Abstract

Electromagnons (Electroactive spin wave excitations) could prove to be decisive in information technologies but they remain fragile quantum objects, mainly existing at low temperatures. Any future technological application requires overcoming these two limitations. By means of synchrotron radiation infrared spectroscopy performed in the THz energy range and under hydrostatic pressure, we tracked the electromagnon in the cupric oxide CuO, despite its very low absorption intensity. We demonstrate how a low pressure of 3.3 GPa strongly increases the strength of the electromagnon and expands its existence to a large temperature range enhanced by 40 K. Accordingly, these two combined effects make the electromagnon of CuO under pressure a more ductile quantum object. Numerical simulations based on an extended Heisenberg model were combined to the Monte-Carlo technique and spin dynamics to account for the magnetic phase diagram of CuO. They enable to simulate the absorbance response of the CuO electromagnons in the THz range.

We investigate the possible emergence of topological Hall effect (THE) in a driven magnetic domain wall (DW). Numerical simulations based on the Landau-Lifshitz-Gilbert-Slonczewski equation shows that the emergent magnetic flux appears when the DW is in a non-equilibrium state. The magnitude of magnetic flux is modulated by the Dzyaloshinskii-Moriya interaction (DMI), providing an experimental test of the predicted THE by a voltage controlled DMI modulation. These results indicate that the THE can be observed even in a topologically trivial magnetic DW, and therefore open up new possibility to electrically detect the dynamical spin structure.

Anticrossing behavior between magnons in the noncollinear chiral magnet Cu2OSeO3 and a two-mode X-band microwave resonator was studied in the temperature range 5-100 K. In the field-induced ferrimagnetic phase, we observed a strong-coupling regime between magnons and two microwave cavity modes with a cooperativity reaching 3600. In the conical phase, cavity modes are dispersively coupled to a fundamental helimagnon mode, and we demonstrate that the magnetic phase diagram of Cu2OSeO3 can be reconstructed from the measurements of the cavity resonance frequency. In the helical phase, a hybridized state of a higher-order helimagnon mode and a cavity mode-a helimagnon polariton-was found. Our results reveal a class of magnetic systems where strong coupling of microwave photons to nontrivial spin textures can be observed.

We theoretically demonstrate that a rotating electric-field component of circularly polarized microwaves or terahertz light can induce electron-spin polarization within a few picoseconds in a two-dimensional electron system with the Rashba spin-orbit interaction by taking advantage of magnetoelectric coupling. The efficiency turns out to be several orders of magnitude greater than that of conventional methods, indicating high potential of this technique in future spintronics.

Nontrivial magnetic orders in the inverse-perovskite manganese nitrides are theoretically studied by constructing a classical spin model describing the magnetic anisotropy and frustrated exchange interactions inherent in specific crystal and electronic structures of these materials. With a replica-exchange Monte Carlo technique, a theoretical analysis of this model reproduces the experimentally observed triangular Γ5g and Γ4g spin-ordered patterns and the systematic evolution of magnetic orders. Our Rapid Communication solves a 40-year-old problem of nontrivial magnetism for the inverse-perovskite manganese nitrides and provides a firm basis for clarifying the magnetism-driven negative thermal expansion phenomenon discovered in this class of materials.

We report on the formation process of skyrmion lattice (SkL) domain boundaries in FeGe using Lorentz transmission electron microscopy and small-angle electron diffraction. We observed that grain boundaries and edges play an important role in the formation of SkL domain boundaries; The SkL domain boundary is stabilized at the intersection of two grains. A micromagnetic simulation using the Landau-Lifshitz-Gilbert equation revealed that the SkL domains separated by a boundary represent the lowest energy configuration. Conversely, in a wide area, SkL domain boundaries were not formed and SkL domains with different orientations rotated to form a single SkL domain. Published by AIP Publishing.

To exploit nanometric magnetic skyrmions as information carriers in high-density storage devices, a method is needed that creates an intended number of skyrmions at specified places in the device preferably at a low energy cost. We theoretically propose that using a system with a fabricated hole or notch, the controlled creation of individual skyrmions can be achieved even when using an external magnetic field applied to the entire specimen. The fabricated defect turns out to work like a catalyst to reduce the energy barrier for the skyrmion creation. Published by AIP Publishing.

It is theoretically proposed that magnetic skyrmions, nanometric spin vortices characterized by a quantized topological number, can be electrically created on a thin-film specimen of chiral-lattice magnetic insulator within a few nanoseconds by applying an electric field via an electrode tip taking advantage of coupling between noncollinear skyrmion spins and electric polarizations. This finding paves the way for utilizing multiferroic skyrmions as information carriers for low-energy-consuming magnetic storage devices without Joule-heating energy losses.

Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions has been limited to metallic magnets so far, their realization was also discovered in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-induced ferroelectricity. Strong magnetoelectric coupling between noncollinear skyrmion spins and electric polarizations mediated by relativistic spin-orbit interaction enables us to drive motion and oscillation of magnetic skyrmions by application of electric fields instead of injection of electric currents. Insulating materials also provide an environment suitable for detection of pure spin dynamics through spectroscopic measurements owing to the absence of appreciable charge excitations. In this article, we review recent theoretical and experimental studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulators. We argue that multiferroic skyrmions show unique coupled oscillation modes of magnetizations and polarizations, so-called electromagnon excitations, which are both magnetically and electrically active, and interference between the electric and magnetic activation processes leads to peculiar magnetoelectric effects in a microwave frequency regime.

The magnetic-field-induced 90 degrees. flop of ferroelectric polarization P in a spin-spiral multiferroic material TbMnO3 is theoretically studied based on a microscopic spin model. I find that the direction of the P flop or the choice of +P-a or -P-a after the flop is governed by magnetic torques produced by the applied magnetic field H acting on the Mn spins and thus is selected in a deterministic way, in contradistinction to the naively anticipated probabilistic flop. This mechanism resolves a puzzle of the previously reported memory effect in the P direction depending on the history of the magnetic-field sweep, and enables controlled switching of multiferroic domains by externally applied magnetic fields. My Monte-Carlo analysis also uncovers that the magnetic structure in the P parallel to a phase under H parallel to b is not a previously anticipated simple ab-plane spin cycloid but a conical spin structure.

Following the early prediction of the skyrmion lattice (SkL)-a periodic array of spin vortices-it has been observed recently in various magnetic crystals mostly with chiral structure. Although non-chiral but polar crystals with C-nv symmetry were identified as ideal SkL hosts in pioneering theoretical studies, this archetype of SkL has remained experimentally unexplored. Here, we report the discovery of a SkL in the polar magnetic semiconductor GaV4S8 with rhombohedral (C-3v) symmetry and easy axis anisotropy. The SkL exists over an unusually broad temperature range compared with other bulk crystals and the orientation of the vortices is not controlled by the external magnetic field, but instead confined to the magnetic easy axis. Supporting theory attributes these unique features to a new Neel-type of SkL describable as a superposition of spin cycloids in contrast to the Bloch-type SkL in chiral magnets described in terms of spin helices.

This paper reports on a theoretical proposal for electrical creation of magnetic skyrmions on a thin-film specimen of a multiferroic chiral magnet by local application of an electric field, instead of an electric current, via an electrode tip. This method can be traced back to the mutual coupling between skyrmion spins and the electric polarizations in multiferroics and represents a unique technique for use in potential skyrmion-based memory devices without Joule-heating losses. (C) 2015 AIP Publishing LLC.

The manipulation of domains by external fields in ferroic materials is of major interest for applications. In multiferroics with strongly coupled magnetic and electric order, however, the magnetoelectric coupling on the level of the domains is largely unexplored. We investigated the field-induced domain dynamics of TbMnO3 in the multiferroic ground state and across a first-order spin-flop transition. In spite of the discontinuous nature of this transition, the reorientation of the order parameters is deterministic and preserves the multiferroic domain pattern. Landau-Lifshitz-Gilbert simulations reveal that this behavior is intrinsic. Such magnetoelectric correlations in spin-driven ferroelectrics may lead to domain wall-based nanoelectronics devices.

We theoretically find that in the multiferroic chiral magnet Cu2OSeO3 resonant magnetic excitations are coupled to the collective oscillation of the electric polarization, and thereby attain simultaneous activity to the ac magnetic field and ac electric field. Because of the interference between these magnetic and electric activation processes, this material hosts a gigantic magnetochiral dichroism for microwaves, that is, a directional dichroism at gigahertz frequencies in the Faraday geometry. The absorption intensity of a microwave differs by as much as similar to 30% depending on whether its propagation direction is parallel or antiparallel to the external magnetic field.

Spontaneously emergent chirality is an issue of fundamental importance across the natural sciences(1). It has been argued that a unidirectional (chiral) rotation of a mechanical ratchet is forbidden in thermal equilibrium, but becomes possible in systems out of equilibrium(2). Here we report our finding that a topologically nontrivial spin texture known as a skyrmion-a particle-like object in which spins point in all directions to wrap a sphere(3)-constitutes such a ratchet. By means of Lorentz transmission electron microscopy we show that micrometre-sized crystals of skyrmions in thin films of Cu2OSeO3 and MnSi exhibit a unidirectional rotation motion. Our numerical simulations based on a stochastic Landau-Lifshitz-Gilbert equation suggest that this rotation is driven solely by thermal fluctuations in the presence of a temperature gradient, whereas in thermal equilibrium it is forbidden by the Bohr-van Leeuwen theorem(4,5). We show that the rotational flow of magnons driven by the effective magnetic field of skyrmions gives rise to the skyrmion rotation, therefore suggesting that magnons can be used to control the motion of these spin textures.

Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant in chiral-lattice magnets, are currently attracting intensive research interest. In particular, their dynamics under external fields is an issue of vital importance because its understanding is crucial both for fundamental science and for technical applications. It has turned out that the skyrmions in an insulating magnet Cu_2OSeO_3 exhibit a multiferroic nature with magnetism-induced ferroelectricity. In this article, we discuss that this multiferroic skyrmion phase shows unique coupled oscillation modes of magnetizations and polarizations, which are both magnetically and electrically active, and the intense interference between their electric and magnetic activation processes leads to an unprecedentedly large diode effect on microwaves. The microwave absorption by this skyrmion phase changes up to 〜20% when the incident direction is reversed. Our results demonstrate that the multiferroic skyrmions can be a promising building block for microwave devices.

Magnetic skyrmions-vortex-like swirling spin structures with a quantized topological number that are observed in chiral magnets-are appealing for potential applications in spintronics because it is possible to control their motion with ultralow current density. To realize skyrmion-based spintronic devices, it is essential to understand skyrmion motions in confined geometries. Here we show by micromagnetic simulations that the current-induced motion of slcyrmions in the presence of geometrical boundaries is very different from that in an infinite plane. In a channel of finite width, transverse confinement results in steady-state characteristics of the skyrmion velocity as a function of current that are similar to those of domain walls in ferromagnets, whereas the transient behaviour depends on the initial distance of the skyrmion from the boundary. Furthermore, we show that a single slcyrmion can be created by an electric current in a simple constricted geometry comprising a plate-shaped specimen of suitable size and geometry. These findings could guide the design of skyrmion-based devices in which skyrmions are used as information carriers.

We theoretically discover that unique eigenmodes of skyrmion crystal (SkX) are not only magnetically active to an ac magnetic field (H-omega) but also electrically active to an ac electric field (E-omega) in a multiferroic chiral-lattice magnet Cu2OSeO3, which amplifies the dynamical magnetoelectric coupling between E-omega and the spin texture. The resulting intense interference between their electric and their magnetic activation processes can lead to an unprecedentedly large diode effect on the microwave, i.e., its absorption by SkX changes up to similar to 20% when the incident direction is reversed. Our results demonstrate that the skyrmion could be a promising building block for microwave devices. DOI:10.1103/PhysRevB.87.134403

Current-driven motion of the magnetic domain wall in ferromagnets is attracting intense attention because of potential applications such as racetrack memory. There, the critical current density to drive the motion is similar to 10(9)-10(12) A m(-2). The skyrmions recently discovered in chiral magnets have much smaller critical current density of similar to 10(5)-10(6) A m(-2), but the microscopic mechanism is not yet explored. Here we present a numerical simulation of Landau-Lifshitz-Gilbert equation, which reveals a remarkably robust and universal current-velocity relation of the skyrmion motion driven by the spin-transfer-torque unaffected by either impurities or nonadiabatic effect in sharp contrast to the case of domain wall or spin helix. Simulation results are analysed using a theory based on Thiele's equation, and it is concluded that this behaviour is due to the Magnus force and flexible shape-deformation of individual skyrmions and skyrmion crystal, which enable them to avoid pinning centres.

Magnetic skyrmion, a topologically stable spin-swirling object, can host emergent electromagnetism, as exemplified by the topological Hall effect and electric-current-driven skyrmion motion. To achieve efficient manipulation of nano-sized functional spin textures, it is imperative to exploit the resonant motion of skyrmions, analogously to the role of the ferromagnetic resonance in spintronics. The magnetic resonance of skyrmions has recently been detected with oscillating magnetic fields at 1-2 GHz, launching a search for new skyrmion functionality operating at microwave frequencies. Here we show a microwave magnetoelectric effect in resonant skyrmion dynamics. Through microwave transmittance spectroscopy on the skyrmion-hosting multiferroic crystal Cu 2 OSeO 3 combined with theoretical simulations, we reveal nonreciprocal directional dichroism (NDD) at the resonant mode, that is, oppositely propagating microwaves exhibit different absorption. The microscopic mechanism of the present NDD is not associated with the conventional Faraday effect but with the skyrmion magnetoelectric resonance instead, suggesting a conceptually new microwave functionality. © 2013 Macmillan Publishers Limited.

We theoretically study spin-wave modes and their intense excitations activated by microwave magnetic fields in the Skyrmion-crystal phase of insulating magnets by numerically analyzing a two-dimensional spin model using the Landau-Lifshitz-Gilbert equation. Two peaks of spin-wave resonances with frequencies of similar to 1 GHz are found for in-plane ac magnetic field where distribution of the out-of-plane spin components circulates around each Skyrmion core. Directions of the circulations are opposite between these two modes, and hence the spectra exhibit a salient dependence on the circular polarization of irradiating microwave. A breathing-type mode is also found for an out-of-plane ac magnetic field. By intensively exciting these collective modes, melting of the Skyrmion crystal accompanied by a redshift of the resonant frequency is achieved within nanoseconds.

We investigated the magnetic structure of an orthorhombic YMnO3 thin film by resonant soft x-ray and hard x-ray diffraction. We observed a temperature-dependent incommensurate magnetic reflection below 45 K and a commensurate lattice-distortion reflection below 35 K. These results demonstrate that the ground state is composed of coexisting E-type and cycloidal states. Their different ordering temperatures clarify the origin of the large polarization to be caused by the E-type antiferromagnetic states in the orthorhombic YMnO3 thin film.

We report on a topological Hall effect possibly induced by scalar spin chirality in a quasi-two-dimensional helimagnet Fe1+delta Sb. In the low-temperature region where the spins on interstitial-Fe (concentration delta similar to 0.3) intervening the 120 degrees spin-ordered triangular planes tend to freeze, a nontrivial component of Hall resistivity with opposite sign of the conventional anomalous Hall term is observed under magnetic field applied perpendicular to the triangular-lattice plane. The observed unconventional Hall effect is ascribed to the scalar spin chirality arising from the heptamer spin clusters around the interstitial-Fe sites, which can be induced by the spin modulation by the Dzyaloshinsky-Moriya interaction.

Magnetoelectric phase diagrams of the rare-earth (R) Mn perovskites RMnO3 are theoretically studied by focusing on crucial roles of the symmetric magnetostriction or the Peierls-type spin-phonon coupling through extending our previous work [M. Mochizuki et al., Phys. Rev. Lett. 105, 037205 (2010)]. We first construct a microscopic classical Heisenberg model for RMnO3 including the frustrated spin exchanges, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. We also incorporate the lattice degree of freedom coupled to the Mn spins via the Peierls-type magnetostriction. By analyzing this model using the replica-exchange Monte Carlo technique, we reproduce the entire phase diagram of RMnO3 in the plane of temperature and magnitude of the orthorhombic lattice distortion. Surprisingly it is found that in the ab-plane spiral spin phase, the (S . S)-type magnetostriction plays an important role for the ferroelectric order with polarization P parallel to a whose contribution is comparable to or larger than the contribution from the (S x S)-type magnetostriction, whereas in the bc-plane spiral phase, the ferroelectric order with P parallel to c is purely of (S x S) origin. This explains much larger P in the ab-plane spiral phase than the bc-plane spiral phase as observed experimentally and gives a clue how to enhance the magnetoelectric coupling in the spin-spiral-based multiferroics. We also predict a noncollinear deformation of the E-type spin structure resulting in the finite (S x S) contribution to the ferroelectric order with P parallel to a, and a wide coexisting regime of the commensurate E and incommensurate spiral states, which resolve several experimental puzzles.

We have studied the impact of the magnetic field on the electromagnon excitations in TbMnO3 crystal. Applying a magnetic field along the c axis, we show that the electromagnons transform into pure antiferromagnetic modes, losing their polar character. Entering in the paraelectric phase, we are able to track the spectral weight transfer from the electromagnons to the magnon excitations and we discuss the magnetic excitations underlying the electromagnons. We also point out the phonons involved in the phase transition process. This reveals that the Mn-O distance plays a key role in understanding the ferroelectricity and the polar character of the electromagnons. Magnetic field measurements along the b axis allow us to detect a new electromagnon resonance in agreement with a Heisenberg model.

We propose a microscopic theory for magnetic switching of electric polarization (P) in the spin-spiral multiferroics by taking TbMnO(3) and DyMnO(3) as examples. We reproduce their phase diagrams under a magnetic field H(ex) by Monte Carlo simulation of an accurate spin model and reveal that competition among the Dzyaloshinskii-Moriya interaction, spin anisotropy, and spin exchange is controlled by the applied H(ex), resulting in magnetic transitions accompanied by reorientation or vanishing of P. We also discuss the relevance of the proposed mechanisms to many other multiferroics such as LiCu(2)O(2), MnWO(4), and Ni(3)V(2)O(4).

We show theoretically with an accurate spin Hamiltonian describing the multiferroic Mn perovskites that the application of the picosecond optical pulse with a terahertz frequency can switch the spin chirality through intensely exciting the electromagnons. There are four states with different spin chiralities, i.e., clockwise and counterclockwise ab/bc-plane spin spirals, and by tuning the strength, shape and length of the pulse, the switching among these states can be controlled at will. Dynamical pattern formation during the switching is also discussed.

We theoretically study origins of the ferroelectricity in the multiferroic phases of the rare-earth (R) Mn perovskites, RMnO(3), by constructing a realistic spin model including the spin-phonon coupling, which reproduces the entire experimental phase diagram in the plane of temperature and Mn-O-Mn bond angle for the first time. Surprisingly we reveal a significant contribution of the symmetric (S . S)-type magneto-striction to the ferroelectricity even in a spin-spiral-based multiferroic phase, which can be larger than the usually expected antisymmetric (S X S)-type contribution. This explains well the nontrivial behavior of the electric polarization. We also predict the noncollinear deformation of the E-type spin structure and a wide coexisting regime of the E and spiral states, which resolve several experimental puzzles.

We study theoretically the electromagnon and its optical spectrum ( OS) of the terahertz-frequency regime in the magnetic-spiral-induced multiferroic phases of the rare-earth-metal (R) Mn perovskites, RMnO(3), taking into account the spin-angle modulation or the higher harmonics of the spiral spin configuration, which has been missed so far. A realistic spin Hamiltonian, which gives phase diagrams in agreement with experiments, resolves a puzzle, i.e., the double-peak structure of the OS with a larger low-energy peak originating from magnon modes hybridized with the zone-edge state. We also predict the magnon branches associated with the electromagnon, which can be tested by neutron-scattering experiment.

In order to investigate the nature of the antiferromagnetic structures in perovskite RMnO3, we study a Heisenberg J(1)-J(2) model with bond alternation using analytical and numerical approaches. The magnetic phase diagram which includes incommensurate spiral states and commensurate collinear states is reproduced. We discuss that the magnetic structure with spin up arrow up arrow down arrow down arrow configuration (E-type structure) and the ferroelectricity emerge cooperatively to stabilize this phase. Magnetoelastic couplings are crucial to understand the magnetic and electric phase diagram of RMnO3.

Orthorhombically distorted perovskite manganites, RMnO3 with R being a trivalent rare-earth ion, exhibit a variety of magnetic and electric phases including multiferroic (i.e., concurrently magnetic and ferroelectric) phases and fascinating magnetoelectric phenomena. We theoretically study the phase diagram of RMnO3 by constructing a microscopic spin model, which includes not only the superexchange interaction but also the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya interaction (DMI). Analysis of this model using the Monte Carlo method reproduces the experimental phase diagrams as functions of the R-ion radius, which contain two different multiferroic states, i.e., the ab-plane spin cycloid with ferroelectric polarization P parallel to a and the bc-plane spin cycloid with P parallel to c. The orthorhombic lattice distortion or the second-neighbor spin exchanges enhanced by this distortion exquisitely controls the keen competition between these two phases through tuning the SIA and DMI energies. This leads to a lattice-distortion-induced reorientation of P from a to c in agreement with the experiments. We also discuss spin structures in the A-type antiferromagnetic state, those in the cycloidal spin states, origin and nature of the sinusoidal collinear spin state, and many other issues.

Magnetic and dielectric properties of Eu1-xYxMnO3 (x = 0 and 0.4) are studied in pulsed magnetic fields up to 55 T. For x = 0, application of magnetic fields higher than 20 T along the b axis causes magnetic transitions accompanied by generation of electric polarization (P) along the a axis. Similar first-order transitions are also observed in crystals of x = 0: 4, in which the ground state at zero magnetic field is already a ferroelectric P parallel to a phase of different origin. Realistic model calculation indicates the presence of a novel multiferroic state induced by the spin exchange striction mechanism in high magnetic fields as an essential nature of the frustrated Mn spin system in this class of manganites.

We theoretically study a competition between two types of spin cycloids (ab-plane and bc-plane ones) in the multiferroic perovskite manganites, which is an origin of intriguing tnagnetoelectric phenomena in these compounds. Analysis of a microscopic model using the Monte-Carlo method reveals that their competition originates from a conflict between the single-ion anisotropy and the Dzyaloshinsky-Moriya interaction. It is demonstrated that the conflict can be controlled by tuning the second-neighbor spin exchanges through the GdFeO3-type distortion, which leads to a cycloidal-plane flop from ab to be observed in the solid-solution systems like Eu1-xYxMnO3 and Gd1-xTbxMnO3 with increasing x.

We report the dielectric dispersion of the giant magnetocapacitance (GMC) in multiferroic DyMnO3 over a wide frequency range. The GMC is found to be attributable not to the softened electromagnon but to the electric-field-driven motion of multiferroic domain wall (DW). In contrast to conventional ferroelectric DWs, the present multiferroic DW motion holds an extremely high relaxation rate of similar to 10(7) s(-1) even at low temperatures. This mobile nature as well as the model simulation suggests that the multiferroic DW is not atomically thin as in ferroelectrics but thick, reflecting its magnetic origin.

The wide range optical spectra on a multiferroic prototype TbMnO(3) have been investigated to clarify the origin of spin excitations observed in the far-infrared region. We elucidate the full band structure, whose high energy edge (133 cm(-1)) exactly corresponds to twice of the highest-lying magnon energy. Thus the origin of this absorption band is clearly assigned to two-magnon excitation driven by the electric field of light. There is an overlap between the two-magnon and phonon energy ranges, where the strong coupling between them is manifested by the frequency shift and transfer of oscillator strength of the phonon mode.

Electronic properties of the sodium cobaltate NaxCoO2 are systematically studied through a precise control of band filling. Resistivity, magnetic susceptibility and specific heat measurements are carried out on a series of high-quality polycrystalline samples prepared at 200 degrees C with Na content in a wide range of 0.35 <= x <= 0.70. It is found that dramatic changes in electronic properties take place at a critical Na concentration x* that lies between 0.58 and 0.59, which separates a Pauli paramagnetic and a Curie-Weiss metals. It is suggested that at x* the Fermi level touches the bottom of the a(1g) band at the Gamma point, leading to a crucial change in the density of states across x* and the emergence of a small electron pocket around the Gamma point for x > x*.

Several thermodynamic measurements for the cobaltate superconductor, NaxCoO2 center dot gamma H2O, have so far provided results inconsistent with each other. In order to solve the discrepancies, we microscopically calculate the temperature dependences of specific heat and superfluid density for this superconductor. We show that two distinct specific-heat data from Oeschler et al. and Jin et al. are reproduced, respectively, for the extended s-wave state and the p-wave state. Two different superfluid-density data are also reproduced for each case. These support our recent proposal of possible two different pairing states,in this material. In addition, we discuss the experimentally proposed large residual Sommerfeld coefficient and extremely huge effective carrier mass.

In order to understand the experimentally proposed phase diagrams of NaxCoO2 center dot yH(2)O, we theoretically study the CoO2-layer-thickness dependence of its magnetic and superconducting (SC) properties by analyzing a multiorbital Hubbard model using the random phase approximation. When the Co valence s is +3.4, we show that the magnetic fluctuation exhibits a strong layer-thickness dependence, where it is enhanced at finite (zero) momentum in the thicker (thinner) layer system. A magnetic order phase appears sandwiched by two SC phases, consistent with the experiments. These two SC phases have different pairing states, where one is the singlet extended s-wave state and the other is the triplet p-wave state. On the other hand, only a triplet p-wave SC phase with a dome-shaped behavior of T-c is predicted when s = +3.5, which is also consistent with the experiments. Controversial experimental results on the magnetic properties are also discussed.

Motivated by recently reported experimental phase diagrams, we study the effects Of CoO6 distortion on the electronic structure in NaxCoO2.yH(2)O. We construct the multiband tight-binding model by employing the LDA result. Analyzing this model, we show the deformation of band dispersions and Fermi-surface topology as functions Of CoO2-layer thickness. Considering these results together with previous theoretical ones, we propose a possible schematic phase diagram with three successive phases: the extended s-wave superconductivity (SC), the magnetic order, and the spin-triplet SC phases when the Co valence number s is +3.4. A phase diagram with only one phase of spin-triplet SC is also proposed for the s = +3.5 case.

We study how the CoO6 distortion along the c-axis affects the magnetic properties and superconductivity in the novel Co-oxide superconductor NaxCoO2.yH(2)O by analyzing the multiorbital Hubbard model using the fluctuation-exchange approximation. It is shown that through generating the trigonal crystal field, the distortion pushes the Co e'(g) bands up and consequently gives rise to the hole-pocket Fermi surfaces, which have been predicted in the band calculations. As the distortion increases, the hole pockets are enlarged and the ferromagnetic fluctuation as well as the pairing instability increases, which is in good aggreement with recent NQR results. (c) 2006 Elsevier B.V. All rights reserved.

The d-vector in possible spin triplet superconductor Na2CoO2 (.) gamma H2O is microscopically analyzed on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. As a result of the perturbation theory, it is shown that the d-vector is parallel to the plane when the pairing symmetry is p-wave, while both d parallel to xy and d parallel to z are possible in the f-wave state. We point out that the multiple phase transitions are expected tinder the in-plane magnetic field when the pairing symmetry is p-wave. (c) 2006 Elsevier B.V. All rights reserved.

The possibility of multiple phase diagram in the novel superconductor Na(x)CoO(2)(.)yH(2)O is analyzed on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. We have shown that the spin triplet pairing state is stable in this model. The p-wave (f-wave) state is stabilized when the Hund's rule coupling is large (small). In the precedent paper, we have determined the direction of d-vector at T = T-c and H = 0 within the linearized Dyson-Gorkov equation. In this paper, the pairing state below T, and under the magnetic field is determined within the weak coupling approximation including the paramagnetic effect. We find that the p + f coexistent state is stabilized at low temperatures in a part of parameter range. We point out that the phase diagram in the H-T plane is quite different between the p-wave, f-wave and p + f-wave superconductivities. The characteristics of each phase are clarified by showing the magnetic susceptibility and specific heat. We discuss the comparison with experimental results and suggest some future experiments to detect the multiple phase transition.

The d-vector in possibile spin triplet superconductor Na xCoO2·yH2O is microscopically investigated on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. As a result of the perturbation theory, we obtain the stable spin triplet superconductivity where the p-wave and f-wave states can be stabilized. If we neglect the spin-orbit coupling, superconducting state has 6-fold (3-fold) degeneracy in the p-wave (f-wave) state. This degeneracy is lifted by the spin-orbit coupling. We determine the d-vector within the linearlized Dyson-Gorkov equation. It is shown that the d-vector is always along the plane when the pairing symmetry is p-wave, while it depends on the parameters in case of the f-wave state. The lifting of degeneracy is significant in the p-wave state while it is very small in the f-wave state. This is because the first order term with respect to the spin-orbit coupling is effective in the former case, while it is ineffective in the latter case. The consistency of these results with NMR and μSR measurements are discussed. ©2005 The Physical Society of Japan.

In the recently discovered Co-oxide superconductor NaxCoO2 center dot yH(2)O, the edge-shared CoO6 octahedra are trigonally contracted along the c-axis in the CoO2-plane. We study how this CoO6 distortion affects the magnetic properties and superconductivity in this compound by analyzing the multiorbital Hubbard model using the fluctuation-exchange approximation. It is shown that through generating the trigonal crystal field, the distortion pushes the Co e'(g) bands up and consequently gives rise to the hole-pocket Fermi surfaces, which have been predicted in the band calculations. As the distortion increases, the hole pockets are enlarged and the ferromagnetic fluctuation as well as the pairing instability increases, which is in good agreement with recent NQR results.

We analyze the multi-orbital model which describes the electronic structure of recently discovered superconductor NaxCoO2 center dot yH(2)O. The instability to the unconventional superconductivity is investigated by means of the perturbation theory. It is shown that the spin triplet superconductivity is stabilized in the wide parameter region, basically owing to the ferromagnetic spin fluctuation. In a small part of the parameter region, the d-wave superconductivity is also stabilized. We point out that the orbital degree of freedom plays an essential role for the superconductivity. (c) 2005 Elsevier B.V. All rights reserved.

Spin and charge fluctuations and superconductivity in Na0.35CoO2 center dot 1.3H(2)O are studied based on a multi-orbital Hubbard model. By applying the fluctuation exchange (FLEX) approximation, we show that the Hund's-rule coupling between the Co t(2g) orbitals causes ferromagnetic spin fluctuation. Triplet pairing is favored by this ferromagnetic fluctuation on the hole-pocket band. We propose that, in Na0.35CoO2 center dot 1.3H(2)O, Co t(2g) orbitals and inter-orbital Hund's-rule coupling play important roles on the triplet pairing, and this compound can be a first example of the triplet superconductor mediated by inter-orbital interaction-induced ferromagnetic fluctuation. (c) 2005 Elsevier B.V. All rights reserved.

Spin and charge fluctuations and superconductivity in Na(x)CoO(2)center dot yH(2)O are studied based on a multiorbital Hubbard model. Tight-binding parameters are determined to reproduce the results of band calculations. By applying the fluctuation-exchange approximation, we show that the Hund's-rule coupling between the Co t(2g) orbitals causes ferromagnetic (FM) spin fluctuation. Triplet f(y(y)(2)-3x(2))-wave and p-wave pairings are favored by this FM fluctuation on the hole-pocket band. We propose that, in Na(x)CoO(2)center dot yH(2)O, the Co t(2g) orbitals and interorbital Hund's-rule coupling play important roles on the triplet pairing, and this compound can be a first example of the triplet superconductor in which the orbital degrees of freedom play substantial roles.

We preform a multi-orbital analysis on the novel superconductivity in Na(x)CoO(2)(.)yH(2)O. We construct a three-orbital model which reproduces the band structure expected from the LDA calculation. The effective interaction leading to the pairing is estimated by means of the perturbation theory. It is shown that the spin triplet superconductivity is stabilized in the wide parameter region. This is basically owing to the ferromagnetic character of spin fluctuation. The p-wave and f-wave superconductivity are nearly degenerate. The former is realized when the Hund's rule coupling is large, and vice versa. In a small part of the parameter space, the d-wave superconductivity is also stabilized. We point out that the orbital degeneracy plays an essential role for these results. In particular, the momentum dependence of wave function of quasi-particles is quite important. The nearly degeneracy of p-wave and f-wave superconductivity is explained by analysing the microscopic character of each Fermi surface. We discuss the validity of some reduced models. While the single-orbital Hubbard model reproducing the Fermi surface is qualitatively inappropriate, we find an effective two-orbital model appropriate for studying the superconductivity. We investigate the vertex corrections higher than the third order on the basis of the two-orbital model. It is shown that the vertex correction induces the screening effect but does not affect qualitative results.

Titanate compounds have been recognized as key materials for understanding the coupling of magnetism and orbitals in strongly correlated electron systems. In the perovskite Ti oxide RTiO3 (where R represents the trivalent rare-earth ions), which is a typical Mott-Hubbard insulator, the Ti t 2g orbitals and spins in the 3d1 state couple each other through the strong electron correlations, resulting in a rich variety of orbital-spin phases. One way of controlling the coupling is to change the tiltings of the TiO6 octahedra (namely the GdFeO3-type distortion) by varying the R ions, through which the relative ratio of the electron bandwidth to the Coulomb interaction is controlled. With this control, these Mott insulators exhibit an antiferromagnetic-to-ferromagnetic (AFM-FM) phase transition, which has turned out to be a consequence of rich orbital physics in these materials. The origin and nature of orbital-spin structures of these Mott insulators have been intensively studied both experimentally and theoretically. When the Mott insulators are doped with carriers, the titanates show touchstone properties of the filling controlled Mott transition. In this paper, we first review the state of the art on the studies for understanding physics contained in the properties of the perovskite titanates. On the properties of the insulators, we focus on the following three topics: (1) the origin and nature of the ferromagnetism as well as the orbital ordering in the compounds with relatively small R ions such as GdTiO3 and YTiO 3, (2) the origin of the G-type antiferromagnetism and the orbital state in LaTiO3 and (3) the orbital-spin structures in other AFM(G) compounds with relatively large R ions (R = Ce, Pr, Nd and Sm). On the basis of these discussions, we discuss the whole phase diagram together with mechanisms of the magnetic phase transition. On the basis of the microscopic (understanding of the orbital-spin states, we show that the Ti t2g degeneracy is inherently lifted in the titanates, which allows the single-band descriptions of the ground-state and the low-energy electronic structures as a good starting point. Our analyses indicate that these compounds offer good touchstone materials described by the single-band Hubbard model on the cubic lattice. From this insight, we also re-analyse the hole-doped titanates R1-xA xTiO3 (where A represents the divalent alkaline-earth ions). Experimentally revealed filling- and bandwidth-dependent properties and the critical behaviour of the metal-insulator transitions are discussed in the light of theories based on the single-band Hubbard models.

The origin of the antiferromagnetic order and puzzling properties of LaTiO_3
as well as the magnetic phase diagram of the perovskite titanates are studied
theoretically. We show that in LaTiO_3, the t_{2g} degeneracy is eventually
lifted by the La cations in the GdFeO_3-type structure, which generates a
crystal field with nearly trigonal symmetry. This allows the description of the
low-energy structure of LaTiO_3 by a single-band Hubbard model as a good
starting point. The lowest-orbital occupation in this crystal field stabilizes
the AFM(G) state, and well explains the spin-wave spectrum of LaTiO_3 obtained
by the neutron scattering experiment. The orbital-spin structures for RTiO_3
with R=Pr, Nd and Sm are also accounted for by the same mechanism. We point out
that through generating the R crystal field, the GdFeO_3-type distortion has a
universal relevance in determining the orbital-spin structure of the perovskite
compounds in competition with the Jahn-Teller mechanism, which has been
overlooked in the literature. Since the GdFeO_3-type distortion is a universal
phenomenon as is seen in a large number of perovskite compounds, this mechanism
may also play important roles in other compounds of this type.

The origin of the G-type antiferromagnetism of RTiO3 with R = La was studied. It was clarified that the crystal field from La lifts the t 2g degeneracy at Ti 3d orbitals. It was suggested that the GdFeO 3-type distortion has a universal mechanism of controlling orbital-spin structure.

The origin of the G-type antiferromagnetism [AFM(G)] and puzzling properties of [Formula presented] with [Formula presented] are studied. We clarify that the crystal field from La caused by the [Formula presented]-type distortion lifts the [Formula presented] degeneracy at Ti [Formula presented] orbitals. The lift stabilizes the AFM(G) with spin-exchange constant in agreement with neutron-scattering results. The orbital-spin structures for [Formula presented], Nd, and Sm are also consistent with experiments. We propose that the [Formula presented]-type distortion has a universal mechanism of controlling orbital-spin structure competing with the Jahn-Teller (JT) mechanism. © 2003 The American Physical Society.

The magnetic phase diagram of the perovskite-type Ti oxides as a function of the GdFeO3-type distortion is examined by using the Hartree-Fock analysis of a multiband d-p Hamiltonian from a viewpoint of competitions of the spin-orbit interaction, the Jahn-Teller (JT) level-splitting and spin-orbital superexchange interactions. Near the anti ferro magnetic (AFM)-to-ferromagnetic (FM) phase boundary, A-type AFM [AFM(A)] and FM states accompanied by a certain type of orbital ordering are lowered in energy at large JT distortion, which is in agreement with the previous strong coupling study. With increasing the GdFeO3-type distortion, their phase transition occurs. Through this magnetic phase transition, the orbital state hardly changes, which induces nearly continuous change in the spin coupling along the c-axis from negative to positive. The strong suppression of T-N and T-C, which is experimentally observed is attributed to the resulting strong two-dimensionality in the spin coupling near the phase boundary. On the other hand, at small GdFeO3-type without JT distortions, which correspond to LaTiO3, the most stable solution is not G-type AFM [AFM(G)] but FM. Although the spin-orbit interaction has been considered to be relevant at the small or no JT distortion of LaTiO3 in the literature, our analysis indicates that the spin-orbit interaction is irrelevant to the AFM(G) state in LaTiO3 and superexchange-type interaction dominates. On the basis of further investigations on the nature of this FM state and other solutions, this discrepancy is discussed in detail.

The possibility of the $D_{3d}$ distortion of ${\rm TiO}_6$ octahedra is
examined theoretically in order to understand the origin of the G-type
antiferromagnetism (AFM(G)) and experimentally observed puzzling properties of
${\rm LaTiO}_3$. By utilizing an effective spin and pseudospin Hamiltonian with
the strong Coulomb repulsion, it is shown that AFM(G) state is stabilized
through the lift of the $t_{2g}$-orbital degeneracy accompanied by a tiny
$D_{3d}$-distortion . The estimated spin-exchange interaction is in agreement
with that obtained by the neutron scattering. Moreover, the level-splitting
energy due to the distortion can be considerably larger than the spin-orbit
interaction even when the distortion becomes smaller than the detectable limit
under the available experimental resolution. This suggests that the orbital
momentum is fully quenched and the relativistic spin-orbit interaction is not
effective in this system, in agreement with recent neutron-scattering
experiment.

The properties and mechanism of the magnetic phase transition of the
perovskite-type Ti oxides, which is driven by the Ti-O-Ti bond angle
distortion, are studied theoretically by using the effective spin and
pseudospin Hamiltonian with strong Coulomb repulsion. It is shown that the
A-type antiferromagnetic (AFM(A)) to ferromagnetic (FM) phase transition occurs
as the Ti-O-Ti bond angle is decreased. Through this phase transition, the
orbital state changes only little whereas the spin-exchange coupling along the
c-axis is expected to change from positive to negative nearly continuously and
approaches zero at the phase boundary. The resultant strong two-dimensionality
in the spin coupling causes rapid suppression of the critical temperature, as
observed experimentally. It may induce large quantum fluctuations in this
region.

Properties and mechanism of the magnetic phase transition of the
perovskite-type Ti oxides, which is driven by the Ti-O-Ti bond angle
distortion, are studied theoretically by using the effective spin and
pseudo-spin Hamiltonian with strong Coulomb repulsion. It is shown that the
A-type antiferromagnetic(AFM(A)) to ferromagnetic(FM) phase transition occurs
as the Ti-O-Ti bond angle is decreased. Through this phase transition, the
orbital state is hardly changed so that the spin-exchange coupling along the
c-axis changes nearly continuously from positive to negative and takes
approximately zero at the phase boundary. The resultant strong
two-dimensionality in the spin coupling causes a rapid suppression of the
critical temperature as is observed experimentally.