Physica 136B (1986) 346-348 North-Holland, Amsterdam

MAGNETIC EXCITATIONS AND SUCCESSIVE PHASE TRANSITION IN RbFeBr3-TYPE MODIFIED TRIANGULAR ANTIFERROMAGNETS

Naoshi S U Z U K I and Masafumi S H I R A I Department of Material Physics, Faculty of Engineering Science, Osaka University, Toyonaka 560, Japan

We study magnetic excitations in RbFeBr3-type singlet-ground-state modified triangular-antiferromagnets (SGS-MTA) in which one third magnetic ions loses the crystallographic equivalence to the others. This SGS-MTA can undergo successive phase transitions, triangular structure (TS)---~ partial disorder (PD)~ paramagnetic (P) or TS---~ ferrimagnetic (FR)~ P, depending on the ratio between the two inequivalent exchange couplings. It is shown that a distinct difference between TS ~ PD and TS ~ FR transitions appears in the temperature dependence of one of the magnon branches (~o3-mode) which originates from the single-ion excitation between the excited states. In case of TS---~ PD the ~o3-mode energy softens with increasing temperature and becomes zero at the TS ~ PD transition temperature, and then remains vanishing in the PD phase. On the other hand, in case of TS--->FR the %-mode energy remains finite in the FR phase. This %-mode is characteristic to the SGS magnets and can be observable by inelastic neturon scattering.

Hexagonal magnetic compounds A B X 3 such as CsCoC13 and RbFeCI 3 are typical examples of model systems for triangular magnets because magnetic B ions located on linear chains form triangular lattice. Among these compounds RbFeBr 3 undergoes a structural phase transition at 120 K [1] to take a modified triangular structure in which one third of the magnetic chains loses the equivalence to the others by shifting along the c-axis (fig. 1). RbFeBr 3 is also a typical example of singlet-ground-state (SGS) magnets with an anisotropy energy DS~ (D > 0, S = 1).

With increasing tempera ture this SGS modified tr iangular-antiferromagnet (MTA) can undergo a successive phase transition [2], triangular struct- ure (TS)-->part ial disorder (PD) for J2/J2 < 1 or TS ~ ferrimangetic ( F R ) ~ P for J~/J2 > 1, where J2 and J~ represent two inequivalent antifer- romagnetic interchain couplings (see fig. 1). In fig. 2 we show a phase diagram in T vs. J~/J2 plane determined by the molecular-field approximation (MFA) for IJll/O--0.5 and J2/J1 =0.1 . Here J1 represents the n.n. intrachain antiferromagnetic coupling which is assumed to be the same for all chains.

By measuring the specific heat of RbFeBr 3 Adachi et al. [2] observed two peaks at T t = 2 K and TN = 5 .6K. They regarded this successive phase transition as TS--* PD ~ P. However , more

theoretical as well as experimental work is needed to elucidate clearly the nature of the successive phase transition. For this purpose we study in this report magnetic excitations of the RbFeBr3-type SGS-MTA on the basis of the M F A which will be sufficient for qualitative discussion.

The effective single-ion Hamil tonian for the i site in the M F A is expressed as

~eff= DS,2 z -- Z BiaSia i

c ~ = x , y

(1)

where Bi~ represents the molecular field:

01 01

j j . l I 02

02

Fig. 1. Structure of magnetic ions of RbFeBr3-type MTA projected on the c-plane. The numbers distinguish sublattices. Sublattice 3 has shifted along the c-axis. Jz and J" represent two inequivalent interchain exchange integrals. Dashed lines indicate the chemical unit cell of the undistorted structure.

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N. Suzuki and M. Shirai / Magnons in RbFeBr3-type antiferromagnets 347

kBTID

2, 1 Para

f i i I. 2. J U &

Fig. 2. Phase diagram in the T vs. J~/~ plane determined by the MFA for the case ofJ~l/D = 0.5 and JJJ1 = 0.1. The spin structure of one of the c-planes is also shown for each phase. The spin directions of adjacent layers are opposite.

B,o = 2 Z 4j (s .o) . (2) J

The equilibrium values (Si~) are determined self-consistently by imposing the usual self-consis- tency condition. The single-ion energy levels of YgTff are easily obtained as

E0 = 1 ( O - W ) , E 1 = D , f 2 = 1 ( D W ) ,

(3)

where W-= (D 2 + 2 1/2 2 1/2 B ibelng (B ix + Biy ) . 4 B i ) , • 2

The magnetic excitations (magnons) in the SOS magnets can be understood on the basis of an exciton picture, namely they can be described as propagating modes of single-ion excitations through the exchange coupling. Corresponding to three single-ion excitations 0---* 1, 0--~ 2 and 1 ~ 2 there are three magnon modes which will be denoted as Wl-, to2-, and to3-mode, respectively. Actual determination of the magnon dispersion is most conveniently implemented by calculating poles of the dynamical susceptibilities of the crystal [3] which are expressed in terms of the single-ion dynamical susceptibilities of y(erf and the Fourier t ransform of exchange integrals.

We first consider the case of undistorted tri- angular structure, namely J; /J2 = 1. In this case the spin structure of the ordered phase is de- scribed as a helical structure with a propagat ion vector Q = (1/3, 1/3, 1/2). By adopting rotating coordinates we can easily calculate the dynamical susceptibilities of the crystal [3] and obtain three magnon modes tol(q), % ( q ) and % ( q ) in the chemical B.Z. scheme. For a given scattering vector q, nine modes toi( q) and wi( q +-- Q ) ( i = 1 - 3) are in principle observable by inelastic neutron scattering. If we use the magnetic B.Z. which is one sixth of the chemical B .Z . , we obtain eigh- teen magnon modes for each q which are obtained by folding toi(q) into the magnetic B.Z. We show in fig. 3 the dispersion curves at T = 0.5 TN along the A - H - L line of the chemical B.Z. calculated for IJ~l/D = 0.5 and J2 /J = 0.1. The N6el temper- ature is k B T N = 1.65D. The solid lines represent magnon modes which are observable in principle by inelastic neutron scattering when scanned along the A - H - L line. In comparing the theoreti-

CO(q)ID

2.

031

(.0 3 O)3

1 ' ~ 601

0. ff',~ Hm 9'm Mr. A H L

Fig. 3. Magnon dispersion curves of a triangular structure along the A-H-L line of the undistorted chemical B.Z.: J'/J2 = 1.0, I J11 / D = 0.5 and J2/J~ = O. 1 ( T = O. 5 T N ). We have plotted these curves by repeating dispersion curves folded into the magnetic B.Z. Note that A and H points correspond to the center of the magnetic B.Z., F=,. The solid lines represent dispersion curves which are observable in principle by inelastic neutron scattering when scanned along the A-H-L line. Six toz-modes which lie around 4.5D are omitted from the figure.

348 N. Suzuki and M. Shirai / Magnons in RbFeBr3-type antiferromagnets

cal disperison curves with the observation, how- ever, we have to take account of the scattering intensity, w 1-modes generally have strong intensi- ty, especially in the vicinity of the H-point. On the other hand, o~3-modes generally have weak intensity, particularly at low temperatures . How- ever, at intermediate temperatures below T N these w3-modes may be observable. As the temp- erature approaches T N the % - m o d e energies soften and become zero at T N because E~ and E 2 become degenerate at T N.

Calculations for the modified triangular struct- ure can be per formed in the same way as for the undistorted triangular structure although the alegebra is rather complicated. We first consider the case of J~/J2 < 1 for which a successive phase transition TS ~ PD---> P occurs. In fig. 4 we show the magnon dispersion curves along the / 'm-Mm line of the magnetic B.Z. calculated for J~/J2 = 0.8, I J1]/D = 0.5 andJ2 /J 1 = 0.1 ( T = 0.5 TN). For these parameters the transition tempera ture of TS---> PD is k B T t = 1.575D and that of PD---> P is k B T N = 1.65D. Comparing fig. 4 with fig. 3 it is clearly seen that the degeneracy at the zone center or edges of the magnetic B.Z. has been removed by the distortion. As shown in fig. 2 the TS for J~/J2 < 1 is modified f rom the pure TS in such a way that the angle between the spins 1 and 2 is larger than 120 °. In the PD phase that angle becomes 180 ° and at the same time the spin momen t of the sublattice 3 vanishes because the molecular field acting on it vanishes. This temper- ature variation of the spin structure strongly affects the single-ion energy level structure, par- ticularly the energy levels of the sublattice 3. Namely, in the PD phase the two excited levels of the sublattice 3 are degenerate. Reflecting this tempera ture variation of the single-ion energy levels magnons in the crystal show quite interest- ing tempera ture dependence. With increasing tempera ture the energies of the lowest oJ3-mode soften and become zero at T t and then remain vanishing in the PD phase.

In the case of J2'/J2 > 1 the TS is modified so that the angle between the spins 1 and 2 is smaller than 120 °. In the FR phase the spin structure

co(q)/D

2.

O.

t01

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = . . . . . = . . . . . . .

: : : : : : : : : : : : : : : : : = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( , 0 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

m b"lm

Fig. 4. Magnon dispersion curves of the distorted structure: J'z/J2=0.8, IJll/D=0.5 and J2/Jl=0.1 (T=O.5TN). Full curves represent tol-modes and dotted curves ~o3-modes. Six oJ2-modes with higher energies are omitted. With increasing temperature the energies of the lowest w3-mode soften most remarkably and vanish at T t.

becomes colinear as shown in fig. 2. In contrast to the PD phase the molecular field acting on the sublattice 3 does not vanish and hence the w 3- mode energies remain finite in the FR phase.

We have shown that the most distinct dif- ference between the TS ~ PD ~ P and TS---> FR---> P successive phase transitions in the SGS-MTA appears in the tempera ture depen- dence of the w3-mode characteristic of the SGS magnets. Therefore , measurements of the mag- non dispersions by inelastic neutron scattering will be very useful to elucidate the nature of the successive phase transition of the SGS-MTA.

References

[1] M. Eibsh/itz, G.R. Davidson and D.E. Cox, AIP Conf. Proc. 18 (1973) 386.

[2] K. Adachi, K. Takeda, F. Matsubara, M. Mekata and T. Haseda, J. Phys. Soc. Jpn 52 (1983) 2202.

[3] N. Suzuki, J. Phys. Soc. Jpn 52 (1983) 3907.