The parable example consists in studing a thin sheet of permalloy with a circular parable shape.

The height of the parable is 22.36 nm.

The parameter $ p $ of the parable defined by $ 2py=x^2$ is 0.70 nm.

The radius of is 1.39 nm.

The geometry size is 1.18 x 22.36 x 2.80 nm^3

The mesh constains 64x128x16 cells such that the cell's size of the mesh is 0.218x0.197x0.175 nm^3

The matter parameters are as follow:

Ms	Aimantations (A/m)	0.17e7
K	Anisotropy (J/m^3)	2.e5
A	Exchange (J/m^3)	1.e-08
L	reference length (m)	0.218e-9
Lex	exchange length (m)	7.421e-08

The exchange length $Lex=\displaystyle \sqrt\frac{2.A}{Mu.Ms.Ms}$ is 74.21 nm. The L/Lex = 2.9e-3

The anisotropy direction U1 is uniformly in the Y-direction with uniaxial crystal type

The initial magnetism M0 is [1,1,1].

The geometry is as follow :


parable geometry	initial magnetization field	first anisotropy direction

The simulation parameters are:

relaxation	taylor expansion
time	optimal
relaxation rate	1.e-8
max iterations number	10 000
toeplitz vector product	LC

All the iterations are done. At 10 000-th iteration, the time vraiation is very small 0.0000019 . the adimensionized energy decreases only from 10914 to 10895 as written in the log file. So the realxation state is the initial state.

The value of magnetism field at equilibrium state are plot as follow:


total magnetic excitation module	equilibrium magnetism field