MAGNETO-OPTICAL ORIENTATION EFFECT INFERROMAGNETIC METALS

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MAGNETO-OPTICAL ORIENTATION EFFECT INFERROMAGNETIC METALS

G. Krinchik

To cite this version:

G. Krinchik. MAGNETO-OPTICAL ORIENTATION EFFECT INFERROMAGNETIC METALS.

Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1058-C1-1060. �10.1051/jphyscol:19711380�.

�jpa-00214419�

JOURNAL DE _PHYSIQUE Colloque C 1, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 1058

MAGNETO-OPTICAL ORIENTATION EFFECT INFERROMAGNETIC METALS

G. S. KRINCHIK

Moscow State University, U. S. S. R.

RBsumB. - Des essais ont kt6 faits pour d6tecter optiquement l'influence de l'orientation du vecteur aimantation sur la structure klectronique d'un m6tal ferromagnktique, effet qui semble rksulter de l'interaction spin-orbite. Un nouvel effet magnkto-optique appel6 effet d'orientation a,, a kt6 dkcouvert dans l'effet Kerr en geomktrie equatoriale. Contrai- rement aux effets magnkto-optiques ordinaires, cet effet est caracterise par une variation particuliere en fonction de la longueur d'onde de la lumiere. Deux mkthodes classiques de description de Sor sont proposkes consistant A introduire un terme supplementaire d'anisotropie dans les composantes diagonales et non diagonales du tenseur de permeabilite diklectrique. Une methode experimentale est proposee permettant de vkrifier la validite de l'un des modeles. Diffkrentes possibilites d'utilisation de a,, pour identifier les transitions entre bandes dans les metaux ou alliages ferromagnktiques sont envisagees.

Abstract. - An attempt was made to detect optically the influence of the orientation of magnetization vector on the electronic structure of a ferromagnetic metal which appears as a result of the spin-orbit interaction. A new magneto- optical effect named orientation effect a,, was discovered at the geometry of the equatorial Kerr effect. In contrast to the usual magneto-optical effects it is characterized by the quadratic dependence on the magnetization, extremely great ani- sotropy and a peculiar dependence on the wavelength of the light. Two methods of classical description of a,, by means of introducing an additional anisotropic term into the diagonal or nondiagonal component of the dielectrical permeability tensor are suggested. A method of experimental determination of the validity of one of these descriptions is given. Different possibilities of using a,, for the identification of the interband transitions in ferromagnetic metals and alloys are considered.

It has been recently discovered that spin-orbit interaction in ferromagnetic metals results in an extremely interesting phenomenon. Investigating Fermi surfaces of ferromagnetic nickel Hodges et al. [I]

have discovered a peculiar change in the form of the hole pockets at the X point and connected this with the fact that the spin-orbit splitting of the twice degenerated band A , J. in the vicinity of the X, point changes from zero to the maximum value of the order of 0.1 eV when the orientation of the magnetization vector I in the crystal changes (see also [2, 31).

I t is essential to point out here, that spin-orbit interaction must affect in the above sense, not only the energy levels of the Fermi surface but also the whole electron energy spectrum of the ferromagnetic metal, and this influence should be especially strong in those regions of Brillouin zone where the energy level degeneration is removed by the spin-orbit inter- action. Hence, it is possible, in principle, to observe the indicated change of the electron structure of a ferro- magnetic metal, following rotation of I, by an optical method at the frequencies of the interband transitions.

The localization of maximum changes of this kind in definite regions of the Brillouin zone gives us hope of a reliable identification of interband transitions are consequently quantitave determining band parameters of ferromagnetic metals-and alloys. Paper [4] discusses the special experiment undertaken to discover the magneto-optical effect of change of electronic struc- ture of a ferromagnetic metal following rotation of the magnetization vector. I n [5] it was stated that this effect, called magneto-optical orientation effect (MOE), was proportional to the square of magnetization component normal t o the plane of incidence of the light. In [6] a detailed study of anisotropy of orienta- tion effect in single crystals of nickel and silicon iron is given, and it is shown that MOE cannot be reduced to the Voigt magneto-optic effect. Let us consider different types of orientation effect due to spin-orbit

interaction, the possibilities of its application to the study of band structure and the phenomenological methods of defining the kind of the tensor of dielec- trical permeability resulting in MOE.

Figure 1, reproduced from [7], gives the scheme of

FIG. 1. -Band structure near symmetry point L

(nla) (1, 1, 1) with the magnetic field along ^(a) the [III] and (b) the

[III] directions.

band structure of ferromagnetic nickel in the vicinity of the point L for two different orientations of I for the electron model with the reverse order of levels [8].

The first possibility for the appearance of MOE is the splitting of degenerated bands in the vicinity of certain lines or points of symmetry. In figure la, for example it is the region of strong splitting of the band A, J for transitions A, J -+ 1, J. in the interval from B t o A. In the vicinity of the point of the inter- section of the band A, J. with Fermi level (the edge A) and in the vicinity of the L point (the edge B) strong optical and magneto-optical orientation effects should be expected since here considerable changes of inter- band density of state take place. In the interval from B t o A only parallel band shifting occurs, while the interband density does not change t o the first approxi- mation, and so, only magneto-optical effects of orien-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711380

MAGNETO-OPTICAL ORIENTATION EFFECT IN FERROMAGNETIC METALS C 1 - 1059 tation type caused by the magnetic circular double

refraction can originate since here we have the ana- logue of Zeeman effect.

The second possible type of MOE is spin-orbit removing of accidental degeneration of the bands in the points of their intersection. From figure l b it is clear that the effect of this kind appears as a result of the intersection of bands L32, f and L32,3 J for transitions E, F, G. In this case there appears an obvious change of the curvature of the bands, effective mass, interband density state occurs which should immediately result in optical and magneto-optical orientation effects. Variations of the appearance of MOE of the second type in the longitudinal direction, for example r X , are possible. Here the following interesting circumstance should be noted. If the identification of any of the peculiarities on the MOE curves with the frequency h a , proves to be valid we shall obtain a direct spectral method of determining the magnitude of exchange splitting of d-band of the ferromagnetic metal AE,. From figure 1 it is clear that though in this case we are dealing with the tran- sitions in the subbands of the same sign of spin L328 f and L,,, f the frequency

as the transition passes to the region of the intersection of bands L32, f and L32a 1. The simultaneous deter- mination of the frequencies h o , and h a , gives a reliable information for estimating the magnitude of exchange splitting of p-bands

since the effective mass of these bands in the longitu- dinal direction may be calculated theoretically [7].

Finally, the width and the shape of the given peculia- rity of the second type at low temperatures should give us some data for the estimation of the spin-orbit splitting parameter.

The third type of MOE may be caused by the shifting of Van Hove singularity out of the Fermi surface during the rotation of I due to the spin-orbit splitting of the bands. Figure 2 shows the scheme of

FIG. 2. - Comparison of band structures near symmetry point X = 2 (nla)

0, 1) for the magnetic field oriented along the

various [001] axes at two positions of the Fermi level.

the third type effect when the turn of I results in the appearance or disappearance of the hole pockets in the point X. In this case certain parts of the bands,

in the vicinity of singularity, are excluded from the interband transitions, and therefore the change of the interband density and the appearance of strictly frequency localized orientation optical and magneto- optical effects are obvious. In order that MOE of the third type should appear, it is necessary that the singularity in the degeneration band should occur near the Fermi surface i. e. at the distance of the order of 0.1 eV. This situation is possible for the shown in figure 2 X5 point in ferromagnetic nickel, the exchange splitting being AE, z 0.3 eV. This situation may be also obtained by means of changing some parameters such as temperature and alloy concentration. In all considered cases it should be born in mind that only one of the equivalent points of Brillouin zone was taken into consideration while it is necessary to find the averaged value of all the analogous in symmetry but now not equivalent points, orientation being fixed. It is natural that the indicated inequality should lead to the characteristic fine struc- ture peculiarity which may be used as an additional information for the identification of the interband transitions.

Let us consider now the possibility of phenomeno- logical determining of the kind of the dielectric per- _- meability tensor? resulting in MOE. It is clear from the symmetry considerations that MOE may be caused by the quadratic in magnetization additions in the diagonal and non-diagonal terms;. To find out which of these additions play the main part is easier by measuring the dependence of MOE on the angle of light incidence.

Let us consider separately the two cases of inserting quadratic in magnetization additions q and r.

Case I :

= cyy = ~ ( 1 - q),. ezz =

= - i82, eXy = cyx = 0 where q = ql - 1q2 is quadratic in magnetization addition, q 4 1. From Maxwell equa- tions for this case with the approximation

4 l and restricting to the linear terms for q we find the following expression for the relative change of the intensity of p-component of reflected light 6' :

= 2 Cos q b(kq2 - n q ~ ) - a(kq1 +-nq2) a 2 +- ^b2 (2)

where

and q the angle of light incidence.

Case I1 :

where u = r , - ir, quadratic in magnetization addi- tion, r < 1. Thus in the same way we receive the following expression for this case :

6" - R - Ro b.rz - a . r l

- ^{--- =} 2 sin 2 rp ---

a 2 -I- b2 - ⁽³⁾

Ro

Comparing (2) and (3) we see that the diagonal

addition q retains its influence in the normal inci-

C 1 - 1060 G . S. KRINCHIK dence of light, while the contribution of the non-

diagonal addition r should vanish. It is interesting to measure the dependencies of MOE on p, the orien- tation of I being along different axes of ferromagnetic crystal. In such measurements the main part for some axes may be played by diagonal additions q, while for the others additions r. Provided this qualitative cha- racteristic of the kind of the tensor; is obtained, it is possible to calculate the corresponding orientation

magneto-optical effects not only when the magnetiza- tion is equatorial but also for the case of polar and meridional magnetization of the ferromagnetic sample, as well as in the case of light passing through the sample with Faraday and Voigt geometry. Experimen- tal detection and measurement of these orientation magneto-optical effects will make the quantitative determination of quadratic in I components q and r possible.

References

[I] HODGES (L.), STONE (D. R.), GOLD (A. V.), Phys. [5] KRINCHIK (G. S.), CHEPUROVA (E. E.), JETP, Letters,

Rev. Lett., 1967, 19, 655. 1970, 11, 105.

[2] STARK (R. W.), TSUI (D. C.), J. Appl. Phys., 1968, L6] KRINcHK (G- S.)y

(E. GusHcH1iv (V. S.)*

39, 1056. this issue.

[7] ZORNBERG (E. I.), Phys. Rev., 1970, B 1, 244.

131 FALICOV (L. M.), RUVALDS (J.), Phys. Rev., 1968, [8] K R I N C H ~ (G. S.), GANSHINA (E. A.), Phys. Lett.,

172, 498. 1966, 23, 294.

[4] KRINCHIK (G. S.), GUSHCHIN ^(V. S.), JETP, Letters, KRINCHIK (G. S.), GUSHCHIN (V. S.), JETP, 1969,

1969, 10, 35. 56, 1833.