Light diffraction by magnetic domain gratings and its applications

JOurnal of Magnetism and Magnetic Materials 19 (1980) 391-394 © North-Holland Publishing Company

LIGHT DIFFRACTION BY MAGNETIC DOMALN GRATINGS AND ITS APPLICATIONS B. KUHLOW

Optisches Institut der Technischen Universitt~tBerlin D-1000 Berlin 12, W. Germany

Magnetic domains arranged in a regular domain grating give rise to light optical diffraction patterns. The diffractions are examined at a stripe domain grating and a hexagonal bubble domain grating. Applications of the diffraction for light deflection and data processing are discussed.

1. Introduction

the cooling below T c a stripe domain pattern aligned in the direction of this field is formed [9]. A suitable strong field inclined to the plane of the crystal applied during the cooling below Tc causes the stripe domains to break into several bubble domains each. In perfect crystals these bubble domains are arranged in a regular hexagonal grating. These domain gratings also remain stable if the external field is switched off [7,9].

Magnetic domains appearing in uniaxial ferro- and ferrimagnetic crystals are magnetized alternately antiparallel in the normal direction to the crystal layer. In perfect crystals these domains are arranged in a regular domain grating [ 1]. It can be observed by means of the magneto-optic effects (Faraday and Kerr effect). As each image formation this observation too is based on the diffraction of light at the domain grating [2]. The Fraunhofer diffraction pattern can be observed in the focal plane of a lens. The diffraction at these domain gratings can be used for some technical applications [ 3 - 6 ] .

3. Light diffraction by magnetic domain gratings The crystals were illuminated with linearly polarized light. The light source was a mercury arc lamp combined with interference filters to select the wavelength k of the light. Domain walls can be neglected, since their width is below the optical resolution. In the case of stripe domains with domain spacing D the different diffraction order maxima appear at angles On according to, fig. 1 :

2. Experimental procedure The investigations were made on thin magnetic uniaxial crystals which were transparent in the optical region and had a sufficiently high value of Faraday rotation/3: (1) a ferrimagnetic crystal with the composition

sin On --- nX/D ; n = 0, +-1, +-2. . . . .

(1)

If the incident light is polarized in the x-direction the intensities of the diffraction orders are given by [2] :

Y1.92 Smo. loCao.98Fe4.o2Geo.98012, 5.3/am thick, grown by liquid phase epitaxy (LPE) on a gadolinium gallium garnet (GGG) substrate (c/green = 1-6°, Tc = 198°C, stripe domain width d ~ 6/am) [7,81. (2) A ferromagnetic CrBr3-crystal, 20/am thick (Tc ~ 33 K, at 15 K: ~green ~ 60° and C/blue ~ 90°, d = 1.3/am) [9,10]. If a magnetic field is applied to the crystal during

I(O)x = E 2 cos2fl ;l(0)y =E2(1 - 2/0)2 sin2c/,

(2)

l(n)x = 0;I(n)y = 4 E 2 sin2c/(sin - - npn] 2 ; n =/=O,

(3)

\

nT~

/

where E is the amplitude of the electrical light-vector and p = diD is the domain factor. In the case of a hexagonal bubble domain grating 391

B. Kuhlow / Light diffraction by magnetic domain gratings

392

Polorizer Domain Structure

Frounhofer Diffraction

l(m, n)x = 0 ;l(m, n)y = 4E 2 sinZflK2(m, n) ; m or n @ 0

(6)

with

K(m, n) = 27rR 2 Jl(27rR/D[n2 + 1/3 (2m - n) 2] t/2) 2nR/D[n 2 + 1/3(2m n)Z] wz The domain factor is p = 2nR2/D2x/~. R is the bubble radius and J1 the Bessel function of the first order.

"x Fig. 1. Light diffraction at a stripe domain structure.

CrBr3 (20/Jm, 15K)

lC

!

d[pm]

the diffraction order m a x i m a appear at the angles ¢, ~7 according to:

®

= 0,

+ l , +-2 .....

I

,j

k 1 sin ~p = nk/D • sin rt = (2m - n) D x / ~ ' n, m

®

idol

!d~;

6

#7

i,+°;#

(4)

where D is the distance between the bubble domains, fig. 2. The intensities of the diffraction order m a x i m a are [7,8]:

I(0, O)x

=

E 2 cos2fl I I 15101

I(0, 0)y = E2(1 - 2p)2 sin 2 3 (Dg~-~) 2

(5)

I I I

I I

100

I i

I

I

150

I

I,

I I,

I I~

200

250

a) Or Br 3 ~E°I

sin~

I

~I [541 nm]

,2

~J I iI (~ [{-1.-21 ,P ,,lCi~

~ (1.2t ~ I) sin(p

', \ \ \. '4'.,~1-2A)(%0) (-1.1J//~ O, ' , , \~'O.2.0RDER.~// "\~"0..... "" 3 Q ~ D E R ' / ~ \\

"O-A.ORDER - O ' I ~ - / /

Fig. 2. Diffraction pattern of a hexagonal bubble domain grating.

ireL

/"°>q0.0

I0

0,5

6

0,3

4

0,2

2

0.1 50

/ //

0.8

100

150

200

'

b) Fig. 3. (a) Measured domain width in a 20 #m thick CrBr 3crystal versus field. (b) Angles of first order diffraction maxima for green and blue light and relative intensities of I(O)y and l(1)y versus field.

B. Kuhlow /Light diffraction by magnetic domain gratings All nonzero-order maxima are polarized perpendicularly to the incident light. This is also true in the case of circular dichroism, while the zero-order maximum is elliptically polarized. In the case of vanishing circular dichroism however it is plane-polarized. The first-order maxir~aa can never vanish as long as the grating exists. The symmetry of the domain grating shows up in the diffraction pattern. The ratio of diameter to distance of the domains in the grating can be changed by an external magnetic field directed normal to the crystal layer. The dependence of domain widths of stripe domains in the CrBr3-crystal on the field is shown in fig. 3a. The diffraction angles of the first-order maxima according to eq. (1) for green light (X = 541 nm) and blue light (X = 490 nm) are shown in fig. 3b. The angle O~ and therefore the direction of the deflected light can be changed by the external magnetic field that influences the domain spacing D. This effect can be used for controllable light deflection [3]. It can also be used to couple light into thin layers in integrated optics. Domain spacing and indices of refraction of the two adjacent layers have to be choosen suitably [6]. Fig. 3b also shows the relative intensities (except the factor sin2/3) of the zero and first-order maximum according to eqs. (2) and (3) polarized in the

•2R ' ~ = 0.85

0.72

393

y-direction, passing through an analyzer perpendicularly set. For a Faraday rotation/~ = 90 ° in the crystal (blue light) the component I(0)x vanishes. For a domain factor p = 1 I(O)y also vanishes and 81% of the light appears in the + first-order maxima. With increasing deviation o f p from the value 19I(O)y increases and I(1)y decreases [ 11 ], thereby limiting the utility of the deflection variation. Nevertheless the domain pattern and consequently the direction of the deflected light can be rotated magnetically. Fig. 4 shows the hexagonal bubble grating and the corresponding diffraction patterns for different values of the external field H. The measured values of domain spacing D and bubble domain diameter 2R are presented in fig. 5. Within the field range o f - 2 8 to +62 A cm -1, changed reversibly, D and consequently the diffraction angles do not change. 2R changes linearly and so does the ratio 2RID that influences the intensity distribution in the diffraction pattern according to eq. (6) [7,8]. The calculated relative intensities I(0, 0)y and I(m, n)y (without factor sin2/3) for the first to fifth-order maxima (cf., fig. 2) are presented in fig. 6. The maximum of the first order is normalized to 1. Within the fixed diffraction spots the intensities vary drastically with variation of the field H (cf., fig. 4). This can be used for data storage largely free from disturban-

0.55

0.35

. . ° , , . . ° , , , ~ ° , . ° ,

~ . , . , ° , , . ° # o . , ° . , , , o . o . . o . o . - o ° ° , . , ~

Fig. 4. Bubble domain gratings and corresponding diffraction patterns for different values of the external magnetic field for the garnet crystal Y1.92Smo.1oCao.98Fe4.02Geo.98012 .

B. Kuhlow / Light diffraction by magnetic domain gratings

394

1415102

I

-13

0

0

Irel~

.........

-12

101

~1 5~

\ /\

/"

//

8

-~z,

/

7 .

®H

-50 J

i

i

-40

h

I

-30

i

-20-I0 i

J

t

L

i

I

i

[

.

.

.

.

lOq--~

1 i

.

i

I

i

L

i

I

i

L

J

~

]o 2o 30 40 5o 60 70 •.- H[~]

L

Fig. 5. Bubble domain spacing D and bubble diameter 2R in the garnet crystal versus field.

ces by optical signal reading in the diffraction pattern. Different states of a domain grating (different stored i n f o r m a t i o n ) have very different intensity patterns in the diffraction. The intensities of the diffraction orders, detected by pin diodes as shown in the triangle in fig. 2, reveal each stored information. The loss o f some domains in the grating, due to crystal defects, does not affect these intensity distributions markedly.

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.

.

.

.

.

.

.

. . . . . . . . . . .

.

-30 -20 -10

0

"

10 20

~

30 ,5,0 50

.

.

.

.

'

60

Fig. 6. Calculated relative intensities of the first to fifth diffraction order maxima and of the component I(0, 0)y for the garnet crystal.

References [1] B.E. Argyle and P. Chaudhari, IBM Techn. Discl. Bull. 18 (1975) 603. [21 B. Kuhlow and M. Lambeck, Physica 80B (1975) 374. [3] T.R. Johansen, D.I. Norman and E.J. Torok, J. Appl. Phys. 42 (1971) 1715. [4] H.W. Fuller, J. Appl. Phys. 42 (1971) 1816. [5] J.F. Dillon Jr., J. Appl. Phys. 29 (1958) 539. [6] G.F. Sauter, M.M. Hanson and D.J. Fleming, Appl. Phys. Lett. 30 (1977) 11. [7] B. Kuhlow, Optik 53 (1979) l l 5 , ibid. 194. [8] B. Kuhlow, Phys. Stat. Sol. (a) 54 (1979) 281. [9] M. Griindler, B. Kuhlow and M. Lambeck, Phys. Lett. 33A (1970) 285. [10] B. Kuhlow and M. Lambeck, Intern. J. Magnetism 3 (1972) 47. [11] B. Kuhlow and M. Lambeck, J. Magn. Magn. Mat. 4 (1977) 337.