Phase diagrams of the classical Heisenberg fluid within the extended van der Waals approximation

Abstract

We use a simple van der Waals theory, suitably extended to the solid phase and to anisotropic interactions, to study the phase behavior of a system of particles with magnetic exchange interactions. A very rich phase behavior is found which indicates, in particular, that the ferromagnetic liquid phase is favored by increasing the range of both the magnetic exchange interactions and of the nonmagnetic interactions. This could well explain why it turns out to be difficult to find such a phase in simulations which use interactions which are cut off at finite range.

Phase separation dynamics in a two-dimensional magnetic mixture

“…This is an exact result within the MF approximation, which has been previously applied also to three-dimensional Heisenberg fluids 23,26,27 as well as in other contexts such as in liquid crystal theory. 37 In the low-temperature ferromagnetic state, the orientational order is uniaxial with respect to a director n. Thus, the angular distribution reduces to h B (r, ω) = h B (r, u), where u = s · n = cos θ .…”

“…The corresponding coexisting densities ρ I , ρ II and concentrations x I , x II are calculated using Eq. (27). Recall that coexisting phases are at equal pressure; we display a number of isobars in the densityconcentration plane, which are indicated by the yellow lines in Fig.…”

“…The integration over orientation in Eq. (19) then becomes 23,27 dω h B (r , ω )s −→ 2π (20) where L(r) = coth B(r) − 1/B(r) is the Langevin function. The latter also defines the local magnetization m(r) = dωh B (r, ω) cos θ = L(r).…”

“…From the theoretical side, the equilibrium properties of one-component Heisenberg fluids, [23][24][25][26][27] as well as other spin fluids with two-dimensional 28 (XY) and Ising spins and mixtures thereof have been extensively studied by MC simulations, integral equation methods, and (mean field (MF)) density functional theories (see Ref. 29 and references therein).…”

“…Heisenberg fluids [23][24][25][26][27] are basic models for continuum systems exhibiting ferromagnetic order, particularly for the description of ferromagnetism in undercooled liquid metal alloys. Mixtures of such systems and, in particular, mixtures of magnetic and non-magnetic particles are promising candidates for the controlled fabrication of patterns on the micron scale.…”