宇田川 将文

We study the interplay of topological bottlenecks and energetic barriers to<br /> equilibration in a Coulomb spin liquid where a short-range energetic coupling<br /> between defects charged under an emergent gauge field supplements their<br /> entropic long-range Coulomb interaction. This work is motivated by the<br /> prevalence of memory effects observed across a wide range of geometrically<br /> frustrated magnetic materials, possibly including the spontaneous Hall effect<br /> observed in Pr2Ir2O7. Our model is canonical spin-ice model on the pyrochlore<br /> lattice, where farther-neighbour spin couplings give rise to a nearest-neighbor<br /> interaction between topological defects which can easily be chosen to be<br /> unnatural or not, i.e. attractive or repulsive between defects of equal gauge<br /> charge. Among the novel features of this model are the following. After<br /> applying a field quench, a rich dynamical approach to equilibrium emerges,<br /> dominated by multi-scale energy barriers responsible for long-lived<br /> magnetization plateaux. These even allow for the metastability of a<br /> &quot;fragmented&quot; spin liquid, an elusive regime where partial order co-exists with<br /> a spin liquid. Perhaps most strikingly, the attraction produces clusters of<br /> defects whose stability is due to a combination of energetic barriers for their<br /> break-up and proximity of opposite charges along with an entropic barrier<br /> generated by the topological requirement of annihilating a defect only together<br /> with an oppositely charged counterpart. These clusters may take the form of a<br /> &quot;jellyfish&quot; spin texture, comprising an arrangement of same-sign gauge-charges,<br /> centered on a hexagonal ring with branches of arbitrary length. The ring<br /> carries a clockwise or counterclockwise circular flow of magnetisation. This<br /> emergent toroidal degrees of freedom provides a possibility for time reversal<br /> symmetry breaking with possible relevance to the spontaneous Hall effect<br /> observed in Pr2Ir2O7.

We study the spin-orbit coupling in spin-triplet Cooper pairs and clarify<br /> multiple superconducting (SC) phases in Sr$_2$RuO$_4$. Based on the analysis of<br /> the three-orbital Hubbard model with atomic LS coupling, we show some selection<br /> rules of the spin-orbit coupling in Cooper pairs. The spin-orbit coupling is<br /> small when the two-dimensional $\gamma$-band is the main cause of the<br /> superconductivity, although the LS coupling is much larger than the SC gap.<br /> Considering this case, we investigate multiple SC transitions in the magnetic<br /> fields for both H // [001] and H // [100] using the Ginzburg-Landau theory and<br /> the quasi-classical theory. Rich phase diagrams are obtained because the spin<br /> degree of freedom in Cooper pairs is not quenched by the spin-orbit coupling.<br /> Experimental indications for the multiple phases in Sr$_2$RuO$_4$ are<br /> discussed.

We show the existence of invariant energy levels in a Kondo lattice model on<br /> an isolated complete graph, such as a triangle and a tetrahedron. These energy<br /> levels always have fixed eigenenergies $t \pm J/2$, irrespective of the<br /> configuration of localized moments ($t$ is the transfer integral of conduction<br /> electrons and $J$ is the spin-charge coupling constant). We also extend the<br /> analysis to geometrically frustrated lattices by using the complete graphs as<br /> basic building blocks. We show that the construction rule for the invariant<br /> energy levels leads to the existence condition of localized states, if the<br /> model is defined on the triangle-based line graphs, such as a kagome lattice.<br /> We further propose a procedure of engineering isolated flat bands with broken<br /> time-reversal symmetry, which are separated from other dispersive bands with<br /> finite energy gaps.

An effective Ising model for the spin-ice type Kondo lattice model is<br /> investigated by the classical Monte Carlo simulation. We clarify the magnetic<br /> phase diagram with four phases: ice-ferro, ice-(0,0,2\pi), 32-sublattice, and<br /> all-in/all-out ordered states. The result well reproduces the phase diagram of<br /> the Kondo lattice model studied previously [H. Ishizuka et al.: J. Phys. Soc.<br /> Jpn. 81 (2012) 113706], which suggests that the RKKY interactions up to third<br /> neighbors are sufficient to describe the magnetic properties of the itinerant<br /> electron model. We discuss the peculiar nature of phase transitions: the<br /> suppression of the critical temperatures down to zero temperature between two<br /> ice phases and the presence of the tricritical points on the phase boundary of<br /> the 32-sublattice ordered state.

We investigate the ground state of the Kondo necklace model on<br /> geometrically-frustrated lattices by the variational Monte Carlo simulation. To<br /> explore the possibility of a partially-ordered phase, we employ an extension of<br /> the Yosida-type wave function as a variational state, which can describe a<br /> coexistence of spin-singlet formation due to the Kondo coupling and magnetic<br /> ordering by the Ruderman-Kittel-Kasuya-Yosida interaction. We show the<br /> benchmark of the numerical simulation to demonstrate the high precision brought<br /> by the optimization of a large number of variational parameters. We discuss the<br /> ground-state phase diagram for the model on the kagome lattice in comparison<br /> with that for the triangular-lattice case.

We have studied the field-orientational dependence of zero-energy density of<br /> states (FODOS) for a series of systems with different Fermi surface and<br /> superconducting gap structures. Instead of phenomenological Doppler-shift<br /> method, we use an approximate analytical solution of Eilenberger equation<br /> together with self-consistent determination of order parameter and a<br /> variational treatment of vortex lattice. First, we compare zero-energy density<br /> of states (ZEDOS) when a magnetic field is applied in the nodal direction<br /> ($\nu_{node}(0)$) and in the antinodal direction ($\nu_{anti}(0)$), by taking<br /> account of the field-angle dependence of order parameter. As a result, we found<br /> that there exists a crossover magnetic field $H^*$ so that $\nu_{anti}(0) &gt;<br /> \nu_{node}(0)$ for $H &lt; H^*$, while $\nu_{node}(0) &gt; \nu_{anti}(0)$ for $H &gt;<br /> H^*$, consistent with our previous analyses. Next, we showed that $H^*$ and the<br /> shape of FODOS are determined by contribution from the small part of Fermi<br /> surface where Fermi velocity is parallel to field-rotational plane. In<br /> particular, we found that $H^*$ is lowered and FODOS has broader minima, when a<br /> superconducting gap has point nodes, in contrast to the result of the<br /> Doppler-shift method. We also studied the effects of in-plane anisotropy of<br /> Fermi surface. We found that in-plane anisotropy of quasi-two dimensional Fermi<br /> surface sometimes becomes larger than the effects of Doppler-shift and can<br /> destroy the Doppler-shift predominant region. In particular, this tendency is<br /> strong in a multi-band system where superconducting coherence lengths are<br /> isotropic. Finally, we addressed the problem of cusp-like singularity in<br /> YNi$_2$B$_2$C and present a possible explanation of this phenomenon.

We study the vortex state of a layered superconductor with vertical line<br /> nodes on its Fermi surface when a magnetic field is applied in the ab-plane<br /> direction. We rotate the magnetic field within the plane, and analyze the<br /> change of low-energy excitation spectrum. Our analysis is based on the<br /> microscopic<br /> Bogoliubov-de Gennes equation and a convenient approximate analytical method<br /> developped by Pesch and Dahm. Both methods give a consistent result. Near the<br /> upper critical field H$_{c2}$, we observe a larger zero-energy density of<br /> states(ZEDOS) when the magnetic field is applied in the nodal direction, while<br /> much below H$_{c2}$, larger ZEDOS is observed under a field in the anti-nodal<br /> direction. We give a natural interpretation to this crossover behavior in terms<br /> of momentum distribution of low-energy quasiparticles. We examine the recent<br /> field angle variation experiments of thermal conductivity and specific heat.<br /> Comparison with our results suggest that special care should be taken to derive<br /> the position of line nodes from the experimental data. Combining the<br /> experimental data of the specific heat and our analyses, we conclude that<br /> Sr$_2$RuO$_4$ has vertical line nodes in the direction of the a-axis and the<br /> b-axis.