OPTICAL GYROTROPY AND BIREFRINGENCE IN MAGNETIC CRYSTALS

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OPTICAL GYROTROPY AND BIREFRINGENCE IN MAGNETIC CRYSTALS

R. Pisarev

To cite this version:

R. Pisarev. OPTICAL GYROTROPY AND BIREFRINGENCE IN MAGNETIC CRYSTALS. Jour- nal de Physique Colloques, 1971, 32 (C1), pp.C1-1051-C1-1052. �10.1051/jphyscol:19711377�. �jpa- 00214415�

JOURNAL DE PHYSIQUE Colloque C I, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1

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OPTICAL GYROTROPY AND BIREFRINGENCE IN MAGNETIC CRYSTALS

R. V. PISAREV

Institute of Semiconductors of the Academy of Sciences of the U. S. S. R., Leningrad D-187, U. S. S. R.

RBsumB. - On discute les effets optiques dans les cristaux ordonnes du point de vue magnktique, a partir des prin- cipes de symktrie magnktique. On montre que du point de vue des phknom&nes optiques, tels que la rotation Faraday et la birkfringence, un moment antiferromagnktique doit avoir les mt5mes effets qu'un moment ferromagnetique. On devrait observer une birefringence antiferromagnetique dans toutes les structures ferri et antiferromagnktiques. On examine d'autres effets optiques possibles. En conclusion, on donne les rksultats &observations expkrimentales de rotation Faraday antiferromagnetique et de birkfringence dans l'hematite.

Abstract. - Optical effects in magnetically-ordered crystals are discussed phenomenologically on basis of magnetic symmetry principles. It is shown that along with such optical phenomena as Faraday rotation and birefringence due to a ferromagnetic moment, the same effects exist at the expense of the antiferromagnetic moment. Antlferromagnetic bire- fringence should be observed in all ferri- and antiferromagnetic structures. A number of other possible optical effects is discussed. In conclusion the results of the experimental observation of antiferromagnetic Faraday rotation and birefrin- gence in hematite are given.

The use of magnetic symmetry arguments is known to lead to the prediction and the discovery of a num- ber of new physical phenomena [I]. The present investigation was carried out in order to examine optical effects following from magnetic symmetry and arising in crystals due to ferromagnetic vector, anti- ferromagnetic vector, electric field and elastic defor- mation [2]. In conclusion the results of the experi- mental investigation of some optical effects in anti- ferromagnetic hematite a-Fe20, will be given.

The light propagation in crystal is characterized by dielectic permeability tensor cij and gyration tensor gij [3]. Let us first consider the possibility of Faraday rotation (FR) that is described by an anti- symmetrical part of E:~. We can represent cFj in the form :

where only linear terms of the expansion are written out. For the simple case of two-sublattices ferri- magnetic or antiferromagnetic, m and 1 are the sum and the difference of the spins of different sublat- tices, i. e.

m = S1

+

Ek and ckn are components of the electric field and elastic deformation tensor respectively.

If one knows the transformation properties of tensors E:~, mk, lk, Ek, ^IS,, [I], the properties of the other tensors in (1) can be found for definite magnetic structure.

Since &Yj are the components of a second-rank polar i-tensor and mk are the components of an axial c- tensor of first-rank, aijk is an axial i-tensor of third rank. This tensor is present in all crystals and as a consequence F R can be always observed in diama- gnetic, paramagnetic crystals and in crystal with spontaneous magnetization (ferro- and ferrimagnets).

Let us consider a possibility of the FR connected with an antiferromagnetic vector 1. It is obvious that such an effect is possible when transformation pro-

perties of 1, coinside with those of m,. This is possible in ferrimagnets where all I, components transform as mk components. Evidently the F R in ferrimagnets can be considered as a summary effect of m and 1 moments. The contribution of the latter can be deter- mined at the magnetic compensation point where m equals to zero.

The antiferromagnetic F R can be exhibited by anti- ferromagnetic crystals in which some of the compo- nents of 1, and mk transform in a similar way. This is possible in antiferromagnetics with weak ferromagne- tism r41. m. .,

In certain magnetic crystals FR can arise in an exter- nal electric field. According to (I) this effect is charac- terized by the third rank polar c-tensor yijk. This effect must be observed in magnetoelectric crystals.

The appearence of FR under elastic stress in magne- tic crystals depends on the fourth rank polar c-tensor which is antisymmetric for the first and second indices and symmetric for the third and forth ones.

The presence of this tensor in crystals coincides with the presence of the third rand axial c-tensor that determines piezomagnetic effect [5].

Now let us analize the expansion of the symmetrical part of the permeability tensor ^8; that determines the optical birefringence. We represent it in a following form :

where &Yj is the dielectric permeability in paramagnetic region. In (3) we have written out only quadratic in m and 1 terms.

Magnetic birefringence characterized by a forth rank polar i-tensor aijk, is a known effect arising in all crystals in a magnetic field or in the presence of the spontaneous magnetization [6].

Forth rank polar i-tensor bijk, determines the anti- ferromagnetic birefringence that must be present in all ferri- and antiferrornagnets, as the 1, 1, and mk m, are transformed in the same way.

Except this antiferromagnetic birefringence speci-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711377

C 1

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birefringence which is bilinear in m and I and charac- terized by the cijk, tensor. This effect may be observed in crystals for which a product mk I,is transformed in the same way as m, m, or 1, 1,. This is possible for crystals with weak ferromagnetism where transformation properties of m, and I, may coincide. This bilinear birefringence must change the sign under reversal of m or 1 that is in contrast to ordinary and antiferro- magnetic birefringence that does not change the sign.

In the same way we have also examined optical activity and gyrotropic birefringence in magnetic crystals expanding the gyration tensor in series of components m,, I,, Ek and o,, [2].

a- Fe, o3

T 1295°K' X =1.15 r

10 H ll c

Now we proceed to the experimental observation of antifermagnetic FR and antiferromagnetic cotton- mouton (C-M) birefringence in hematite a-Fe203. The measurements of these effects were made on a single crystal platelet of about 1 mm thickness at wave-length, 1.15 y. The light travels along optical axis of the crystal which was perpendicular to the platelet. Figure 1 shows field dependence of F R at room temperature.

Figure 2 shows the temperature dependence of C-M

FIG. 2. -Temperature dependence of C M birefringence in hematite at 1 = 1.1 5 ^p and H = 8 kOe. The effect is observed when the antiferromagnetic moment I is oriented perpendicular

to the direction of light propagation.

0 ^{I I I} ,

/

H , ^{~ o e} direction of optical axis into the basic plane. It is FIG. 1. - Magnetic field dependence of FR in hematite ^a- interesting to note large magnitude of the antiferro- Fez03 at T = 295 OK (weak ferromagnetic state) and I ⁼ 1.15 p. magnetic birefringence that is n,, - n, = 2.1 ^X

References

[I] BIRSS (R. R.), Symmetry and magnetism, North- 32,1547, 1957 (translation) : Soviet Physics-IETP, Holland Publishing Company, Amsterdam, 1964. 1957, 5, 1259.

[2] PISAREV (R. V.), J. Exp. Theor. Phys., 1970, 58, 1421. 151 BOROV"-RoMANoV (A. J. ex^. Phys.9 U . S. S. R, 38, 1088, 1960 (translation) : Soviet [3] LANDAU (L. D.), LIFSHITZ (E. M.), Electrodynamics Physics-JETP, 1960, 11, 786.

of Continuous Media, Oxford, Pergamon, 1960. [6] PISAREV (R. v.), SINY (I. G.) and SMOLENSKY (G. A.), [4] DZIALOSHINSKII (I. E.), J. Exp. Theor. Phys., U. S. S. R., Solid State Communications, 1969,7, 23.