Pauli Spin Research Articles

ELECTRON CORRELATION EFFECT AT FINITE TEMPERATURE

The Gutzwiller variational scheme is extended to finite temperature by constructing an orthogonal set of trial functions for the correlated electrons and by deriving the entropy from the thermodynamic equations. The enhancements of the electron effective mass, the Pauli spin suscepti- bility and the Knight shift are obtained for the entire range of temperature and correlation strength. However, the electronic specific heat is enhanced only for k~ T/A 2 0.11 (A = bandwith). The theory is used to explain the experimental results on phosphorus-doped silicon.

Properties of chromium hydride

Measurements of the low-temperature electrical resistivity, magnetic susceptibility, and heat capacity, have been made on a non-stoichiometric chromium hydride sample of the composition CrH0.97, prepared by an electrochemical method. A T2-dependence of the electrical resistivity was observed in the low-temperature region, indicating an s-electron-paramagnon scattering to be the dominant factor contributing to the electrical resistivity. Heat capacity data show a high value of the electron density of states, (N(Ef) = 0.96 states per electron volt per chromium atom) and a much softer lattice as compared with pure Cr metal. Magnetic data show a stronglyenhanced Pauli spin susceptibility and a pronounced density of d-states at the Fermi level, associated with a peak at or near the Fermi level. Results of these measurements suggest that CrH0.97 is metal-like and that its electronic structure is similar to that of pure Pd metal.

Induced magnetic form factor of chromium

Expressions in terms of Bloch wave functions are derived for the induced nondiagonal magnetic susceptibility $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}},0)$. The expressions for the important contributions are shown to reduce in the tight-binding limit to the usual Pauli spin, Van Vleck orbital, and core diamagnetic terms. Each of these contributions was evaluated for Cr using augmented-plane-wave energy bands and wave functions. The results are in good agreement with the recent measurement of the induced magnetic form factor by Stassis, Kline, and Sinha if an exchange enhancement factor of 2.53 is assumed for the spin contribution. The calculated orbital form factor is isotropic and is essentially identical to the free-ion orbital form factor of Freeman and Watson. The limitations and reasons for the sucess of the free-ion model are discussed.

Electronic structure and magnetic properties of scandium

The Van Vleck orbital and Pauli spin paramagnetic contributions to the magnetic susceptibility of single-crystal and polycrystalline scandium are calculated using the augmented-plane-wave method in conjunction with a linear-combination-of-atomic-orbitals interpolation scheme, which uses $s\ensuremath{-}$, $p\ensuremath{-}$, and $d\ensuremath{-}$-type functions in the tight-binding representation. The warped-muffin-tin potential was obtained from overlapping charge densities, which were derived from the atomic configuration $3{d}^{2}4s$; the exchange interaction was included in full Slater ${\ensuremath{\rho}}^{\frac{1}{3}}$ approximation. The Fermi energy is found to lie in a sharp peak in the density-of-states curve. The anisotropy in the magnetic susceptibility and the low-temperature variation of the susceptibility of scandium, particularly the hump around 25\ifmmode^\circ\else\textdegree\fi{}K observed by Spedding and Croat, are successfully explained. The large enhancement of the low-temperature specific heat due to spin fluctuations calculated from the molecular-field parameter in random-phase approximation is shown to account for the absence of superconductivity in scandium.

Magnetization Mössbauer Effect and Superconductivity in Fe2Te3

The magnetization and Mössbauer effect in Fe2Te3 have been measured between liquid helium temperatures and 300 K and the Meissner effect has been studied between 1.7 and 4.2 K. Both the Mössbauer effect and the magnetization indicate that Fe2Te3 undergoes a weak ferromagnetic transition at about 10 K and has an internal field of 11 kOe at the lowest temperatures. The superconducting transition predicted by Atzeri and Mula was not observed. Above 10 K the temperature variation of the susceptibility is probably a reflection of the energy dependence of the d band density of states on the Pauli spin susceptibility of the material.

Weyl Transform and the Magnetic Susceptibility of a Relativistic Dirac Electron Gas

The Weyl transform in relativistic quantum dynamics is formulated in terms of the coordinate eigenfunction and momentum eigenfunction that correspond to the ordinary and magnetic Wannier function and ordinary and magnetic Bloch function, respectively, in solid-state theory. Using this method, a rigorous but fairly simple dynamical derivation of the magnetic susceptibility of a relativistic Dirac electron gas (which includes the effect of an anomalous magnetic moment) is given. The terms coming from the Landau-Peierls formula and Pauli spin paramagnetism are cancelled by the terms arising from the second-order effect of spin and by an unfamiliar dynamical effect due to the inherent spread of the electron (approximately equal to its Compton wavelength). The very simple result reduces to the sum of Landau orbital diamagnetism and Pauli spin paramagnetism in the nonrelativistic limit. It is suggested that different physical processes dominate in the very-low-electron-density limit as compared to that in the very-high-electron-density limit. Striking similarities with the magnetic properties of the electrons in bismuth crystal are pointed out.

Electronic states in Ag-Pd alloys

Electronic densities of states functions are calculated for the random substitutional alloy system Ag-Pd for a number of compositions across the complete range of concentrations. The calculations are based on the coherent potential approximation. It was found necessary to extend the simple model Hamiltonian method previously used to describe Cu-Ni alloys because of the stronger dependence of the lattice constant on composition in the Ag-Pd system. It is shown that the results are consistent with published photoemission and optical absorption data, and low temperature specific heat and Pauli spin susceptibility experiments. The possibility of s-d charge transfer in this alloy system is discussed.

Effect of Electron Correlation in a Narrow Band

Gutzwiller's variational method is used to investigate the Pauli spin susceptibility and the spin waves in a degenerate narrow band. It is found that the susceptibility tends to become negative for sufficiently strong correlation if the number of holes is small and if large density of states occurs at the top of the band near the Fermi energy. For Ni, a numerical analysis is performed using the simplified density-of-states curve proposed by Kanamori. The conditions for the occurrence of ferromagnetic Ni agree with those obtained by Kanamori. The energies of spin waves in ferromagnetic metals are obtained by examining the normal modes of spin excitations in the correlated ground state. Only the improvement upon the random-phase-approximation (RPA) result which is due to correlated electron hoppings is considered. In the long-wavelength limit, the coefficient $C$ in the expression $\ensuremath{\hbar}{\ensuremath{\omega}}_{q}=C{q}^{ 2}$ is reduced from the RPA value by this correlation effect, in agreement with the predictions of other theories.

Semiconductor electrons in electric and magnetic fields

Optical properties of semiconductors in the simultaneous presence of electric and magnetic fields are reviewed, with particular emphasis on the possibilities of modulation techniques. First, the problem of an electron in crossed and parallel fields is solved in the one-level effective mass approximation (EMA), and the results are used to interpret the experimental interband transitions in Ge, with due account of the degenerate character of the valence band in this material. The limitations of the one-level EMA are discussed, and the two-level model is introduced, which correctly describes the experimentally observed transition from a magnetic type to an electric type of motion in increasing transverse electric field. Possibilities to observe electric field effects in cyclotron resonance transitions are discussed in this approximation. Finally, the three-level model is used to describe properly both orbital and spin properties of conduction electrons. It is demonstrated that in a small-gap semiconductor with large spin-orbit interaction a sufficiently strong transverse electric field destroys the Landau orbital quantization but not the Pauli spin quantization. Possible experimental consequences of this situation are discussed. Influence of finite dimensions of the sample on the character of the electron motion in crossed and parallel fields is examined. A possibility to achieve the semiconductor-semimetal transition in a symmetryinduced zero-gap semiconductor in crossed field configuration is predicted and described, taking into account the Luttinger effects in the magnetic level structure.

A unified formalism for polarization optics by using group theory

A unified treatment of three polarization calculus methods - Jones matrix, Mueller matrix and Poincare sphere - is accomplished by using the concept of the Lie group. In the case of the totally transparent system, it is related to the compact Lie group, and in the case of the partially transparent system, it is related to the homogeneous Lorentz group. The physical meaning of the Pauli's spin matrices is given and the generator is introduced and used extensively.

Bulk nuclear polarization of solid3He

Measurements are given on the bulk nuclear spin polarization in a liquid-solid3He mixture cooled by compressional cooling to below 5 mK in a magnetic field of 54.5 kG. Owing to the low Pauli spin susceptibility of liquid3He, the observed polarization is primarily due to solid3He. A maximum average nuclear polarization of 47% was observed, although the corresponding solid3He polarization is believed to be higher. Our novel detection system, using a dual directional coupler for cw NMR, is a simple and versatile means of working in the awkward frequency range around 180 MHz. We also report transient heating measurements in the3He system which indicate that the internal thermal equilibrium time in bulk solid3He on the3He melting curve appears to be quite short (less than 5 min) at these temperatures. One type of transient measurement is complicated by the dramatic effect of the contribution of the3He nuclear magnetization to the total local magnetic field. This contribution is considered via a simple model.

Lower Critical Field Measurements in NbN Bulk and Thin Films

Low-field magnetization measurements have been made at 4.2°K on thin-film and bulk NbN samples using a vibrating-sample Foner magnetometer. These data can be used to calculate the upper critical field, Hc2, without having to resort to resistivity data, which, particularly in the case of NbN, yield very anomalous results. In the present work the experimental value of Hc1 is obtained from the magnetization curves and Hc2 is then calculated using the GLAG equations. These calculations and the significance of the Pauli spin paramagnetism and spin-orbit scattering in these materials are discussed.

Paramagnetic effects on fluctuation-induced diamagnetism in superconductors

The effects of Pauli spin paramagnetism on the fluctuation-induced diamagnetism are studied in superconductors with arbitrary scattering lengths. Including these effects, ( M( T c) - M 0)/√ HT c is no longer a universal function of HT c -2 and (1− T/ T c) even for pure superconductors.

SL 2,C symmetry of the gravitational field

In a previous paper the symmetry of the gravitational-field dynamical variables was discussed. A scheme was given according to which the spin coefficients and the Riemann tensor were represented in the form of linear combinations of the infinitesimal generators of the groupSL2,C, similar to the way Yang and Mills write their dynamical variables in terms of the Pauli spin matrices, where the spin coefficients take the role of the Yang-Mills-like potentials and the Riemann tensor takes the role of the fields. In this paper we use this representation of the gravitational-field dynamical variables in order to write the field equations of general relativity, and obtain a simple and attractive representation for the field equations of Newman and Penrose. Comparison between the present method and that of Utiyama, based on the Yang-Mills theory, is discussed and the possibility of using it as a basis for quantization is briefly mentioned.

Indirect Measurement of the Superconducting Pair Density aboveTcinLa3−xGdxIn Due to Thermodynamic Fluctuations

We observed a temperature-dependent lowering of the paramagnetism of Gd ions in ${\mathrm{La}}_{3\ensuremath{-}x}{\mathrm{Gd}}_{x}$ In ($x=0.064$) above the critical temperature. We attribute this effect to the influence of thermodynamic fluctuations of the superconducting order parameter on the Pauli spin susceptibility affecting in this way the indirect coupling of Gd spins. The result is in qualitative agreement with recent calculations by Fulde and Straessler.

Electron-Phonon Interaction and Paramagnetic Susceptibilities for Transition Metals

The influence of the electron-phonon interaction of the paramagnetic susceptibilities for transition metals is discussed. While the electronic specific heat is influenced by this interaction, the Pauli spin paramagnetic susceptibility and the orbital paramagnetic susceptibility are not influenced. In the case where the spin-orbit interaction exists, however, the spin paramagnetic susceptibility χ s , the orbital paramagnetic susceptibility χ orb and the mixed contribution due to the spin and orbital angular momentums χ so are influenced. In f. c. c. 4 d and 5 d and h. c. p. 5 d transition metals the modifications of χ s , χ orb and χ so due to the electron-phonon interaction are conceivable, but in other transition metals these modifications are very small. Finally, some discussions of this effect on the diamagnetic susceptibilities are given.

SL(2, C) Symmetry of the Gravitational Field Dynamical Variables

We represent the spin coefficients and the Riemann tensor in the form of linear combinations of the infinitesimal generators of the group SL(2, C). This representation is similar to the way Yang and Mills write their dynamical variables in terms of the Pauli spin matrices. The spin coefficients take the role of the Yang-Mills-like potentials, whereas the Riemann tensor takes the role of the fields.

Relevance of Knight Shift Measurements to the Electronic Density of States.

The Knight shift, , measures the magnetic hyperfine field at the nucleus produced by the conduction electrons which are polarized in a magnetic field. Knight shifts are often dominated by the Pauli term and, in its most simple form, can be written as . Here χ p is the conduction electron Pauli spin susceptibility which depends on the density of states at the Fermi level, N(E f ), and 〈a〉 is an average magnetic hyperfine coupling constant associated with the wave function character at the nucleus, ∣ψ F (0)∣2, for conduction electrons at the Fermi surface. The Knight shift therefore provides, through 〈a〉, insight into the wave-function character associated with N(E F ). Calculations of 〈a〉 involving an averaging over k-space have been attempted for a few simple metals up to the present time. For alloys and intermetallic compounds, rather different 〈a〉's are experimentally observed for different local environments, indicating that samples the variation in local wave-function character, or a variation in local density of states. There is no unique way of separating the local variation of N(E F ) from ∣ψ F ∣(0)∣2. In this article the methods developed for relating to the electronic properties for most of the types of cases encountered in the literature are reviewed. We discuss "simple" metals including problems of orbital magnetism and changes in caused by electronic transitions such as melting. Knight shifts and their temperature dependence in metals and intermetallic compounds involving unfilled d shells, are discussed. We give estimates of atomic hyperfine fields due to single electrons, appropriate to those cases where problems due to electronic configurations do not make deductions from experiment too ambiguous. A density of states curve calculated for Cu is given, showing the relative importance of s-p, and d character for that metal. In a qualitative sense this Cu curve implies such information for other transition metals. We discuss alloy solid solutions for the cases where a "rigid" band model might be used to explain the results, and for cases where local effects have to be taken into account. The charge oscillation and RKKY approaches and their limitations are reviewed for cases of dilute nonmagnetic and d- or f-type impurities.

Statistical Mechanics of Alternant Spin Waves

The statistical mechanics of the Heisenberg antiferromagnetic ring of doublet sites with alternating exchange coupling is investigated by an approximate method based on the equivalence, established by the Jordan–Wigner transformation, of Pauli spin matrices and Fermi annihilation and creation operators. Mathematically, the theory is somewhat similar to the pseudospin approach of Soos, but the physical interpretation is quite different, being analogous to that in Anderson's theory of antiferromagnetism. Unlike Soos' work, the present formulation requires the sublattice magnetization to vanish at all temperatures, in agreement with the exact result of Mermin and Wagner. Different magnetic susceptibility valves are derived which are in better agreement with the numerical results of Duffy and Barr.

Superconducting fluctuations in a magnetic field

The rounding of the transition curve is measured for superconducting bismuth films in a perpendicular magnetic field. The contribution of the fluctuating superconducting wave function to the conductivity aboveTc in an applied magnetic field is calculated with a simple model. The allowed states of the fluctuations are cylinders in momentum space. During their life time the fluctuating superconducting electrons can be accelerated by an electrical field and contribute to the conductivity. Experiment and theory are in fair agreement. We obtain some information about the Pauli spin paramagnetism of the electrons.