Magnetostatic energies in crystals of paramagnetic particles

We derive a multiscale framework that combines contributions from the lattice symmetry, shape, and interfacial effects to calculate the total magnetostatic energy and effective susceptibility of crystalline paramagnetic particle aggregates. Demagnetizing tensor fields are calculated through a Fourier-space method developed by Beleggia and M. De Graef [M. Beleggia and M. De Graef, J. Magn. Magn. Mater. 263, L1 (2003)10.1016/S0304-8853(03)00238-5] to account for shape anisotropy. A planewise Ewald summation method developed by Massidda [V. Massidda and J. Hernando, Physica B + C 101, 159 (1980)0378-436310.1016/0378-4363(85)90065-8] supplies local field factors in the constant dipole approximation which account for the effect of crystal structure on internal fields, while explicitly accounting for field perturbations at surfaces. The effective energy and susceptibility scales illustrate the dependence of magnetic properties on both aggregate shape and internal organization and successfully predicts the occurrence of giant susceptibility in structured aggregates of paramagnetic particles.