This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

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

Optical Properties of (Zn, Mn) and (Cd, Mn) Chalcogenide Mixed Crystals and Superlattices

Thin Cd1−xMnxTe semiconductor films with x ranging from 0 to 0.9 have been grown on CdTe (111) substrates using the atomic layer epitaxy method. The films grow epitaxially at all concentrations and show no manganese interdiffusion. The films are characterized by low‐energy electron diffraction, Auger electron spectroscopy and angle‐resolved UV photoemission.

Growth of Cd1−xMnxTe films with 0<x<0.9 by atomic layer epitaxy

We report on dynamic magnetic properties at low temperatures (4.2T30 K) of the disordered Heisenberg frustrated antiferromagnet ${\mathrm{Cd}}_{0.6}$${\mathrm{Mn}}_{0.4}$Te over an extended range of frequencies or of corresponding observation times ${(10}^{\mathrm{\ensuremath{-}}6}$${t}_{\mathrm{obs}3\ifmmode\times\else\texttimes\fi{}{10}^{3}}$ s). At high frequencies, the real (${\ensuremath{\chi}}_{\ensuremath{\nu}}^{\mathcal{'}}$) and imaginary (${\ensuremath{\chi}}_{\ensuremath{\nu}}^{\mathcal{'}\mathcal{'}}$) parts of the susceptibility are determined from accurate Faraday-rotation experiments while the dynamics for longer characteristic times are investigated in a weak field, through superconducting quantum-interference device (SQUID) measurements of the magnetization. Starting from two different dynamic criteria, (i) the significant change of the relaxation of the in-field magnetization to step variations of the temperature and (ii) the appearance of long-time thermoremanent magnetization relaxation, we deduce a value ${T}_{f0}$=12.9\ifmmode\pm\else\textpm\fi{}0.1 K for the freezing temperature.Fortunately, it also corresponds to the coalescence between the temperature of appearance of irreversibilities and that corresponding to the maximum of the ac susceptibility at very low frequencies. The Vogel-Fulcher law is unable to describe the dynamics over so large a frequency range. Thus, the spin freezing has been analyzed in terms of a critical slowing down above the static freezing temperature ${T}_{f0}$ using the power law \ensuremath{\tau}/${\ensuremath{\tau}}_{0}$=A[(T-${T}_{f0}$)/T${]}^{\mathrm{\ensuremath{-}}z\ensuremath{\nu}\mathcal{'}}$ with reasonable values of ${\ensuremath{\tau}}_{0}$=3.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}14}$ s and of the dynamic critical exponent z\ensuremath{\nu}'=9.7. This exponent is consistent with simulations obtained recently for three-dimensional Ising spin-glasses. We get independently a similar estimation of ${T}_{f0}$ by other approaches. We also determined the (H,T) magnetic phase diagrams of ${\mathrm{Cd}}_{0.6}$${\mathrm{Mn}}_{0.4}$Te for different values of ${t}_{\mathrm{obs}}$ up to 100 s. The field dependence of the temperature corresponding to the onset of irreversibilities, even for long observation times, looks like a Gabay-Toulouse line, associated with a transverse spin freezing. This behavior, uncommon for classical spin-glasses, is assumed to be related to the particular frustrated structure in this Heisenberg disordered antiferromagnet.

Dynamics of the spin-glass freezing in Cd0.6Mn0.4Te.

Magnetic phases of a Heisenberg spin glass in strong magnetic fields: High field faraday rotation in Cd1−xMnxTe

Monte Carlo simulation of a Heisenberg spin glass in external magnetic fields: Cd0.45Mn0.55Te

Anomaly in dilatation, linear birefringence and susceptibility of NiO at 400 K

What can be learned from magnetooptic measurements

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Papers

Magnetic phases of a Heisenberg spin glass in strong magnetic fields: High field faraday rotation in Cd1−xMnxTe

Monte Carlo simulation of a Heisenberg spin glass in external magnetic fields: Cd0.45Mn0.55Te

Anomaly in dilatation, linear birefringence and susceptibility of NiO at 400 K

What can be learned from magnetooptic measurements