Spin glass transition of single-crystalline TmFe₂O_4-δ

TmFe₂O₄is one kind of multiferroic material in which equivalent amounts of Fe²⁺and Fe³⁺occupy a two-dimensional triangular lattice, leading to charge and spin frustrations. The spin frustration is expected to be increased as the fraction of Fe²⁺(Fe³⁺) becomes larger than that of Fe³⁺(Fe²⁺). We have grown single-crystalline TmFe₂O_4-δwith oxygen vacancies by using floating zone melting method and examined its magnetic properties. On cooling the compound, a long-range magnetic ordering develops around ∼240 K. With further cooling, a maximum of zero-field-cooled (ZFC) magnetization is observed at 186.2 K. The ac magnetic susceptibility obtained by ZFC process also manifests a maximum in its temperature dependence, and the variation of spin-freezing temperature with frequency of ac magnetic field is explainable in terms of the dynamic scaling law with the critical component of 8.68(8). This value suggests that the spin glass transition occurs at 186.2 K. The effect of external dc magnetic field on the irreversible transition temperature is coincident with the de Almeida-Thouless (AT) line. Aging-memory and rejuvenation effect is also observed below the spin-freezing temperature. These facts support the idea that TmFe₂O_4-δundergoes spin glass transition below the ferrimagnetic transition temperature. In other words, TmFe₂O_4-δcan be regarded as a reentrance spin glass. It is thought that the oxygen vacancies bring about unequal number of Fe²⁺and Fe³⁺ions and thereby strengthen the magnetic frustration among the iron ions coupled with antiferromagnetic interactions, leading to the spin glass behavior.