We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties---optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

The theory and properties of randomly disordered crystals and related physical systems

Calculations are made of the magnetic excitations in the random systems Rb2NiF4/Rb2MnF4 and K2MnF4/K2ZnF4 using various approximations based upon the single-site coherent potential approximation. For the former system, three different ways were used to treat the transverse part of the exchange interaction; the most successful was to reduce the disorder in the transverse exchange interactions by appropriate scaling of the single-site Green functions. The calculations then gave good agreement with recent measurements. In the calculations for the latter system, two approximations have been used for treating the transverse part of the interactions and two ways of keeping the magnetic excitations off the non-magnetic zinc ions. The results predict considerable structure which is absent in theories which average the single-site energies.

Magnetic excitations in two-dimensional random antiferromagnets

For pt.II, see ibid., vol.8, no.1, p.2688 (1975). The problem of off-diagonal disorder is analysed in the fermion-field picture of configuration averaging. The idea of bond-CPAS reported earlier in this series is studied in detail.

Fermion-field theory and configuration averaging. III. Off-diagonal disorder and bond CPA

Studies local magnetic moments in binary alloys as a function of alloy concentration. A two-sublattice model accounts also for the antiferromagnetic solutions found in the Cr-rich region. The effect of local atomic configuration is considered and the shift in atomic energy levels due to charge transfer is taken into account. The continued fractions technique is employed for calculations of the Local Green functions. The Coulomb repulsion term is treated in the alloy analogy approximation and the intra-atomic exchange term is treated by the Hartree-Fock approximation. Calculations are performed for parameters corresponding to Fe-Cr alloys. The magnetic moments of Cr and Fe agree with experimental data: ferromagnetic (up to 70 at.% Cr) and antiferromagnetic (above 83 at.% Cr) phases were found. The ferromagnetic moment of Fe decreases linearly against the number of Cr atoms in the vicinity; the rate, however, is concentration dependent. The magnetic moment of Fe in pure chromium is 1.5 mu B and Fe is antiferromagnetically coupled to Cr atoms.

Magnetic moments for different local atomic configurations in Fe-Cr alloys

A theory for spin waves in diluted uniaxial antiferromagnets with random interactions in both exchange and single-ion anisotropy has been developed by extending a recent work on the related ferromagnets. As in the paper for the ferromagnets, the kind of coherent potential approximation (CPA) the authors consider here taking into account the dynamical effects of fluctuations in the exchange and local-anisotropy fields on the same level. For a two-sublattice antiferromagnet, however, the effective medium is self-consistently determined in terms of three parameters which, after using the time-reversal symmetry into the usual CPA T matrix condition for a pair of nearest-neighbour sites, may be reduced to only two independent parameters in the whole energy space. The concentration dependence, at zero temperature, of the zero-field antiferromagnetic resonance (or, equivalently, of the antiferromagnetic-'spin-flop' critical field) is analysed as a function of a local-anisotropy parameter and of the relative size of the anisotropy in the pure magnetic system. For systems with random non-competitive anisotropy, it is found that the general behaviour of these quantities with dilution is very much more sensitive to changes in both the random and non-random parts of the anisotropy than predicted by virtual-crystal approximation.

CPA approach for randomly diluted anisotropic antiferromagnets: spin-flop transition and AFMR

A coherent potential approximation for insulating antiferromagnetic alloys is presented, in which the off-diagonal (transfer) parts of the exchange interaction are treated on the same basis as the diagonal parts. The theory uses three parameters which are adjusted to ensure no net scattering on average from a nearest-neighbour pair of atoms when immersed in the coherent crystal. This type of treatment is especially suitable for Heisenberg exchange where the diagonal and off-diagonal terms have the same magnitudes. Results are presented for the one-magnon densities of states at various concentrations for the systems K(Mn, Ni)F3, K(Ni, Zn)F3 and K2(Mn, Ni)F4.

J B Parkinson

Papers

Coherent potential approximation for insulating Heisenberg antiferromagnetic alloys