Derivation of phenomenological expressions for transition matrix elements for electron-phonon scattering

In the literature on electron-phonon scatterings very often a phenomenological expression for the transition matrix element is used which was derived in the textbooks of Ashcroft/Mermin and of Czycholl. There are various steps in the derivation of this expression. In the textbooks in part different arguments have been used in these steps, but the final result is the same. In the present paper again slightly different arguments are used which motivate the procedure in a more intuitive way. Furthermore, we generalize the phenomenological expression to describe the dependence of the matrix elements on the spin state of the initial and final electron state

Electronic correlations in vanadium chalcogenides: BaVSe3 versus BaVS3

Albeit structurally and electronically very similar, at low temperature the quasi-one-dimensional vanadium sulfide BaVS3 shows a metal-to-insulator transition via the appearance of a charge-density-wave state, while BaVSe3 apparently remains metallic down to zero temperature. This different behavior upon cooling is studied by means of density functional theory and its combination with the dynamical mean-field theory and the rotationally-invariant slave-boson method. We reveal several subtle differences between these chalcogenides that provide indications for the deviant behavior of BaVSe3 at low temperature. In this regard, a smaller Hubbard U in line with an increased relevance of the Hund's exchange J plays a vital role.Comment: 16 pages, 11 figures, published versio

Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions

A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic corrections. The analysis focuses primarily on the odd sector of the model (i.e., that associated with magnetic exponents), and in particular on its Lee-Yang zeros, which are determined to high accuracy. Scaling relations are used to connect to the even (thermal) sector, and a first analysis of the density of zeros yields information on the specific heat and its corrections. The analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections.Comment: 15 pages, 3 figures. Published versio

Magnetism in systems with various dimensionality: A comparison between Fe and Co

A systematic ab initio study is performed for the spin and orbital moments and for the validity of the sum rules for x-ray magnetic circular dichroism for Fe systems with various dimensionality (bulk, Pt-supported monolayers and monatomic wires, free-standing monolayers and monatomic wires). Qualitatively, the results are similar to those for the respective Co systems, with the main difference that for the monatomic Fe wires the term in the spin sum rule is much larger than for the Co wires. The spin and orbital moments induced in the Pt substrate are also discussed.Comment: 4 page

Effective critical behaviour of diluted Heisenberg-like magnets

In agreement with the Harris criterion, asymptotic critical exponents of three-dimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration- and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field--theoretical renormalization group approach to explain this observation and to calculate the effective critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point $T_c$ as observed experimentally. In the asymptotic limit (at $T_c$) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion.Comment: 15 pages, 4 figure

Random Exchange Quantum Heisenberg Chains

The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite size systems.Comment: 13 pages, RevTex, 12 figures available on request ([email protected]

Calculation of magnetic anisotropy energy in SmCo5

SmCo5 is an important hard magnetic material, due to its large magnetic anisotropy energy (MAE). We have studied the magnetic properties of SmCo5 using density functional theory (DFT) calculations where the Sm f-bands, which are difficult to include in DFT calculations, have been treated within the LDA+U formalism. The large MAE comes mostly from the Sm f-shell anisotropy, stemming from an interplay between the crystal field and the spin-orbit coupling. We found that both are of similar strengths, unlike some other Sm compounds, leading to a partial quenching of the orbital moment (f-states cannot be described as either pure lattice harmonics or pure complex harmonics), an optimal situation for enhanced MAE. A smaller portion of the MAE can be associated with the Co-d band anisotropy, related to the peak in the density of states at the Fermi energy. Our result for the MAE of SmCo5, 21.6 meV/f.u., agrees reasonably with the experimental value of 13-16 meV/f.u., and the calculated magnetic moment (including the orbital component) of 9.4 mu_B agrees with the experimental value of 8.9 mu_B.Comment: Submitted to Phys. Rev.

Universality, frustration and conformal invariance in two-dimensional random Ising magnets

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferro- and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $\gamma/\nu$, $\alpha/\nu$ and $\nu$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure--Ising exponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point along either the temperature axis or the Nishimori line, one finds non-diverging specific heats. A percolation-like ratio $\gamma/\nu$ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems.Comment: RevTeX code for 10 pages, 9 eps figures, to appear in Physical Review B (September 1999

Critical properties of random anisotropy magnets

The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different theoretical approaches give evidence for a second order phase transition for anisotropic distributions of the local anisotropy axes, while for the case of isotropic distribution such transition is absent. This outcome is described by renormalization group in its field theoretical variant on the basis of the random anisotropy model. Considerable attention is paid to the investigation of the effective critical behaviour which explains the observation of different behaviour in the same universality class.Comment: 41 pages, 10 figure