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Diffuse scattering of light by ferromagnetic domains in EuS
Solid State Communications, Vol. 6, pp. 805- 807, 1968.
Pergamon Press. Printed in Great Britain
DIFFUSE SCATTERING OF LIGHT BY FERROMAGNETIC DOMAINS IN EuS F.Rys Seminar f. Theoretische Physik ETH, ZUrich and P. Wachter Laboratorium fur Festkörperphystk ETH, Zurich (Received 20 July 1968 by G. Busch)
The diffuse scattering of light by EuS-single crystals was measured in function of temperature and wavelength. The ferromagnetic domains can be described by a position-dependent dielectric tensor. For wavelengths larger than the size of the domains Rayleigh-type scattering is derived, which agrees well with the experiment.
STRONG scattering of light near the absorption edge has been observed for EuS below the Curie point. ~ ~ The dimensions of the magnetic domains show a strong size effect. In thin evaporated layers the domains are larger than the wavelength of light; however, in single crystals Individual domains can only be observed by an electron microscope, the domain size being smaller than the wavelength of light. 2 ~ By applying a saturating magnetic field a single domain crystal can be achieved,
observing this crystal with a polarizing microscope at low temperatures. Maximal magnetic scattering is obtained at 4. 2°K. The scattering intensity is normalized by comparison with the residual scattering of a single domain crystal at 4. 2°Kusing a wavelength rather separated from the absorption edge. Above the Curie temperature the magnetic scattering is found to be exactly zero, so that the onset of scattering can be used as a determination of the critical temperature (Fig. 1). The magnetic scattering as a function of wavelength has been measured by comparing the transmitted light intensity of a multi-domain crystal with a single domain crystal at 4. 2°K (Fig. 2).
Monochromatic light is focussed with a small aperture on the crystal. The transmitted light passes a lens with a much larger diameter than the light beam and is recorded by a multiplier. By covering the center or the rim part of this lens with corresponding diaphragms the ratio of transmitted to scattered light can be determined (assuming that the angular dependence of the scattered light remains constant and the size of the scatterer always remains smaller than the wavelength of light). A small residual scattering of light is observed at room temperature mostly being caused by scattering in the glass windows of the cryostat, but is found to be the same below the Curie point in a single domain crystal. Special care has been taken to select a EuS single crystal without strain, which was ascertained by
A single domain crystal of EuS is optically active in the ferromagnetic temperature region. Light with longer wavelengths than the absorption edge is subject to different refractive indices n4 and n. for right and left hand circular polarization, respectively, if the wave vector Is parallel to the magnetization The dielectric tensor for this case has the form: / •M O\ for ~ = M ~ ~.
c —
805
=
f ( ioM \\ 0
c 0
0
\ J
/
and cubic symmetry. (1)
806
DIFFUSE SCATTERING OF LIGHT
1,0
Vol. 6, No.11
—_..~
!Ii
\\
4J4•
—U
~
“I
70
,~
—______
—
-
________
\ 4
8
l~
1
H,
20
24
28
~‘~-~•otte
30
.K
FIG. 1
I =
aM (c~ c_)=—.~—-
~
0,7
-
0,15
(2)
A multi domain crystal is characterized by M (x), varying in direction from one domain to another and being constant within the same domain. Using (1) the dielectric tensor now will be a domain function: ~k
+
~
=
+
ia ~
1,5
1,0
2~ ~
Wavelength
This difference is responsible for the large Faraday effect in the Eu-Chalcogenides. Due to a small anisotropy energy a single domain is obtamed with external fields smaller than 100 Oe, which therefore, can be neglected in the calculation.
e~,(~)= c
-4
20
nM is calculated from the spin exchange and the spin orbit interaction in second order perturbation theory, using a simple band model.4 The difference of the refractive indices is related to = ± i t~, by: n.~-n..
~
—
Scattering of light due to magnetic dothains in EuS at 0. 9 ~i.
=
I
w1~~~,nQ 1YC9,,t,C
~
30
~
~
I(~.H,)
I 0
-
log X ~
FIG. 2 Scattering of light due to magnetic domains in EuS at 4. 2°K. order in ~c by: D.’
E~’
=
+
(4)
~
The last term plays the role of a source; the scattered wave in a distance R~from the scatterer is therefore given in the wave zone approximation by: elk R
~
E
=
0 ~R
4
k ,~
G
(5)
3] is decomposed into =d’i =I E X+ I’M where ~ (x)with ~~iqx respect dx to the direction of l~’, and where
M~(~)(3) E=
The light with a wavelength (X 9000 ~) larger than the size of the domain (d 10~cm) is scattered by the small-volume deviations of the dielectric constant similarly as in the case of Rayleigh scattering. We neglect multiple scattering and shall assume elastic scattering. In the scattered terms of the incoming (primed)field (unprimed) is given radiation in first field
E 0e
-
q
-
X
~,
and
~ -
For a crystal in thermal equilibrium the scattering is completely described 4 by the tensor: I,jq) = 16r2k 2R~ (6)
Vol. 6, No. 11
DIFFUSE SCATTERING OF LIGHT
(where i,k refer to components in the plan orthogonal to li’) which is given in terms of the domain spin correlation function:
807
100 cm_i (8) (~)4 ~ M2 v 3rr C defining an “extinction length” h ~ = 10_a cm in agreement with the experiment. h
=
.-~—
nv (~)= ‘ d3x Id3y c M 1(~)Mk(.i-~)> e~’~ (7)
(3) The 2 v;temperature according todependence a roup model of h E IsE given by M volume v goes like M the domain yielding h(T) M (T) in good agreement with Fig. 1. .
-~
Discussion (1) The total scattered intensity per unit energy flux of the incoming radiation ( = extinction coefficient h) depends on X~by equa-
(4) The measurement of the dtfferenttal scattering cross-section furnishes Information on the domain structure through the spin correlation function r
1~(i).
tion (6) in excellent agreement with Fig. 2. (2) For qd <<1 (d being the domain size) neglecting the correlation between different domains one gets with the above values:
As an example, a periodic domain structure will give rise to discrete peaks in the scattering similar to von Laue diffraction.
References 1.
SUITS J.C.,
J. appl. Phys. 38, 1498 (1967).
2.
WACHTER P., Phys. kondens. Materie 7, 1 (1968).
3.
KNEER G. und ZINN W., Ber. v.d. Jahrestagung d. Arbeitsgem. Magnetismus, Munster (1968).
4.
RYS F., Helv. Phys. Acta 41, 395 (1968).
5.
KITTEL C., Introduction to Solid State Physics, pp. 488. John Wiley, New York (1963).
6.
KANAMORI J.,
Rado and Suhi, Magnetism 1, pp. 127. Academic Press (1963). Diffuse Lichtstreuung an EuS-Einkristallen wurde in Abh~ngigkeit der Temperatur und der Wellenlänge gemessen. Die ferromagnetischen Dom~nenkönnen durch elnen ortsabh~ngigenDielektrizit~tstensor beschrieben werden. Fur Wellenlangen, die grosser als die Domanen sind, ergibt sich em Rayleigh-ahnliches Streuverhalten in guter Uebereinstimmung mit dem Experiment.
Pergamon Press. Printed in Great Britain
DIFFUSE SCATTERING OF LIGHT BY FERROMAGNETIC DOMAINS IN EuS F.Rys Seminar f. Theoretische Physik ETH, ZUrich and P. Wachter Laboratorium fur Festkörperphystk ETH, Zurich (Received 20 July 1968 by G. Busch)
The diffuse scattering of light by EuS-single crystals was measured in function of temperature and wavelength. The ferromagnetic domains can be described by a position-dependent dielectric tensor. For wavelengths larger than the size of the domains Rayleigh-type scattering is derived, which agrees well with the experiment.
STRONG scattering of light near the absorption edge has been observed for EuS below the Curie point. ~ ~ The dimensions of the magnetic domains show a strong size effect. In thin evaporated layers the domains are larger than the wavelength of light; however, in single crystals Individual domains can only be observed by an electron microscope, the domain size being smaller than the wavelength of light. 2 ~ By applying a saturating magnetic field a single domain crystal can be achieved,
observing this crystal with a polarizing microscope at low temperatures. Maximal magnetic scattering is obtained at 4. 2°K. The scattering intensity is normalized by comparison with the residual scattering of a single domain crystal at 4. 2°Kusing a wavelength rather separated from the absorption edge. Above the Curie temperature the magnetic scattering is found to be exactly zero, so that the onset of scattering can be used as a determination of the critical temperature (Fig. 1). The magnetic scattering as a function of wavelength has been measured by comparing the transmitted light intensity of a multi-domain crystal with a single domain crystal at 4. 2°K (Fig. 2).
Monochromatic light is focussed with a small aperture on the crystal. The transmitted light passes a lens with a much larger diameter than the light beam and is recorded by a multiplier. By covering the center or the rim part of this lens with corresponding diaphragms the ratio of transmitted to scattered light can be determined (assuming that the angular dependence of the scattered light remains constant and the size of the scatterer always remains smaller than the wavelength of light). A small residual scattering of light is observed at room temperature mostly being caused by scattering in the glass windows of the cryostat, but is found to be the same below the Curie point in a single domain crystal. Special care has been taken to select a EuS single crystal without strain, which was ascertained by
A single domain crystal of EuS is optically active in the ferromagnetic temperature region. Light with longer wavelengths than the absorption edge is subject to different refractive indices n4 and n. for right and left hand circular polarization, respectively, if the wave vector Is parallel to the magnetization The dielectric tensor for this case has the form: / •M O\ for ~ = M ~ ~.
c —
805
=
f ( ioM \\ 0
c 0
0
\ J
/
and cubic symmetry. (1)
806
DIFFUSE SCATTERING OF LIGHT
1,0
Vol. 6, No.11
—_..~
!Ii
\\
4J4•
—U
~
“I
70
,~
—______
—
-
________
\ 4
8
l~
1
H,
20
24
28
~‘~-~•otte
30
.K
FIG. 1
I =
aM (c~ c_)=—.~—-
~
0,7
-
0,15
(2)
A multi domain crystal is characterized by M (x), varying in direction from one domain to another and being constant within the same domain. Using (1) the dielectric tensor now will be a domain function: ~k
+
~
=
+
ia ~
1,5
1,0
2~ ~
Wavelength
This difference is responsible for the large Faraday effect in the Eu-Chalcogenides. Due to a small anisotropy energy a single domain is obtamed with external fields smaller than 100 Oe, which therefore, can be neglected in the calculation.
e~,(~)= c
-4
20
nM is calculated from the spin exchange and the spin orbit interaction in second order perturbation theory, using a simple band model.4 The difference of the refractive indices is related to = ± i t~, by: n.~-n..
~
—
Scattering of light due to magnetic dothains in EuS at 0. 9 ~i.
=
I
w1~~~,nQ 1YC9,,t,C
~
30
~
~
I(~.H,)
I 0
-
log X ~
FIG. 2 Scattering of light due to magnetic domains in EuS at 4. 2°K. order in ~c by: D.’
E~’
=
+
(4)
~
The last term plays the role of a source; the scattered wave in a distance R~from the scatterer is therefore given in the wave zone approximation by: elk R
~
E
=
0 ~R
4
k ,~
G
(5)
3] is decomposed into =d’i =I E X+ I’M where ~ (x)with ~~iqx respect dx to the direction of l~’, and where
M~(~)(3) E=
The light with a wavelength (X 9000 ~) larger than the size of the domain (d 10~cm) is scattered by the small-volume deviations of the dielectric constant similarly as in the case of Rayleigh scattering. We neglect multiple scattering and shall assume elastic scattering. In the scattered terms of the incoming (primed)field (unprimed) is given radiation in first field
E 0e
-
q
-
X
~,
and
~ -
For a crystal in thermal equilibrium the scattering is completely described 4 by the tensor: I,jq) =
Vol. 6, No. 11
DIFFUSE SCATTERING OF LIGHT
(where i,k refer to components in the plan orthogonal to li’) which is given in terms of the domain spin correlation function:
807
100 cm_i (8) (~)4 ~ M2 v 3rr C defining an “extinction length” h ~ = 10_a cm in agreement with the experiment. h
=
.-~—
nv (~)= ‘ d3x Id3y c M 1(~)Mk(.i-~)> e~’~ (7)
(3) The 2 v;temperature according todependence a roup model of h E IsE given by M volume v goes like M the domain yielding h(T) M (T) in good agreement with Fig. 1. .
-~
Discussion (1) The total scattered intensity per unit energy flux of the incoming radiation ( = extinction coefficient h) depends on X~by equa-
(4) The measurement of the dtfferenttal scattering cross-section furnishes Information on the domain structure through the spin correlation function r
1~(i).
tion (6) in excellent agreement with Fig. 2. (2) For qd <<1 (d being the domain size) neglecting the correlation between different domains one gets with the above values:
As an example, a periodic domain structure will give rise to discrete peaks in the scattering similar to von Laue diffraction.
References 1.
SUITS J.C.,
J. appl. Phys. 38, 1498 (1967).
2.
WACHTER P., Phys. kondens. Materie 7, 1 (1968).
3.
KNEER G. und ZINN W., Ber. v.d. Jahrestagung d. Arbeitsgem. Magnetismus, Munster (1968).
4.
RYS F., Helv. Phys. Acta 41, 395 (1968).
5.
KITTEL C., Introduction to Solid State Physics, pp. 488. John Wiley, New York (1963).
6.
KANAMORI J.,
Rado and Suhi, Magnetism 1, pp. 127. Academic Press (1963). Diffuse Lichtstreuung an EuS-Einkristallen wurde in Abh~ngigkeit der Temperatur und der Wellenlänge gemessen. Die ferromagnetischen Dom~nenkönnen durch elnen ortsabh~ngigenDielektrizit~tstensor beschrieben werden. Fur Wellenlangen, die grosser als die Domanen sind, ergibt sich em Rayleigh-ahnliches Streuverhalten in guter Uebereinstimmung mit dem Experiment.