dipolar operators package for Stoch Magnet module contains dipolar classes.

This package implements the dipolar operator ond the demagnetized operators on macro cells of the network.

The dipolar magnetic energy of a spin i is $ E^i_{dip}= \displaystyle \frac{\mu_0.\mu_s^2}{4 \pi} \sum_{j!=i} \frac{1}{r_{ij}^3} \left ( (S_i,S_j) - 3 (S_i,U_{ij}) . (S_j,U_{ij}) \right ) $ where

$ X_i $ is the position of the spin i
$ r_{ij}=|X_j-X_i| $
$ U_{ij}=\frac{1}{r_{ij}} (X_j-X_i) $

The corresponding dipolar magnetic field which verifies $ H^i = - \frac{1}{\mu_s} \frac{\partial E}{\partial S_i} $ is

$ H^i_{dip}= \displaystyle -\frac{\mu_0.\mu_s}{4 \pi} \sum_{j!=i} \frac{1}{r_{ij}^3} \left ( S_j - 3 (S_j,U_{ij}). U_{ij} \right ) $.

The total dipolar energy of the system is $ E_h=\displaystyle \frac{1}{2} \sum_i E^i_h=\frac{1}{2} . \sum_i \frac{\mu_0.\mu_s^2}{4 \pi} \sum_{j!=i} \frac{1}{r_{ij}^3} \left ( (S_i,S_j) - 3 (S_i,U_{ij}) . (S_j,U_{ij}) \right )$

As the dipolar magnetic field or energy has an heavy cpu cost, an other approach may be used: the particles are gathered in a macro cell which is considered as a particle whose the position is at the magnetic mass center of the particles in it and its magnetic moment is the sum of the magnetic moment of the particles included in it. Then a demagnetized field is computed in it and the dipolar magnetic field is the demagnetized field of the macro cell which contains the particles.

If the demagnetized field is considered as external field applied on each particle of the macro cell such that the Energy of the spin is considered as a Zeeman energy: $ E^i_{dem}=-\mu_s <H^{mc}_{dem},S_i> $ and total energy of the system $ E_{dem}=\sum_i E^i_{dem} $ where $mc $ is the macro cell containing the spin i.

If the demagnetized field is not considered as an external field but a field that changes at any time: the computation of the dipolar field is computed from direction of magnetic moment S on particles p to magnetic field $H$ on particles with intermediate computation on magnetization field M and demagnetized field $H^{dem}$ on macro cells c:

$ S_p \mapsto M_c \mapsto H^{dem}(M_c) \mapsto H_p $.

The class of the package is :

SM_DipolarOperator to compute the dipolar field
SM_MacroCellsDemagnetizedOperator is the base class of the demagnetied operators:
- SM_MacroCellsContinuousDemagnetizedOperator is the implementation of Demagnetized opertor when the computing of the demagnetozed field over the macro cells of the network is updated at each step
- SM_MacroCellsExternalDemagnetizedOperator is the implementation of Demagnetized opertor when the computing of the demagnetozed field over the macro cells of the network is updated at each n steps

The demagnetied field and dipolar field are computed in dipolar/demagnetized fields computing package

The UML organization of the package is as follow: