By using atomic force microscopy (resolution of 40 nm) the effect of surface roughness and internal inhomogeneities on the fine structure of domain walls of different types in thin transparent orthoferrite samples cut perpendicular to the optic axis for YFeO3 and axis [001] for DyFeO3 has been studied.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3366

Abakumov, P.V.

Dobromyslov, M.B.

Kuzmenko, A.P.

Roslyakova, L.I.

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 5 No 4, 04039(2pp) (2013) Том 5 № 4, 04039(2cc) (2013)   The article was reported at the International Conference «Physics and Technology of Nanomaterials and Structures», Kursk, 21-22 November, 2013 2077-6772/2013/5(4)04039(2) 04039-1  2013 Sumy State University Short Communication  Interrelation of Shape and Structure of Domain Walls with Magnetic Inhomogeneities  A.P. Kuzmenko1, P.V. Abakumov1, L.I. Roslyakova1, M.B. Dobromyslov2  1 Southwest State University, 94, 50 Let Oktyabrya Str., 305040 Kursk, Russia 2 Pacific National University, 136, Tihookeanskaya Str., 680035 Khabarovsk, Russia  (Received 24 October 2013; published online 10 December 2013)  By using atomic force microscopy (resolution of 40 nm) the effect of surface roughness and internal  inhomogeneities on the fine structure of domain walls of different types in thin transparent orthoferrite samples cut perpendicular to the optic axis for YFeO3 and axis [001] for DyFeO3 has been studied.  Keywords: Domain structure, Scanning probe microscopy types of domain walls.   PACS numbers: 42.65.Dr, 75.60.Ch   Devices for storage and processing information that utilize materials with electric and magnetic ordering increasingly find application [1]. A special place in this series is taken by orthoferrites that have four magnetic sublattices for both d-subsystem (magnetic ions Fe3+), and f-subsystem (Y3+ and rare-earth ions R3+).  f-subsystem being many-electron one dictates the orig-ination of the electric ordering. In addition to this, in certain phases a spontaneous electric polarization ap-pears at phase transitions, induced by magnetic field, in f- and d-subsystems. Those structural features are responsible for magneto-electric interactions in RFeO3. The basic mechanism of magnetization reversal in the-se materials is the motion of domain walls (DWs), which is of a nonlinear nature and occurs at supersonic speeds and is accompanied by the appearance of gyro-scopic vortices [2] that propagate along DW.    Fig. 1 – Confocal magneto-optical image of domain structure YFeO3  Domain structure (DS) and the fine structure of DW in RFeO3, -Fe2O3 and FeВO3 were studied earlier  [3, 4] by using Raman microspectral scattering. In the present paper magnetic force microscopy (MFM) has been used to investigate the way roughness of surfaces and internal inhomogeneities (grows nonmagnetic in-homogeneities) influence the fine structure of DW of various types in lamellar transparent orthoferrite sam-ples cut perpendicular to the optic axis for YFeO3 and axis [001] for DyFeO3 with a space resolution of 40 nm. At the initial state DS and DW have been visualized with the modified for magneto-optic studies confocal microscope, which was a component of the microspec-trometer (OmegaScope) integrated with the atomic force microscope (SmartSPM). In a uniformly magnet-ized lamellar sample RFeO3 multi-domain structure was created (Fig. 1) with a rectangular and sinusoidal shape that had excessive free energy. It had DW of both Neel and Bloch type. Topographic image of the surface is indicative of submicron-scale defects as tracks of mechanical polish-ing (Fig. 2a). The distribution of the normal component of the magnetic field gradient in the neighborhood of DW according to MFM is given in Fig. 2b. MFM made it possible to reveal on DS and DW magnetic kink-like formations that are immediately associated with these surface defects. To study these two- pass scanning technique was used combining semicontact atomic-force and magnetic-force studies.           a    b  Fig. 2 – Image of a surface site of YFeO3 sample in the neigh-borhood of DW: a – image of surface topography; b – MFM image of a kink-like bend of DW  By one-pass scanning along sinusoidal DW data about its structure within the bend head-to-head have been obtained (Fig. 3). It was established that the DW knee was made up of piecewise linear sites inked by special points (breather-like formations). This can be explained by the fact that to minimum of the free ener-gy in orthoferrites there corresponds stripe DS. It must be noted that the DW width along the full length to the inflection point remained constant and was of the order of 2 m. After the passage of the point of extremum its width increased to 3 m in a jump fashion. Interrelation between the DW orientation and crys-tallographic axes in DyFeO3 sample whose plane was perpendicular to axis [001] was studied by MFM meth-ods. This kind of sample orientation due to birefringence significantly reduces magneto-optic quality factor, which  A.P. KUZMENKO, P.V. ABAKUMOV, ET. AL J. NANO- ELECTRON. PHYS. 5, 04039 (2013)   04039-2 does not allow one to determine the location and shape of DW in a magneto-optic fashion. For studying this only one-pass MFM technique was used. Curvature radius     Fig. 3 – MFM image of DW within the bend region (head-to-head)  (40 nm) of the cantilever probe made it possible to im-prove the accuracy of MFM measurements by an order of magnitude compared to optical resolution. DWs of various types were studied, which were of different shapes and width. Fig. 4a, b shows MFM images of Bloch DW and Neel DW, the formation of which is typi-cal for such orientation of the DyFeO3 sample. On the right-hand side shown is a “magnetic profile” of varia-tion in magnetic momentum along the line perpendicu-lar to the DW plane. From Fig. 2 it follows that the wall thickness was 3 and 0.7 m for Bloch DW and Neel DW, respectively. In orthoferrites one-axis anisot-ropy plays an important role, which makes the origina-tion of two types of DWs equally probable with orienta-tion perpendicularly either to axis [100] (Neel) or axis [010] (Bloch), whose surface energy is determined: N,B  (AK1,2)1/2. Here N and B are the energy of Neel DW (at K1  K2) and Bloch DW (at K2  K1); A is the exchange interaction constant; K1, K2 are the one-axis anisotropy constants. It follows from this that for such orientation of the plate of the DyFeO3 sample DW of the Bloch type is energetically more favorable: B  N. DW corresponds to the magnetized wave of the soli-ton-like type as it follows from the solutions of the non-linear sine-Gordon equation that describes the motion of vector   ⃗ for both DW types considering the boundary conditions. In DW of ac type (Bloch DW) the rotation of vectors   ⃗ and  ⃗⃗ ⃗⃗⃗ takes place in the plane ac, corre-sponding to variation of vector  ⃗⃗ ⃗⃗⃗:        [   ] ,     ,         [   ] . For DW of ab type (Neel DW) typical is the rotation of vector   ⃗ in the plane ab. In this case at angles    ,       the rotation of vector   ⃗ leads to the change in direction and magnitude of vector  ⃗⃗⃗  up to a zero value at the DW center. The equations for changes in  ⃗⃗⃗  along the Y-axis perpendicular to the DW surface:     ,     ,        [   ] . The varia-tions of the weak ferromagnetic moment obtained from these equations are in correlation with “magnetic pro-files” derived from MFM for each DW type, corroborat-ing the good efficiency of the technique for the analysis of the fine structure of DW and DS.   REFERENCES  1. A.P. Pyatakov, A.K. Zvezdin, Usp. Fiz. Nauk 182, 6 (2012).  2. M.V. Chetkin, Yu.N. Kurbatova, T.B. Shapaeva, J. Magn. Magn. Mater. 321, 7 (2009). 3. A.P. Kuz’menko, P.V. Abakumov, M.B. Dobromyslov,  J. Magn. Magn. Mater. 324, 1262 (2012). 4. A.P. Kuzmenko, P.V. Abakumov, M.B. Dobromyslov, N.I. Shumakova, J. Nano- Electron. Phys. 5 No3, 03025 (2013).  

Interrelation of Shape and Structure of Domain Walls with Magnetic Inhomogeneities

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 5 No 4, 04039(2pp) (2013) Том 5 № 4, 04039(2cc) (2013) 
 
 
The article was reported at the International Conference «Physics and Technology of Nanomaterials and Structures», Kursk, 21-22 November, 2013 
2077-6772/2013/5(4)04039(2) 04039-1  2013 Sumy State University 
Short Communication 
 
Interrelation of Shape and Structure of Domain Walls with Magnetic Inhomogeneities 
 
A.P. Kuzmenko1, P.V. Abakumov1, L.I. Roslyakova1, M.B. Dobromyslov2 
 
1 Southwest State University, 94, 50 Let Oktyabrya Str., 305040 Kursk, Russia 
2 Pacific National University, 136, Tihookeanskaya Str., 680035 Khabarovsk, Russia 
 
(Received 24 October 2013; published online 10 December 2013) 
 
By using atomic force microscopy (resolution of 40 nm) the effect of surface roughness and internal  
inhomogeneities on the fine structure of domain walls of different types in thin transparent orthoferrite 
samples cut perpendicular to the optic axis for YFeO3 and axis [001] for DyFeO3 has been studied. 
 
Keywords: Domain structure, Scanning probe microscopy types of domain walls. 
 
 PACS numbers: 42.65.Dr, 75.60.Ch 
 
 
Devices for storage and processing information that 
utilize materials with electric and magnetic ordering 
increasingly find application [1]. A special place in this 
series is taken by orthoferrites that have four magnetic 
sublattices for both d-subsystem (magnetic ions Fe3+), 
and f-subsystem (Y3+ and rare-earth ions R3+).  
f-subsystem being many-electron one dictates the orig-
ination of the electric ordering. In addition to this, in 
certain phases a spontaneous electric polarization ap-
pears at phase transitions, induced by magnetic field, 
in f- and d-subsystems. Those structural features are 
responsible for magneto-electric interactions in RFeO3. 
The basic mechanism of magnetization reversal in the-
se materials is the motion of domain walls (DWs), 
which is of a nonlinear nature and occurs at supersonic 
speeds and is accompanied by the appearance of gyro-
scopic vortices [2] that propagate along DW. 
 
 
 
Fig. 1 – Confocal magneto-optical image of domain structure 
YFeO3 
 
Domain structure (DS) and the fine structure of DW 
in RFeO3, -Fe2O3 and FeВO3 were studied earlier  
[3, 4] by using Raman microspectral scattering. In the 
present paper magnetic force microscopy (MFM) has 
been used to investigate the way roughness of surfaces 
and internal inhomogeneities (grows nonmagnetic in-
homogeneities) influence the fine structure of DW of 
various types in lamellar transparent orthoferrite sam-
ples cut perpendicular to the optic axis for YFeO3 and 
axis [001] for DyFeO3 with a space resolution of 40 nm. 
At the initial state DS and DW have been visualized 
with the modified for magneto-optic studies confocal 
microscope, which was a component of the microspec-
trometer (OmegaScope) integrated with the atomic 
force microscope (SmartSPM). In a uniformly magnet-
ized lamellar sample RFeO3 multi-domain structure 
was created (Fig. 1) with a rectangular and sinusoidal 
shape that had excessive free energy. It had DW of 
both Neel and Bloch type. 
Topographic image of the surface is indicative of 
submicron-scale defects as tracks of mechanical polish-
ing (Fig. 2a). The distribution of the normal component 
of the magnetic field gradient in the neighborhood of 
DW according to MFM is given in Fig. 2b. MFM made 
it possible to reveal on DS and DW magnetic kink-like 
formations that are immediately associated with these 
surface defects. To study these two- pass scanning 
technique was used combining semicontact atomic-
force and magnetic-force studies. 
 
        
 
a    b 
 
Fig. 2 – Image of a surface site of YFeO3 sample in the neigh-
borhood of DW: a – image of surface topography; b – MFM 
image of a kink-like bend of DW 
 
By one-pass scanning along sinusoidal DW data 
about its structure within the bend head-to-head have 
been obtained (Fig. 3). It was established that the DW 
knee was made up of piecewise linear sites inked by 
special points (breather-like formations). This can be 
explained by the fact that to minimum of the free ener-
gy in orthoferrites there corresponds stripe DS. It must 
be noted that the DW width along the full length to the 
inflection point remained constant and was of the order 
of 2 m. After the passage of the point of extremum its 
width increased to 3 m in a jump fashion. 
Interrelation between the DW orientation and crys-
tallographic axes in DyFeO3 sample whose plane was 
perpendicular to axis [001] was studied by MFM meth-
ods. This kind of sample orientation due to birefringence 
significantly reduces magneto-optic quality factor, which 
 A.P. KUZMENKO, P.V. ABAKUMOV, ET. AL J. NANO- ELECTRON. PHYS. 5, 04039 (2013) 
 
 
04039-2 
does not allow one to determine the location and shape 
of DW in a magneto-optic fashion. For studying this only 
one-pass MFM technique was used. Curvature radius  
 
 
 
Fig. 3 – MFM image of DW within the bend region (head-to-head) 
 
(40 nm) of the cantilever probe made it possible to im-
prove the accuracy of MFM measurements by an order 
of magnitude compared to optical resolution. DWs of 
various types were studied, which were of different 
shapes and width. Fig. 4a, b shows MFM images of 
Bloch DW and Neel DW, the formation of which is typi-
cal for such orientation of the DyFeO3 sample. On the 
right-hand side shown is a “magnetic profile” of varia-
tion in magnetic momentum along the line perpendicu-
lar to the DW plane. From Fig. 2 it follows that the 
wall thickness was 3 and 0.7 m for Bloch DW and 
Neel DW, respectively. In orthoferrites one-axis anisot-
ropy plays an important role, which makes the origina-
tion of two types of DWs equally probable with orienta-
tion perpendicularly either to axis [100] (Neel) or axis 
[010] (Bloch), whose surface energy is determined: 
N,B  (AK1,2)1/2. Here N and B are the energy of Neel 
DW (at K1  K2) and Bloch DW (at K2  K1); A is the 
exchange interaction constant; K1, K2 are the one-axis 
anisotropy constants. It follows from this that for such 
orientation of the plate of the DyFeO3 sample DW of 
the Bloch type is energetically more favorable: B  N. 
DW corresponds to the magnetized wave of the soli-
ton-like type as it follows from the solutions of the non-
linear sine-Gordon equation that describes the motion 
of vector   ⃗ for both DW types considering the boundary 
conditions. In DW of ac type (Bloch DW) the rotation of 
vectors   ⃗ and  ⃗⃗ ⃗⃗⃗ takes place in the plane ac, corre-
sponding to variation of vector  ⃗⃗ ⃗⃗⃗:    
 
   [   ]
 ,    
 ,     
 
   [   ]
 . For DW of ab type (Neel DW) typical 
is the rotation of vector   ⃗ in the plane ab. In this case 
at angles    ,       the rotation of vector   ⃗ leads to 
the change in direction and magnitude of vector  ⃗⃗⃗  up 
to a zero value at the DW center. The equations for 
changes in  ⃗⃗⃗  along the Y-axis perpendicular to the 
DW surface:     ,     ,     
   [   ]
 
. The varia-
tions of the weak ferromagnetic moment obtained from 
these equations are in correlation with “magnetic pro-
files” derived from MFM for each DW type, corroborat-
ing the good efficiency of the technique for the analysis 
of the fine structure of DW and DS. 
 
 
REFERENCES 
 
1. A.P. Pyatakov, A.K. Zvezdin, Usp. Fiz. Nauk 182, 6 (2012).  
2. M.V. Chetkin, Yu.N. Kurbatova, T.B. Shapaeva, J. Magn. 
Magn. Mater. 321, 7 (2009). 
3. A.P. Kuz’menko, P.V. Abakumov, M.B. Dobromyslov,  
J. Magn. Magn. Mater. 324, 1262 (2012). 
4. A.P. Kuzmenko, P.V. Abakumov, M.B. Dobromyslov, 
N.I. Shumakova, J. Nano- Electron. Phys. 5 No3, 03025 (2013). 
 


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Interrelation of Shape and Structure of Domain Walls with Magnetic Inhomogeneities

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