Quadrupole Susceptibility of Gd-Based Filled Skutterudite Compounds

It is shown that quadrupole susceptibility can be detected in Gd compounds contrary to our textbook knowledge that Gd$^{3+}$ ion induces pure spin moment due to the Hund's rules in an $LS$ coupling scheme. The ground-state multiplet of Gd$^{3+}$ is always characterized by $J$=7/2, where $J$ denotes total angular momentum, but in a $j$-$j$ coupling scheme, one $f$ electron in $j$=7/2 octet carries quadrupole moment, while other six electrons fully occupy $j$=5/2 sextet, where $j$ denotes one-electron total angular momentum. For realistic values of Coulomb interaction and spin-orbit coupling, the ground-state wavefunction is found to contain significant amount of the $j$-$j$ coupling component. From the evaluation of quadrupole susceptibility in a simple mean-field approximation, we point out a possibility to detect the softening of elastic constant in Gd-based filled skutterudites.Comment: 8 pages, 4 figure

Electric Dipolar Susceptibility of the Anderson-Holstein Model

The temperature dependence of electric dipolar susceptibility \chi_P is discussed on the basis of the Anderson-Holstein model with the use of a numerical renormalization group (NRG) technique. Note that P is related with phonon Green's function D. In order to obtain correct temperature dependence of P at low temperatures, we propose a method to evaluate P through the Dyson equation from charge susceptibility \chi_c calculated by the NRG, in contrast to the direct NRG calculation of D. We find that the irreducible charge susceptibility estimated from \chi_c agree with the perturbation calculation, suggesting that our method works well.Comment: 4 pages, 4 figure

Kondo Effect in an Electron System with Dynamical Jahn-Teller Impurity

We investigate how Kondo phenomenon occurs in the Anderson model dynamically coupled with local Jahn-Teller phonons. It is found that the total angular moment composed of electron pseudo-spin and phonon angular moments is screened by conduction electrons. Namely, phonon degrees of freedom essentially contribute to the formation of singlet ground state. A characteristic temperature of the Kondo effect due to dynamical Jahn-Teller phonons is explained by an effective $s$-$d$ Hamiltonian with anisotropic exchange interaction obtained from the Jahn-Teller-Anderson model in a non-adiabatic region.Comment: 5 pages, 3 figure

Generation of twist on magnetic flux tubes at the base of the solar convection zone

Using two-dimensional magnetohydrodynamics calculations, we investigate a twist gen- eration mechanism on a magnetic flux tube at the base of the solar convection zone based on the idea of Choudhuri, 2003, Sol. Phys., 215, 31 in which a toroidal mag- netic field is wrapped by a surrounding mean poloidal field. During generation of the twist, the flux tube follows four phases. (1) It quickly splits into two parts with vortex motions rolling up the poloidal magnetic field. (2) Owing to the physical mechanism similar to that of the magneto-rotational instability, the rolled-up poloidal field is bent and amplified. (3) The magnetic tension of the disturbed poloidal magnetic field re- duces the vorticity, and the lifting force caused by vortical motion decreases. (4) The flux tube gets twisted and begins to rise again without splitting. Investigation of these processes is significant because it shows that a flux tube without any initial twist can rise to the surface in relatively weak poloidal fields.Comment: 10 pages, 6 figur

Singular Vertices in the Strong Coupling Phase of Four-Dimensional Simplicial Gravity

We study four-dimensional simplicial gravity through numerical simulation with special attention to the existence of singular vertices, in the strong coupling phase, that are shared by abnormally large numbers of four-simplices. We attempt to cure this disease by adding a term to the action which suppresses such singular vertices. For a sufficiently large coefficient of the additional term, however, the phase transition disappears and the system is observed to be always in the branched polymer phase for any gravitational constant.Comment: 11 pages, 7 Postscript figure

Effective Crystalline Electric Field Potential in a j-j Coupling Scheme

We propose an effective model on the basis of a $j$-$j$ coupling scheme to describe local $f$-electron states for realistic values of Coulomb interaction $U$ and spin-orbit coupling $\lambda$, for future development of microscopic theory of magnetism and superconductivity in $f^n$-electron systems, where $n$ is the number of local $f$ electrons. The effective model is systematically constructed by including the effect of a crystalline electric field (CEF) potential in the perturbation expansion in terms of $1/\lambda$. In this paper, we collect all the terms up to the first order of $1/\lambda$. Solving the effective model, we show the results of the CEF states for each case of $n$=2$\sim$5 with $O_{\rm h}$ symmetry in comparison with those of the Stevens Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF energy levels in an intermediate coupling region with $\lambda/U$ in the order of 0.1 corresponding to actual $f$-electron materials between the $LS$ and $j$-$j$ coupling schemes. Note that the relevant energy scale of $U$ is the Hund's rule interaction. It is found that the CEF energy levels in the intermediate coupling region can be quantitatively reproduced by our modified $j$-$j$ coupling scheme, when we correctly take into account the corrections in the order of $1/\lambda$ in addition to the CEF terms and Coulomb interactions which remain in the limit of $\lambda$=$\infty$. As an application of the modified $j$-$j$ coupling scheme, we discuss the CEF energy levels of filled skutterudites with $T_{\rm h}$ symmetry.Comment: 12 pages, 7 figures. Typeset with jpsj2.cl

Efficient small-scale dynamo in solar convection zone

We investigate small-scale dynamo action in the solar convection zone through a series of high resolution MHD simulations in a local Cartesian domain with 1$R_\odot$ (solar radius) of horizontal extent and a radial extent from 0.715 to 0.96$R_\odot$. The dependence of the solution on resolution and diffusivity is studied. For a grid spacing of less than 350 km, the root mean square magnetic field strength near the base of the convection zone reaches 95% of the equipartition field strength (i.e. magnetic and kinetic energy are comparable). For these solutions the Lorentz force feedback on the convection velocity is found to be significant. The velocity near the base of the convection zone is reduced to 50% of the hydrodynamic one. In spite of a significant decrease of the convection velocity, the reduction in the enthalpy flux is relatively small, since the magnetic field also suppresses the horizontal mixing of the entropy between up- and downflow regions. This effect increases the amplitude of the entropy perturbation and makes convective energy transport more efficient. We discuss potential implications of these results for solar global convection and dynamo simulations.Comment: 46 pages, 25 figures, 1 table, accepted by Ap