Search Results (68 total)

The interpretation given in our recent x-ray scattering study of Pr_1-xCa_xMnO₃ in terms of charge and orbital ordering is questioned in the preceeding Comment by Garcia and Subias. They argue that anisotropy of the charge distribution induced by local distortions gives rise to the so-called charge order reflections. In this Reply we suggest that the two different pictures are reconcilable.

We present the results of a systematic x-ray scattering study of the charge and orbital ordering in the manganite series Pr_1-xCa_xMnO₃ with x=0.25, 0.4, and 0.5. The temperature dependence of the scattering at the charge and orbital wavevectors, and of the lattice constants, was characterized throughout the ordered phase of each sample. It was found that the charge- and orbital-order wavevectors are commensurate with the lattice, in striking contrast to the results of electron and neutron diffraction studies of samples with x=0.5. High-momentum-transfer resolution studies of the x=0.4 and 0.5 samples further revealed that while long-range charge order is present, long-range orbital order is never established. Above the charge and orbital ordering temperature T₀, the charge-order fluctuations are more highly correlated than the orbital fluctuations. This suggests that charge order drives orbital order in these samples. In addition, a longitudinal modulation of the lattice with the same periodicity as the charge and orbital ordering was discovered in the x=0.4 and 0.5 samples. For x=0.25, only long-range orbital order was observed with no indication of charge ordering, nor of an additional lattice modulation. We also report the results of a preliminary investigation of the loss of charge and orbital ordering in the x=0.4 sample by application of a magnetic field. Finally, the polarization and azimuthal dependence of the charge and orbital ordering in these compounds are characterized both in the resonant and nonresonant limits, and compared with the predictions of current theories. The results are qualitatively consistent with both cluster and local density approximation +U calculations of the electronic structure.

We report resonant x-ray scattering studies of charge and orbital order in Pr_1-xCa_xMnO₃ with x  =  0.4 and 0.5. Below the ordering temperature, T_O  =  245 K, the charge and orbital order intensities follow the same temperature dependence, including an increase at the antiferromagnetic ordering temperature, T_N. High resolution measurements reveal, however, that long range orbital order is never achieved. Rather, an orbital domain state is formed. Above T_O, the charge order fluctuations are more highly correlated than the orbital fluctuations. We conclude that the charge order drives the orbital order at the transition.

Dipole resonant x-ray scattering from ordered Mn 3d orbitals in LaMnO₃ has been observed near the Mn K-absorption edge. The polarization of the scattered photons is rotated from σ to π^′ and the azimuthal angle dependence shows a characteristic twofold symmetry. A theory for the resonant scattering mechanism has been developed by considering the splitting of the Mn 4p levels due to the Mn 3d orbital ordering. The order parameter of the orbital ordering decreases above the Néel temperature ( T_N  =  140 K) and disappears at T_O  =  780 K, concomitant with a structural phase transition.

Large resonant magnetization-sensitive x-ray scattering is predicted to occur in the vicinity of L_II, L_III, and M_II-M_V absorption edges in the rare-earth and actinide elements, and at the K and L edges in the transition elements. These "magnetic" resonances result from electric multipole transitions, with the sensitivity to the magnetization arising from exchange. For some transitions, the magnetic scattering will be comparable to the charge scattering. The general features of the observed L_III resonance in Ho are discussed.

We calculate the polarization dependence of the x-ray scattering cross section, including magnetic terms, using the Poincaré representation for the polarization. General expressions are given for the polarization dependence of the cross section of the pure magnetic scattering and of the interference between charge and magnetic scattering, and for the polarization of the scattered beam in both cases. These expressions are compared to the equivalent results for magnetic neutron scattering. The general results are then specialized to several typical cases, including the scattering of linearly and circularly polarized radiation from spiral, uniaxially modulated, and ferromagnetic structures. It is shown that detailed magnetic-structure determinations are possible using synchrotron radiation. It is further demonstrated that the orbital- and spin-angular-momentum contributions of both ferromagnets and antiferromagnets may be separately measured in a variety of simple geometries. It is found that, although the efficiency is very low, linearly polarized radiation can be completely converted to circular polarization by scattering from a magnetic spiral. Finally, it is shown that, in addition to the interference between charge and magnetic scattering, there is an interference involving the spin- and orbital-angular-momentum scattering, which can couple moments in different spatial directions.

Densities of states are obtained for ∼ 10 000-atom three-dimensional alloy models with site-diagonal disorder, and the results are compared with the single-site coherent-potential approximation. The numerical approach contains several improvements over our previous calculations.

A detailed quantitative study of the low-temperature spin-wave dynamics has been made for the classical Heisenberg-coupled chain using computer simulation. Results for the relaxation rates are presented and compared with dynamic scaling and other predictions.

A general expression is given for the polarization density matrix of electromagnetic radiation emitted in the presence of fluctuating surroundings. This has been utilized to compute numerically the polarization state of the entire emission line within the framework of various stochastic models. It is concluded that polarization analysis of the Mössbauer lines can be a useful tool for the exploration of the hyperfine interactions and relaxation phenomena.

The order parameters which are induced in dysprosium aluminum garnet (DyAlG) by a direct magnetic field have been studied using group-theoretical techniques. We find seven order parameters which are induced by the field both above and below the transition. Four of these order parameters involve magnetic moments along local hard directions, and they represent deviations from the ideal Ising-like behavior of DyAlG. The results of the neutron-scattering experiment of Corliss and Hastings, obtained with magnetic field along the [111], [100], and [110] directions are discussed, and several experiments are suggested.

We have calculated the phase diagrams for an Ising antiferromagnet in an external field when the transverse g factors of the two sublattices are unequal. We find that the induced staggered magnetic field allows the external field to couple to the antiferromagnetic order parameter, preventing the occurrence of second-order phase transitions except at isolated critical points. Quantitative results based on mean-field theory are presented.

Using a sum-rule argument and calculations based on a self-consistent approximation for the correlation functions, we show that the electronic system can distort the NMR line shape and shift the peak frequency in exchange-coupled magnetic systems. This contribution to the line shape is especially important at low fields.

We report magnetic-form-factor measurements for Ir in the cubic antiferromagnet K₂IrCl₆ (T_N=3.05 K). Even though the Ir ions lie on an fcc lattice and are surrounded by octahedra of Cl, the magnetization density deviates strongly from the cubic symmetry that the charge density shows. This unusual asymmetry is dramatically magnified by the large amount of covalent bonding of the single 5d(t_2g) magnetic hole to the Cl₆ complex.

We have used computer simulations to study the dynamic behavior at infinite temperature of a threedimensional Heisenberg magnet with impurities. Computation has been done for the case of a simple-cubic lattice (maximum size: 27 × 27 × 27 spins) with nearest-neighbor exchange. The spin self-correlation function as well as the first four near-neighbor correlation functions are obtained for times t out to the order of 3/J. While it is not clear that these data may be extrapolated to obtain long-time behavior, particularly at low concentration, the self-correlation function appears to fall off less rapidly than the t^-3/2 law consistent with spin diffusion, even at concentrations well above the percolation limit.

A general two-beam dynamical theory of the elastic scattering of a thermal neutron from arbitrary magnetic structures is presented. Using a density-matrix formalism, general expressions are developed to compute the scattering cross section as well as the final state of polarization of the emerging neutron. Emphasis is placed on those features of scattering which arise due to the spin of the neutron. Detailed calculations have been carried out for spiral structures, ferromagnetic and antiferromagnetic spin arrangements, and the results are compared with those of kinematical theory. As an illustration, the calculation for the flipping ratio R for the MnF₂ (210) peak in the symmetrical Laue configuration indicates that according to dynamical theory R can take arbitrary values when the thickness of the crystal or wavelength of the incident neutron is varied.

A stochastic theory of line shape is considered for describing molecular reorientational processes in liquids. The theory takes into account both secular and nonsecular terms in the interaction Hamiltonian. A general solution for the line shape is given in a matrix form by assuming a Markovian modulation for the random process. The usefulness of the theory is demonstrated by doing perturbation theory calculations in the motionally narrowed limit. A resolvent-operator technique is employed for collecting higher-order terms in perturbation theory. Two models for molecular motion, (i) rotational diffusion and (ii) strong-collision approximation, are treated and their predictions compared. In the case of the rotational-diffusion model, the results are illustrated by considering a g-tensor interaction in liquids. Expressions for line width and shift are given up to fourth order in perturbation theory, and a detailed comparison is made with the existing theories.

The Ising chain with random bonds in a magnetic field H=-ΣiJ_iσ_iσ_i+1-hΣiσ_i, where J_i=± 1 at random, and ΣiJ_i=0, represents a model of a magnetic glass, or of heteropolymer melting. Calculations of the thermodynamic properties of the chain as a function of field strength and temperature have been performed by Monte Carlo techniques. These results are compared with perturbation calculations for small and large values of h/T. The Monte Carlo results show, in agreement with the perturbation calculations, that the field-induced magnetization is generally smaller for the random bond model than for a chain of noninteracting spins. As T→0 the magnetization approaches the result for noninteracting spins.

Densities of states and spectral functions are obtained for large (∼8000 atoms) three-dimensional alloy models with cell localized disorder and are compared with the single-site coherent-potential approximation (CPA). We find that the CPA agrees remarkably well with the exact numerical results. In particular, the overall structure of the electronic spectrum and the transition from one- to two-band behavior are well described. There is, however, some substructure which is not reproduced by the single-site approximation.

We present theoretical results for the thermodynamic properties and time-independent spin-spin correlation functions for the classical Heisenberg magnetic chain in an applied magnetic field. The calculations are performed by numerical solution of the transfer-matrix integral equation. In addition, approximate variational procedures and low-temperature expansions yield some analytic results. The procedures used are applicable to any near-neighbor interaction for classical spins in a linear chain. The most unusual behavior found is for antiferromagnetic coupling, where the specific heat shows oscillations as a function of field, and the longitudinal uniform susceptibility and the transverse staggered susceptibility increase with field for low fields.

Uniform magnetic fields may couple in higher order to the antiferromagnetic order parameter in a large class of compensated antiferromagnets. We describe this coupling as an induced staggered field. In this paper we give the general rules which determine when the coupling is allowed by the symmetry of the order parameter. We also discuss the dependence of the coupling on field direction. Some implications of these results for the behavior of transition-metal fluorides and for metamagnetic tricritical points are given. In particular we find that there is no induced staggered field in systems such as FeCl₂ while a coupling is expected in FeCO₃ and FeF₂, as well as in the recently discussed case of dysprosium aluminum garnet. In all these systems, however, the staggered field should vanish along certain symmetry directions for which metamagnetic tricritical points should exist.

The random-phase-approximation result derived in the preceding paper is used to study the EPR line shape of CO₂^- defects in CaCO₃. Relaxation is caused by a thermally activated mechanism due to which the oxygen ions hop between three equivalent sites in the (111) plane. As a result, the Zeeman Hamiltonian jumps at random between three different forms with equal probability. The calculated spectra for different values of the relaxation rate agree well with the experimental results of Hughes and Soos. At high temperatures, an additional spin-relaxation mechanism is shown to account for the observed residual linewidth when the external magnetic field is along the crystal trigonal axis.