Classical Theory of the Temperature Dependence of Magnetic Anisotropy Energy

Abstract

The consequences are analyzed of the following two assumptions: (1) the effect of temperature upon magnetic anisotropy arises solely from the introduction of local deviations in the direction of magnetization; and (2) the local deviation in an elementary region is the resultant of a very large number of independent deviations. The influence of these local deviations upon the magnetic anisotropy is most conveniently expressed by representing the magnetic energy as a series of surface harmonics. The coefficient of the $n\mathrm{th}$ harmonic is found to vary with temperature as {$\frac{{J}_{s}(T)}{{J}_{s}(0)}$} raised to the power $\frac{n(n+1)}{2}$. The first two exponents for cubic crystals have values of 10 and 21, respectively. The exponent 10 expresses almost precisely the observed temperature dependence of ${K}_{1}$ in iron. In nickel the anisotropy decreases much more rapidly than predicted. It is deduced that the above two assumptions are applicable to iron but not to nickel.