ZQZ_Q Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices

Adiabatic $Z_Q$ invariants by quantized Berry phases are defined for gapped electronic systems in $d$-dimensions ($Q=d+1$). This series includes Polyacetylene, Kagome and Pyrochlore lattice respectively for $d=1,2$ and 3. The invariants are quantum $Q$-multimer order parameters to characterize the topological phase transitions by the multimerization. This fractional quantization is protected by the global $Z_Q$ equivalence. As for the chiral symmetric case, a topological form of the $Z_2$-invariant is explicitly given as well.Comment: 4 pgages, 4 figure

Kagom\'{e} ice state in the dipolar spin ice Dy_{2}Ti_{2}O_{7}

We have investigated the kagom\'{e} ice behavior of the dipolar spin-ice compound Dy_{2}Ti_{2}O_{7} in magnetic field along a [111] direction using neutron scattering and Monte Carlo simulations. The spin correlations show that the kagom\'{e} ice behavior predicted for the nearest-neighbor (NN) interacting model, where the field induces dimensional reduction and spins are frustrated in each two-dimensional kagom\'{e} lattice, occurs in the dipole interacting system. The spins freeze at low temperatures within the macroscopically degenerate ground states of the NN model.Comment: 5 pages, 3 figures, submitted to PR

Theory of Metal-Insulator Transition in PrRu4P12 and PrFe4P12

All symmetry allowed couplings between the 4f^2-electron ground state doublet of trivalent praseodymium in PrRu4P12 and PrFe4P12 and displacements of the phosphorus, iron or ruthenium ions are considered. Two types of displacements can change the crystal lattice from body-centred cubic to simple orthorhombic or to simple cubic. The first type lowers the point group symmetry from tetrahedral to orthorhombic, while the second type leaves it unchanged, with corresponding space group reductions Im3 --> Pmmm and Im3 --> Pm3 respectively. In former case, the lower point-group symmetry splits the degeneracy of the 4f^2 doublet into states with opposite quadrupole moment, which then leads to anti-quadrupolar ordering, as in PrFe4P12. Either kind of displacement may conspire with nesting of the Fermi surface to cause the metal-insulator or partial metal-insulator transition observed in PrFe4P12 and PrRu4P12. We investigate this scenario using band-structure calculations, and it is found that displacements of the phosphorus ions in PrRu4P12 (with space group reduction Im3 --> Pm3) open a gap everywhere on the Fermi surface.Comment: 6 page

Metal-insulator transition in PrRu4_4P12_{12} and SmRu4_4P12_{12} investigated by optical spectroscopy

Electronic structures of the filled-skutterudite compounds PrRu$_4$P$_{12}$ and SmRu$_4$P$_{12}$, which undergo a metal-insulator transition (MIT) at $T_{\rm MI}$ = 60 K and 16 K, respectively, have been studied by means of optical spectroscopy. Their optical conductivity spectra develop an energy gap of $\sim$ 10 meV below $T_{\rm MI}$. The observed characteristics of the energy gap are qualitatively different from those of the Kondo semiconductors. In addition, optical phonon peaks in the spectra show anomalies upon the MIT, including broadening and shifts at $T_{\rm MI}$ and an appearance of new peaks below $T_{\rm MI}$. These results are discussed in terms of density waves or orbital ordering previously predicted for these compounds.Comment: 4pages, 4figures, submitted to Physical Review

Quantum-Classical Reentrant Relaxation Crossover in Dy2Ti2O7 Spin-Ice

We have studied spin relaxation in the spin ice compound Dy2Ti2O7 through measurements of the a.c. magnetic susceptibility. While the characteristic spin relaxation time is thermally activated at high temperatures, it becomes almost temperature independent below Tcross ~ 13 K, suggesting that quantum tunneling dominates the relaxation process below that temperature. As the low-entropy spin ice state develops below Tice ~ 4 K, the spin relaxation time increases sharply with decreasing temperature, suggesting the emergence of a collective degree of freedom for which thermal relaxation processes again become important as the spins become highly correlated

Anisotropic Release of the Residual Zero-point Entropy in the Spin Ice Compound Dy2Ti2O7: Kagome-ice Behavior

We report the specific heat and entropy of single crystals of the spin ice compound Dy2Ti2O7 at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions: [100], [110], [111] and [112]. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches Rln2. However, in the intermediate field region, the entropy in fields along the [111] direction is different from those for the other three field directions. For the [111] direction the frustration structure changes from that of three-dimensional(3D) pyrochlore to that of two-dimensional(2D) Kagome-like lattice with constraint due to the ice rule, leading to different values of zero-point entropy.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

Low Temperature Specific Heat of Dy2_2Ti2_2O7_7 in the Kagome Ice State

We report the specific heat of single crystals of the spin ice compound Dy$_2$Ti$_2$O$_7$ at temperatures down to 100 mK in the so-called Kagome ice state. In our previous paper, we showed the anisotropic release of residual entropy in different magnetic field directions and reported new residual entropy associated with spin frustration in the Kagome slab for field in the [111] direction. In this paper, we confirm the first-order phase transition line in the field-temperature phase diagram and the presence of a critical point at (0.98 T, 400 mK), previously reported from the magnetization and specific-heat data. We newly found another peak in the specific heat at 1.25 T below 0.3 K. One possible explanation for the state between 1 T and 1.25 T is the coexistence of states with different spin configurations including the 2-in 2-out one (Kagome ice state), the 1-in 3-out state (ordered state) and paramagnetic one (free-spin state).Comment: 14 pages, 7 figure

Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice

We report a study of the low temperature bulk magnetic properties of the spin ice compound Dy2Ti2O7 with particular attention to the (T < 4 K) spin freezing transition. While this transition is superficially similar to that in a spin glass, there are important qualitative differences from spin glass behavior: the freezing temperature increases slightly with applied magnetic field, and the distribution of spin relaxation times remains extremely narrow down to the lowest temperatures. Furthermore, the characteristic spin relaxation time increases faster than exponentially down to the lowest temperatures studied. These results indicate that spin-freezing in spin ice materials represents a novel form of magnetic glassiness associated with the unusual nature of geometrical frustration in these materials.Comment: 24 pages, 8 figure