Surface energies in crystals of mutually polarizing dipolar particles

Interfacial energy affects the internal field distribution and the macroscopic morphology of dipolar colloidal aggregates. We compute the surface energy of crystalline assemblies of polarizable spheres that explicitly accounts for mutual polarization among particle dipoles. Applying this approach to simple cubic, body-centered cubic, face-centered cubic, diamond cubic, and body-centered tetragonal lattices, we recover known constant dipole results in the low-contrast limit for transversely magnetized surfaces and reveal pronounced differences as the particle-medium contrast increases. The dependence of surface energies on orientation relative to the external field suggests that low-energy crystal shapes will be smooth and elongated along the field axis, providing insights into the expected equilibrium crystal shapes. The (110) surface is the most energetically favorable for the lowest energy lattice, a body-centered tetragonal crystal, consistent with observations from simulations and experiments. These findings underscore the importance of interfacial effects in the analysis and design of reconfigurable, tunable dipolar materials.