Magnetic field tuning of spin resonance in TmFeO₃ single crystal probed with THz transient

TmFeO₃, a canted antiferromagnet, has two intrinsic spin resonance modes in the terahertz (THz) frequency regime: quasi-ferromagnetic (q-FM) mode and quasi-antiferromagnetic (q-AFM) mode. Both the q-FM and q-AFM modes show strong magnetic field and temperature dependence. Hereby, by employing THz time-domain spectroscopy combined with external magnetic field and low temperature system, we systematically investigated the magnetic field induced frequency shift of q-FM and q-AFM modes as well as the temperature driven spin reorientation phase transition in TmFeO₃ single crystal. In contrast to the isotropic temperature dependent two-mode, the magnetic field dependence of two-mode is strongly anisotropic: the magnetic field applied along c-axis (a-axis) can harden (soften) the spin resonance frequency of q-FM mode for Γ₄ phase of TmFeO₃, and the field applied along b-axis shows negligible frequency shift for the q-FM mode, with the q-AFM mode relatively stable. The present study provides solid evidence that the magnetic anisotropy in rare earth orthoferrite plays a dominant role in the q-FM mode and the occurrence of spin reorientation phase transition. With the magnetic anisotropic energy obtained from the temperature dependent q-FM and q-AFM mode frequencies, we can predict both magnetic field and temperature dependence of spin resonance in TmFeO₃ single crystal via phenomenological analysis.