Table of contents

The well known argument of Peierls that a 1D electron-phonon system is unstable against an arbitrary small lattice distortion at q=2k_F is modified for nonlinear lattices with commensurate ground states of period p not=1 and rational values of the Fermi vector k_F. For a suitable lattice potential an electronically induced metal-insulator transition is described in the presence of a soft mode. In this case a lattice deformation of wavevector q does not imply a Fermi vector of k_F=q/2.

Recently, a Letter by Chacon et al. (ibid., vol.16, L187, 1983) appeared, in which they claim that improvements have been made on the authors' previous calculations of the surface tension of liquid metals (Hasegawa and Watabe, ibid., vol.15, p.353, 1982). However, they have overlooked an important point of the density functional theory and there is no physical foundation supporting their calculations.

Comment by M. Hasegawa and M. Watabe, ibid., vol.16, L699, 1983. The authors show that no important point of the density functional theory has been overlooked in the calculations presented in the Letter written by Chacon et al. (ibid., vol.16, L187, 1983). The physical foundations supporting the calculations are discussed.

The authors have delineated certain important aspects of the use of theoretical Compton profiles for estimating cohesive energy, energy of mixing, etc. Inclusion of electron-electron correlation in the calculation of Compton profiles seems to be essential in order to get the correct values of ground state energy differences. Some model calculations have also been performed for the energy change as a result of 'switching on' correlation in a homogeneous electron gas at zero temperature. Numerical estimates of this 'correlation energy' have been obtained for free-electron-like metals, viz Na and Li.

A class of linear Jahn-Teller systems characterised by a three-diagonal Hamiltonian is examined. It covers the E(X) epsilon , Gamma ₈(X) tau ₂ and Gamma ₈(X)( epsilon (X) tau ₂) systems (also in an external field) as well as the dimer. It is shown that the energy of these systems will lie on a baseline E+D=v+¹/₂ if the system parameters j, G and D satisfy a three-diagonal determinantal equation of finite order.

The diffusion model is extended to the geometry of long thin wires. In the weak localisation limit, the author obtains the same result as that found by perturbation diagrammatic techniques. In the region where perturbation theory is not applicable, it is found that sigma varies as 1//L² when the length L of the wire is of the order of the Thouless (1977, 1980) localisation length L_c and that the AC conductivity is given by sigma varies as omega ¹//². It is suggested that transport in a long thin wire at non-zero temperatures may be dominated by a pseudo-gap which makes the conductivity rapidly vanish as T to 0. This may explain the recent data of Dean and Pepper (1983).

The authors report ODMR (optically detected magnetic resonance) studies of near infrared luminescence from nominally undoped cubic ZnSe. The magnetic resonances of shallow donors and isolated Fe³⁺ ions are detected in a prominent band at 980 nm. A similar band in ZnS has recently been identified by Skowronski and Liro (1981, 1982) as the internal ³T₁ to ⁵E transition of Fe²⁺. It is concluded that ODMR detects the radiationless distant shallow donor to Fe³⁺ deep donor electron transfer. This process creates the excited Fe²⁺(³T₁) state which in turn emits the 980 nm photon in a transition to the 5_E ground state.

The authors find that the lifetime of the 1.9 eV luminescence of cis-polyacetylene is <or approximately=9 ps. The relevance of this result to the understanding of relaxation processes in optically excited material is discussed.

The authors present an exact solution for the diffusion of pairs of indistinguishable particles in a non-interacting lattice gas with site-blocking. The experimental relevance of the pair density correlation function is emphasised. Analytic results obtained for one dimension are discussed and related to the spin dynamics of the Heisenberg ferromagnet.

Lattice parameter measurements of LiYF₄ and LiY_0.5Tb_0.5F₄ made between -100 degrees C and +550 degrees C show that the anisotropy of the thermal expansion ( alpha ₁₁> alpha ₃₃) of these scheelite structure fluorides has the opposite sense to oxide scheelites ( alpha ₃₃> alpha ₁₁). This, together with corresponding differences found between the anisotropy of linear compressibility and elastic stiffness constants, can be understood if the oxides, but not the fluorides, are considered to show a tendency towards layer-like behaviour. Pulse echo overlap measurements of ultrasonic wave velocities have been used to obtain the hydrostatic pressure derivatives delta C_IJ/ delta P of the elastic constants of CaWO₄. Since the acoustic symmetry axes do not shift appreciably with pressure, the pressure derivatives delta C_IJ/ delta P, like the elastic constants C_IJ themselves, can be transformed (with useful simplification) to reference bases comprised of acoustic symmetry axes (( kappa and kappa + pi /2) or ( gamma and gamma + pi /2)) and the Z axis. The acoustic mode Gruneisen gammas in the long-wavelength limit obtained for CaWO₄ show that shear acoustic mode softening occurs under pressure along the gamma and gamma + pi /2 acoustic symmetry axes, in contrast to that for LiYF₄ and LiY_0.5Tb_0.5F₄ which takes place along the other type ( kappa and kappa + pi /2) of acoustic symmetry axes in the (001) plane.

A method is presented of approximating the vibrational density of states of an infinite one-dimensional alloy with a random mass distribution. The method involves solving for the vibrational Green function of a finite chain of particles with an exactly treated mass distribution, embedded in a virtual-crystal approximation to represent the rest of the alloy. Detailed results are given for binary alloys.

Expressions for the exchange energy of a relativistic polarised electron gas have been derived. These expressions have been evaluated numerically over a wide range of densities and polarisations. The leading-order relativistic corrections for the transverse exchange energy, which are of most importance in practice, have been evaluated analytically. The numerical results have been fitted to a simple form, suggested by the analytic leading-order-correction expressions, which should be useful for local-density-approximation applications.

Using the band-structure model proposed by Bodnar (1977), the authors have calculated the dielectric function of Cd₃As₂ in the presence of a magnetic field. This calculation, which is carried out in full detail only for waves propagating along the direction of the magnetic field, which may, however, be in an arbitrary crystallographic direction, permits the analysis of cyclotron resonance as well as measurements of magnetoreflectivity or absorption. Numerical calculations are presented for propagation along or perpendicular to the c axis.

From an analysis of the scattering theory for a model of a wire with a disordered section, the asymptotic properties of the electrical conductance are derived as the length of the disordered section tends to infinity. It is proved that the conductance decreases exponentially with the length of the disordered section. It is shown that the exponent is two times the smallest Ljapunov exponent associated with a product of random matrices derived from the stationary Schrodinger equation for the system. The distribution of the conductance is asymptotically log-normal. These results are derived from similar properties obtained for the elements of the transmission matrix. The results for the transmission matrix hold equally for the disordered harmonic strip and bar.

When superconductivity coexists with a spin-density wave (SDW) for the same electrons, both spin-singlet and spin-triplet Cooper-pair amplitudes of comparable magnitude must occur. Physical properties of the coexistence states are strongly affected by the amplitude of spin-triplet Cooper pairs even when the electron-electron interaction for triplet pairing, and hence the triplet pair potential, are both zero. The coexistence phase may occur in (TMTSF)₂X organic superconductors where SDW and superconductivity phases meet on the temperature-pressure phase diagram. Compared with the superconductivity-only phase, the SDW superconductivity coexistence state is predicted to have a higher Pauli-limited critical magnetic field and a reduced sensitivity of the transition temperature to non-magnetic impurities.

The authors investigate numerically the magnetic properties of a random superconducting network, which models random superconductor-insulator mixtures. Bonds between nearest-neighbour sites on a square lattice are chosen to be independently superconducting with probability p, and insulating with probability 1-p. A new numerical method is used to investigate loop statistics in these percolating networks. The diamagnetic susceptibility chi as a function of the superconducting fraction p is calculated. Close to the percolation threshold p_c, chi shows a singular behaviour as a function of (p_c-p). The numerical results exhibit a finite-size scaling which enables one to deduce the critical exponent of chi from calculations on relatively small samples. The numerical results are in good agreement with the predictions of recent scaling theory and differ from those made by previous workers.

The authors study the thermodynamic behaviour of two-component random Ising systems in the formalism of Eggarter and Eggarter (1977) properly extended to include site correlations. This formalism is exact in the case of a Bethe lattice, while it leads to the Bethe-Peierls approximation for real lattices. The authors consider such systems with antiferromagnetic couplings, different values of the magnetic moments and placed in a magnetic field. They calculate their magnetic properties and discuss them in connection with relevant experimental studies. They also study the phase diagrams of such systems, concentrating on cases relevant to other theoretical as well as experimental studies.

The authors study the positional (site) correlation of the magnetic 'atoms' in a two-component random Ising system, induced in the liquid state by attractive or repulsive interactions U among them. This site correlation strongly influences the magnetic properties of the system. The T_cr versus concentration phase diagrams of such systems are studied for various values of the interaction U and the results compared to observe phase diagrams of relevant real systems.

Reports on the stress- and magnetic-field-induced linear birefringence (LB) in some simple two-sublattice antiferromagnets-the cubic perovskites RbMnF₃, KNiF₃ and KCoF₃. Study of variations with temperature and stress allows one to separate the natural lattice part Delta n₁ of the LB from the magnetic contribution Delta n_m appearing below T_N. Low stresses (few tens of bars) are enough to get a single-T-domain sample and for higher stresses it is shown that the variation of the LB with stress arises mainly from lattice deformations. The magnetic contribution Delta n_m increases strongly from RbMnF₃ to KCoF₃ as does the spin-orbit coupling for these compounds. A macroscopic description is given for interpreting the stress- and magnetic-field-induced LB. Following a treatment reported by Pisarev and co-workers (1971, 1972, 1975) for garnets the author deduces the magneto-optical anisotropy coefficient a=0.21 for RbMnF₃ from an in-field sample-rotation experiment. The author demonstrates that the microscopic origin of the LB is the spin-orbit coupling and/or the anisotropic exchange interaction and that the data cannot be explained in terms of the magnetostriction.

The contributions to the principal linear birefringences (LB) of BaMnF₄ due to the structural and magnetic phase transitions at T_c=252K and T_N=26K, respectively, are essentially determined by fluctuations of the respective order parameters. It is possible to separate the LB contributions of the structural order parameter and of its fluctuations. The critical exponent beta =0.28 thus obtained confirms the vicinity of a Lifshitz point. The magnetic LB is quantitatively described by the nearest-neighbour spin-correlation function Gamma ₁ of a 2d Heisenberg S=5/2 antiferromagnet. Slight deviations from this model at T<T_n seem to indicate a small contribution due to magneto-electric coupling. The absorption intensity of the two-exciton transition 2(⁶A_1g to ⁴T_1g) fits the theoretical predictions exceptionally well. It allows the detection of contributions due to biquadratic correlation functions in addition to Gamma ₁.

The Vernon et al. (1981) theory of spin relaxation of F in PbF₂ due to the hyperfine interaction of F with paramagnetic Mn impurities involves the analysis of encounters between the diffusing F^- ions and the fixed Mn impurities. Vernon et al. assumed in their analysis that the motion of an ion is that on an empty lattice and that once an ion leaves the vicinity of an impurity the probability of return is negligible. The theory is developed more rigorously to include the effect of return visits of the ions and also for a model in which the ions move by the vacancy mechanism. It is found that the relaxation rates are essentially the same for motion of a single ion on a lattice and for motion by the vacancy mechanism. The effect on the relaxation rates of including return visits to the impurity is significant and best-fit parameters to the experimental data lead to reduced values of the high-temperature hyperfine interaction parameters.

Mossbauer parameters of ⁵⁷Fe-doped MnS₂, MnSe₂ and MnTe₂ are analysed in terms of the trigonal crystal-field parameter Delta , spin-orbit interaction constant lambda and exchange field parameters J_eff, phi _ex and theta _ex, at the Fe²⁺ site. In MnS₂+0.5 at.% ⁵⁷Fe, the Mn²⁺ spin direction is found to be close to (103) in the cubic-axis system; a multi-axis spin system is inferred. In MnSe₂+2at.%⁵⁷Fe the Mossbauer parameters are consistent with the spin direction deduced from neutron diffraction (ND) studies, namely a cubic (100) direction. In MnTe₂+2at.%⁵⁷Fe the spins are directed approximately along (111) (cubic) below T_N, in approximate agreement with earlier ND and ¹²⁵Te Mossbauer studies; however, a magnetic spin rearrangement reported at 60K is not observed. Transition to the antiferromagnetic state appears to be first order in all three substances.

Dynamic scaling for a number of ferroelectric transitions is demonstrated by the use of diagrammatic techniques. A particular feature of the observations is the identification, for the first time, of a factor defining the discontinuity in lattice frequencies. This factor is given a clear visual presentation and allows a quantitative evaluation of the first-order character of the transition.

The dielectric response of finite-grain-sized, uranium-doped, ceramic perovskites are examined and characterised. It is shown that the dopant forms dipolar centres such that an activated population of reversed dipoles exists in the ferroelectric phase. These centres also take part in the polarisation fluctuations near the critical temperature, thereby limiting the correlation length of the main ferroelectric fluctuations and preventing finite-grain-size effects from being observed.

Inelastic scattering of light in magnetic semiconductors related with s-d (d-f) exchange interactions and spin-orbit coupling is discussed. Calculations of the differential cross section for the case of localised d as well as for the nonlocalised s conduction band are performed. It is shown that a new Raman process, related with excitation of spin-flip in the conduction band and of magnons, should occur in the energy range of 0.05-0.5 eV as a consequence of RKKY interaction. In the case of this process and for typical values of s-d exchange interaction lying between 0.05 and 0.1 eV, the differential cross sections range from 10^-9 to 10^-11 cm²sr^-1 and from 10^-7 to 10^-9 cm²sr^-1 s for ferromagnetic and antiferromagnetic semiconductors, respectively. For the Raman scattering from spin-flip and electronic excitations caused by spin-orbit interaction, selection rules for the polarisations of the incident and scattered photons are derived. The differential cross section for spin-flip Raman scattering in europium chalcogenides is found to be 10^-9 cm²sr^-1s. The results show that using Raman spectroscopy one can measure the values of the d-f (s-d) exchange integral and spin-orbit interaction parameter. The analysis of the dependence of the energy of the magnon-spin-flip Raman processes on an external magnetic field allows one to determine the sign of the RKKY interaction and to find the g-factor for the conduction electrons. The feasibility of applying spin-flip and magnon-spin-flip Raman processes in magnetic semiconductors in the tuning of electromagnetic radiation in Raman lasers is analysed briefly.

Thermal emission spectra of metal-backed thin films of SrF₂ are observed at elevated temperatures in the frequency regions around the transverse optical mode and the longitudinal optical mode. Considerable changes in the spectra are found for films prepared under different conditions. The frequency and the intensity of the emission peaks show anomalies in the temperature dependence for the as-deposited film. Spectral analysis based on the virtual-mode theory gives physically meaningful results only for the heat-treated film. The temperature dependence of the observed spectra is discussed in terms of a theory of phonon anharmonicity.