Reaction field and dipolar interaction in quasi‐onedimensional heisenberg systems. Application to CsNiF₃

Abstract

An improved mean field theory, the reaction field approximation, which was previously used for a Heisenberg paramagnet, is extended to include the magnetic dipolar interaction. It is shown that in spin chains, when the intra-chain interaction is ferromagnetic, the dipolar inter-chain interaction plays an important role in explaining the phase transition to an antiferromagnetic three-dimensional order a t low temperature. A study of the magnetic susceptibility of CsNiF3 is presented as an explicit example. Values for the intra-chain J and inter-chain J' exchange parameters are derived from TN and x i ( TN). The temperature dependence of X I is very well reproduced by the model.Le modhle du champ de rbaction, un calcul de champ moyen ambliorb, prhcbdemment applique B un systeme paramagnbtique de Heisenberg, permet bgalement de tenir compte des interactions dipolaires. Ce modAle montre que pour chaines de spins, lorsque I'interaction intra-chaine est ferromagnhtique, les couplages dipolaires entre chaines jouent un role capital dans l'htablissement de l'ordre antifenomagnbtique tri-dimensionnel observe A basse temphrature. A titre d'example, nous prbsentons une btude de la susceptibilitk magnbtique dans CsNiF,. Les parametres d'bchange intra-chaine J et inter-chaines J' sont obtenus Bpartir des valeurs TN et xl(T~). La variation de X I en fonction de la temperature est trhs bien reproduite par le mod&.

Correlated effective field theory in transition metal compounds

“…RFA was originally proposed by Onsager [67] and was extended to the Ising system by Brout et al [68] and to an arbitrary spin system S in the entire phase space (both below and above T c ) by Scherer et al [69][70][71][72][73].…”

Spinteract: A Program to Refine Magnetic Interactions to Diffuse Scattering Data

“…This requires either analytical approximations, such as field theories, or numerical simulations, such as Monte Carlo simulations. Spinteract uses a self-consistent extension of mean-field theory called Onsager reaction-field theory [48][49][50][51][52][53]. This approach takes account of thermal fluctuations in an approximate way, but has been shown to give results in excellent agreement with Monte Carlo simulations [24,54].…”

Mean-field transfer-matrix study of the magnetic phase diagram ofCsNiF3

“…1) which is different from the 120 • structure of CsMnBr 3 , an XY system having strong AF coupling along the chains. This difference is due to the relatively strong dipolar field originating from the neighboring ferromagnetic chains 11 . This dipolar field depends strongly on the angle between the magnetic sub-lattices and it can be shown quite easily that there is no interchain dipolar field present on a given site at H c , where the magnetization of all the sub-lattices are parallel to the field.…”

“…It is important to note that dipolar field is almost nonexistant if the ordering along the chains is antiferromagnetic (AF), as it is in many other ABX 3 compouds such as CsMnBr 3 and CsNiCl 3 . 10 This strong dipolar field is responsible for the particular planar AF arrangement 11 of CsNiF 3 which is different from the expected 120 • structure of a system with only AF interactions on a triangular lattice. This magnetic phase occurs for temperatures smaller than T N ≃ 2.77 K. 12 .…”