Theory of the magnetic torque anisotropy of the samarium iron garnet

Abstract

A theory for the contribution of Sm3+ ions to the anisotropy of the iron garnet is developed through several stages of approximation on the assumption that the crystalline Stark and exchange fields at each of the rare-earth sites in the garnet have predominantly, though not perfectly, cubic symmetry. The ground state of each Sm3+ ion is first assumed to have had its angular momentum partially and anisotropically quenched by the cubic component of the Stark field. Still in the cubic approximation, the theory is refined to include (i) a partial decoupling of the spin from the orbital angular momentum by the Stark field and (ii) an enhancement dependent on temperature of the average spin angular momentum by the exchange field. The assumption of perfect cubic symmetry is then dropped, and local rhombic distortions of the exchange and Stark fields are introduced and treated perturbatively. It is found that as long as the rhombic distortions are not too large there is a region in temperature in which the anisotropy varies as the inverse third power of the temperature. It is suggested that this behaviour is realized experimentally to a good approximation in the magnetic torque data obtained between 80 and 300 °K by Pearson. From Pearson's data, a value βHex(T = 0 °K)/k approximately equal to 29 °K is extracted for the isotropic component of the exchange field. This value for the exchange field, when inserted in the perfectly cubic theory, gives approximate agreement with the anisotropy measured at low temperatures in garnets lightly doped with samarium. For the concentrated samarium garnet, however, the perfectly cubic theory gives the wrong direction of easy magnetization and, with this value for the exchange field, a Schottky anomaly at too low a temperature. The discrepancies are removed by inclusion of rhombic distortions. In particular, one choice for these distortions, appropriate for the concentrated garnet, leads correctly to the prediction that the (110) is the easy direction of magnetization, explains satisfactorily the ionic contribution to the specific heat between 5 and 20 °K, and locates correctly a prominent ionic absorption level which has been observed in the far infra-red.