Classical generalized constant coupling model for geometrically frustrated antiferromagnets

Abstract

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagomé lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.

Correlations, spin dynamics, defects: the highly frustrated kagomé bilayer

“…54 to the signature of a moderate increase of the spin-spin correlations of the Kagomé bilayer which, however, must remain short ranged given the absence of any phase transition. This conclusion was confirmed by neutron measurements on SCGO for temperatures ranging from 200 K down to 1.5 K [63], and by susceptibility calculations performed on the Kagomé and the pyrochlore lattices with Heisenberg spins, in which the spin-spin correlation length is kept of the order of the lattice parameter [64]. These calculations, using the so-called «generalized constant coupling» method (GCC) [64], consists in computing the susceptibility of isolated spin-clusters (triangles for the Kagomé and tetrahedras for the pyrochlore) and in coupling these clusters following a mean field approach.…”

“…In this case, the ground state of a cluster is non-magnetic and the spin gap is between the S = 0 ground state and the magnetic S = 1 excited states. In the case of the Kagomé lattice, the ground state of the triangle is magnetic (S / total = 1 2) which gives rise to the nonphysical divergence in the susceptibility as T ® 0, due to the choice of a particular cluster [64]. The GCC simulations for the S / = 3 2 Kagomé and pyrochlore lattices, in between which the Kagomé bilayer's susceptibility is expected to lie, are presented in Fig.…”

Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants

“…6,67 Several theoretical models, mostly for classical spins, have been developed to explain this. 68,69 Basically, frustration leads to individual plaquettes or spin clusters behaving essentially independently. However, our models are less frustrated than that and hence always develop substantial correlations.…”

Effects of site dilution on the magnetic properties of geometrically frustrated antiferromagnets

“…In a series of recent papers 12,13,14 , the present authors have shown how very simple models based on small clusters can provide a very accurate description of the universal cooperative paramagnetic regime in these systems, when compared with both Monte Carlo (MC) and experimental data. The purpose of the present work is to study what are the effects of site dilution by non magnetic impurities of the otherwise perfect pyrochlore and kagome lattices on the magnetic properties in this same regime.…”

“…In the simplest approach, these interactions can be modeled as a mean field. A more refined approximation consists on treating these interactions as created by an effective field which is fixed by a self consistency condition, the so called generalized constant coupling (GCC) approach 13,14 . This self consistency condition is constructed in the following way: we consider the magnetization per spin of a unit with p spins (a triangle for the kagome lattice or a tetrahedron for the pyrochlore lattice, for example), in the presence of the internal field created by the neighboring p − 1 spins outside the unit, and the magnetization of an isolated spin in the presence of the internal field created by the 2(p − 1) neighboring spins, and we equate both quantities, obtaining in this way an equation for the internal field…”