On the Origin of the Magnetic Anisotropy Energy of Ferrites

Abstract

Possible sources of the anisotropy energy are investigated for ferromagnetic ferrites, i.e., Ni-, Co-, Fe- and Mn-ferrites. The cubic anisotropy energy which arises from the anisotropy of the crystalline field acting on magnetic ions and is described by the function of the spin operator of one ion identically vanishes for ions with spin less than 2, so that this kind of anisotropy energy vanishes for Ni2+ and Co2+ ions. The anisotropy energy arising from the magnetic dipole-dipole interaction which appears for cubic crystals in its second order perturbation was calculated for Mn- and Ni-ferrites and that arising from the anisotropic exchange interaction calculated for Ni-ferrite but they were found to be too small to account for the experimental values. Therefore, it is concluded that the major part of the anisotropy energy for Ni-ferrite arises from the anisotropy energy of Fe3+ ions, for magnetite from the anisotropy energy of Fe2+ and Fe3+ ions, and for Mn-ferrite from the anisotropy energy of Fe3+ and Mn2+ ions. Especially it is shown that the experimental anisotropy energy of magnetite extrapolated to the absolute zero of temperature is in good agreement with the sum of the experimental anisotropy energy of Ni-ferrite and the calculated value of the anisotropy energy of Fe2+ ions. For Co-ferrite, its large anisotropy energy seems to come from the pseudo-quadrupole and anisotropic exchange interactions among Co and Fe ions, but the situation is too complex to carry out the calculation of the anisotropy energy in this case. Finally, the temperature dependence of the cubic anisotropy energy is calculated for Mn-ferrite, and is shown to decrease as (Tc-T)2 near the Curie temperature. Further, the sum of the coefficient,a of the cubic anisotropy Hamiltonian for Mn2+ and Fe3+ ions of the octahedral sites and that for Fe3+ ion of the tetrahedral sites have been determined for Mn-ferrite by adjusting the calculated the small a-value of Mn2+ ions, that the a-value of Fe3+ ions on octahedral sites has five times as large an absolute value as that of Fe3+ ions on tetrahedral sites and that the former has the opposite sign to the latter.