The magnetization σ of the ferromagnetic compound CrO2 was measured as a function of field H and temperature T near the Curie point Tc. From isotherms of σ2 vs H/σ, the initial susceptibility χ0 above Tc was obtained, which when tested against the relationship χ0−1 ∝ (T−Tc)γ gives a constant γ of 1.63±0.02 from just above Tc (386.5°K) up to about 1.15 Tc. This γ value contrasts with the values near43 recently computed for the Heisenberg model and later found experimentally in various ferromagnetic metals and compounds. At higher temperatures the effective γ decreases rapidly towards unity. Up to the highest field used (25 kOe), the critical isotherm obeys the relationship σ∝H1/δ with δ=5.75±0.05, which differs markedly from the theoretical δ values of 3 (molecular field) and 5.2 (3-dimensional Ising) and from various experimental values. Gradual departure from this relationship below 1.5 kOe is attributed to the magnetocrystalline anisotropy that persists at Tc. Furthermore, we find that all the σ(H, T) data for CrO2 just above Tc can be represented by a universal function of the form, σ/σ′=f(H/H′), in which σ′ ∝ (T−Tc)λ and H′ ∝ (T−Tc)λ+γ, where λ=0.34. This ``corresponding states'' representation is the exact magnetic analog of an equation of state recently proposed by Widom for a fluid near its critical point.

The magnetization-field-temperature characteristics of Cr${\mathrm{O}}_{2}$ and nickel just above their ferromagnetic Curie points, though quantitatively very different, are found to obey the same special type of equation of state, which is isomorphic with that recently proposed for the critical-point behavior of a fluid.

This paper describes the observations and associated analyses of the microwave resonance absorption of very small, apparently highly perfect, single crystal samples of ferromagnetic metals. The primary focus of this study is on nickel but iron and cobalt are also considered. From the point of view of magnetic resonance, the observed narrow line-widths of these samples suggests that they are of high quality compared to bulk material. The general conclusions drawn are that the limited penetration of the microwave energy into a conducting ferromagnet makes an important contribution to the observed resonance absorption linewidth and shape. A damping term of the Landau-Lifshitz form is also identified and gives, quite accurately, the observed linewidth and shape behaviour both in temperature and frequency; this without an explicit temperature or frequency dependence of the damping `constant'. There is no evidence for surface spin pinning being present and, in fact, strong experimental evidence against it playing a role in these studies is presented. The magnetocrystalline anisotropy constants and the g value of nickel metal are deduced from the data. Both ${K}_{1}$ and ${K}_{2}$ are found to be negative over the entire range studied ($\mathit{130}\ifmmode^\circ\else\textdegree\fi{}$ to $\mathit{635}\ifmmode^\circ\else\textdegree\fi{}K$) and both have rapidly decreasing magnitudes with increasing temperature. The spectroscopic splitting factor, g, is determined to be $\mathit{2.22}\ifmmode\pm\else\textpm\fi{}\mathit{.03}$ and is independent of temperature and frequency.

Gadolinium metal is a system of relative simplicity as far as exchange interactions and ionic states are concerned. The 8S7/2 state of Gd3+ is consistent with the observed 7μb/atom and the moment contributing f electrons are most likely exchange coupled via conduction electrons. The present work concerns the measurement of the ferromagnetic resonance behavior of a single crystal at frequencies of 21 and 35 Gc/sec and at temperatures from above the Curie point (20°C) to 4.2°K. The resonance absorptions are well defined at both frequencies and at all temperatures for most crystal orientations. The minimum linewidth observed is about 400 Oe but the line shape and width degrade when the applied field departs from the easy axis, particularly at the lower frequency and at low temperatures. Strong, well-defined domain wall resonances are also frequently observed. The deduced magnetocrystalline anisotropy energy is accurately described by the standard uniaxial expansion EA = K1 sin2θ+K2 sin4θ+⋯, about the hexagonal axis. The anisotropy constants derived from the resonance data agree reasonably well with those measured by Graham1 using static torque methods. The samples used in these experiments are from the same source.2 The demagnetization fields at the surface of the coin-shaped sample are measured directly from the shift in the resonance field of a small chip of the free radical DPPH in intimate contact with the sample surface.3 The corresponding demagnetization factors lie between that calculated by Schlömann4 for a uniformly magnetized right cylinder (an accurate description of our sample shape) and that calculated for an oblate spheroid of the same axial ratio, tending toward the latter at low temperatures. Using the magnetization measurements of Graham (as a function of temperature and applied field) we find that the spectroscopic splitting factor, g, is 2.00±0.02 below 0°C, changing smoothly to 1.94±0.02 at 28°C in the paramagnetic region. This latter values agrees well with those reported by Kip5 and by Popplewell and Tebble.6 The g value at low temperatures, also deduced from the resonance data, gives better (but still not exact) agreement between the directly measured saturation magnetization and that implied by the 8S7/2 ionic state.

If in the Heisenberg interaction J (S̄a·S̄b), J is separation dependent and the lattice is distortable, then an extended system of arbitrary angular momentum yields more long-range order at a given temperature than the molecular field predicts for the ``clamped crystal.'' Both MnO and NiO show such departures from molecular field prediction and earlier estimates based on isotropic deformations could not account for the observed behavior. Anisotropic deformations have not previously been considered in this regard. The form of these anisotropic distortions is a contraction along the [111] crystallographic direction perpendicular to the sublattice magnetization. In NiO this trigonal deformation corresponds to a change in angle of the original cubic cell from 90° to 90°06′. This distortion accounts for only a small part of the sublattice magnetization's deviation from molecular field prediction. For MnO, on the other hand, neutron diffraction data indicate that this angle is as large as 90°26′, a distortion that would account for about a third of the observed estimate. We have made a direct x-ray diffraction measurement of this deformation and fully confirm this value. The x-ray data supply additional evidence that the disordering transition in MnO is thermodynamically of first order.

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.

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.

The high magnetic field behavior of gadolinium metal and the comparison between that behavior and the predictions of the molecular field model are reported. Measurements were made on a c-axis oriented single crystal of gadolinium in pulsed fields to 140 k-oersted and over a range of temperatures.

Some transitions between ordered and disordered magnetic states that take place via transitions of first order are tabulated. Among these transitions are some of the order-disorder type. The theoretical basis for such a transition to occur is indicated using a simple physical model that assumes: (1) a strain dependent exchange interaction and (2) a compressible lattice. The necessary condition for first-order behavior is determined, and the theory is compared to the behavior of a real material, MnAs. It is found to be in substantial agreement with the behavior of that compound. The system represented by the simple model employed here possesses ferro-, antiferro-, and paramagnetic states. The equilibrium boundaries between these states are determined in the pressure-temperature plane as an illustration of the possible transitions that may be observed with this model.

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 $\ensuremath{\eta}\ensuremath{\equiv}\frac{40NkK{T}_{0}{\ensuremath{\beta}}^{2}{[j(j+1)]}^{2}}{[{(2j+1)}^{4}\ensuremath{-}1]}>1$. 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.