Thermodynamics of the frustrated $J_1$-$J_2$ Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

Abstract

We use the spin-rotation-invariant Green's function method as well as the high-temperature expansion to discuss the thermodynamic properties of the frustrated spin-$S$ $J_1$-$J_2$ Heisenberg magnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighbor bonds $J_1<0$ and antiferromagnetic next-nearest-neighbor bonds $J_2\ge 0$ and arbitrary spin $S$. We find that the transition point $J_2^c$ between the ferromagnetic ground state and the antiferromagnetic one is nearly independent of the spin $S$, i.e., it is very close to the classical transition point $J_2^{c,\mathrm{clas}}=\frac{2}{3}|J_1|$. At finite temperatures we focus on the parameter regime $J_2<J_2^c$ with a ferromagnetic ground-state. We calculate the Curie temperature $T_C(S,J_2)$ and derive an empirical formula describing the influence of the frustration parameter $J_2$ and spin $S$ on $T_C$. We find that the Curie temperature monotonically decreases with increasing frustration $J_2$, where very close to $J_2^{c,\mathrm{clas}}$ the $T_C(J_2)$-curve exhibits a fast decay which is well described by a logarithmic term $1/\text{log}(\frac{2}{3}|J_1|-J_2)$. To characterize the magnetic ordering below and above $T_C$, we calculate the spin-spin correlation functions $⟨{\mathbf{S}}_0{\mathbf{S}}_{\mathbf{R}}⟩$, the spontaneous magnetization, the uniform static susceptibility $\ddot{I}{‡}_0$ as well as the correlation length $\hat{I}¾$. Moreover, we discuss the specific heat $C_V$ and the temperature dependence of the excitation spectrum. As approaching the transition point $J_2^c$ some unusual features were found, such as negative spin-spin correlations at temperatures above $T_C$ even though the ground state is ferromagnetic or an increase of the spin stiffness with growing temperature.

19 pages, 10 figures, version as in EPJB