INELASTIC LIGHT SCATTERING BY MAGNONS IN ANTIFERROMAGNETIC EuTe

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INELASTIC LIGHT SCATTERING BY MAGNONS

IN ANTIFERROMAGNETIC EuTe

S. Demokritov, L. Klinkova, N. Kreines, V. Kudinov

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Supplement au no 12, Tome 49, dkembre 1988

INELASTIC LIGHT SCATTERING BY MAGNONS IN ANTIFERROMAGNETIC

EuTe

S. 0. Demokritov, L. A. Klinkova, N. M. Kreines and V. I. Kudinov

Institute for Physical Problems, Academy of Sciences, Moscow, U.S.S.R.

Abstract. - One-magnon inelastic light scattering in EuTe by thermal magnons belonging to both branches of the excitation spectrum is studied. The dependences of the magnon frequency and of the intensity of the scattered light on the magnetic field are measured. The contribution to the intensity of one-magnon light scattering from exchange mechanism, which is of decisive importance for strongly canted magnetic sublattices, is separated.

The magnetic properties and magnetic structure of EuTe have by now been sufficiently well investigated. It has been shown that below

TN=

9.8 K it is antiferromagnet (AF) with magnetic anisotropy of easy plane type. The effective exchange field HE is 36 kOe. The spins are ferromagnetically ordered in the (111) plane and their directions in the two neighbor- ing planes are reversed. The effective anisotropy field HA is N 10 kOe. The weak anisotropy in the (111)

plane (effective field

--

10 Oe) arises easy axes of type [112]. The EuTe is turned in an external magnetic field from AF state into the state of a saturated para- magnet (spin-flip transition) [I, 21. At the light wave- length (A = 632.8 nm) used by us, EuTe crystals in a magnetically ordered state exibit, besides a relative transparency (penetration depth is 0.3 mm), strong magneto-optic effects (MOE). Thus, according to [3- 41, the Faraday effect (FE) reaches z 2 x 10' deg/cm (n+

-

n- = 0.07) at saturation and the isotropic magnetic refraction (IMR) is An = 0.05. The actual linear magnetic birefringence (LMB) is smaller by two orders. The presence of large MOE alongside relatively small absorption is attributed to the fact that the energy of a X = 632.8 nm photon is close to the fundamen- tal absorption edge Eg = 2.05 eV due to the 4f-5dt2, electrodipole transition.

We investigated in the experiments Brillouin- Mandelstam scattering (BMS) under backscattering conditions, i.e. with the wave vectors of the investigated magnon q, of the incident and scattered light

kl and k2 parallel to one other. The value of q at X = 632.8 nm is 3

x

10' cm-l. We used two experimental geometries, with q parallel and perpendicular to the magnetisation vector. The principal part of the experimental setup was an optical system compris- ing a high-contrast high-resolution spectrometer. the setup construction is described in detail in [5]. Fig- ure 1 shows a typical scattering spectrum. It can be seen that we have succeded in detecting

BMS

from magnons belonging t o both branches of the spin-wave spectrum of an easy plane AF. The satellites labeled

Fig. 1. - Spectrum of scattered light. T = 2 K, q = 3 x 10' cm-l, q

//

[OlO] I M , H = 25 kOe.

MY

and MfS correspond to scattering by magnons of the low-frequency branch of the spectrum and those labeled M: and MtS correspond to the high-frequency branch. Thus, one such recording yielded the magnon frequencies of two branches for given magnetic field and a given direction of the wave-vector qrelative to the magnetization vector. Figure 2 shows the field dependence of the magnon frequencies of both branches for q // M and q l M . In a zero magnetic field both spectrum branches have gaps. The gap in the low- frequency branch, A1 = Y ( ~ H , H E ) ' / ~ , is due t o the presence of intraplanar anisotropy Ha. The gap in the high-frequency branch is basically due to the presence of easy-plane anisotropy HA, A2 = 7

AN HA HE)'''

.

As seen from figure 2, the frequencies of magnons propagating along the field differ from those of the magnons propagating in the perpendicular direction. The result of frequencies field dependence calculation is shown by the solid lines in figure 2. The calculation that takes the magnetodipole interaction into account is based on the macroscopic Landau-Lifshitz equations.

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C8 - 1582 JOURNAL DE PHYSIQUE 3,O

-

s i

-

.- 1-0 0 20 40 60 H [kOel

0

Fig. 3. -Field dependence of intensity of BMS by magnons

Iff 2ff

fn

60 4lu8 of the low-frequency branch of EuTe at q

//

N. Points

-

experimental results, curves 1, 2, 3 -respective results of Fig. 2.

-

Spin-wave spectrum in EuTe at T = 2 K. ( m )

calculation of the contributions of linear magnetic birefrin- - _[ll1].(*) - [Ool]

,

q

//

*,

(V) -

//

[Ool] 7 gence, of the Faraday effect _andisotropic magnetic refrac-

q l M . _{tion, 4net result.}

The measured field dependence of the intensity BMS by magnons of the low-frequency branch at q

// M is

shown in figure 3. It can be seen that the scattered intensity is large in weak fields, decreases rapidly with an increase of the field, and begins to increase again only at H > 10 kOe. To analyse these results we calculated the intensity of one-magnon light scattering for an easy-plane antiferromagnet (the details of calculation were published in [6]). One can express the magnetic part of the dielectric tensor Aaij in the form:

where the first first term describes FE, the second LMB due to the vector L, and the third IMR. The fluctuations of the dielectric tensor, which lead to light scattering, are related by equation (1) with the fluctuations of L and M. Each term in (1) leads, gener- ally speaking, t o light scattering. Comparison of the experimental results with calculations has shown that the best agreement is obtained if account is taken of the BMS contributions from all three MOE, mentioned above.

In weak fields, BMS by magnons of the low- frequency branch is mainly due to LMB. In spite of the relative weakness of LMB in EuTe (two order smaller than e.g. FE), the anomalously large fluctuations of the vector L in the easy plane lead to appreciable intensity of the BMS in weak fields. With increase of the projection of the magnetic field on the easy plane the BMS intensity decreases like H - ~ and the LMB ceases to make a noticeable contribution to the light scattering even in fields 5-7 kOe.

The FE makes a rather small contribution to light scattering by magnons of the low-frequency branch. In BMS by magnons of the high-frequency branch, how-

ever, it does play a decisive role. The fact that scattering by such magnons was detected also in weak fields can be explained only when account is taken of the FE. Moreover, the intensity of BMS by high-frequency magnons in strong fields depended dramatically on the direction of k. No BMS were detected in fields

H

> 40 kOe at k

//

H, whereas at k l H the BMS intensity was relatively large and showed no tendency to decrease with increase of H. All this is in agreement

with the calculation result for the FE contribution. In fields stronger than 20 kOe the main contribution to BMS by low-frequency magnons is made by IMR, which is due to d-f exchange interaction. The intensity of the BMS due to IMR is isotropic, i.e. independent of the direction of k relative to H as is observed in experiments. The solid curves of figure 3 show the calculated contributions of each of the described MOE to the BMS intensity and total scattering intensity.

It should be emphasized that in this work we suc- ceeded in detecting one-magnon BMS due to the exchange interaction.

[I] Jonson, W. R. and McColum, P. C., Phys. Rev. B 22 (1980) 2435.

[2] Oliveira, N. F., Foner, S., Shapira, J., Reed, T. B., Phys. Rev. B 5 (1972) 2634.

[3] Demokritov, S. O., Kreines, N. M., Kudinov, V.

I., JET? Lett. 41 (1985) 46.

[4] Schoenes, J. and Wachter, P., Physica B 86-88 (1977) 125.

[5] Borovik-Romanov, A. S., Demokritov, S. O., Kreines, N. M., Kudinov, V. I., Sov. Phys. JETP 61 (1985) 1348.