The spin-Hamiltonian (SH) parameters for the ${}_{}{}^4{}_{}{}^{}$${\mathit{A}}_2$(F) state of 3${\mathit{d}}^3$/3${\mathit{d}}^7$ ions for tetragonal and trigonal symmetries are studied as a function of the crystal-field (CF) parameters based on simultaneous diagonalization of the electrostatic, CF, and the spin-orbit-coupling Hamiltonians. The results obtained are compared to those in earlier works. The CF and SH parameters of ${\mathrm{Cr}}^{3+}$ ions at the A and M vacancies and at codoped ${\mathrm{Li}}^{+}$ sites in the cubic fluoroperovskites AM${\mathrm{F}}_3$ are investigated by taking into account the contributions of the defects and the defect-induced lattice distortion. Suitable models are proposed for the lattice distortion, and the distortion parameters are obtained by adjusting them to fit to the observed data for the SH parameters and the energy of the first excited state.

Finite-size effects in the correlation function G(R,T;L) of a spherical-model ferromagnet, confined to geometry ${\mathrm{L}}^{\mathrm{d}\mathrm{-}\mathrm{d}\prime }$×${\mathrm{\infty }}^{\mathrm{d}\prime }$ (2<d<4,d′⩽2) and subjected to twisted boundary conditions, are analyzed. Focusing our attention on the region of first-order phase transition (T<${\mathrm{T}}_{\mathrm{c}}$), we examine the influence of the twist parameter τ on the function G(R,T;L) in different regimes of the distance parameter ɛ (=R/L). We find that the functional dependence of the function G on the parameter ɛ is highly anisotropic, in that it depends very differently on the components, ${\mathrm{\varepsilon }}_{\mathrm{\perp }}$ and ${\mathrm{\varepsilon }}_{\mathrm{\parallel }}$, of ɛ pertaining to the finite and the infinite directions, respectively. While the long-range order in the direction of ${\mathrm{\varepsilon }}_{\mathrm{\perp }}$ is significantly altered by the parameter τ, it is curtailed very seriously in the direction of ${\mathrm{\varepsilon }}_{\mathrm{\parallel }}$. In fact, for ${\mathrm{\varepsilon }}_{\mathrm{\parallel }}$≫1, the qualitative features of the correlation function acquire characteristics of a d′-dimensional bulk system, though the correlation length ξ appearing therein still pertains to the actual, finite-sized system. The net result is that long-range order in the direction of ${\mathbf{R}}_{\mathrm{\parallel }}$ persists only to distances small in comparison with ξ which, for d′<2, is known to be O{L(L/a${)}^{\left(\mathrm{d}\mathrm{-}2\right)/(2\mathrm{-}\mathrm{d}\prime )}$}, a being the lattice constant.

The observation of spin-dependent photoelectron diffraction using circularly polarized x rays is reported for Fe films on Cu(001). Circularly polarized x rays produce spin-polarized photoelectrons from the Fe 2p doublet, and intensity asymmetries in the 2${\mathit{p}}_{3/2}$ level are observed. Fully spin-specific multiple-scattering calculations reproduce the experimentally determined energy and angular dependences. An analytical procedure is introduced which removes exchange shift contributions to the Fe 2p asymmetry, and focuses instead upon intensity variations due to spin-dependent diffraction.

The spatial distributions of magnetization (i.e., domain structures due to magnetic interaction) in metals under conditions of strong de Haas–van Alphen (dHvA ) oscillations at any magnetic field within the period of magnetic oscillations (PMO) are investigated. At fields away from the center of the PMO the distribution of magnetization is markedly different from the well-known strictly symmetrical domains, which exist only at the center of the PMO. For temperatures near the diamagnetic phase transition distributions of magnetization without sharp domain walls are found. Similar results are predicted for domain structures in uniaxial ferroelectrics or ferromagnetics. The discovered structures are strongly asymmetrical with narrow spikelike domains separating wide domains of opposite magnetization. Spikelike domains of more complex structures, which may be important in kinetic processes, are obtained at sufficiently low temperatures. In contrast to the existing theory, which yields a temperature-independent magnetic susceptibility below the phase transition, we find a minimum in the spatially averaged differential susceptibility just below the phase transition, which reflects strong interactions between diamagnetic domain walls. The form and magnitude of the calculated dHvA oscillations is in good agreement with the experimentally observed magnetic oscillations in gold, which exhibit significant deviations from the Lifshitz-Kosevich theory.

The tetragonal intermetallic compounds ${\mathrm{U}}_2$${\mathrm{Pd}}_2$In and ${\mathrm{U}}_2$${\mathrm{Pd}}_2$Sn have been studied by means of magnetic susceptibility, magnetization, specific heat, electrical resistivity, and x-ray- and neutron-diffraction techniques. The compounds order antiferromagnetically at 36 and 41 K, respectively, and have enhanced electronic specific-heat coefficients γ of 393 and 203 mJ/mol f.u. ${\mathrm{K}}^2$, respectively. At low temperature, the nearest-neighbor U-U spacing is along the c axis in both compounds, though in ${\mathrm{U}}_2$${\mathrm{Pd}}_2$Sn the in-plane U-U distance is shorter at room temperature. This crossover is due to motion of the U atoms within the cell rather than anisotropy of the thermal contraction. It is now well established in several classes of (1:1:1) uranium ternary intermetallic compounds that the strong magnetic anisotropy is correlated with the direction of nearest-neighbor U-U links; the moments are almost invariably oriented perpendicular to such links. This is also the case for ${\mathrm{U}}_2$${\mathrm{Pd}}_2$In and ${\mathrm{U}}_2$${\mathrm{Pd}}_2$Sn, where the moments lie in the tetragonal basal plane in a canted arrangement along [110] and [11¯0] directions. Of four such Shubnikov subgroups of P4/mbm, one is clearly preferred by the data. At 10 K, the magnetic moments extracted are (1.6±0.2)${\mathrm{\mu }}_{\mathit{B}}$ and (2.0±0.1)${\mathrm{\mu }}_{\mathit{B}}$ per U atom in ${\mathrm{U}}_2$${\mathrm{Pd}}_2$In and ${\mathrm{U}}_2$${\mathrm{Pd}}_2$Sn, respectively.

We examine the effects of vacancies on a triangular spin-1/2 antiferromagnet within spin-wave theory. We find that frustration is dominant in determining the properties of the defective lattice. For a single vacancy the on-site magnetization is significantly modified over a large region. For more than one vacancy the change in the magnetization is found to depend on their relative positions and not simply on their distance of separation. The qualitative behavior may be understood in terms of the relief of frustration. We also consider kagome$iaa— patches of various sizes embedded in an infinite triangular lattice, and find that the change in the density of states leads to a low-temperature peak in the specific heat.

Theoretical and experimental results are presented for high-resolution frequency scans of 45° oblique-incidence far-infrared reflectivity spectra of ${\mathrm{FeF}}_2$ in the vicinity of the antiferromagnetic resonance frequency. The magnetic field is vertical and the plane of incidence horizontal. Calculations are presented and illustrated numerically for an arbitrary angle θ between the crystal c axis and the magnetic field ${\mathit{H}}_0$. The main point of principle is that the equilibrium spin configuration and therefore the magnetic susceptibility depend on θ. The reflectivity R is nonreciprocal, i.e., R(-${\mathit{H}}_0$)≠R(${\mathit{H}}_0$). For θ=0° magnetic features are seen only in s polarization (E field vertical), but otherwise they are seen in both polarizations. Except for θ=0° and 90° weak s to p and p to s reflections are predicted. We discuss the instrumental developments required for the high resolution that is necessary for this spectroscopy. Experimental results for θ=45° are presented (θ=0° and 90° are in a previous publication). The whole range of spectra, including the s to p and p to s reflections, are accounted for with the same set of parameters as were used previously to fit the θ=0° and 90° results.

We present numerical results for the magnetic susceptibility of a Heisenberg antiferromagnetic spin ladder as a function of temperature and the spin-spin interaction strengths ${\mathit{J}}_{\mathrm{\perp }}$ and ${\mathit{J}}_{\mathrm{\parallel }}$. These are contrasted with bulk-limit results for the dimer chain. A fit to the experimental susceptibility of the candidate spin-ladder compound vanadyl pyrophosphate, (VO${)}_2$${\mathrm{P}}_2$${\mathrm{O}}_7$, gives the parameters ${\mathit{J}}_{\mathrm{\perp }}$=7.82 meV and ${\mathit{J}}_{\mathrm{\parallel }}$=7.76 meV. With these values we predict a singlet-triplet energy gap of ${\mathit{E}}_{\mathrm{gap}}$=3.9 meV, and give a numerical estimate of the ladder triplet dispersion relation ω(k). In contrast, a fit to the dimer-chain model leads to ${\mathit{J}}_1$=11.11 meV and ${\mathit{J}}_2$=8.02 meV, which predicts a gap of ${\mathit{E}}_{\mathrm{gap}}$=4.9 meV.

Bulk ferromagnetic microprobes, as commonly used in magnetic force microscopy, have been analyzed by electron holography. Using the double exposure technique, detailed holograms have been obtained from nickel probes. The resulting two-dimensional interferograms can be well reproduced by numerical calculations which are based on the assumption that the probes stray field is produced by a macrodipole of several micrometers in length. By treating the dipole charge as a variational free parameter to be fitted against the experimental data, it is possible to determine the stray field produced by the probes, their effective leakage flux, and the surface area of a sample which may seriously be affected by the probes stray field. The results are considered especially important for those applications of magnetic force microscopy where the sample is likely to be magnetically perturbed by the stray field which is produced by the imaging probe itself.

The most general spin-3/2 Ising model with up-down symmetry is investigated on a honeycomb lattice. The partition function on a surface in the space spanned by the coupling constants J, K, L, and M was found exactly. The explicit expression for the quadrupolar order parameter with the inclusion of an external crystal field of strength Δ is obtained. It is shown that this order parameter exhibits in general a simple power-law dependence on T-${\mathit{T}}_{\mathit{c}}$ near ${\mathit{T}}_{\mathit{c}}$.

A Mössbauer-effect experiment, with γ-ray wave vector k directed both along and normal to the c axis of a siderite (${\mathrm{FeCO}}_3$) single-crystal platelet, has been systematically performed in the temperature range 50<T<300 K. The T dependence of the integrated area S(T)=${\mathit{S}}_{\mathrm{\pi }}$(T)+${\mathit{S}}_{\mathrm{\sigma }}$(T) under the quadrupole doublet reveals that at 300 K the Debye-Waller factors are ${\mathit{f}}_{\mathit{c}}$=0.72(2) and ${\mathit{f}}_{\mathrm{\perp }\mathit{c}}$=0.75(2). Independently, the area ratios ${\mathit{S}}_{\mathrm{\pi }}$/${\mathit{S}}_{\mathrm{\sigma }}$ under the π and σ quadrupole components, measured at 300 K, confirm the lack of a spatial anisotropy of the f factor but, more significantly, confirm the theoretically predicted polarization-dependent resonant-absorption cross section in transmission through the crystal.

Schwinger-boson mean-field theory (SBMFT) is discussed for the two-dimensional antiferromagnetic Heisenberg model with a square lattice. It is known that the SBMFT violates the local constraint of the Schwinger-boson number. In this paper, by means of the projector technique, an exact and direct result is given for the distributions and fluctuations in the local Schwinger-boson number.

We discuss the problem of static chaos in spin glasses. In the case of magnetic-field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free-energy cost is determined by the finite-temperature fixed-point exponents. In this framework, numerical results suggest that mean-field chaos exponents are probably exact in finite dimensions. If we use the droplet approach, numerical results suggest that the zero-temperature fixed-point exponent θ is very close to (d-3)/2. In both approaches d=3 is the lower critical dimension in agreement with recent numerical simulations.

We investigate through Monte Carlo simulations the critical behavior of the antiferromagnetic Heisenberg model on a hexagonal lattice. Critical exponents associated with both magnetic and chiral orderings were estimated. The transition temperatures of these two kinds of order were found to be the same within error margins, in agreement with previous results. The calculation of the Binder parameter also demonstrates that the transition is most likely continuous. The exponents obtained agree, for the most part, with those of Kawamura and thus provide further support for the existence of a new universality class.

The dynamics of spin waves in dilute Heisenberg magnets becomes critical at concentrations p near the percolation threshold ${\mathit{p}}_{\mathit{c}}$ where, by virtue of the divergence of the percolation correlation length ξ, the systems become self-similar. The resulting crossover in dispersion relation and density of states from hydrodynamic to critical behavior affects static thermal properties influenced by excitation of spin waves. In a previous work we showed that, in fact, the crossover in dynamics induces a crossover in the magnetization behavior. In this work we investigate the effects of the dynamic crossover on another thermal property, the specific heat. The study of the specific heat involves new aspects since it includes the contribution of the excitations on the whole distribution of finite clusters, besides the contribution of the excitations on the infinite cluster, while the magnetization involves only the excitations on the infinite cluster. It is shown that for low temperatures T and small δp=(p-${\mathit{p}}_{\mathit{c}}$) the specific heat of a dilute ferromagnet at concentrations p>${\mathit{p}}_{\mathit{c}}$ is C(p,T)=δ${\mathit{p}}^{\nu \mathit{d}}$g(δ${\mathit{p}}^{\nu \mathit{z}}$J/${\mathit{k}}_{\mathit{B}}$T), where ν is the percolation-correlation-length exponent, z the dynamic critical exponent, d the Euclidean dimensionality, and J the exchange constant. At concentrations p<${\mathit{p}}_{\mathit{c}}$ no crossover is observed because of the structure of the cluster. The different asymptotic forms of the scaling function g(y) for y≪1 and y≫1 imply a crossover in the specific heat from standard hydrodynamic behavior ${\mathit{T}}^{\mathit{d}/2\mathrm{}}$, however, with a nontrivial δp-dependent coefficient because of mode softening, for T<${\mathit{T}}^{\mathrm{*}}$(p), to an anomalous behavior ${\mathit{T}}^{\mathit{d}/\mathit{z}}$ for T>${\mathit{T}}^{\mathrm{*}}$(p), where the crossover temperature is ${\mathit{T}}^{\mathrm{*}}$(p)∝δ${\mathit{p}}^{\nu \mathit{z}}$. This crossover, similar to that found previously for the magnetization, is additional to the usual percolation-thermal crossover which determines the transition temperature ${\mathit{T}}_{\mathit{c}}$(p).

A detailed study of magnetoresistance and magnetization is reported on the Laves-phase compound Ce(${\mathrm{Fe}}_{0.92}$${\mathrm{Al}}_{0.08}$${)}_2$ in the temperature range of 4.4 to 250 K and in magnetic fields up to 45 kOe. The measurements indicate a paramagnetic to ferromagnetic transition at 170 K and rule out the possibility of a spin-glass transition as had been earlier reported in some studies. The magnetoresistance measurements clearly indicate that the compound has an antiferromagnetic state below 100 K as suggested by earlier neutron-scattering measurements. The antiferromagnetic state is found to undergo a metamagnetic transition which could be observed in the present study above 60 K.

For the spin-1/2 Heisenberg antiferromagnet on the kagomé lattice we calculate the high-temperature series for the specific heat and the structure factor. A comparison of the series with exact-diagonalization studies shows that the specific heat has further structure at lower temperature in addition to a high-temperature peak at T≊2/3. At T=0.25 the structure factor agrees quite well with results for the ground state of a finite cluster with 36 sites. At this temperature the structure factor is less than two times its T=∞ value and depends only weakly on the wave vector q, indicating the absence of magnetic order and a correlation length of less than one lattice spacing. The uniform susceptibility has a maximum at T≊1/6 and vanishes exponentially for lower temperatures.

The spin-wave stiffness ${\mathrm{\rho }}_{\mathit{s}}$ of the Heisenberg antiferromagnet at zero temperature is calculated in two ways, by spin-wave theory and by series expansion about the Ising limit, extending previous results. The two methods give values of ${\mathrm{\rho }}_{\mathit{s}}$ for the isotropic model which are in good agreement, and which satisfy the hydrodynamic relation.

We present a selection rule for matrix elements of local spin operators in the S=1/2 Haldane-Shastry model. Based on this rule we extend a recent exact calculation by Haldane and Zirnbauer of the ground-state dynamical spin correlation function ${\mathit{S}}^{\mathit{a}\mathit{b}}$(n,t)=〈0‖${\mathit{S}}^{\mathit{a}}$(n,t)${\mathit{S}}^{\mathit{b}}$(0,0)‖0〉 and its Fourier transform ${\mathit{S}}^{\mathit{a}\mathit{b}}$(Q,E) of this model to a finite magnetic field. In zero field, only two-spinon excitations contribute to the spec tral function; in the (positively) partially spin-polarized case, there are two types of elementary excitations: spinons (Δ${\mathit{S}}^{\mathit{z}}$=±1/2) and magnons (Δ${\mathit{S}}^{\mathit{z}}$=-1). The magnons are divided into left- or right-moving branches. The only classes of excited states contributing to the spectral functions are (I) two spinons, (II) two spinons+one magnon, (IIIa) two spinons+two magnons (moving in opposite directions), and (IIIb) one magnon. The contributions to the various correlations are ${\mathit{S}}^{\mathrm{-}+}$: (I); ${\mathit{S}}^{\mathit{z}\mathit{z}}$: (I)+(II); ${\mathit{S}}^{+\mathrm{-}}$: (I)+(II)+(III). In the zero-field limit there are no magnons, while in the fully polarized case, there are no spinons. We discuss the relation of the spectral functions to correlations of the Calogero-Sutherland model at coupling λ=2.

We present an effective electromagnetic Lagrangian in a charged anyon gas at arbitrary temperature, which enables us to study the electromagnetic properties of the anyonic system at both zero and finite temperature (i.e., in the superconductive and the normal phases) with equal facility. The temperature dependences of magnetic and dielectric permeabilities are derived. It is shown directly how the particle excitations are ‘‘dressed’’ to become electromagnetic vortices. The induced quantum numbers of those excitations are found at arbitrary T.