Spin Hall effect in Sr2RuO4 and transition metals (Nb,Ta)

We study the intrinsic spin Hall conductivity (SHC) and the $d$-orbital Hall conductivity (OHC) in metallic $d$-electron systems based on the multiorbital tight-binding model. The obtained Hall conductivities are much larger than that in $p$-type semiconductors. The origin of these huge Hall effects is the "effective Aharonov-Bohm phase" induced by the signs of inter-orbital hopping integrals as well as atomic spin-orbit interaction. Huge SHC and OHC due to this mecahnism is ubiquitous in multiorbital transition metals.Comment: 4 pages, 3 figures, Proceedings of SNS conference in Sendai, 200

Theory of Thermal Conductivity in High-Tc Superconductors below Tc: Comparison between Hole-Doped and Electron-Doped Systems

In hole-doped high-Tc superconductors, thermal conductivity increases drastically just below Tc, which has been considered as a hallmark of a nodal gap. In contrast, such a coherence peak in thermal conductivity is not visible in electron-doped compounds, which may indicate a full-gap state such as a (d+is)-wave state. To settle this problem, we study the thermal conductivity in the Hubbard model using the fluctuation-exchange (FLEX) approximation, which predicts that the nodal d-wave state is realized in both hole-doped and electron-doped compounds. The contrasting behavior of thermal conductivity in both compounds originates from the differences in the hot/cold spot structure. In general, a prominent coherence peak in thermal conductivity appears in line-node superconductors only when the cold spot exists on the nodal line.Comment: 5 pages, to be published in J. Phys. Soc. Jpn. Vol.76 No.

Theory of Thermoelectric Power in High-Tc Superconductors

We present a microscopic theory for the thermoelectric power (TEP) in high-Tc cuprates. Based on the general expression for the TEP, we perform the calculation of the TEP for a square lattice Hubbard model including all the vertex corrections necessary to satisfy the conservation laws. In the present study, characteristic anomalous temperature and doping dependences of the TEP in high-Tc cuprates, which have been a long-standing problem of high-Tc cuprates, are well reproduced for both hole- and electron-doped systems, except for the heavily under-doped case. According to the present analysis, the strong momentum and energy dependences of the self-energy due to the strong antiferromagnetic fluctuations play an essential role in reproducing experimental anomalies of the TEP.Comment: 5 pages, 8 figures, to appear in J. Phys. Soc. Jpn. 70 (2001) No.10. Figure 2 has been revise

Universality in heavy-fermion systems with general degeneracy

We discuss the relation between the T^{2}-coefficient of electrical resistivity $A$ and the T-linear specific-heat coefficient $\gamma$ for heavy-fermion systems with general $N$, where $N$ is the degeneracy of quasi-particles. A set of experimental data reveals that the Kadowaki-Woods relation; $A/\gamma^{2} = 1*10^{-5} {\mu\Omega}(K mol/mJ)^{2}$, collapses remarkably for large-N systems, although this relation has been regarded to be commonly applicable to the Fermi-liquids. Instead, based on the Fermi-liquid theory we propose a new relation; $\tilde{A}/\tilde{\gamma}^2=1\times10^{-5}$ with $\tilde{A} = A/(1/2)N(N-1)$ and $\tilde{\gamma} = \gamma/(1/2)N(N-1)$. This new relation exhibits an excellent agreement with the data for whole the range of degenerate heavy-fermions.Comment: 2 figures, to appear in Phys. Rev. Let

Effect of Nonmagnetic Impurity in Nearly Antiferromagnetic Fermi Liquid: Magnetic Correlations and Transport Phenomena

In nearly antiferromagnetic (AF) metals such as high-Tc superconductors (HTSC's), a single nonmagnetic impurity frequently causes nontrivial widespread change of the electronic states. To elucidate this long-standing issue, we study a Hubbard model with a strong onsite impurity potential based on an improved fluctuation-exchange (FLEX) approximation, which we call the GV^I-FLEX method. This model corresponds to the HTSC with dilute nonmagnetic impurity concentration. We find that (i) both local and staggered susceptibilities are strongly enhanced around the impurity. By this reason, (ii) the quasiparticle lifetime as well as the local density of states (DOS) are strongly suppressed in a wide area around the impurity (like a Swiss cheese hole), which causes the ``huge residual resistivity'' beyond the s-wave unitary scattering limit. We stress that the excess quasiparticle damping rate caused by impurities has strong momentum-dependence due to non-s-wave scatterings induced by many-body effects, so the structure of the ``hot spot/cold spot'' in the host system persists against impurity doping. This result could be examined by the ARPES measurements. In addition, (iii) only a few percent of impurities can causes a ``Kondo-like'' upturn of resistivity ($d\rho/dT<0$) at low temperatures when the system is very close to the AF quantum critical point (QCP). The results (i)-(iii) obtained in the present study, which cannot be derived by the simple FLEX approximation, naturally explains the main impurity effects in HTSC's. We also discuss the impurity effect in heavy fermion systems and organic superconductors.Comment: 22 pages, to be published in PR

Theory of Anomalous Hall Effect in a Heavy fermion System with a Strong Anisotropic Crystal Field

In a heavy fermion system, there exists the anomalous Hall effect caused by localized $f$-orbital freedom, in addition to the normal Hall effect due to the Lorentz force. In 1994, we found that the Hall coefficient caused by the anomalous Hall effect ($R_H^{AHE}$) is predominant and the relation $R_H^{AHE} \propto \rho^2$ ($\rho$ is the electrical resistivity) holds at low temperatures in many compounds. In this work, we study the system where the magnetic susceptibility is highly anisotropic due to the strong crystalline electric field on $f$-orbitals. Interestingly, we find that $R_H^{AHE}$ is nearly isotropic in general. This tendency is frequently observed experimentally, which has casted suspicion that the anomalous Hall effect may be irrelevant in real materials. Our theory corresponds to corrections and generalizations of the pioneering work on ferromagnetic metals by Karplus and Luttinger.Comment: 4 pages, revtex, to be published in J. Phys. Soc. Jpn. (No.8

Optical Conductivity and Hall Coefficient in High-Tc Superconductors: Significant Role of Current Vertex Corrections

We study AC conductivities in high-Tc cuprates, which offer us significant information to reveal the true electronic ground states. Based on the fluctuation-exchange (FLEX) approximation, current vertex corrections (CVC's) are correctly taken into account to satisfy the conservation laws. We find the significant role of the CVC's on the optical Hall conductivity in the presence of strong antiferromagnetic (AF) fluctuations. This fact leads to the failure of the relaxation time approximation (RTA). As a result, experimental highly unusual behaviors, (i) prominent frequency and temperature dependences of the optical Hall coefficient, and (ii) simple Drude form of the optical Hall andge for wide range of frequencies, are satisfactorily reproduced. In conclusion, both DC and AC transport phenomena in (slightly under-doped) high-Tc cuprates can be explained comprehensively in terms of nearly AF Fermi liquid, if one take the CVC's into account.Comment: 5 page

Transport phenomena in three-dimensional system close to the magnetic quantum critical point: The conserving approximation with the current vertex corrections

It is known that various transport coefficients strongly deviate from conventional Fermi-liquid behaviors in many electron systems which are close to antiferromagnetic (AF) quantum critical points (QCP). For example, Hall coefficients and Nernst coefficients in three-dimensional heavy fermion CeCoIn5 and CeCu6-xAux increase strikingly at low temperatures, whose overall behaviors are similar to those in high-Tc cuprates. These temperature dependences are too strong to explain in terms of the relaxation time approximation. To elucidate the origin of these anomalous transport phenomena in three-dimensional systems, we study the current vertex corrections (CVC) based on the fluctuation exchange (FLEX) approximation, and find out decisive role of the CVC. The main finding of the present paper is that the Hall coefficient and the Nernst coefficient strongly increase thanks to the CVC in the vicinity of the AF QCP, irrespective of dimensionality. We also study the relaxation time of quasi-particles, and find that "hot points" and "cold lines" are formed in general three-dimensional systems due to strong AF fluctuations.Comment: 11 pages, 18 figures. Accepted for publication in Phys. Rev.

Giant Extrinsic Spin Hall Effect due to Rare-Earth Impurities

We investigate the extrinsic spin Hall effect in the electron gas model due to magnetic impurities, by focusing on Ce- and Yb-impurities. In the dilute limit, the skew scattering term dominates the side jump term. For Ce-impurities, the spin Hall angle $\alpha_{\rm SH}$ due to skew scattering is given by $-8\pi\sin\delta_2/7$, where $\delta_2 (\ll 1)$ is the phase shift for$d (l=2)$ partial wave. Since $\alpha_{\rm SH}$ reaches $O(10^{-1})$ if \delta_2 \simge 0.03, the spin Hall effect is anticipated to be considerable in metals with rare-earth impurities. The giant extrinsic SHE originates from the large orbital angular momentum, which is also significant for the intrinsic SHE.Comment: 5 pages, 3 figures, to be published in New Journal of Physic

Indication of intrinsic spin Hall effect in 4d and 5d transition metals

We have investigated spin Hall effects in 4$d$ and 5$d$ transition metals, Nb, Ta, Mo, Pd and Pt, by incorporating the spin absorption method in the lateral spin valve structure; where large spin current preferably relaxes into the transition metals, exhibiting strong spin-orbit interactions. Thereby nonlocal spin valve measurements enable us to evaluate their spin Hall conductivities. The sign of the spin Hall conductivity changes systematically depending on the number of $d$ electrons. This tendency is in good agreement with the recent theoretical calculation based on the intrinsic spin Hall effect.Comment: 5 pages, 4 figure