Experiment
Experiment: thing ferromagnetic films
Base model
Stationary Landau-Lifshitz equation
 
d 
M   M  H eff
dt

W
H eff 
M
 
M  H eff  0
Energy of magnetic
Stationary Landau-Lifshitz equation
l0  effective magnetic length,

l0
2
 ,  1



H eff  H   M   M z
Radial and spherical coordinates
Symmetry of magnetization distribution:
r,   q   0 ( r )
2
2
M  M0

M  M 0 (cos  sin  , sin  sin  , cos )
1D equation
( )  q  , simplest case q  1
d2
1d
1

 (r) 
 ( r )  sin  cos   2   
2
dr
r dr
r

d2
2R
exp( r )  R,


sin

cos

(
1


e
)
2
dR
The equation is the same as for the
pendulum with not constant gravity

Numeric investigation (easy-plane)
• Method of shooting in phase plane
Asymptotic of magnetization    / 2 is the
asymptotic of only single solution
Numeric investigation (easy-axes)
• Method of shooting in phase plane
The conservation low of energy in pendulum model
don’t allow to construct a solution with right asymptotic
Solution:
  0,   const
• Example of magnetization distribution

at H  0
Solution: magnetic “Targets”
• Example of magnetization distribution

at H  0 (non constant anisotropy)


2R
2R
F  1e , F    e
Contence
• Introduction
• Model of magnets
•
1. From 2D model to 1D model
2. Solutions
Conclusion
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