A synchrotron X-ray study of the phases and phase transitions in the mixed Ising-XY magnet Fe_xCo_1−x TiO₃

Abstract

We report a detailed synchrotron x-ray scattering study of the phases and phase transitions in the mixed Ising-XY magnetic system with quenched randomness: Fe_xCo_1−x TiO₃ (x=0.35, 0.50, 0.65 and 0.75). For concentrations x=0.35, 0.50 and 0.65, we observe at high resolution a breakup of both the magnetic and the atomic structures of the crystal into domains, as well as a uniform lattice distortion following the ordering of the XY spin components. We argue that this breakup into domains in the XY phases results from random anisotropy, random field and magnetoelastic effects in Fe_xCo_1−x TiO₃. In particular, we find that in random anisotropy XY magnets, there exists a novel phase transition which is critical, but involves no long-range ordered phase. In addition to the XY behavior, the Ising spin component in the mixed phase (x=0.65) is found to break into domains following the (short range) ordering of the XY spin components. Specifically, the scattering profiles of the low temperature mixed states are well described by a Lorentzian squared cross-section, which in three dimensions corresponds to exponential decay of the real space spin-spin correlations. This loss of the long-range order of the Ising order due to the ordering of the XY spin components after initial establishment of the Ising order on cooling is difficult to understand within our current picture of the random field Ising model. We have also carried out a detailed study of the magnetic field effects on phase transitions in the mixed Ising random magnet Fe_0.75Co_0.25TiO₃, for fields up to 2.9T. It is found, as in the diluted Ising antiferromagnets Mn_xZn_1−x F₂ and Fe_xZn_1−x F₂, that when the sample is cooled in the presence of a field, it evolves from the high temperature paramagnetic phase to a low temperature domain state. The low temperature scattering profiles are well described by a Lorentzian squared cross-section. However, if the sample is cooled below the Neél temperature T _N in the absence of a field, and a magnetic field is subsequently applied, the long range magnetic order persists on warming, up to a well defined field-dependent metastability temperature, T _M(H). The shedding of this LRO in the metastable region is consistent with the “trompe l’oeil critical behavior” description, with a β _ZFC∼0.17. The depression of the metastability temperature in magnetic fields can be well described by the form T _M(H)=T _N(0)−bH ²−aH ^2/φ, with the best fit value for the crossover exponent φ=1.2(1). This smaller value (than the theoretical value φ=1.4) for φ probably arises from the close proximity of a multicritical point at higher fields. At the superlattice reciprocal lattice point (1, 1,–1.5), we observe a drastic field-dependence of the x-ray, but not the neutron, scattering intensity. This additional x-ray intensity is believed to arise from an induced staggered charge density. In particular, the quadratic magnetic field dependence of the additional intensity is consistent with a lattice and magnetism coupling of the form, ρ _s M _s M, where ρ _ss is a staggered charge density, M _s the staggered magnetization and M the uniform magnetization.