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

Understanding the correlation between magnetic properties and nanostructure involves collaborative efforts between chemists, physicists, and materials scientists to study both fundamental properties and potential applications. This article introduces a classification of nanostructure morphology according to the mechanism responsible for the magnetic properties. The fundamental magnetic properties of interest and the theoretical frameworks developed to model these properties are summarized. Common chemical and physical techniques for the fabrication of magnetic nanostructures are surveyed, followed by some examples of recent investigations of magnetic systems with structure on the nanometer scale. The article concludes with a brief discussion of some promising experimental techniques in synthesis and measurements.

Magnetic Properties of Nanostructured Materials

https://engineering.purdue.edu/~tsfisher/ME595M/Lepri%20thermal%20cond%20review%202004.pdf

Thermal conduction in classical low-dimensional lattices

The character of the ground state of an antiferromagnetic insulator is fundamentally altered following addition of even a small amount of charge1. The added charge is concentrated into domain walls across which a π phase shift in the spin correlations of the host material is induced. In two dimensions, these domain walls are ‘stripes’ which can be insulating2,3 or conducting4,5,6 — that is, metallic ‘rivers’ with their own low-energy degrees of freedom. However, in arrays of one-dimensional metals, which occur in materials such as organic conductors7, interactions between stripes typically drive a transition to an insulating ordered charge-density-wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large compared tothe CDW coupling between stripes. As a consequence, there should exist electronic quantum liquid-crystal phases, which constitute new states of matter, and which can be either high-temperature superconductors or two-dimensional anisotropic ‘metallic’ non-Fermi liquids. Neutron scattering and other experiments in the copper oxide superconductor La1.6−xNd0.4SrxCuO4 already provide evidence for the existence of these phases in at least one class of materials.

Electronic liquid-crystal phases of a doped Mott insulator

TOPICAL REVIEW: Nanomagnetics

We summarize and extend our study (using real-space response and correlation functions) of the properties of a continuous-symmetry ferromagnet with random anisotropy, distinguishing between the cases of weak and strong random anisotropy. For the weak-anisotropy case we find three different magnetic regimes, according to the strength of the external magnetic field H. In zero H, the net magnetization is zero, although the ferromagnetic correlation length (FCL) is large. We call a ferromagnet in this first regime a correlated spin glass (CSG). It has a very large magnetic susceptibility, and hence a relatively small coherent anisotropy converts it into a nearly typical ferromagnetic domain structure. Also, a relatively small magnetic field nearly aligns the CSG, producing the second regime, which we call a ferromagnet with wandering axis (FWA). The FWA is a slightly noncollinear structure in which the tipping of the magnetization with respect to the field varies over the system. The tipping angle is correlated over a (field-dependent) correlation length which is smaller than the FCL of the CSG. As the field increases the correlation length in the FWA decreases, until the third regime is reached, wherein the tipping angles (which are smaller than in the FWA) are completely uncorrelated from site to site. We obtain the magnetization or susceptibility (as appropriate) for each of these three regimes. We also show that the temperature dependence of the (single-ion) random anisotropy strength can provide a plausible explanation for certain classes of reentrant phenomena and susceptibility cusps observed in magnetization studies. Neutron scattering studies appear to be consistent with the predicted ${H}^{\mathrm{\ensuremath{-}}1/2}$ dependence of the FCL in the FWA regime, and display the expected rise of the FCL in the CSG regime as the random anisotropy strength decreases with increasing temperature.

Ordering in ferromagnets with random anisotropy.

The hydrodynamic theory of spin waves is extended to a magnetic system such as a spin glass or a crystal with helical spin order, in which there are equilibrium magnetizations on different sites, with spin directions that are not collinear. If the total magnetization is zero and if the interactions are assumed to be isotropic in spin space, one predicts well-defined spin waves at small wave vectors $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$, with a linear dispersion relation, and three polarizations for each value of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$. The hydrodynamic assumption of a finite spin-stiffness constant may be questionable, however, for the spin glass. Nonzero magnetization is discussed briefly.

Hydrodynamic theory of spin waves in spin glasses and other systems with noncollinear spin orientations

Ultrathin ferromagnetic films with perpendicular spin anisotropy can possess an alternating up-down stripe-domain structure, with widths L\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta} Considering the two inequivalent types of stripe domains to form a single unit, this structure may be thought of as a two-dimensional smectic crystal It is subject to a weak stripe orientation energy With increasing temperature the domain system changes from a smectic crystal phase to an ``Ising nematic'' phase, and then to a ``tetragonal liquid'' phase We discuss its possible phase diagrams, in (${\mathit{H}}_{\mathrm{\ensuremath{\perp}}}$, ${\mathit{H}}_{\mathrm{\ensuremath{\parallel}}}$, T) space This sequence of phases can occur whether or not the system ultimately undergoes a spin reorientation transition to a planar phase

Phase diagram of ultrathin ferromagnetic films with perpendicular anisotropy.

We present the analog of the Khalatnikov theory for the Kapitza conductance ${h}_{\ensuremath{\kappa}}$ at the boundary between two dissimilar classical one-dimensional harmonic chains of atoms. We then perform steady-state molecular-dynamics computer experiments to determine ${h}_{\ensuremath{\kappa}}$ directly. The phonon mismatch theory gives only order-of-magnitude agreement with the computer experiments. Preliminary calculations indicate that anharmonicity increases the Kapitza conductance.

One-dimensional Kapitza conductance: Comparison of the phonon mismatch theory with computer experiments

Recently developed techniques to find the eigenmodes of a ferromagnetic particle of arbitrary shape, as well as the absorption in the presence of an inhomogeneous radio-frequency field, are extended to treat infinite lattices of such particles. The method is applied to analyze the results of recent ferromagnetic resonance experiments and yields substantially good agreement between theory and experiment.

http://arxiv.org/pdf/cond-mat/0703273.pdf

W. M. Saslow

Papers

Ordering in ferromagnets with random anisotropy.

Hydrodynamic theory of spin waves in spin glasses and other systems with noncollinear spin orientations

Phase diagram of ultrathin ferromagnetic films with perpendicular anisotropy.

One-dimensional Kapitza conductance: Comparison of the phonon mismatch theory with computer experiments

Dynamic magnetic response of infinite arrays of ferromagnetic particles