One-ion mechanism of magnetocrystalline surface anisotropy energy: Yttrium iron garnet

Abstract

A quantitative calculation of magnetocrystalline surface anisotropy energy on the basis of a one-ion mechanism is presented. It involves, in the case of yttrium iron garnet (YIG), the quadratic axial term of the ferric ion spin Hamiltonian and two plausible assumptions concerning the structure of the crystal surface. For a {001} surface of YIG the absolute value of the calculated surface anisotropy constant is 0.0115 ${\mathrm{ergcm}}^{-2\mathrm{}}$ at 0°K and 0.0070 ${\mathrm{ergcm}}^{-2\mathrm{}}$ at 296°K. The latter agrees within experimental error with the most recent absolute value 0.008 ${\mathrm{ergcm}}^{-2\mathrm{}}$ measured at room temperature. For a {111} surface of YIG the surface anisotropy predicted by the present mechanism is zero at all temperatures.