Magnetic Ordering in the Rare-Earth Metals with More than Half-Filled 4 f Shells

Abstract

The effect of the anisotropy energy on the screw spin structrtre is investigated. Various spin structures found in dysprosium, holmium and erbium are shown to be stable if the anisotropy constants of second, fourth and sixth orders have appropriate magnitudes and signs. The anisotropy energies decrease with rising temperature at different rates according to their orders. This temperature variation of the anisotropy energy causes the magnetic transitions between different spin structures in these rare-earth metals. It is shown that the state with the oscillation of the z component of the spin which has been observed in the high temperature phase of erbium is always stable just below the Neel temperature when the second order anisotropy makes the easy axis of the spin parallel to the c axis. The change of the pitch of the screw with temperature clue to the quadrupole interaction is also calculated on the basis of the molecular field approximation and it is shown to be too small compared with the experimental result.