Microscopic theory on charge transports of a correlated multiorbital system

Current vertex correction (CVC), the back-flow-like correction to the current, comes from conservation laws, and the CVC due to electron correlation contains information about many-body effects. However, it has been little understood how the CVC due to electron correlation affects the charge transports of a correlated multiorbital system. To improve this situation, I studied the inplane resistivity, $\rho_{ab}$, and the Hall coefficient in the weak-field limit, $R_{\textrm{H}}$, in addition to the magnetic properties and the electronic structure, for a $t_{2g}$-orbital Hubbard model on a square lattice in a paramagnetic state away from or near an antiferromagnetic (AF) quantum-critical point (QCP) in the fluctuation-exchange (FLEX) approximation with the CVCs arising from the self-energy ($\Sigma$), the Maki-Thompson (MT) irreducible four-point vertex function, and the main terms of the Aslamasov-Larkin (AL) one. Then, I found three main results about the CVCs. First, the main terms of the AL CVC does not qualitatively change the results obtained in the FLEX approximation with the $\Sigma$ CVC and the MT CVC. Second, $\rho_{ab}$ and $R_{\textrm{H}}$ near the AF QCP have high-temperature region, governed mainly by the $\Sigma$ CVC, and low-temperature region, governed mainly by the $\Sigma$ CVC and the MT CVC. Third, in case away from the AF QCP, the MT CVC leads to a considerable effect on only $R_{\textrm{H}}$ at low temperatures, although $R_{\textrm{H}}$ at high temperatures and $\rho_{ab}$ at all temperatures considered are sufficiently described by including only the $\Sigma$ CVC. I also achieved the qualitative agreement with several experiments of Sr$_{2}$RuO$_{4}$ or Sr$_{2}$Ru$_{0.975}$Ti$_{0.025}$O$_{4}$. Moreover, I showed several better points of this theory than other theories.Comment: 43 pages, 23 figures, 1 table; published versio

Vector chirality for effective total momentum JeffJ_{\textrm{eff}} in a nonfrustrated Mott insulator: Effects of strong spin-orbit coupling and broken inversion symmetry

I propose the emergence of the spin-orbital-coupled vector chirality in a non-frustrated Mott insulator with the strong spin-orbit coupling due to $ab$-plane's inversion-symmetry (IS) breaking. I derive the superexchange interactions for a $t_{2g}$-orbital Hubbard model on a square lattice with the strong spin-orbit coupling and the IS-breaking-induced hopping integrals, and explain the microscopic origins of the Dzyaloshinsky-Moriya (DM) -type and the Kitaev-type interactions. Then, by adopting the mean-field approximation to a minimal model including only the Heisenberg-type and the DM-type nearest-neighbor interactions, I show that the IS breaking causes the spin-orbital-coupled chirality as a result of stabilizing the screw state. I also highlight the limit of the hard-pseudospin approximation in discussing the stability of the screw states in the presence of both the DM-type and the Kitaev-type interactions, and discuss its meaning. I finally discuss the effects of tetragonal crystal field and $J_{\textrm{eff}}=\frac{3}{2}$ states, and the application to the iridates near the $[001]$ surface of Sr$_{2}$IrO$_{4}$ and the interface between Sr$_{2}$IrO$_{4}$ and Sr$_{3}$Ir$_{2}$O$_{7}$.Comment: 11 pages, 3 figures; published versio

Orbital-cooperative spin fluctuation and orbital-dependent transport in ruthenates

Unusual transport properties deviating from the Fermi liquid are observed in ruthenates near a magnetic quantum-critical point (QCP). To understand the electronic properties of the ruthenates near and away from an antiferromagnetic (AF) QCP, I study the electronic structure and magnetic and transport properties for the $t_{2g}$-orbital Hubbard model on a square lattice in fluctuation-exchange approximation including Maki-Thompson (MT) current vertex correction (CVC). The results away from the AF QCP reproduce several experimental results of Sr$_{2}$RuO$_{4}$ qualitatively and provide new mechanisms about the enhancement of spin fluctuation at $Q_{\textrm{IC-AF}}\approx (0.66\pi,0.66\pi)$, larger mass enhancement of the $d_{xy}$ orbital than that of the $d_{xz/yz}$ orbital, and nonmonotonic temperature dependence of the Hall coefficient. Also, the results near the AF QCP explain the $T$-linear inplane resistivity in Sr$_{2}$Ru$_{0.075}$Ti$_{0.025}$O$_{4}$ and give an experimental test on the obtained temperature dependence of the Hall coefficient. I reveal spatial correlation including the self-energy of electrons beyond mean-field approximations is essential to determine the electronic properties of the ruthenates. I also show several ubiquitous transport properties near an AF QCP and characteristic transport properties of a multiorbital system by comparison with results of a single-orbital system near an AF QCP.Comment: 6 pages, 3 figure

Microscopic theory of Dzyaloshinsky-Moriya interaction in pyrochlore oxides with spin-orbit coupling

Pyrochlore oxides show several fascinating phenomena, such as the formation of heavy fermions and the thermal Hall effect. Although a key to understanding some phenomena may be the Dzyaloshinsky-Moriya (DM) interaction, its microscopic origin is unclear. To clarify the microscopic origin, we constructed a $t_{2g}$-orbital model with the kinetic energy, the trigonal-distortion potential, the multiorbital Hubbard interactions, and the $LS$ coupling, and derived the low-energy effective Hamiltonian for a $d^{1}$ Mott insulator with the weak $LS$ coupling. We first show that lack of the inversion center of each nearest-neighbor V-V bond causes the odd-mirror interorbital hopping integrals. Those are qualitatively different from the even-mirror hopping integrals, existing even with the inversion center. We next show that the second-order perturbation using the kinetic terms leads to the ferromagnetic and the antiferromagnetic super exchange interactions. Then, we show the most important result: the third-order perturbation terms using the combination of the even-mirror hopping integral, the odd-mirror hopping integral, and the $LS$ coupling causes the DM interaction due to the mirror-mixing effect, where those hopping integrals are necessary to obtain the antisymmetric kinetic exchange and the $LS$ coupling is necessary to excite the orbital angular momentum at one of two sites. We also show that the magnitude and sign of the DM interaction can be controlled by changing the positions of the O ions and the strength of the Hubbard interactions. We discuss the advantages in comparison with the phenomenological theory and Moriya's microscopic theory, applicability of our mechanism, and the similarities and differences between our case and the strong-$LS$-coupling case.Comment: 23 pages, 8 figures; published versio

Many-body effects on the resistivity of a multiorbital system beyond Landau's Fermi-liquid theory

I review many-body effects on the resistivity of a multiorbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point. These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multiorbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multiorbital systems. To improve this situation, I formulate the resistivity of a multiorbital Hubbard model using the extended \'{E}liashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki-Thompson term. The results away from and near the antiferromagnetic quantum-critical point reproduce the temperature dependence observed in Sr$_{2}$RuO$_{4}$ and Sr$_{2}$Ru$_{0.075}$Ti$_{0.025}$O$_{4}$, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems.Comment: 26 pages, 9 figures; published as an invited brief review article in Modern Physics Letters

Magnon Dispersion and Specific Heat of Chiral Magnets on the Pyrochlore Lattice

Chiral magnets are magnetically ordered insulators having spin scalar chirality, and magnons of chiral magnets have been poorly understood. We study the magnon dispersion and specific heat for four chiral magnets with Q=0 on the pyrochlore lattice. This study is based on the linear-spin-wave approximation for the S=1/2 effective Hamiltonian consisting of two kinds of Heisenberg interaction and two kinds of Dzyaloshinsky-Moriya interaction. We show that the three-in-one-out type chiral magnets possess an optical branch of the magnon dispersion near q=0, in addition to three quasiacoustic branches. This differs from the all-in/all-out type chiral magnets, which possess four quasiacoustic branches. We also show that all four chiral magnets have a gapped magnon energy at q=0, indicating the absence of the Goldstone type gapless excitation. These results are useful for experimentally identifying the three-in-one-out or all-in/all-out type chiral order. Then, we show that there is no qualitative difference in the specific heat among the four magnets. This indicates that the specific heat is not useful for distinguishing the kinds of chiral orders. We finally compare our results with experiments and provide a proposal for the three-in-one-out type chiral magnets.Comment: 11 pages, 11 figure

Tunneling between chiral magnets: Spin current generation without external fields

Magnons can generate a spin current, and the standard generating mechanism requires at least one external field. Since this mechanism is often applied to a multilayer system including a magnet and a paramagnetic metal, the system can possess not only the charge current induced by the spin current but also the charge current induced by the external field. The latter is an unnecessary accompaniment. Here we show that the tunneling of a magnon pair between chiral magnets can generate a spin current even without external fields. This phenomenon originates from a phase difference between magnon pairs of separate, weakly coupled chiral magnets, and is essentially different from the mechanism using the angle degree of freedom of the magnon Bose-Einstein condensates. The pair's tunneling is possible in chiral magnets due to lack of the Goldstone-type gapless excitations. This phenomenon opens the door to spintronics not requiring any external field and using the magnon pair tunneling.Comment: 8 pages, 2 figure

Fermi surface versus Fermi sea contributions to intrinsic anomalous and spin Hall effects of multiorbital metals in the presence of Coulomb interaction and spin-Coulomb drag

Anomalous Hall effect (AHE) and spin Hall effect (SHE) are fundamental phenomena, and their potential for application is great. However, we understand the interaction effects unsatisfactorily, and should have clarified issues about the roles of the Fermi sea term and Fermi surface term of the conductivity of the intrinsic AHE or SHE of an interacting multiorbital metal and about the effects of spin-Coulomb drag on the intrinsic SHE. Here we resolve the first issue and provide the first step about the second issue by developing a general formalism in the linear response theory with appropriate approximations and using analytic arguments. The most striking result is that even without impurities the Fermi surface term, a non-Berry-curvature term, plays dominant roles at high or slightly low temperatures. In particular, this Fermi surface term causes the temperature dependence of the dc anomalous Hall or spin Hall conductivity due to the interaction-induced quasiparticle damping and the correction of the dc spin Hall conductivity due to the spin-Coulomb drag. Those results revise our understanding of the intrinsic AHE and SHE. We also find that the differences between the dc anomalous Hall and longitudinal conductivities arise from the difference in the dominant multiband excitations. This not only explains why the Fermi sea term such as the Berry-curvature term becomes important in clean and low-temperature case only for interband transports but also provides the useful principles on treating the electron-electron interaction in an interacting multiorbital metal for general formalism of transport coefficients. Several correspondences between our results and experiments are finally discussed.Comment: 23 pages 4 figure; published versio

Competition between spin fluctuations in Ca2−x_{2-x}Srx_{x}RuO4_{4} around x=0.5x=0.5

We study the static susceptibilities for charge and spin sectors in paramagnetic states for Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ in $0.5\leq x \leq 2$ within random phase approximation on the basis of an effective Ru $t_{2g}$ orbital Hubbard model. We find that several modes of spin fluctuation around \boldq=(0,0) and \boldq\sim(0.797\pi,0) are strongly enhanced for the model of $x=0.5$. This enhancement arises from the increase of the corresponding susceptibilities for the $d_{xy}$ orbital due to the rotation-induced modifications of the electronic structure for this orbital (i.e., the flattening of the bandwidth and the increase of the density of state near the Fermi level). We also find that the ferromagnetic spin fluctuation becomes stronger for a special model than for the model of $x=0.5$, while the competition between the modes of spin fluctuation at \boldq=(0,0) and around \boldq\sim (\pi,0) is weaker for the special model; in this special model, the van Hove singularity (vHs) for the $d_{xy}$ orbital is located on the Fermi level. These results indicate that the location of the vHs for the $d_{xy}$ orbital, which is controlled by substitution of Ca for Sr, is a parameter to control this competition. We propose that the spin fluctuations for the $d_{xy}$ orbital around \boldq=(0,0) and \boldq\sim (\pi,0) play an important role in the electronic states around $x=0.5$ other than the criticality approaching the usual Mott transition where all electrons are localized.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Negative magneto-thermal-resistance in a disordered two-dimensional antiferromagnet

We demonstrate that a weak external magnetic field can induce negative magneto-thermal-resistance for magnons in a disordered two-dimensional antiferromagnet. We study the main effect of a weak external magnetic field on the longitudinal thermal conductivity, $\kappa_{xx}$, for a disordered antiferromagnet using the weak-localization theory for magnons. We show that the weak-localization correction term of $\kappa_{xx}$ positively increases with increasing the magnetic field parallel to the ordered spins. Since this increase corresponds to a decrease of the thermal resistivity, this phenomenon is negative magneto-thermal-resistance for magnons. This negative magneto-thermal-resistance and the weak localization of magnons will be used to control the magnon thermal current in antiferromagnetic spintronics devices. We also discuss several implications for further experimental and theoretical studies for disordered magnets.Comment: 8 pages, 1 figure; published versio