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

Ferroelectric and magnetic materials are a time-honoured subject of study and have led to some of the most important technological advances to date. Magnetism and ferroelectricity are involved with local spins and off-centre structural distortions, respectively. These two seemingly unrelated phenomena can coexist in certain unusual materials, termed multiferroics1,2,3,4,5,6,7,8,9,10,11. Despite the possible coexistence of ferroelectricity and magnetism, a pronounced interplay between these properties has rarely been observed6,12. This has prevented the realization of multiferroic devices offering such functionality13. Here, we report a striking interplay between ferroelectricity and magnetism in the multiferroic TbMn2O5, demonstrated by a highly reproducible electric polarization reversal and permanent polarization imprint that are both actuated by an applied magnetic field. Our results point to new device applications such as magnetically recorded ferroelectric memory.

Electric polarization reversal and memory in a multiferroic material induced by magnetic fields.

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

This paper compares theory and experiment for behavior very near critical points. The primary experimental results are the "critical indices" which describe singularities in various thermodynamic derivatives and correlation functions. These indices are tabulated and compared with theory. The basic theoretical ideas are introduced via the molecular field approach, which brings in the concept of an order parameter and suggests that there are close relations among different phase transition problems. Although this theory is qualitatively correct it is quantitatively wrong, it predicts the wrong values of the critical indices. Another theoretical approach, the "scaling law" concept, which predicts relations among these indices, is described. The experimental evidence for and against the scaling laws is assessed. It is suggested that the scaling laws provide a promising approach to understanding phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.

Static Phenomena Near Critical Points: Theory and Experiment

The dielectric relaxation of a solid solution of 10‐mol % lead titanate in lead magnesium niobate is found to be similar to the magnetic relaxation in spin‐glass systems.1–3 Based on this analogy, it is proposed that the relaxor ferroelectric is a polar‐glassy system which has thermally activated polarization fluctuations above a static freezing temperature. An activation energy and freezing temperature of 0.0407 eV and 291.5 K, respectively, were found by analyzing the frequency dependence of the temperature of the dielectric maximum using the Vogel–Fulcher relationship.4,5 It has also been shown that a macroscopic polarization is sustained on heating up to this freezing temperature. A coupling between nanometer scale clusters is believed to control the kinetics of the fluctuations and the development of a frustration as the system freezes into states of local equilibrium. The possibility of an orientational freezing associated with the ferroelastic nature of the nanosized polar regions in the rhombohedr...

Freezing of the polarization fluctuations in lead magnesium niobate relaxors

The theory of the Vogel-Fulcher law of spin glasses

Observation of electron hopping in 151Eu3S4 by Mössbauer spectroscopy

The orthoferrite DyFeO3, weakly ferromagnetic at room temperature, was found to become antiferromagnetic at 36°K. Symmetry considerations suggest that at this transition point the iron spin‐axis rotates out of the plane perpendicular to the Moriya‐Dzyaloshinsky vector, becoming parallel to it. On this basis the magnetic point group mmm is assigned to DyFeO3 below the transition. Further evidence for the correctness of this assignment has been obtained by the observation of a linear dependence of the susceptibility on the magnetic field χxy=CHz, and cyclic permutations as allowed by the mmm symmetry. Another transition, which we associate with an antiferromagnetic ordering of the Dy3+ moment, is found at TN=3.7°K. The magnetization curves measured below 4.2°K at fields up to 40 kG are interpretable, to a good approximation, in terms of |±15/2〉 Kramers' doublet whose axis lies in the mirror plane of the crystal, making an angle of approximately 30° with the [010] axis. Below TN metamagnetic transitions were...

Magnetic Properties of an Antiferromagnetic Orthoferrite

Magnetic structure of some rare-earth orthochromites

Curie temperatures of 14 different orthoferrites with the chemical formula RFeO3, (R = Y, La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) were measured by differential thermal analysis Hyperfine interactions of the Fe57 nucleus in the same materials were determined from their Mossbauer spectra The quadrupole splittings (except for Sm), isomer shifts, Curie temperatures, and internal fields vary regularly with the ionic radius of R

S. Shtrikman

Papers

The theory of the Vogel-Fulcher law of spin glasses

Observation of electron hopping in 151Eu3S4 by Mössbauer spectroscopy

Magnetic Properties of an Antiferromagnetic Orthoferrite

Magnetic structure of some rare-earth orthochromites

Differential Thermal Analysis and Mössbauer Studies in Rare‐Earth Orthoferrites