ANTISYMMETRIC EXCHANGE INTERACTION IN KCuF3 : ITS DOMINANT EFFECT ON THE EPR LINE

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ANTISYMMETRIC EXCHANGE INTERACTION IN

KCuF3 : ITS DOMINANT EFFECT ON THE EPR

LINE

I. Yamada

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Supplkment au no 12, Tome 49, d6cembre 1988

ANTISYMMETRIC EXCHANGE INTERACTION IN KCuF3: ITS DOMINANT

EFFECT ON THE EPR LINE

I. Yamada

Department of Physics, Faculty of Science, Chiba University, Yayoi-cho, Chiba-260, Japan

Abstract. - We point out theoretically that the one-dimensional Heisenberg antiferromagnet KCuF3 should have the interaction of diiSi x S with c&jlc-axis. From the measurements of EPR linewidth, we have confirmed this prediction.

1. Introduction 2. Calculation of dii In spite of its pseudo-cubic crystal structure (a =

4.14

A

and c = 3.92 A) [I], KCuF3 has one- dimensional magnetic properties

(Jc

= -203 K and

Ja = +2 K) as a result of the strong orbital coupling dong the c-axis and lack of that in the c-plane caused by the cooperative Jahn-Teller effect (21. The crystal structure and the orbitals of the ground state is shown in figure 1. The magnetic structure so far accepted is as follows; Spins lie in the c-plane owing to the small XY-like anisotropy arising both from the dipo- lar and the anisotropic exchange interactions. They couple antiferromagnetically along the c-axis with J,

and ferromagnetically in the c-plane with Ja. When

we pay attention to its crystal structure, however, we find that there is no inversion center halfway between a Cu-Cu bond on the c-axis and also in the c-plane. Thus, there is a possibility that this compound has the Dzyaloshinsky-Moriya (DM) antisymmetric exchange interaction x d i j S i x Sj. If this interaction is effec- tive in this compound, the magnetic structure so far accepted should be modified; further, spin dynamics should be also strongly affected. An absorption line of electron paramagnetic resonance (EPR) is one of the representative quantities that reflect this interaction. In this report, we shall show that KCuF3 has the DM interaction with dijlc-axis from both theoretical and the experimental point of view.

The formulation of dij is given by Moriya [3] as

where Eo and Em are the energy levels of the ground and the excited states, respectively, (0 ILiI m) a matrix element of the angular momentum a t dsite, X the con- stant of spin-orbit coupling and J (00m0) the exchange

interaction. If the orbital states are known, then we can calculate dij. First, we take up spins on the c-axis. As shown in figure 1, there are two inequivalent Cu- sites, Cu(a) and Cu(b). When we denote [aacl-axes as

[xyz], respectively, the hole orbitals of Cu(a) and Cu(b) are expressed as follows.

C u ( 4 Cu(b) E4 : 14) = ds,,, 14) = -dezx, E3 : 13) = ds,,

,

13) = d ~ z y , E2 : 12) = d~,,, 12) = -dexp,

E l : (1) =C1dyX-, -Cdyz, Il)=-ddyx-,-Cdy,, E o : 10)=Cdy,-,+C1dy,, lo)= -Cd%-,+C1dyz,

where dyx-, = (x2

-

y2) 12, dy, = (3z2

-

r2) 1 2 6 , de,, = xy, de,, = zx and de,, = zy. The order of energy levels for de,,, de,, and d ~ , , is not essential. The coefficients

C

and C' are given as 0.577 and 0.816, respectively 111. Using equations (1) and (2), we can calculate each component of dij; the result show that dTj

#

0,

ej

#

0 and d t = 0. Therefore, it becomes clear that dij is perpendicular to the c-axis. On the other hand, dij

#

0 is also derived between spins in the c-plane. Each dij lies in the c-plane and orthogonal or parallel t o each other. With such dij and the exchange interaction in the c-plane, it is easy to show that spins Fig. 1. - Crystal structure and the ground state orbitals of do not cant. Thus, the DM interaction between spins KCuF3. in the c-plane is absolutely ineffective.

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C8 - 1494 _JOURNALDE PHYSIQUE

3. _{Experimental evidence of dii}

_#

₀and d i j l c - axis

When the DM interaction is overwhelmingly strong as compared with other perturbation terms such as the dipole-dipole (dd) and the anisotropic exchange (ae) interactions, EPR lines are governed by the DM interaction. In the present case, we can see that the DM overwhelms others by comparing each second moment MFM, M t d and M F ; namely, each calculated value is MfM N 10'' 0 e 2 , M T 10' 0 e 2 and M F

lo6

0e2. In the calculation, we have used ( ~ ~Jc 1for the ~ ) ~ parameter of the ae interaction, (Aglg) J, for that of the DM interaction and the g-values, g, = 2.27 and gc = 2.15 determined in the present study. Thus it becomes clear that the DM interaction is the main origin of line broadening of EPR line; The contribution of the ae and the dd interactions is a few percent. Since spin diffusion does not enhance the secular part of the DM interaction [4], the line width at high temperatures is estimated as M2/we where we N J l h . The angular part

~f~

is

M~~~ C(

(2

+

sin20) for dijlc-axis, (3)

{

(1

+

cos20) for d i j

11

c-axis (4) where 8 is the angle between the c-axis and the external field. Our experimental result, namely @-

dependence of the derivative peak-to-peak linewidth AHpp is shown in figure 2. Its angular behavior is like (2

+

sin2@) and the ratio AHpp (0 = 90')

1

AHpp (0 = 0') = '1.4 agrees quite well with the theoretical prediction 1.5 given by equation (3);

In conclusion, dijlc-axis derived theoretically is confirmed by the

EPR

experiment. As a result, the

spin structure so far accepted should be modified. The direction of dij reverses alternately along the c-axis. Thus, there should be a c-componer~t of spin on each c-axis, but a macroscopic net weak moment cannot be expected because the c-component has opposite direction On adjacent c-axes. The expected c-component is (Aglg) times the a-component; namely, about 10 % of the a-component.

Fig. 2. - Angular dependence of the (derivative peak-to- peak linewidth at 300 K.

[I] Tsukuda, N. and Okazaki, A.,

J:

Phys. Soc. Jpn 33 (1972) 1088.

[2] Kadota, S., Yarnada, I., Yoneyama, S. and Hi- rakawa, K., J. Phys. Soc. Jpn 23 (1967) 751. [3] Moriya, T., Phys.

Rev.

120 (19150) 91.