Rare earth single-ion anisotropy and the magnetic structures of the RTiO3 perovskites: R = Tb,Dy, Ho,Er and Tm

Attention is drawn to common features in the magnetic structures of the isostructural RMO₃ phases where R = Tb, Dy, Ho, Er and Tm and M = Al, Ti, Cr, Fe and Co. The orientation of the rare earth magnetic moment with respect to the orthorhombic c-axis depends only on R. For R = Er and Tm the moments are parallel to the c-axis while for R = Tb, Dy and Ho they lie in the a-b plane. The in-plane moments are canted with respect to the a and b axes with both ferromagnetic and antiferromagnetic components and the canting angles are constant for a given R independent of M. Using symmetry arguments we show that the above systematics can be understood in terms of the rare earth single-ion anisotropy. Detailed calculations incorporating a crystal field of C_s symmetry determined for Er³⁺ in YAlO₃ and an isotropic molecular field of magnitude appropriate to the RTiO₃ compounds produce results in agreement with the experimental observations. Essentially the same results are obtained for a crystal field of D_4h symmetry. The B²₀O²₀ term in the crystal field Hamiltonian is identified as the factor which determines the orientation of the rare earth moment.