The Effective Field

$$\mbox{\bf H}_{\mbox{\scriptsize loc}}= -\frac{dE_{\mbox{\scriptsize tot}}}{d\mbox{\bf m}}$$

Contributions to the effective field:

• external applied field

  $$E_{\mbox{\scriptsize external}} = - \sum_{\mbox{\scriptsize... ...}}\mbox{\bf m}_i \cdot \mbox{\bf H}_{\mbox{\scriptsize ext}}$$

• dipole field
  Each magnetic moment gives rise to a magnetic dipole field. Due to the linearity of maxwells equations (and the superposition principle), the contributions from each moment can be summed together to calculate the effective dipole field.

  $$E_{\mbox{\scriptsize dipole}} = \frac{\mu_0}{4 \pi} \sum_{... ... (\mbox{\bf m}_j \cdot \mbox{\bf r}_{ij})}{r_{ij}^5} \right]$$

• exchange field
  The exchange interaction is a quantummechanical effect which forces magnetic moments to align parallel (ferromagnetism) or antiparallel (antiferromagnetism).

  $$E_{\mbox{\scriptsize exchange}} = -A\!\!\!\!\!\!\!\!\sum_{\... ... pairs}} \!\!\!\!\!\!\!\!\mbox{\bf m}_i \cdot \mbox{\bf m}_j$$

• anisotropy field
  The anisotropy field describes the interaction of the magnetic moments with the crystal lattice.

  $$E_{\mbox{\scriptsize anisotropy}} = -\sum_{\mbox{\scriptsize spins}} K_i (\mbox{\bf m}_i \cdot \mbox{\bf a}_i)^2$$