This review describes a new paradigm of electronics based on the spin degree of freedom of the electron. Either adding the spin degree of freedom to conventional charge-based electronic devices or using the spin alone has the potential advantages of nonvolatility, increased data processing speed, decreased electric power consumption, and increased integration densities compared with conventional semiconductor devices. To successfully incorporate spins into existing semiconductor technology, one has to resolve technical issues such as efficient injection, transport, control and manipulation, and detection of spin polarization as well as spin-polarized currents. Recent advances in new materials engineering hold the promise of realizing spintronic devices in the near future. We review the current state of the spin-based devices, efforts in new materials fabrication, issues in spin transport, and optical spin manipulation.

http://science.sciencemag.org/content/sci/294/5546/1488.full.pdf

Spintronics: a spin-based electronics vision for the future.

On a generalised approach to first and second order magnetic transitions

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

Magnetocaloric effect: From materials research to refrigeration devices

The exchange interaction that gives rise to ordered magnetic states depends upon interatomic spacing. If the lattice is deformable, then a spontaneous distortion of the lattice will occur in the ordered state. We have calculated, in the molecular field approximation, the properties of a system in which the exchange energy dependence is given by ${T}_{c}={T}_{0}[1+\frac{\ensuremath{\beta}(v\ensuremath{-}{v}_{0})}{{v}_{0}}]$. ${T}_{c}$ is the Curie temperature appropriate to a lattice volume $v$ while ${v}_{0}$ is the equilibrium volume in the absence of magnetic interactions. The course of the magnetization with temperature of such a system depends upon the steepness $\ensuremath{\beta}$ of the exchange interaction dependence on interatomic distance, the compressibility $K$, and ${T}_{0}$. The behavior may be the usual second-order transition to paramagnetism, but it can in fact become a first-order transition with the properties usually associated thereto, e.g., latent heat and discontinuous density change. In the absence of an externally applied pressure, the transition will be of the first order if $\ensuremath{\eta}\ensuremath{\equiv}\frac{40NkK{T}_{0}{\ensuremath{\beta}}^{2}{[j(j+1)]}^{2}}{[{(2j+1)}^{4}\ensuremath{-}1]}g1$. In this inequality, $N$ is the number per unit volume of magnetic ions of angular momentum $j\ensuremath{\hbar}$ while $k$ is the Boltzmann constant.We have reviewed the experimental evidence on the nature of the first-order magnetic transition in MnAs. We find that this evidence indicates the transition to be one from ferromagnetism to paramagnetism rather than ferromagnetism to antiferromagnetism as has been generally assumed. Application of the theory noted above gives $\ensuremath{\eta}=2$ for this transition. In addition, we derive a value for the volume strain sensitivity, $\ensuremath{\beta}=19$ and infer the compressibility to be 2.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{2}$/d.

Magnetic Disorder as a First-Order Phase Transformation

This paper describes an experimental and theoretical examination of a 10-\ensuremath{\mu}g $c$-axis-oriented single crystal of MnAs. The critical magnetic field for the first-order transition to the ferromagnetic phase has been measured as a function of temperature (15 to 65\ifmmode^\circ\else\textdegree\fi{}C) and pressure (0 to 1000 bars gauge), using miniature-coil pulsed fields to 110 kOe. Data analysis substantiates the thesis of the recent Bean-Rodbell theory on magnetic first-order phase transitions that the transition in MnAs near 45\ifmmode^\circ\else\textdegree\fi{}C is between ferromagnetic and paramagnetic phases and arises from a sufficiently sensitive dependence of exchange energy on lattice strain and a sufficiently high compressibility. The match between theory and experiment yields a compressibility $K$ of 4.55\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ ${\mathrm{dyn}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{2}$, a lattice thermal expansion coefficient $\ensuremath{\alpha}$ of 5.71\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$/\ifmmode^\circ\else\textdegree\fi{}C, an apparent paramagnetic Curie temperature ${{T}_{0}}^{*}$ of 277.1\ifmmode^\circ\else\textdegree\fi{}K, and a Curie-temperature dependence on volume strain, $\ensuremath{\beta}[\ensuremath{\equiv}(\frac{d{T}_{c}}{{T}_{0}}){(\frac{\mathrm{dV}}{{V}_{0}})}^{\ensuremath{-}1}]$, of 18.9, where ${T}_{0}$ is the Curie temperature of the unstrained specimen at 0\ifmmode^\circ\else\textdegree\fi{}K. Discrepancies in the match suggest a primary need to include short-range order in the theory. Auxiliary experiments show the magnetocrystalline anisotropy sum, ${K}_{1}+2{K}_{2}+3{K}_{3}$, to be about -7.6 and -12.0\ifmmode\times\else\texttimes\fi{}${10}^{6}$ ergs/${\mathrm{cm}}^{3}$ at 299 and 77\ifmmode^\circ\else\textdegree\fi{}K, respectively.

Magnetic First-Order Phase Transition in Single-Crystal MnAs

The experimental and theoretical effects of magnetocrystalline anisotropy upon the magnetic first‐order phase transition in the compound MnAs are here described. A 3°C orientation‐dependent difference in the transition temperature is observed near 20 kOe for a single‐crystal specimen. Anisotropy measurements using Shenker's method give anisotropy sums, ΣnnKn, varying from −11.9×106 ergs/cm3 at 77°K to −5.6× 106 ergs/cm3 at 314°K, where Kn are the anisotropy terms in the energy representation, EK=ΣnKn sin2nθ, that is appropriate for this hexagonal material. A separate method gives an anisotropy field of 18.3 kOe at 35°C. Data analysis indicates that three constants, K1, K2, and K3, are needed to describe the anisotropy. Their values at 35°C are −5.75, +1.5, and −1.15×106 ergs/cm3, respectively. Theoretical checks using the magnetic form of the Clausius‐Clapeyron equation are in close accord with the experimental data and the determined constants.

Magnetic First‐Order Phase Transition and Anisotropy in Single‐Crystal MnAs

The nuclear magnetic resonance spectrum of ${\mathrm{Co}}^{59}$ in metallic powders is presented. This spectrum contains three lines in addition to the already well-known line of ${\mathrm{Co}}^{59}$ in face-centered cubic cobalt (213.1 Mc/sec at 25\ifmmode^\circ\else\textdegree\fi{}C). The other lines are higher in frequency, the highest located 10.0 Mc/sec above the fcc resonance and is much less intense than the fcc. This highest lying resonance is identified to be due to ${\mathrm{Co}}^{59}$ nuclei in hexagonal close-packed cobalt, and we qualitatively account for the lower intensity by examining the effect on the resonance of the nuclear quadrupole moment in a noncubic environment.

D. S. Rodbell

Papers

Magnetic Disorder as a First-Order Phase Transformation

Magnetic First-Order Phase Transition in Single-Crystal MnAs

Magnetic First‐Order Phase Transition and Anisotropy in Single‐Crystal MnAs

Nuclear Magnetic Resonance Spectrum of Co 59 in Metallic Cobalt Powders