Velocity dependent interactions and a new sum rule in bcc He

Recent neutron scattering experiments [PRL,{\bf 88},p.195301 (2002)] on solid $^4$He, discovered a new optic-like mode in the bcc phase. This excitation was predicted by a recently proposed model that describes the correlated atomic zero-point motion in bcc Helium in terms of dynamic electric dipole moments. Modulations of the relative phase of these dipoles between different atoms describes the anomalously soft T$_1$(110) phonon and two new optic-like modes, one of which was recently found in the neutron scattering experiments. In this work we show that the correlated dipolar interactions can be written as a velocity dependent interaction. This then results in a modified f-sum rule for the T$_1$(110) phonon, in good agreement with the recent experimental data.Comment: 5 pages, 3 figure

Bcc 4^4He as a Coherent Quantum Solid

In this work we investigate implications of the quantum nature of bcc $^{4}$% He. We show that it is a unique solid phase with both a lattice structure and an Off-Diagonal Long Range Order of coherently oscillating local electric dipole moments. These dipoles arise from the local motion of the atoms in the crystal potential well, and oscillate in synchrony to reduce the dipolar interaction energy. The dipolar ground-state is therefore found to be a coherent state with a well defined global phase and a three-component complex order parameter. The condensation energy of the dipoles in the bcc phase stabilizes it over the hcp phase at finite temperatures. We further show that there can be fermionic excitations of this ground-state and predict that they form an optical-like branch in the (110) direction. A comparison with 'super-solid' models is also discussed.Comment: 12 pages, 8 figure

Damping of spin waves and singularity of the longitudinal modes in the dipolar critical regime of the Heisenberg-ferromagnet EuS

By inelastic scattering of polarized neutrons near the (200)-Bragg reflection, the susceptibilities and linewidths of the spin waves and the longitudinal spin fluctuations were determined separately. By aligning the momentum transfers q perpendicular to both \delta S_sw and the spontaneous magnetization M_s, we explored the statics and dynamics of these modes with transverse polarizations with respect to q. In the dipolar critical regime, where the inverse correlation length kappa_z(T) and q are smaller than the dipolar wavenumber q_d, we observe:(i) the static susceptibility of \delta S_sw^T(q) displays the Goldstone divergence while for \delta S_z^T(q) the Ornstein-Zernicke shape fits the data with a possible indication of a thermal(mass-)renormalization at the smallest q-values, i.e. we find indications for the predicted 1/q divergence of the longitudinal susceptibility; (ii) the spin wave dispersion as predicted by the Holstein-Primakoff theory revealing q_d=0.23(1)\AA^{-1}in good agreement with previous work in the paramagnetic and ferromagnetic regime of EuS; (iii) within experimental error, the (Lorentzian) linewidths of both modes turn out to be identical with respect to the q^2-variation, the temperature independence and the absolute magnitude. Due to the linear dispersion of the spin waves they remain underdamped for q<q_d. These central results differ significantly from the well known exchange dominated critical dynamics, but are quantitatively explained in terms of dynamical scaling and existing data for T>=T_C. The available mode-mode coupling theory, which takes the dipolar interactions fully into account, describes the gross features of the linewidths but not all details of the T- and q-dependencies. PACS: 68.35.Rh, 75.40.GbComment: 10 pages, 7 figure

Pressure-dependence of electron-phonon coupling and the superconducting phase in hcp Fe - a linear response study

A recent experiment by Shimizu et al. has provided evidence of a superconducting phase in hcp Fe under pressure. To study the pressure-dependence of this superconducting phase we have calculated the phonon frequencies and the electron-phonon coupling in hcp Fe as a function of the lattice parameter, using the linear response (LR) scheme and the full potential linear muffin-tin orbital (FP-LMTO) method. Calculated phonon spectra and the Eliashberg functions $\alpha^2 F$ indicate that conventional s-wave electron-phonon coupling can definitely account for the appearance of the superconducting phase in hcp Fe. However, the observed change in the transition temperature with increasing pressure is far too rapid compared with the calculated results. For comparison with the linear response results, we have computed the electron-phonon coupling also by using the rigid muffin-tin (RMT) approximation. From both the LR and the RMT results it appears that electron-phonon interaction alone cannot explain the small range of volume over which superconductivity is observed. It is shown that ferromagnetic/antiferromagnetic spin fluctuations as well as scattering from magnetic impurities (spin-ordered clusters) can account for the observed values of the transition temperatures but cannot substantially improve the agreeemnt between the calculated and observed presure/volume range of the superconducting phase. A simplified treatment of p-wave pairing leads to extremely small ($\leq 10^{-2}$ K) transition temperatures. Thus our calculations seem to rule out both $s$- and $p$- wave superconductivity in hcp Fe.Comment: 12 pages, submitted to PR