Low-temperature spin dynamics in the TmFeO 3 orthoferrite with a non-Kramers ion

We investigate the magnetic dynamics of the orthorhombic perovskite ${\mathrm{TmFeO}}_{3}$ at low temperatures, below the spin reorientation transition at ${T}_{\mathrm{SR}}\ensuremath{\approx}80$ K, by means of time-of-flight neutron spectroscopy. We find that the magnetic excitation spectrum combines two emergent collective modes associated with different magnetic sublattices. The Fe subsystem orders below ${T}_{\mathrm{N}}\ensuremath{\sim}632$ K into a canted antiferromagnetic structure and exhibits sharp, high-energy magnon excitations. We describe them using linear spin-wave theory, and reveal a pronounced anisotropy between in- and out-of-plane exchange interactions, which was mainly neglected in previous reports on the spin dynamics in orthoferrites. At lower energies, we find two crystalline electrical field (CEF) excitations of ${\mathrm{Tm}}^{3+}$ ions at energies of $\ensuremath{\sim}2$ and 5 meV. In contrast to the sister compound ${\mathrm{YbFeO}}_{3}$, where the ${\mathrm{Yb}}^{3+}$ ions form quasi-one-dimensional chains along the $c$ axis, the Tm excitations show dispersion along both directions in the $(0KL)$ scattering plane. Analysis of the neutron scattering polarization factor reveals a longitudinal polarization of the 2 meV excitation. To evaluate the effect of the CEF on the ${\mathrm{Tm}}^{3+}$ ions, we perform point-charge model calculations, and their results quantitatively capture the main features of Tm single-ion physics, such as energies, intensities, and polarization of the CEF transitions, and the type of magnetic anisotropy.