Mean-field treatment of nonlinear susceptibilities for a ferromagnet of arbitrary spin

Abstract

The intrinsic linear and nonlinear magnetic susceptibilities, χn, for a ferromagnet of arbitrary spin, calculated using the mean-field approximation, are shown to diverge in the asymptotic critical region (ACR) with the exponent γn = nγ + (n − 1)β and n = 1, 2, . . . . This behaviour of χn in the ACR is consistent with the scaling equation of state. With increasing spin, the divergence in χn(T ), as the ferromagnetic-paramagnetic phase transition temperature, TC , is approached from below or above, progressively slows down with the result that the width of the ACR increases. For a given spin, the higher the order of nonlinear susceptibility, the narrower the ACR. These results are in qualitative agreement with the critical behaviour of χn(T ) observed in an archetypal ferromagnet.

Anomalous and Anisotropic Nonlinear Susceptibility in the Proximate Kitaev Magnet $α$-RuCl$_3$

“…χ2 on the other hand exhibits such a discontinuity only for type A (e.g. ferromagnet) where time reversal symmetry is broken [15]. In comparison, in the other two cases it is zero.…”

“…We illustrate in fig. 1(a-c) the three known types of characteristic behavior of both the linear (χ 1 ) and the nonlinear (χ 2 and χ 3 ) susceptibilities for typical ferromagnets, bipartite antiferromagnets and spin glasses, respectively [15,[17][18][19]. In all three cases, significant non zero χ 3 is found only in the vicinity of the critical temperature.…”

“…where the coefficients represent the various order susceptibilities. In particular, the coefficient χ 2 is non zero when time reversable symmetry is broken, while preserving lattice symmetry as for instance [15] in ferromagnets.…”

Evidence for a re-entrant character of magnetism of σ-phase Fe–Mo alloys: Non-linear susceptibilities

“…In other words, two magnetic orderings viz. SG and FM co-exist in the ground magnetic state of these treatment that does not account for magneto-crystalline and shape anisotropies [17]. Anyway, it should be mentioned that a positive, peak-like shaped 2 curve was also observed in a ferromagnetically ordered Ga0.6Mo2S4 spinel [15].…”

“…Concerning 2(T), the first even term, it should be absent for the pure SG, whereas for the FM it should be negative for T < TC (with a divergence at TC) and equal to zero for T > TC [17].…”