COTTON-MOUTON BIREFRINGENCE IN FERRIMAGNETIC GARNETS

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COTTON-MOUTON BIREFRINGENCE IN FERRIMAGNETIC GARNETS

G. Smolensky, R. Pisarev, I. Siny, N. Kolpakova

To cite this version:

G. Smolensky, R. Pisarev, I. Siny, N. Kolpakova. COTTON-MOUTON BIREFRINGENCE IN FER- RIMAGNETIC GARNETS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1048-C1-1050.

�10.1051/jphyscol:19711376�. �jpa-00214414�

EFFETS OP TIQUES ^(2' partie)

COTTON-MOUTON BIREFRINGENCE IN FERRIMAGNETIC GARNETS

G. A. SMOLENSKY, R. V. PISAREV, I. G. SINY, N. N. KOLPAKOVA

Institute of Semiconductors of the Academy of Sciences of the U. S. S. R., Leningrad, U. S. S. R.

R6sum6. - Nous donnons une description phenom6nologique de la birefringence magnetique B l'aide de la pola- risabilit6 Blectronique d'un cristal like au spin. Nous discutons plus en detail la birefringence d'un cristal cubique magn6- tique ; dans lequel l'effet peut &re decrit par trois coefficients magneto-optiques

et

Nous avons etudie expkrimentalement la birefringence magnetique dans les ferrites grenats d'ythium et de terresrares.

Le rapport a

(2

est introduit pour la description des resultats. La valeur de a caractkrise l'anisotropie magneto-optique du cristal.

Abstract. - A phenomenological description of magnetic birefringence is given in terms of spin-dependent electronic polarizability of the crystals. In more details is discussed the birefringence in cubic magnetic crystals, where the effect can be described by three magneto-optical coefficients p

p

and

The experimental study of magnetic birefringence has been performed in yttrium and rare-earth iron garnets. For the description of the results the ratio a

(2

was introduced. The value of a characterizes magneto-optical anisotropy of the crystal.

Let us consider magnetic birefringence in terms of the spin dependent polarizability tensor. Such tensor was recently discussed by Moriya [I] to account one and two-magnon light scattering. Birefringence of the light is described by symmetrical components of the polarizability tensor and the expansion of this tensor must contains only quadratic products of the spin components

where @:(a) is the polarizability of ion at a-site in paramagnetic region, S,(a)-1-component of spin of a-ion.

The other symmetrical contribution to the polari- zability tensor arise due to interaction of a-ion with ions at the other crystallographical sites

where b designates ion at b-site.

No microscopical theory of birefringence in magne- tic crystals has been developed so far. It follows from (1) and (2), that different mechanisms can give a contribution to the birefringence. From (1) the bire- fringence can be connected with spin-orbit coupling and from (2) with exchange interaction. The precise estimate of the magnitude of the effect is next to impossible. Here we only say that the close analogy must exist between magnetic birefringence and two- magnon light scattering as it is the case between Faraday rotation and one-magnon light scattering [I].

Contribution to birefringence from second rank n,-tensor in (2) must be isotropic. On the contrary the contribution of the forth-rank Piklm ^and-

tensors will depend on the direction of magnetization with respect to the crystal axes. We shall discuss here only cubic crystals. When the magnetization lie along [loo] and [ I l l ] crystal axes and the light propa- gates perpendicular t o the magnetization the bire- fringence may be written as in the case of electro- optical effects in the form

where P l l = P l l l l , PI, = PI,,,, P44 = P4444 are magneto-optical coefficients that characterize the contribution to birefringence from n, P and y-tensors, no-index of refraction at M = 0 ; n and n,-indexes

'i

of refraction for light polarized para lely and perpen- dicular to the derection of the magnetization.

When the magnetization lies along arbitrary direc- tion in crystals the birefringence may be represented as a product of (3) and (4) and the direction cosines ai of the magnetization and the cosines Pi of the direc- tion, perpendicular to the magnetization

Expressions (3-5) include only one magnetization M and must be valid for simple ferromagnets and anti- ferromagnets. In the case of ferrimagnets each sublat- tice must give the contribution to the observed bire- fringence that depends on the polarizability and the magnetization of the ions of this sublattice.

Now we shall discuss the results on magnetic bire- fringence in yttrium and rare-earth iron garnets [2-41.

The results at room temperature are presented in table I, where we gave the values of birefringence according to formulas (3) and (4). The validity of formula (5), that gives birefringence when the magne- tization lies along some arbitrary direction in crystal was examined on different samples cut parallel to main crystallographical planes (loo), (1 10) and (1 11).

The experiment reported here consisted in measuring the birefringence as a function of direction of magneti-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711376

COTTON-MOUTON BIREFRINGENCE I N FERRIMAGNETIC GARNETS

Garnet

Magnetic birefringence of ferrimagnetic garnets

at T = 295

1 = 1,15 ,u and H = 20 kOe (in degrees per centimeter)

- - -

Y3Fe5012 125 160

Y3Fe4,3Ga0,7012 50 90

Sm3Fe5012

250 155

E"3Fe50~2

320 312

Gd3Fe501z

124 160

Tb3Fe5012

45 1 20

D~3Fe501z

30 110

Ho3Fe501, 40 150

ErsFe5012 100 190

L"3Fe50~z

100 150

zation in these principal planes with monochromatic magnetization at a = 1 cubic crystal transforms to light (1 = 1,15 p) linearly polarized at the angle 45O uniaxial and optical axis coincides with the direc- with respect to the magnetization. As it was expected tion of magnetization. One can see that all the garnets according to ( 5 ) no angle dependence of birefringence at the room temperature are divided into two groups was found when light travels parallel to [ I l l ] axes. when a > 1 and a < 1. Rather large magneto-opti- The example of angle dependence for light propaga- cal anisotropy is observed in HoIG (a = 3,75) and ting along [I101 direction is shown at figure 1 for DyIG (a = 3,7).

holmium iron garnet (HoIG). When a # 1 crystals from cubic transform to

ORIEATATION OF MAGNETIC P1EI.D IA (110) PLARE

biaxial and optical axis do not lie along the magneti- zation. So even when light travels along the magneti-

o

zation we must observe magnetic birefringence (longi-

0

0 - I -

C

I 1 1

[OOI] [IIIJ [IIO]

I 1 t

-

tudinal birefringence !) and as usually Faraday rotation.

So two light waves in crystal will be elliptically pola- rized. The phase difference between these two waves will be a superposition of phase differences between -

two circularly polarized waves as in the case of Fara-

a

#I

day geometry if there were no birefringence and of

i

phase difference between two linearly polarized

- -

I - 2 -

waves as in the case of Cotton-Mouton geometry

c

if there were no rotation

a

W U

y.

-.-so ;

0

2 nl

<3 2

( A d 2 = ( T ) (Ant-M + A d .

E

P (7)

W 0

R

H

Such gyroanisotropical behaviour was observed

a

b d

experimentally in TbIG [5]. Figure 2 shows changes

U

" of the ellipticity of the light at the exit of (110) crystal

g

0

-

plate when the phase difference changes periodically

-.

I05 te

- 5 '

- -

r ..

FIG. 1. - Magnetic birefringence in HoIG versus direction of magnetization in the (110) plane at room temperature,

1

1,15 p, H

16 kOe.

"

r

For the description of the results on magnetic ^-

birefringence of garnets it is conviniente to introduce

the ratio of magnitudes given by (3) and (4)

13'1 200 30; ^O

a = 2 P44

(6)

P11 - P12

FIG. 2. - Temperature dependence of the depolarization of that characterize magneto-o~tical anisotropy of the the light at the exit of (110) plane of TbIG (t

0,275 cm), crystal. It is easy to show that under the influence of ¹

1,15 p, H

6,7 kOe.

69

2,Zl

₁₁

I ^-

C 1 - 1050 G. A. SMOLENSKY, R. V. PISAREV, I. G. SINY, N. N . KOLPAKOVA due to magnetic birefringence and Faraday rotation

change with temperature.

Now we discuss briefly temperature dependence of magnetic birefringence in garnets. At figure 3 we show birefringence in TbIG for two general cases when magnetization lies along forth and third order axis of the crystal. In both cases light propagates along [110]

axes perpendicular to the magnetization.

FIG. 3. - Temperature dependence of magnetic birefringence of the light in TbIG at M 11 [I001 (upper curve) and M 11 [In1

(lower curve).

When the temperature is lowed birefringence chan- ges the sign for H 11 [loo]. At liquid nitrogen tempera- tures effect has large value of An = + ^{70. and}

An = - 72. lo5. So besides large value of the effect in different directions there is very large anisotropy : when magnetization is rotated nearly 500from [100] to

[I 111 direction birefringence is changed by -- 4 700°/cm.

It was found that experimental curves can not be fitted by simple quadratic dependence of the bire- fringence from net magnetization. We believe that this is connected with multi-sublattice structure of the garnets and the results need more detailed analysis.

When the contributions of different sublattices are of different signs, competition between sublattices can lead to complex thermal behaviour of the net bire- fringence. When the coefficient of larger magnitude is associated with the sublattice magnetization which drops of more rapidly with increasing temperature, a magneto-optical birefringence compensation tem- perature and reversal of sign of the effect can ensue.

Probably this is the case for An,,, in TbIG (Fig. 3).

Some difficulties in thermal behaviour of birefringence may arise from non-colinear magnetic structure, magnetostrictional deformations, and crystallogra- phical distortions.

In the paper [4] no dispersion of linear magnetic birefringence was found in the garnets in the range from 1.4 to 2.0 p. In our study we observe small dispersion in the range from 1.15 p to 3.39 p.

References

[I] MORIYA (T.), J. Appl. Phys., 1968, 39, 1042. [41 DILLON, IR. (J. F.), REMEIKA (J. P.), STATON (C. R.) [2] PISAREV (R. V.), SINY (I. G.), SMOLENSKY (G. A.), J. Appl. Phys., 1969, 40, 1510.

Pis'ma _{1969, 9,} Thurn. _294. tear. phis., 19699 9 , ; [5] PISAREV (R. V.), SINY (I. G.), SMOLENSKY (G. A.), [3] PISAREV (R. V.), SINY (I. G.), SMOLENSKY (G. A.), Phis. tverd. tela, 1970, 12, 118.

Zhurn. exp. teor, phis., 1969, 57, 737.