Magnetic anisotropy of single-domain particles

The competition between uniaxial and cubic magnetic anisotropies of single-domain particles is analyzed theoretically. As long as $K_{1c}/K_{1u}<$ 5 ($K_{1c}$ and $K_{1u}$ are the first constants of the crystallographic and uniaxial anisotropies), the value of $K_{1u}$ noticeably affects coercive force $H_c$ and relative residual magnetization $j_r$ of particle ensembles. If the uniaxial anisotropy direction coincides with crystallographic axis $\langle$111$\rangle$ or $\langle$100$\rangle$, the dependences of $H_c$ and $j_r$ on ratio $K_{1c}/K_{1u}$ have a minimum. The competition between the induced uniaxial anisotropy and cubic anisotropy was detected experimentally when the effect of temperature $T$ on the $H_c(T)$ and $j_r(T)$ dependences for single-domain spherical particles of magnetic 3$d$ alloys and $\gamma$-Fe$_2$O$_3$ oxide was investigated. For all single-domain particles studied here, the effect of crystallographic anisotropy on $H_c$ and $j_r$ is manifested at low temperatures, while uniaxial anisotropy plays a decisive role in the temperature range $T >$ 250 K. The effect of second constant $K_2$ on $H_c$ and $j_r$ of ensembles of single-domain particles with uniaxial and cubic anisotropies is investigated theoretically. It is shown that the value of $K_2$ may substantially change the value of $H_c$ for a particle ensemble, preserving the value of $j_r$ unchanged.