Two-layer model of reflectiveferromagnetic films interms of magneto-optical ellipsometry studies Текст научной статьи по специальности «Физика»

УДК 517.9

Two-layer Model of Reflective Ferromagnetic Films in Terms of Magneto-optical Ellipsometry Studies

Olga A. Maximova* Sergey G. Ovchinnikov^

Kirensky Institute of Physics Federal Research Center KSC SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036

Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041

Russia

Nikolay N. Kosyrev*

Kirensky Institute of Physics Federal Research Center KSC SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036

Russia

Sergey A. Lyaschenko§

Kirensky Institute of Physics Federal Research Center KSC SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036

Reshetnev Siberian State Aerospace University Krasnoyarsky Rabochy, 31, Krasnoyarsk, 660037

Russia

Received 17.11.2016, received in revised form 16.01.2017, accepted 02.02.2017 An approach to analysis of magneto-optical ellipsometry measurements is presented. A two-layer model of ferromagnetic reflective films is in focus. The obtained algorithm can be used to control optical and magneto-optical properties during films growth inside vacuum chambers.

Keywords: Magneto-optical ellipsometry, Kerr effect, two-layer model, ferromagnetic metal, reflection, growth control.

DOI: 10.17516/1997-1397-2017-10-2-223-232.

Recently it has become necessary to synthesize new materials that would be applied in spin-tronics devices. This field of study has significantly developed and it dictates the properties that materials should have in order to be used for its purposes. It is well-known that the simplest method of generating a spin-polarised current in a metal is to pass the current through a ferromagnetic material. That is why, one of the perspective materials for spintronics is a ferromagnetic/semiconductor two-layered structure [1].

* maximo.a@mail.ru

1 sgo@iph.krasn.ru

^ kosyrev@inbox.ru

§ fenics_star@mail.ru © Siberian Federal University. All rights reserved

In order to synthesize them and control their properties we have to use the methods that are non-destructive, precise, easy to use, applicable for in situ investigations in the high-vacuum chambers of molecular beam epitaxy. We suggest that magneto-optical ellipsometry is a technique that reflects these requirements. Magneto-optical ellipsometry usually combines the features of conventional ellipsometry and of magneto-optical Kerr effect measurements [2-6]. Applied to the sample magnetic field changes the ellipsometric parameters, this difference can be examined and used to investigate magneto-optic properties of the sample.

In this work we give detailed explanation how to analyse magneto-ellipsometric data and obtain information on magneto-optical and optical properties of the material.

1. General approach to magneto-ellipsometric data processing

Our approach is based on the analysis of a well-known equation that relates the experimental ellipsometric parameters ^ and A with complex reflection coefficients corresponding to in-plane (Rp) and out-of-plane (Rs) light polarizations [7-8]. Ellipsometric parameters ^ and A can be presented as a sum of conventional parameters and Ao measured without external magnetic field and additional ellipsometric parameters 5^ and SA that are the result of magnetic field application. We suggest to consider real and imaginary parts of these coefficients, so we mark them by ' and " respectively:

tan(^o + 5^) exp(i(Ao + 5A)) = RpR-1 = (Rp — iRp)(R'S — iR'S(1)

We are interested in magneto-optical properties of the sample. That is why it seems to be reasonable to present reflection coefficients as a sum of magnetic (subscript 1) and non-magnetic (subscript 0) summands [9-11]:

Rp = Rpp + Rps = RPo + RPi — i(RP'o + RP'i) (2)

Rs = Rss + Rsp = Rso = RSo — iR'So- (3)

This paper focuses on the case of transverse magneto-optic Kerr effect when the magnetization is perpendicular to the plane of incidence and parallel to the surface of the sample. That is why there are no magnetic summands for s-plane polarization.

From (1-3) four equations can be obtained. Two of them correspond to non-magnetic condition: _

, , / (RpoRSo + RSoRp'o)2 + (RSoRpo — Rp'oRSo)2 tan V>o = ]l -R2 + R2---> (4)

T) 2 I D"

Rso + Rso

Ac = arctan RR ~ , (5)

and two equations demonstrate the influence of an external magnetic field:

6A = A - Ac = arctan R^(Rp0 + Rpi) - R'so(R'p0 + Ki) - aQj (6)

RS0(Rp0 + Rp1) + RS0(Rp0 + Rp1)

= ^ — ^0 = arctan (F tan(^0)) — ^0, (7)

where F is a multiplier in

tan ('o + 5') = F tan 'o =

41

= tan 'M 11 + + R'p2 + 2(RoRpi + RpoRpi))(R2o + R2) (8)

(Rp0RS0 + RS0R'p0)2 + (RS0Rp0 — R'p0R's0)2

These equations do not depend on the number of layers in a sample, so can be used for every type of reflective nanostrustures models. Below, a two-layer model is presented.

2. Data processing for the case of a two-layer model

As it was mentioned above, ferromagnetic/semiconductor two-layer structures are a subject of interest nowadays. So in this chapter let us discuss a model consisting of an upper ferromagnetic layer 1 (the refraction index Ni = ni — iki), a middle non-magnetic layer 2 (the refraction index N2 = n2 — ik2) and a substrate 3 (the refraction index N3 = n3 — ik3). The light electromagnetic wave is incident from non-magnetic dielectric medium 0 (e.g. vacuum, characterized by the refraction index N0 = n0 — ik0) onto the upper layer. In the setup, a Cartesian coordinate system is defined with the x axis normal to the interfaces and pointing into the substrate from the sample surface. The y and x axis lie in the plane of incidence. We consider T-configuration (transverse) in which magnetization is z-axis directed, i.e perpendicular to the plane of incidence and parallel to the surface. So YX plane is a plane of incidence, YZ plane is a boundary plane.

For a two-layer model it is necessary to consider each interface (0-1, 1-2, 2-3) as each of them impacts the values of ellipsometric angles. The purpose of the data processing is to characterize a ferromagnetic layer.

The first step is carrying out ellipsometric and magneto-ellipsometric measurements. Here we do not focus on ellipsometric data analysis as there is a lot of research in this field [7,8,12]. So from ellipsometric measurements we can find complex refractive indices N0, Ni, N2, N3, thicknesses of both layers, while magneto-ellipsometric parameters spectra are necessary for magneto-optical properties study of a ferromagnetic layer.

Fresnel coefficients that reflect magneto-optical properties can be derived from the scattering matrix:

S = I01L1I12L2123, (9)

where Iab is an interface matrix and Lc is a layer matrix [7].

Rs = ^, (10)

(Sii)s

Rp =(Sr¥, (11)

(Sii)p

Rs = rois + ri2 S e-i2/31 + rois ri2 s r23 se^2?2 + r23 s

1 + roisri2se-i2/31 + ri2sr23se-i2?2 + roisr23se-i2(?l+?2)'

r = roip + ri2pToip e-i231 — roipr2ipr23pe-i232 + r23pToipTi2pe-i2(3l+32) (13) p 1 — riopri2pe-i231 — r2ipr23pe-i232 — riopr23pTi2pe-i2(3l+32) '

where

Toip = tioptoip — roipriop, (14)

т 12p — t21ptl2p — r12pr21p-

(15)

So, in order to process magneto-ellipsometric data the following expressions are necessary:

roip

N1 cos ф0 — N0 cos ф1 . 2QN§ sin ф0 cos ф0

- - i-

N1 cos ф0 + N0 cos ф1 (N1 cos ф0 + N0 cos ф1)2 '

r12p —

2QN2

1 sin ф1 cos ф1

N2 cos ф1 — N1 cos ф2

- - i

N2 cos ф1 + N1 cos ф2 (N2 cos ф1 + N1 cos ф2)2 '

N3 cos ф2 — N2 cos ф3

r10p

r23p лт

N3 cos Ф2 N0 cos ф1 — N1 cos ф0

+ i

r21p —

N0 cos ф1 + N1 cos ф0

N1 cos w2 — N2 cos w1

- + i

N1 cos ф2 + N2 cos ф1 (N1 cos ф2 + N2 cos ф1)2 '

N0 cos ф0 — N1 cos ф1

N2 cos фз '

2QN1 sin ф1 cos ф1 (N0 cos ф1 + N1 cos ф0)2 '

2QN| sin ф2 cos ф2

l01p

t10p —

r01S

Г12Б —

r23S

2N0 cos ф0

N0 cos ф0 + N1 cos ф1 '

N1 cos ф1 — N2 cos ф2 N1 cos ф1 + N2 cos ф2 '

N2 cos ф2 — N3 cos ф3 N2 cos ф2 + N3 cos фз '

2QN3 sin ф0 cos ф0

t12p

t21p

N1 cos ф0 + N0 cos ф1

2N1 cos ф1 N1 cos ф0 + N0 cos

2N1 cos ф1 N2 cos ф1 + N1 cos ф2

2N2 cos ф2

+ i

+ i

N1 (N1 cos ф0 + N0 cos ф1)2 '

2QN3 sin ф1 cos ф1 N0(N1 cos ф0 + N0 cos ф1)2 '

2QN3 sin ф1 cos N2(N2 cos ф1 + N1 cos ф2)2 '

2QN2 sin ф2 cos ф2

N2 cos ф1 + N1 cos ф2 N1 (N2 cos ф1 + N1 cos ф2)2 ' 2n

в1 — "T" N1 cos ф1d1, л

2n

в2 — -Г"N2 cos ф23,2, л

(16)

(17)

(18)

(19)

(20) (21) (22)

(23)

(24)

(25)

(26)

(27)

(28) (29)

where f31 and (32 are phase thicknesses of layer 1 and layer 2, respectively, d1 and d2 are thicknesses of layers 1 and 2. Subscripts 01, 12, 23 correspond to the wave propagation from medium 0 to medium 1, from 1 to 2 and from 2 to 3 respectively, while subscripts 10 and 21 correspond to the backward wave propagation. Indices r are refractive indices for the mentioned above interfaces, indices t are transmission coefficients. Angles 1 and 2 are related with (the angle of incidence) by Snell's law. Q is a magneto-optical coupling parameter that is responsible for non-diagonal elements of dielectric tensor. It means that if we know this parameter we can fully describe the dielectric permitivity, not only diagonal elements. Hereinafter we present the

i

formulae necessary for identifying Q from magneto-ellipsometric measurements. Let us rewrite (12-18) in the same manner as (2, 3):

rois = (RSo)oi — i(RSo)oi, (30)

ri2S = (RSo)i2 — i(RSo)i2, (31)

r2ís = (RSo)23 — i(RSo)23, (32)

r23p = (Rpo)23 : — i(Rpo)23 = rr'23 — i rÍ23, (33)

ro1P = (R'po)oi + (R'pi)oi — i((Rpo)oi + (Rpi)oi) = rroi — i rioi, (34)

r12P = (Rpo) i2 + (R'pi)i2 — i((Rpo)i2 + (Rpi)i2) = rri2 — i rii2, (35)

r2íP = (Rpo)23 + (Rpi)23 — i((Rpo)23 + (Rpi)23) = rf'23 — i ri23, (36)

r1oP = (Rpo)io — (Rpi)io — i((R^o)io — (Rpi)io) = rrio — i riio, (37)

r21P = (Rpo)2i — (Rpi)2i — i((Rpo)2i — (R^i)n) = rr2i — i ri2i, (38)

toip = = (Tpo)oi + (Tpi)oi — i((Tp'o)oi + (Tpi)oi) = troi — i tioi, (39)

tl2p = = (Tpo)i2 + (Tpi) i2 — i((Tpo ) 12 + (Tpi ) 12) = tr 12 — i ti 12, (40)

tiop - = (Tpo)io — (Tpi)io — i((Tp'o) i o — (Tpi) i o) = tr i o — i ti i o, (41)

t2ip - = (Tpo)2i — (Tpi)2i — i((Tp'o)2i — (Tpi)2i)= tr2i — i tin, (42)

(RSo)oi, (RSo)oi , (Rpo)oi, (Rpo)oi, Rpi)oi, (Rpi)oi correspond to R'so,R'So, Rpo, í?" í?' Rpo, Rpi,

Rpi in the model of a homogeneous semi-infinite medium, respectively [11]. Subscript 01 denotes the electromagnetic wave incidence from ambient medium 0 onto layer 1. Indices (R'so)i2, (R'so)i2, (R'po)i2, (Rpo)i2, (R'pi)i2, (R'Pi)i2 are also calculated by formulae for the model of a homogeneous semi-infinite medium, the only difference is that subscript 12 denotes the electromagnetic wave incidence from layer 1 onto layer 2 that leads to the following changes in the formulae for the model of a homogeneous semi-infinite medium: cos po ^ cos pi, cos pi ^ cosp2, sinpo ^ siny>i, ni ^ n2, no ^ ni, ki ^ k2, ko ^ ki. Likewise, indices (Rpo)io, (R'po)io, (R'pi)io, (Rpi)io describe the electromagnetic wave propagation from layer 1 to medium 0: cospo ^ cospi, sinpo ^ sinpi, no ^ ni, ko ^ ki. Indices (R'po)2i, (R'po)2i, (R'pi)2i, (R'Pi)2i correspond to the electromagnetic wave propagation from layer 2 to layer 1: cos po ^ cos p2, sin po ^ sin p2, no ^ n2, ko ^ k2. Finally, indices (R'so)23, (RSo)23, (Rpo)23, (Rpo)23, (Rpi)23, (Rpi)23 describe the electromagnetic wave incidence from layer 2 on substrate 3: cospo ^ cosp2, cospi ^ cosp3, sinpo ^ sinp2, ni ^ n3, no ^ n2, ki ^ k3, ko ^ k2.

Transmission coefficients necessary for data processing are the following:

(TP0)oi (TP'0)oi

2

2

(noni + koki )(a2 + c2) + (n20 + kl )(ab + cd)

Aí+B2 :

(n0 + k0)(ad — bc) + (niko — n0 ki)(a2 + c2)

AíTB2 :

Qi(pq + rs) — Q2(pr — sq)

(TPi)oi =2 (TP'i)oi = 2

(ni + k2)(A2 + B2)2 :

Ql(pr — sq) + Q2 (pq + rs)

(n

k2)(A2 + B2)2

(43)

(44)

(45)

2

1

where

A3 = n\a + k\c + nob + kod, (47)

B3 = kia — n\c + kob — nod, (48)

p = N (3n2ko — k3) + P (n0 — 3nokl), (49)

q = ni(Al — B32) — 2A3B3ki, (50)

r = ki (B32 — A3) — 2A3B3ni, (51)

s = N (n3 — 3nok2) — P (3n22ko — k3), (52)

a = Re(cos po), (53)

b = Re (cos p1), (54)

c = Im(cos ^0), (55)

d = Im(cos ^1), (56)

N = Re(sin p0 )a — Im(sin p0)c, (57)

P = — Re(sin p0)c — Im(sin p0)a. (58)

Transmission coefficients with subscripts 10, 12, 21 correspond to the electromagnetic wave propagation from layer 1 to medium 0, from layer 1 to layer 2, from layer 2 to layer 1, respectively. The changes in the formulae are the same as proposed for refractive indices.

Let us take into account N0 = n0 — ik0, N1 = n1 — ik1, N2 = n2 — ik2, Q = Q1 — iQ2 and compare expressions (12, 13) with (2, 3). Thus we obtain expressions for R'p0, R'po, Rp1,Rpi, R's0 and RSo in terms of numerators and denominators:

r = numeratorRso _ Re(n(Rso)) — i Im(n(Rso)) (59) denominatorRso Re(d(Rso)) — i Im(d(Rso)) '

R = Re(n(Rpo)) — i Im(n(Rpo)) (60)

po Re(d(Rpo)) — i Im(d(Rpo)) ' 1 J

R = Re(n(Rp)) — i Im(n(Rp)) (61)

p Re(d(Rp)) — i Im(d(Rp)), (6)

where n stands for numerator and d - for denominator. As a result, we have

r = Re(n(Rpo)) Re(d(Rpo)) + Im(n(Rpo)) Im(d(Rpo)) (62)

po (Re(d(Rpo)))2 + (Im(d(Rpo)))2 , ( )

= Im(n(Rpo)) Re(d(Rpo)) — Im(d(Rpo)) Re(n(Rpo)) (63)

po = (Re(d(Rpo)))2 + (Im(d(Rpo)))2 , (63)

R = Re(n(Rp)) Re(d(Rp)) + Im(n(Rp)) Im(d(Rp)) R (64)

p1 (Re(d(Rp)))2 + (Im(d(Rp)))2 po' J

'p)) Re(d(Rp)) — Im(d(Rp)) Rei (Re(d(Rp)))2 + (Im(d(Rp)))2

= Im(n(Rp)) Re(d(Rp)) — Im(d(Rp)) Re(n(Rp)) (65)

Rp1 (Re(d(R )))2 + (Im(d(R )))2 RP0, (65)

R = Re(n(Rso)) Re(d(Rso)) + Im(n(Rso)) Im(d(Rso)) (66)

so (Re(d(Rso)))2 + (Im(d(Rso)))2 , ( )

= Im(n(Rso)) Re(d(Rso)) - Im(d(Rso)) Re(n(Rso)) ( )

so (Re(d(Rso)))2 + (Im(d(Rso)))2 ' ( )

where the following notations are used:

Re(n(Rpo)) = (RPo)oi + CiRPo)i2 - ni(RPo)i2 + Lom&R'pohs - mR'Pohs)--Moi12(UKo)23 + n2(RPo)23) + (RPo)23(CiC2 - ni- Ro^fem + CmO

Im(n(Rpo)) = (Rp'o)oi + ni(RPo)i2 + CiR'o )i2 + LomfeRo^ + %(RPo)23) + + Moii2(C2(RPo)23 - n2(RP'o)23) + RoMC^ - n^) + RPo)23foni + Ci^),

Re(d(RPo)) = 1 + LomCi - Momm + C2L223 - mMi223+ + (CiC2 - ViV2)Loi23 - fam + Cin2)Moi23,

Im(d(RPo)) = Loii2ni + MomCi + C2Mi223 + n2^i223+ + (CiC2 - nin2)Moi23 + (C2ni + Cim)Loi23,

Re(n(RP)) = rroi + (Ci^ri2 - nirii2)(«i)oi - (Ci^«i2 + nirri2)(«2)oi--(rroirr2i - r«oiri2i)(C2rr23 - mri23) + (r«oirr2i + rroiri2i)(C2ri23 + n2rr23)+ + (rr23(CiC2 - nin2) - ri23(C2ni + Cin2))((«i)oi(«i)i2 - (K2)oi(K2)i2)--(r«23(CiC2 - nin2) + rT23(£im + niC2))((Ki)oi(K2)i2 + («i)i2 («2)oi),

Im(n(RP)) = rioi + (Cirii2 + nirri2)(«i)oi + (Cirri2 - nirii2)(«2)oi--(r«oirr2i + rroiri2i)(C2rr23 - n2ri23) - (rroirr2i - rioiri2i)(C2ri23 + n2rr23) + + (ri23(CiC2 - nins) + rr23(C2ni + Cin2))((«i)oi(«i)i2 - («2)oi(«2)i2) + + (rr23 (Ci C2 - ni m) - ri23 (Cin2 + niC2))((«i)oi(«2)i2 + («i) i2 («2 )oi),

Re(d(R)) = 1 - Ci(rriorri2 - riiorii2) + ni(riiorri2 + rriorii2)--C2(rr2irr23 - ri2iri23) + n2(ri2irr23 + ri23rr2i)-((«i )i2(rriorr23 - riio ri23) - («2 )i2(riiorr23 + ri23rrio))(CiC2 - nin2) + + ((«i)i2)(riiorr23 + ri23rrio) + («2)i2(rriorr23 - riiori23))(C2ni + Cin2),

Im(d(RP)) = -Ci(riiorri2 + rrwrii2) - ni(rrwrri2 - riwrii2)--C2(ri2irr23 + rr2iri23) - m(rr2irr23 - ri23«2i)-((«i)i2(riiorr23 + rriori23) + («2)i2(rriorr23 - ri23riio))(CiC2 - nim)--((«i)i2)(rriorr23 - ri23riio) - («2)i2(riiorr23 + rriori23))(C2ni + Cim),

Re(n(Rso)) = (R'so)oi + Ci(Rso)i2 - ni(Rso)i2 + Hoii2^2^)23 - m^o)23)--Joii2(C2(Rso)23 + m(R'so)23) + (Rso)23(CiC2 - m^) - (R'so)23(C2ni + C№),

(68)

(69)

(70)

(71)

(72)

(73)

(74)

(75)

Im(n(Rso)) = (R'so)oi + m(R'so )i2 + UR'Sohi + HoiniUR'Sohz + m&'sohs )+ +Jon2(&(R'soh3 - m(R'Sohs) + (R'Sohs^i& - mm) + (R'sohs&m + tim), Re(d(Rso)) = 1 + Hoii2ti - Joii2m + t2H1223 - V2J1223+ +(tit2 - mm)Hoi23 - (&m + tim)Joi23, lm(d(Rso)) = Hoii2 ni + Joii2ti + £,2-Ji223 + mHi223 + +(tit2 - mm)Joi23 + (&m + tim)Hoi23,

(77)

(78)

(79)

ti = Re(e-i231 ), (80)

ni = - Im(e-i231 ), (81)

t2 = Re(e-i232 ), (82)

n2 = - Im(e-i232 ), (83)

Loii2 = (Rpo)i2 (RPo)oi - (R'Po)i2(R'Po)oi, (84)

Moii2 = (Rpo)oi (Rpo)i2 + (R'Po)oi(R'po)i2, (85)

Li223 = (Rpo)23 (Rpo)i2 - (Rpo)23(Rpo)i2i (86)

Mi223 = (Rpo)i2 (Rpo)23 + (Rpo) i2 (Rpo)237 (87)

Loi23 = (Rpo)23 (Rpo)oi - (Rpo)23(Rpo)oi: (88)

Moi23 = (Rpo)oi (Rpo)23 + (Rpo)oi (Rpo)23: (89)

Hoii2 = (R'so)i2(R'so)oi - (R'so)i2(R'so)oi, (90)

Joii2 = (RSo)oi (RSo) i2 + (R'so)oi(R'so)i2, (91)

Hi223 = (R'so)23(R'so)i2 - (R'so)23(R'so)i2, (92)

Ji223 = (R'so)i2(R'so)23 + (R'so)i2(R'so)23, (93)

Hoi23 = (R'so)23(R'so)oi - (Rso)23(Rso)oi, (94)

Joi23 = (R'so)oi(R'so)23 + (R'so)oi(R'so)23, (95)

(ki)oi = triotroi - tiiotioi - rroirrio + rioiriio, (96)

(«2)oi = tiiotroi + triotioi - rroiriio - rioirrio, (97)

(Ki)i2 = tr2itri2 - ti2itii2 - rr2irri2 + ri2irii2, (98)

(K2)i2 = tii2tr2i + tri2ti2i - rruri2i - riurr2i. (99)

So all necessary expressions that relate measured ellipsometric and magneto-ellipsometric parameters with refraction indices, coefficients of extinction, magneto-optical coupling parameter in case of a two-layer model are obtained. The final step is giving the best fit to the experimental data by the use of the wavelength-to-wavelength Nelder-Mead minimization [13] of the

ellipsometric angles. It yields real and imaginary parts of magneto-optical parameter Q, thus information about all elements of the dielectric permittivity tensor can be obtained from the experiment.

Conclusion

To conclude, we have proposed an approach to studying two-layer nanomaterials by means of magneto-ellipsometry. The algorithm of experimental data analysis (^o, So, ^o + S^, Ao + SA) is presented. As a result, optical and magneto-optical properties can be easily and reliably characterized during films growth through the presented formulae that are to be used in the software for magneto-optical ellipsometry set-ups.

The reported study was funded by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund to the research project 16-42-243058. The work was supported partly by the Russian Foundation for Basic Research, Grant No. 16-32-00209 mola, Grant No. 14-02-01211; the Complex program of SB RAS No. II.2P, project 0358-2015-0004; the Ministry of Education and Science of the RF (State task No. 16.663.2014); grant Scientific School 7559.2016.2.

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Двухслойная модель отражающих ферромагнитных пленок для исследования тонких пленок методом магнитоэллипсометрии

Ольга А. Максимова Сергей Г. Овчинников

Институт физики им. Л. В. Киренского, КНЦ СО РАН Академгородок, 50/38, Красноярск, 660036

Сибирский федеральный университет Свободный, 79, Красноярск, 660041

Россия

Николай Н. Косырев

Институт физики им. Л. В. Киренского, КНЦ СО РАН Академгородок, 50/38, Красноярск, 660036

Россия

Сергей А. Лященко

Институт физики им. Л. В. Киренского, КНЦ СО РАН Академгородок, 50/38, Красноярск, 660036

СибГАУ им. академика М. Ф. Решетнева Красноярский рабочий, 31, Красноярск, 660037

Россия

Представлен метод анализа магнито-эллипсометрических измерений. Детально 'рассматривается двуслойная модель ферромагнитных отражающих пленок. Полученный алгоритм может использоваться для контроля оптических и магнито-оптических свойств пленок в процессе их роста в вакуумных камерах.

Ключевые слова: магнито-оптическая эллипсометрия, эффект Керра, двухслойная модель, ферромагнетик, отражение, контроль роста.