Description of a Heisenberg ferromagnet above the Curie point as a spin liquid

Abstract

A Heisenberg ferromagnet (F) with spin S=1/2, found in a spin-liquid (SL) state at temperatures above the Curie point τC, is considered. In this spin-liquid state there is no long-range magnetic order but the short-range order is preserved, and the spin correlation functions are isotropic. The spin liquid is described in the framework of a second-order theory by the method of temperature Green functions. The main thermodynamic characteristics of the spin liquid are found as the result of a self-consistent numerical solution of a system of three integral equations. The Curie point τC+, at which the dc magnetic susceptibility at wave vector q=0 diverges, is determined. A comparison of the thermodynamic characteristics of the system in the F state (τ⩽τC, spin-wave theory) and in the SL state (τ⩾τC+) is made. It is shown that τC+>τC, and a modification of spin-wave theory in which τC reaches the value τC+ is indicated. At the point of the F-SL phase transition the spin correlation functions suffer a finite discontinuity, and with increasing temperature they fall off ∝ 1/τ. The heat capacity of the ferromagnet at τ→τC goes to infinity, while in the SL state the heat capacity remains finite at the point τC+ and falls off for τ≫τC+ in proportion to 1/τ2. The susceptibility obeys the Curie-Weiss law.