anisotropy operators package for Stoch Magnet module contains anisotropy classes.
anisotropy operators package for Stoch Magnet module contains anisotropy classes.
The Anistropy energy of a spin is \( E^i_a=\displaystyle k_U . \phi_U(S_i) \) where $U$ is the anistropy directions
The corresponding Anisotropy magnetic field which verifies \( H^i = - \frac{1}{\mu_s} \frac{\partial E}{\partial S_i} \) is
\( H^i_a= \displaystyle -\frac{k_U}{\mu_s} \nabla \phi_U (S_i) \).
The total Anisotropy energy of the system is \( E_a=\displaystyle \sum_i E^i_a= \sum_i k_U \phi_U(S_i) \)
The package contains the classes:
- SM_AnisotropyOperator<I> describes the generic anistrop operator with templated abstract method SM_AnisotropyOperator::computePhi() and SM_AnisotropyOperator::computePhiDerivatives()
- SM_UniaxialAnisotropyOperator describes the uniaxial anisotropy with
- \( \phi_U(S)= - (S,U_0)^2 \)
- \( \nabla \phi_U(S)= -2.(S,U_0).S\)
- SM_PlanarAnisotropyOperator describes the planar anisotropy with
- \( \phi_U(S)= (S,U_0)^2 \)
- \( \nabla \phi_U(S)= 2.(S,U_0).S\)
- SM_CubicAnisotropyOperator describes the cubic anisotropy with
- \(\phi_U(S)= \displaystyle \frac{1}{2} \sum_{d=0}^{d=2} (S,U_d)^4 \)
- \( \nabla \phi_U(S)= 2. \sum_{d=0}^{d=2} (S,U_d)^3 U_d \)
The UML organization of the package is as follow:
