Qualitative mechanism in line with experimental data on visualization of the domain structure and fine structure of the domain wall in weak ferromagnets has been proposed. The mechanism is based on the phenomenological consideration of Faraday rotation, optical absorption, and atom polarization in response to the radiation exciting Raman scattering. Qualitative agreement of estimates on the scattered radiation intensity in oppositely- magnetized domains with experimental results is good, which made it possible to attack problems of visualization of magnetic entities with nanoscale resolution.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3197

Abakumov, P.V.

Dobromyslov, M.B.

Kuzmenko, A.P.

Shumakova, Nataliia Ivanivna

Шумакова, Наталия Ивановна

Шумакова, Наталія Іванівна

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 5 No 3, 03025(3pp) (2013) Том 5 № 3, 03025(3cc) (2013) 
 
 
2077-6772/2013/5(3)03025(3) 03025-1  2013 Sumy State University 
Short Communication 
 
Justification of Visualization Technique of Domain Structure with Raman Scattering 
 
A.P. Kuzmenko1,*, P.V. Abakumov1, M.B. Dobromyslov2, N.I. Shumakova3 
 
1 South-West State University, 94, 50 let Oktyabrya st., 305040 Kursk, Russia 
2 Pacific National University, 136, Tihookeanskaya st., 680035 Khabarovsk, Russia 
3 Sumy State University, 2, Rymsky-Korsakov st., 40007 Sumy, Ukraine 
 
(Received 22 May 2013; revised manuscript received 01 July 2013; published online 12 July 2013) 
 
Qualitative mechanism in line with experimental data on visualization of the domain structure and fi-
ne structure of the domain wall in weak ferromagnets has been proposed. The mechanism is based on the 
phenomenological consideration of Faraday rotation, optical absorption, and atom polarization in response 
to the radiation exciting Raman scattering. Qualitative agreement of estimates on the scattered radiation 
intensity in oppositely- magnetized domains with experimental results is good, which made it possible to 
attack problems of visualization of magnetic entities with nanoscale resolution. 
 
Keywords: Polarizability, Optical absorption, Faraday rotation, Raman spectroscopy, Domain structure. 
 
 PACS numbers: 42.65.Dr, 75.60.Ch 
 
 
 
                                                          
* apk3527@mail.ru 
The intensity of the inelastically scattered light is a 
function of both polarizability and the number of mole-
cules (elementary cells) within the scattering area. One 
of the critical drawbacks of Raman scattering is its low 
effectivity, which amounts to only IMRS / I0 ~ 10 – 6 of 
the exciting intensity (I0) [1], which gives reason to 
believe the effect of Raman scattering is low. The small 
probability of Raman scattering per one molecule 
makes its observation a rather difficult task, which 
requires advanced hardware. Therefore, the factors, on 
which the intensity of the Raman signal depends, can 
be divided into two classes, namely, hardware and 
natural. The hardware part includes the power and the 
frequency of the exciting radiation, geometry of the 
experiment, numerical aperture of the lens, and the 
detector sensitivity. To the natural factors belong the 
parameters of the medium studied, namely, polarizabil-
ity of molecules and atoms ( P E ), the absorption 
coefficient on wavelengths of exciting and scattered 
radiation, optical activity, and magnitudes of electro- 
and magnetooptical parameters. 
Earlier in the experiment on visualization of the do-
main structure in a plane sample (100 m) cut out per-
pendicular to the optic axis of yttrium orthoferrite 
(YFeO3) the difference in the intensity of Raman scatter-
ing (34 %) in domains with oppositely oriented magnetic 
moments was observed (Fig. 1). The present paper pro-
poses qualitative explanation of the observation of do-
main structure and domain wall with the help of hyper-
spectral distribution of intensity variations on one line of 
the Raman spectrum (221 cm – 1) proposed in [2]. 
In analyzing we take into consideration that the ex-
citing (L) and scattered (R) electromagnetic waves 
are distinct in frequency R  L  k, where k is the 
natural frequency of one of possible oscillations in the 
medium studied. Difference in frequency between excit-
ing and scattered waves allows one to consider them 
individually. Each follows both absorption laws and 
Faraday rotation. 
Consider the scattered radiation, which was record-
ed by a spectroscopic camera CCD 1024  256 pixel 
(pixel size 26 m). 
 
 
 
Fig.1 – Hyperspectral distribution of Raman scattering in 
domains with oppositely-oriented magnetization and within 
domain wall (top), and its profile (bottom) 
 
Due to Faraday rotation characteristic of YFeO3 (on 
  532 nm, F  3000 о/cm) the electric strength vector 
of the scattered light rotates through a mirror-
symmetric angle in domains with oppositely oriented 
magnetizations. To the Glan prism, which was an ana-
lyzer, light landed from various domains with distinct 
polarizations. According to Malus’s law I  I0cos2, 
where I0 and I are the incoming and outgoing intensi-
ties, respectively, the outgoing intensity from various-
ly-magnetized domains is not changed. In other words, 
the Faraday rotation of scattered light does not con-
tribute to the intensity variations of Raman scattering 
in oppositely- magnetized domains. 
Let us analyze variations in the orientation of the 
electric strength of the exciting radiation. Geometry of 
the experiment was not changed for a sample with 
variously-magnetized domains. The observed varia-
 A.P. KUZMENKO, P.V. ABAKUMOV, M.B. DOBROMYSLOV, ET AL. J. NANO- ELECTRON. PHYS. 5, 03025 (2013) 
 
 
03025-2 
tions in the Raman intensity in neighboring domains 
can be described with a ratio W2 / W1, where W2 and W1 
are the Raman intensity in the first and second do-
mains, respectively, which in classical approximation 
are determined by the magnitudes of projection of the 
E-vector of exciting radiation onto the polarization 
vector P of atoms. The vector diagram (Fig. 2) illus-
trates those changes of vectors 0E , 1E and 2E . The 
rotation of 0E  is due to the Faraday rotation 
 
    Fd, (1) 
 
where φ is the rotation angle of vector, θF is specific 
Faraday rotation, d is the radiation penetration depth 
into a sample. 
 
 
 
Fig.2 – Vector diagram of mutual orientation of E  and P  
vectors: left and right for domains with opposite magnetiza-
tion 
 
To the first approximation anti-Stokes components 
W2 and W1 are determined by expression [3]: 
 
 24 2 0( )L kW A E    , (2) 
 
where A is a constant; L и k are the frequencies of 
the exciting radiation and atom natural vibrations, 
respectively; ε is polarizability; 0E  is the electric field 
vector. 
Consider the effect of optical absorption on the ex-
citing intensity. To pinpoint the limiting penetration 
depth of exciting radiation into a sample, when the 
Raman signal is still recorded, the following experi-
ment was conducted. Exciting laser (532 nm, 50 mW) 
radiation was focused on the sample surface. With a 
neutral slackening filter the laser intensity was de-
creased with a step of 0.5 dB. The dependence obtained  
 
 
 
Fig.3 – Effect of optical absorption on the amount of Raman 
scattering 
 
(Fig. 3) made it possible to establish the fact that the 
minimum intensity of the exciting radiation I, at which 
the Raman recording with the use of the hard-and-
software complex was possible, reached I0 / I  50. 
Therefore, the penetration depth of exciting radiation 
can be assessed according to the Lambert-Bouguer law 
 
 d0  – ln(I/I0) /  (3) 
 
Substitution of the optical absorption coefficient , 
whose value for YFeO3 at   532 nm is 200 cm – 1 [4] , 
into (3) gives d0  on the order of 20 m. With the use of 
this d0 we obtain, from expression (1), the rotation angle 
 (Fig. 2) of the vector E  dictated by the Faraday rota-
tion. In this case, for neighboring domains    60. 
The angle 0 0P E
  (Fig. 2), at which the result-
ing projections of 1E  or 2E  onto P  vary under the 
influence of Faraday rotation in such a way that when 
the projection of 1E  is maximum, the projection of 2E  
satisfies the condition 1 2lim limE E . To calculate the 
maximum value of the resulting projection of 1E  onto 
P  one may use the following equation 
 
 0
0
0
0
cos 0
d
E d
d
 

 


   (4) 
 
where τ is the variable angle, considering the Faraday 
rotation. Extreme of the integration (4) provides 
0   / 2  30. 
The exciting radiation power (50 mW) suffices to 
depolarize atoms. In other words, at the sample sur-
face, when the incident power is maximum, the pola-
rizability vector turns to be parallel to the 0E -vector –
P  0E . As the incident radiation penetrates the mat-
ter its power drops and, as a consequence, its influence 
on the polarizability vector decreases and this vector 
tends to take its initial position. Under these condi-
tions, in the first domain vectors P and E  rotate with 
different velocities in one direction, and in the second 
one they do in mutually opposite directions, which 
brings about the decrease in Raman intensity. 
Expression (3) and dependence in Fig. 3 allow one 
to evaluate the penetration depth d1 of the incident 
radiation (I0) at which its depolarization effect termi-
nates. In doing so, vector, due to Faraday rotation, 
rotates through 1   Fd1. From Fig. 2 the angle 
( ^ )P E   is found in the following way: 
 
      F
dd e
 
(5) 
 
where  is the angle of polarization variation. Here the 
first term corresponds to the rotation of the incident 
strength vector for variously- magnetized domains. The 
second term is relevant to the rotation of the atom 
polarizability vector; polarizability decreases with an 
increase in penetration depth. 
To evaluate the observed variations in Raman in-
tensities in neighboring domains characterized by  
expression W2/W1, we make use of (2), which takes the 
form for neighboring domains 
 JUSTIFICATION OF VISUALIZATION TECHNIQUE OF DOMAIN… J. NANO- ELECTRON. PHYS. 5, 03025 (2013) 
 
 
03025-3 
0 1 0
0 0 1
0 0 1
0 1 0
0
2
1 0
1 (cos ) (cos )
1 (cos ) (cos )
E d dW
W E d d
   
  
  
   
   
   
 


 
  
 
  
 
 
 
 (6) 
 
Here 1 is determined from (5) after substitution of d1. 
For calculated data, according to (6), we get 
W2 / W1  0.356, which agrees well with obtained differ-
rence in scattered radiation intensities of 0.34 [2]. 
Some difference can be attributed to the fact that the 
real-world crystal structure is not perfect and there is, 
in this geometry, birefringence, which stems from the 
error in the sample orientation perpendicular to the 
optic axis (52 from [001]). 
 
Work performed under the Agreement on scientific 
and technological cooperation between Universities. 
 
 
REFERENCES 
 
1. A.G. Milehin, N.A. Eryukov, L.L. Sveshnikova, et al. J 
Exp. Theor. Phys. 140, 983 (2011).  
2. A.P. Kuzmenko, P.V. Abakumov, M.B. Dobromyslov, J. 
Magn. Magn. Mater. 324, 1262 (2012). 
3. B.A. Kolesov, Raman-spectroscopy in inorganic chemistry 
and mineralogy (Russian Academy of Sciences, Siberian 
branch, Institute of inorganic chemistry: Novosibirsk: 
2009) (In Russian). 
4. G.A. Smolensky, V.V. Lemanov, Ferrites and their techno-
logical application (Nauka: Leningrad Branch: 1975) (In 
Russian). 
 


Justification of Visualization Technique of Domain Structure with Raman Scattering

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 5 No 3, 03025(3pp) (2013) Том 5 № 3, 03025(3cc) (2013)   2077-6772/2013/5(3)03025(3) 03025-1  2013 Sumy State University Short Communication  Justification of Visualization Technique of Domain Structure with Raman Scattering  A.P. Kuzmenko1,*, P.V. Abakumov1, M.B. Dobromyslov2, N.I. Shumakova3  1 South-West State University, 94, 50 let Oktyabrya st., 305040 Kursk, Russia 2 Pacific National University, 136, Tihookeanskaya st., 680035 Khabarovsk, Russia 3 Sumy State University, 2, Rymsky-Korsakov st., 40007 Sumy, Ukraine  (Received 22 May 2013; revised manuscript received 01 July 2013; published online 12 July 2013)  Qualitative mechanism in line with experimental data on visualization of the domain structure and fi-ne structure of the domain wall in weak ferromagnets has been proposed. The mechanism is based on the phenomenological consideration of Faraday rotation, optical absorption, and atom polarization in response to the radiation exciting Raman scattering. Qualitative agreement of estimates on the scattered radiation intensity in oppositely- magnetized domains with experimental results is good, which made it possible to attack problems of visualization of magnetic entities with nanoscale resolution.  Keywords: Polarizability, Optical absorption, Faraday rotation, Raman spectroscopy, Domain structure.   PACS numbers: 42.65.Dr, 75.60.Ch                                                              * apk3527@mail.ru The intensity of the inelastically scattered light is a function of both polarizability and the number of mole-cules (elementary cells) within the scattering area. One of the critical drawbacks of Raman scattering is its low effectivity, which amounts to only IMRS / I0 ~ 10 – 6 of the exciting intensity (I0) [1], which gives reason to believe the effect of Raman scattering is low. The small probability of Raman scattering per one molecule makes its observation a rather difficult task, which requires advanced hardware. Therefore, the factors, on which the intensity of the Raman signal depends, can be divided into two classes, namely, hardware and natural. The hardware part includes the power and the frequency of the exciting radiation, geometry of the experiment, numerical aperture of the lens, and the detector sensitivity. To the natural factors belong the parameters of the medium studied, namely, polarizabil-ity of molecules and atoms ( P E ), the absorption coefficient on wavelengths of exciting and scattered radiation, optical activity, and magnitudes of electro- and magnetooptical parameters. Earlier in the experiment on visualization of the do-main structure in a plane sample (100 m) cut out per-pendicular to the optic axis of yttrium orthoferrite (YFeO3) the difference in the intensity of Raman scatter-ing (34 %) in domains with oppositely oriented magnetic moments was observed (Fig. 1). The present paper pro-poses qualitative explanation of the observation of do-main structure and domain wall with the help of hyper-spectral distribution of intensity variations on one line of the Raman spectrum (221 cm – 1) proposed in [2]. In analyzing we take into consideration that the ex-citing (L) and scattered (R) electromagnetic waves are distinct in frequency R  L  k, where k is the natural frequency of one of possible oscillations in the medium studied. Difference in frequency between excit-ing and scattered waves allows one to consider them individually. Each follows both absorption laws and Faraday rotation. Consider the scattered radiation, which was record-ed by a spectroscopic camera CCD 1024  256 pixel (pixel size 26 m).    Fig.1 – Hyperspectral distribution of Raman scattering in domains with oppositely-oriented magnetization and within domain wall (top), and its profile (bottom)  Due to Faraday rotation characteristic of YFeO3 (on   532 nm, F  3000 о/cm) the electric strength vector of the scattered light rotates through a mirror-symmetric angle in domains with oppositely oriented magnetizations. To the Glan prism, which was an ana-lyzer, light landed from various domains with distinct polarizations. According to Malus’s law I  I0cos2, where I0 and I are the incoming and outgoing intensi-ties, respectively, the outgoing intensity from various-ly-magnetized domains is not changed. In other words, the Faraday rotation of scattered light does not con-tribute to the intensity variations of Raman scattering in oppositely- magnetized domains. Let us analyze variations in the orientation of the electric strength of the exciting radiation. Geometry of the experiment was not changed for a sample with variously-magnetized domains. The observed varia- A.P. KUZMENKO, P.V. ABAKUMOV, M.B. DOBROMYSLOV, ET AL. J. NANO- ELECTRON. PHYS. 5, 03025 (2013)   03025-2 tions in the Raman intensity in neighboring domains can be described with a ratio W2 / W1, where W2 and W1 are the Raman intensity in the first and second do-mains, respectively, which in classical approximation are determined by the magnitudes of projection of the E-vector of exciting radiation onto the polarization vector P of atoms. The vector diagram (Fig. 2) illus-trates those changes of vectors 0E , 1E and 2E . The rotation of 0E  is due to the Faraday rotation      Fd, (1)  where φ is the rotation angle of vector, θF is specific Faraday rotation, d is the radiation penetration depth into a sample.    Fig.2 – Vector diagram of mutual orientation of E  and P  vectors: left and right for domains with opposite magnetiza-tion  To the first approximation anti-Stokes components W2 and W1 are determined by expression [3]:   24 2 0( )L kW A E    , (2)  where A is a constant; L и k are the frequencies of the exciting radiation and atom natural vibrations, respectively; ε is polarizability; 0E  is the electric field vector. Consider the effect of optical absorption on the ex-citing intensity. To pinpoint the limiting penetration depth of exciting radiation into a sample, when the Raman signal is still recorded, the following experi-ment was conducted. Exciting laser (532 nm, 50 mW) radiation was focused on the sample surface. With a neutral slackening filter the laser intensity was de-creased with a step of 0.5 dB. The dependence obtained     Fig.3 – Effect of optical absorption on the amount of Raman scattering  (Fig. 3) made it possible to establish the fact that the minimum intensity of the exciting radiation I, at which the Raman recording with the use of the hard-and-software complex was possible, reached I0 / I  50. Therefore, the penetration depth of exciting radiation can be assessed according to the Lambert-Bouguer law   d0  – ln(I/I0) /  (3)  Substitution of the optical absorption coefficient , whose value for YFeO3 at   532 nm is 200 cm – 1 [4] , into (3) gives d0  on the order of 20 m. With the use of this d0 we obtain, from expression (1), the rotation angle  (Fig. 2) of the vector E  dictated by the Faraday rota-tion. In this case, for neighboring domains    60. The angle 0 0P E  (Fig. 2), at which the result-ing projections of 1E  or 2E  onto P  vary under the influence of Faraday rotation in such a way that when the projection of 1E  is maximum, the projection of 2E  satisfies the condition 1 2lim limE E . To calculate the maximum value of the resulting projection of 1E  onto P  one may use the following equation   0000cos 0dE dd     (4)  where τ is the variable angle, considering the Faraday rotation. Extreme of the integration (4) provides 0   / 2  30. The exciting radiation power (50 mW) suffices to depolarize atoms. In other words, at the sample sur-face, when the incident power is maximum, the pola-rizability vector turns to be parallel to the 0E -vector –P  0E . As the incident radiation penetrates the mat-ter its power drops and, as a consequence, its influence on the polarizability vector decreases and this vector tends to take its initial position. Under these condi-tions, in the first domain vectors P and E  rotate with different velocities in one direction, and in the second one they do in mutually opposite directions, which brings about the decrease in Raman intensity. Expression (3) and dependence in Fig. 3 allow one to evaluate the penetration depth d1 of the incident radiation (I0) at which its depolarization effect termi-nates. In doing so, vector, due to Faraday rotation, rotates through 1   Fd1. From Fig. 2 the angle ( ^ )P E   is found in the following way:        Fdd e (5)  where  is the angle of polarization variation. Here the first term corresponds to the rotation of the incident strength vector for variously- magnetized domains. The second term is relevant to the rotation of the atom polarizability vector; polarizability decreases with an increase in penetration depth. To evaluate the observed variations in Raman in-tensities in neighboring domains characterized by  expression W2/W1, we make use of (2), which takes the form for neighboring domains  JUSTIFICATION OF VISUALIZATION TECHNIQUE OF DOMAIN… J. NANO- ELECTRON. PHYS. 5, 03025 (2013)   03025-3 0 1 00 0 10 0 10 1 0021 01 (cos ) (cos )1 (cos ) (cos )E d dWW E d d                           (6)  Here 1 is determined from (5) after substitution of d1. For calculated data, according to (6), we get W2 / W1  0.356, which agrees well with obtained differ-rence in scattered radiation intensities of 0.34 [2]. Some difference can be attributed to the fact that the real-world crystal structure is not perfect and there is, in this geometry, birefringence, which stems from the error in the sample orientation perpendicular to the optic axis (52 from [001]).  Work performed under the Agreement on scientific and technological cooperation between Universities.   REFERENCES  1. A.G. Milehin, N.A. Eryukov, L.L. Sveshnikova, et al. J Exp. Theor. Phys. 140, 983 (2011).  2. A.P. Kuzmenko, P.V. Abakumov, M.B. Dobromyslov, J. Magn. Magn. Mater. 324, 1262 (2012). 3. B.A. Kolesov, Raman-spectroscopy in inorganic chemistry and mineralogy (Russian Academy of Sciences, Siberian branch, Institute of inorganic chemistry: Novosibirsk: 2009) (In Russian). 4. G.A. Smolensky, V.V. Lemanov, Ferrites and their techno-logical application (Nauka: Leningrad Branch: 1975) (In Russian).  

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Justification of Visualization Technique of Domain Structure with Raman Scattering

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