Two-spin Cluster Research Articles

Random anisotropy magnetism in amorphous rare-earth alloys

The random anisotropy model is extended to the case of antiferromagnetic interaction between the rare-earth ions. A self-consistent two-spin cluster approximation is used for calculating the magnetization curve, the magnetoresistivity and its anisotropy for both ferro and antiferromagnetic cases. The model can account for the magnetic properties of alloys like DyNi 3 with a ferromagnetic interaction, and those of alloys like TbAg with an antiferromagnetic one.

Discussion of random Heisenberg models in a cluster approximation

Recently, Bhargava and Kumar studied the random bond and the random site problem for a Heinsenberg model. They calculated the critical temperature ${T}_{c}$ as a function of the bond or site concentration $x$ using a two-spin cluster expansion. In contrast to their paper it can be shown that ${T}_{c}(x)$ is the same in both cases.

Amorphous rare earth alloys: Random-anisotropy ferromagnetism in the pair approximation

A self-consistent two-spin cluster approximation is used to calculate magnetization curves and correlation functions for a ferromagnetic amorphous alloy within the random-anisotropy model for the case of unit total angular momentum ( j = 1) and correlations between the anisotropy axes.

Magnetoresistivity of amorphous rare earth alloys

The magnetoresistivity is studied in the framework of exchange scattering by a system of magnetic ions distributed over an amorphous structure. The resistivity depends on the magnetisation and the nearest-neighbour spin correlation, which are calculated in a self-consistent two-spin cluster approximation within the random anisotropy model. Theoretical curves are presented for both ferromagnetic and antiferromagnetic interaction between the rare earth ions; the former account for experimental data on DyNi3 and HoNi3 alloys, while the latter account for those on the TbAg alloy.

Amorphous rare-earth alloys: random-anisotropy antiferromagnetism

The model of randomly oriented single-ion uniaxial anisotropy field is extended to the case of antiferromagnetic exchange interaction between rare-earth ions. A self-consistent two-spin cluster approximation is used to calculate the magnetization curves for a model system of spin 1. The results are in good qualitative agreement with experimental data on amorphous RE x Cu 1− x and RE x Ag 1− x alloys (RE = Tb, Dy, Ho). In particular, the observed increase of the “coercive” field with increasing x in RE x Cu 1− x alloys is accounted for.

Cluster expansion of random heisenberg ferromagnets

In this paper the two-spin cluster expansion is applied to a random ferromagnet.

The Kirkwood expansion for spin systems in statistical mechanics

The Kirkwood expansion for spin systems involving a priori averages within states of a given long-range order in the cumulant expansion of the free energy is examined. By defining a generating function for the averages the inconvenient averages can be replaced by a suitable canonical average in the thermodynamic limit. This modified Kirkwood expansion is generalized to the case of arbitrary spin. Simple applications to the Ising model and the spin one model of 3He-4He mixtures are illustrated. A two-spin cluster approximation for the Ising model gives estimates of the critical temperature in good agreement with the Bethe-Peierls approximation.

Approximate Free Energies for Heisenberg Ferromagnets

A systematic discussion is given of the approximate free energies and Curie temperatures that can be obtained by using trial density matrices (which describe various possible decompositions of the ferromagnet into clusters) in a variational calculation of the free energy. Single-spin clusters lead to the molecularfield model (as is well known) and two-spin clusters yield the Oguchi pair model. The relation of the "constant-coupling" method to these approximations is clarified. A rigorous calculation using three-spin $\ensuremath{\Lambda}$ clusters is found to give results differing from those of Oguchi. Finally, the Bethe-Peierls-Weiss approximation is considered within the framework of this paper.

On the Two-Spin Cluster Theory of Ferro- and Antiferromagnetism

On the Two-Spin Cluster Theory of Ferro- and Antiferromagnetism

Two-Particle Cluster Theory of Antiferromagnetism

The two-spin cluster theory of Strieb, Callen and Horwitz, previously applied by the present authors to ferromagnets, is extended to antiferromagnets. The theory is formulated to include nearest and next-nearest neighbor exchange ( J 1 and J 2 ) and to apply to those types of antiferromagnetic Neel phases in which equal numbers of spins are nominally “up” and “down”. When J 2 =0 the theory reduces to the antiferromagnetic constant coupling theory of Kasteleijn and van Kranendonk. Consequently the theory suffers from the defect of an anti-Neel transition at low temperatures.

Ferromagnetic Transitions and the One-Third-Power Law

Experiments have shown that the reduced magnetization of insulating ferromagnets varies as m(T) = D(1-T/Tc)f for T>0.9Tc, and that f=⅓. We report calculations of the magnetization of the Heisenberg model which give, over a wide temperature range, both the observed exponent f=⅓ and the observed co-efficient D, within 2% of the experimental value. This result is obtained for a two-spin cluster theory; similar but slightly less satisfactory agreement is demonstrated by two forms of Green function theory. Because these theories are not satisfactory in the immediate vicinity of the phase transition, and because the experimental ⅓-power law extends far from the transition [in terms of m(T)], we suggest that the ⅓-power law may be a property of the stable ferromagnetic phase rather than a reflection of the phase transition in the sense of the Landau theory.