Magnetic behavior and complete high-field magnetic phase diagram of the orthoferrite ErFeO3

Magnonic superradiant phase transition

“…In such a two-sublattice model of Fe 3þ , as depicted in Fig. 1a, the two spins ŜA=B are ordered antiferromagnetically along the c axis at T c < T ≲ 90 K, but are slightly canted toward the a axis and show weak magnetization (the Fe 3þ spins exhibit the so-called spinreorientation transition at 90 K ≲ T ≲ 100 K [26][27][28] ). In contrast, the Er 3þ spins are paramagnetic at T > T c , and they are directed along the a axis by the weak Fe 3þ magnetization.…”

“…The actual values of the parameters appearing in our proposed spin model are provided in "Parameters" together with a description of how they were determined based on recent experimental results of terahertz magnetospectroscopy 31 and magnetization measurements 26 .…”

“…In this study, using an ErFeO 3 spin model reproducing both the phase diagrams obtained via magnetization measurements 26 and terahertz magnetospectroscopy results 31 , we derived an extended Dicke Hamiltonian that accounts for Er 3þ -Er 3þ exchange interactions as well as the cooperative coupling between the Er 3þ spins and Fe 3þ magnon modes. We found that the LTPT in ErFeO 3 can be caused solely by Er 3þ -magnon coupling (in the absence of Er 3þ -Er 3þ exchange interactions).…”

“…The anisotropic g-factors g Er x , g Er y , and g Er z of the Er 3þ spins are free parameters, and could easily change the critical DC fields. T c and three critical DC fields obtained from the magnetization measurements 26 were not sufficient to determine the above parameters.…”

“…These values were utilized to fit Fig. 2 roughly to the phase diagrams reported by Zhang et al 26 . The precise values of J Er , J, and D y were mainly determined to fit our calculated spin resonance frequencies B DC ==c to the corresponding terahertz absorption spectrum in our experiments 31 , which are both shown in Supplementary Fig.…”