We review the physical properties of diluted magnetic semiconductors (DMS) of the type AII1−xMnxBVI (e.g., Cd1−xMnxSe, Hg1−xMnxTe). Crystallographic properties are discussed first, with emphasis on the common structural features which these materials have as a result of tetrahedral bonding. We then describe the band structure of the AII1−xMnxBVI alloys in the absence of an external magnetic field, stressing the close relationship of the sp electron bands in these materials to the band structure of the nonmagnetic AIIBVI ‘‘parent’’ semiconductors. In addition, the characteristics of the narrow (nearly localized) band arising from the half‐filled Mn 3d5 shells are described, along with their profound effect on the optical properties of DMS. We then describe our present understanding of the magnetic properties of the AII1−xMnxBVI alloys. In particular, we discuss the mechanism of the Mn++‐Mn++ exchange, which underlies the magnetism of these materials; we present an analytic formulation for the magnetic susc...

Diluted magnetic semiconductors

The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their interrelations. The experimental observations are surveyed and the analogies between different physical systems - fluids, magnets, superfluids, binary alloys, etc. - are developed phenomenologically. An exact theoretical basis for the analogies follows from the equivalence between classical and quantal `lattice gases' and the Ising and Heisenberg-Ising magnetic models. General rigorous inequalities for critical exponents at and below Tc are derived. The nature and validity of the `classical' (phenomenological and mean field) theories are discussed, their predictions being contrasted with the exact results for plane Ising models, which are summarized concisely. Pade approximant and ratio techniques applied to appropriate series expansions lead to precise critical-point estimates for the three-dimensional Heisenberg and Ising models (tables of data are presented). With this background a critique is presented of recent theoretical ideas: namely, the `droplet' picture of the critical point and the `homogeneity' and `scaling' hypotheses. These lead to a `law of corresponding states' near a critical point and to relations between the various exponents which suggest that perhaps only two or three exponents might be algebraically independent for any system.

https://iopscience.iop.org/article/10.1088/0034-4885/30/2/306/pdf

The theory of equilibrium critical phenomena

“…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...

Experiments on simple magnetic model systems

Percolation theory, the theory of the properties of classical particles interacting with a random medium, is of wide applicability and provides a simple picture exhibiting critical behaviour, the features of which are well understood and amenable to detailed calculation In this review the concepts of percolation theory and the general features associated with the critical region about the onset of percolation are developed in detail In particular, several dimensional invariants are examined which make it possible to unify much of the available information, and to extend the insights of percolation theory to processes which have not yet received numerical study The compilation of the results of percolation theory, both exact and numerical, is believed to be complete through 1970 A selective bibliography is given In a concluding chapter several recent applications of percolation theory to classical and to quantum mechanical problems are discussed

An introduction to percolation theory

This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems.

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Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations

The aim of this series of papers is to help bridge the gap in our knowledge of the properties of the Ising and Heisenberg models between very short-range forces corresponding to nearest-neighbour interactions, and very long-range forces corresponding to the mean-field approximation. The present paper is concerned with the equivalent neighbour model in which the interactions between a spin and a certain finite number of its neighbours are equal, and the remaining interactions are all zero. Methods derived previously for obtaining series expansions at high temperatures are generalized to include second- and third-neighbour shells for standard two- and three-dimensional lattices. It is found that as the co-ordination number q increases the properties of the model approach an asymptotic value which depends on dimension, and on q in a given dimension, but not significantly on the type of lattice structure. An estimate is made of this asymptotic behaviour as a function of q.

N W Dalton

Papers

Crystal statistics with long-range forces: I. The equivalent neighbour model