-Co and Jf~-N~ in RbzCo0.sNi0.sF4 decrease to 0.94 and 0.79 t imes smal ler than those in pure mater ials , respec- tively.

3. Discussion and conclusion

We consider the overal l d ispers ions in the mixed crystal. We extend Walker ' s mean-crystal model [4] to systems with an anisotropic exchange Hami l ton ian and an arbi t rary atomic concentrat ion c. We take a standard four-sublat- tice model and take a conf igurat ional average over all possible local env i ronments of a specific type of ion. The equat ion of mot ion based on a Green- funct iona l formal ism with a Tyabl ikov

approx imat ion is solved to give the expression

(.0 4 - - (H2A~ + H~ - h2AA -- 2hABhBA -- h2B)to 2

+ ( (H~. - 2 2 h AA)(HB~ -- h 2B) - 2hABhsAHA,,HB~

_1_ 2 2 9 2 2 h AB h BA - - ,h AA h BB -- 2hAAhABhuAhBB) = 0 , (1)

where

HA,~ = --2Z(JXASA + ]SfBSB)- gAIXBHA

HBa = --2Z(]}~.SA + J}~BSB)- gBI.tBHA

hAA = 2ZJXASA3'~

hA~ = 2ZJ~SA3'k

hBA = 2Z]ffASBTk

h~B = 2ZY'ffBSB3'k

Jie o = JieoC o (P, Q = A , B and i = zz, xx )

Yk =zl .~, ei k .o (z = 4)

It should be noted that this expression reduces to a result of Wa lker ' s four-sublatt ice model in the limit of c = 0.5 and J.~o = J~'}).

We should also note that in fitting the overal l observed dispersion to the calculat ion as is depicted in fig. 2 both branches are given with the same reduct ion factors of 0.94 and 0.79 on J~',,-co and J~%Ni and the fixed anisotropy fields of gAP, BHA (Nil = 0.28 meV and gBl~BHA (Co) = 0.(I.

We next consider the effect of the deviat ion of the exchange constants from those in pure crystals. We have calculated the NOel temperature and the sublatt ice magnet izat ion using the same Green- functional formal ism in the f ramework of the mean-f ield approx imat ion. The parameters of the exchange constants necessary in the calculat ion have been fixed as obta ined in the present exper iments (see table I). Here we discuss only the concentrat ion dependence of the NOel tem- perature. Results are summar ized in fig. 3, which shows the var iat ion of TN with respect to the alloy concentrat ion c together with the measured up- ward concave character ist ic [7]. A l though the quant i tat ive agreement between calculation and exper iment is, as expected, not excellent, one

196 H. lkeda et al. / Magnetic excitations in Rb2CocNiFcF4

200

v I ,L

23 F--

150 LLI [3_

DJ t'--

z lOOd ~

Rb2CocNi l _cF 4 I I I F I I I I

-" "o

] r F l [ [ l l ] 0.5 1.0

C

Fig. 3. Concentration dependence of the N6el temperature. The solid line (c - 0.5) is a result from the calculations based on a linear spin-wave theory with the exchange parameters of RbeCo05Ni0.sF4. Open circles are observed N6el temperatures [7].

important experimental fact, that TN deviates more than the geometrical mean, seems to be reproduced in this calculation. Consequently, the observed modification of the exchange constants seems to play an essential role in the concentration dependence of TN. As a matter of fact, we do not think that the thermodynamic quantities in these random mixtures obey well in the mean-field ap- proximation but we trust that the physical realiza- tion is well understood in this approximation.

In conclusion, inelastic neutron scattering measurements on two-dimensional mixed antifer- romagnet Rb2Co0sNi0 5F4 show two bands of exci- tation throughout the Brillouin zone. The excita- tion spectrum is well explained within the linear spin-wave theory with considerably modified exchange parameters from the pure materials. Thus, it is important to take a resulting change of the superexchange constants owing to the modification of the lattice parameters, if any, into consideration of the magnetic excitations in ran- domly mixed magnetic systems.

References

[1] R.A. Cowley, R.J. Birgeneau and G. Shirane, in: Ordering in Strongly Fluctuating Condensed Matter, ed., T. Riste (Plenum, New York, 198[)) p. 157.

12] W. J .L Buyers, T.M. Holden, E.C. Svensson, R.A. Cowley and R.W.H. Stevenson, Phys. Rev. Len. 27 (1971) 1442.

I3] G.J. Coombs, R.A. Cowley, D.A. Jones, G. Parisot and D. Tochetti, A.I.P. Conf. Proc. 29 (1976) 254.

14] R.J. Birgeneau, L.R. Walker, H.J. Guggenheim, J. Als- Nielsen and G. Shirane, J. Phys. C8 11975) L328.

[5] J. Als-Nielsen, R.J. Birgeneau, H.J. Guggenheim and G. Shirane, Phys. Rev. BI2 (1975) 4963.

[61 H. Ikeda, T. Riste and G. Shirane, J. Phys. Soc. Jpn. 49 11978) 5O4.

[7] H. lkeda, T. Abe and I. Hatta, J. Phys. Soc. Jpn. 51) (1981) 1488.

[8] H. Ikeda and M.T. Hutchings, J. Phys. C 11 (1978) L529. 19] K. Nagata and Y. Tomono, J. Phys. Soc. Jpn. 36 (1974) 78.