arXiv subjects

Yukitoshi Motome

Publications and source records attributed to Yukitoshi Motome.

At least 73 records · Page 4Linked to original sources

arXiv2022

Anomalous Hall effect in antiferromagnetic perovskites

We theoretically study the anomalous Hall effect (AHE) in perovskites with antiferromagnetic (AFM) orderings. By studying the multiorbital Hubbard model for $d$ electrons in perovskite transition metal oxides under the GdFeO$_3$-type distortion within the Hartree-Fock approximation, we investigate the behavior of intrinsic AHE owing to the atomic spin-orbit coupling via the linear response theory. We consider the cases where there exist two ($d^2$) and three ($d^3$) electrons in the $t_{2g}$ orbitals, and show that AFM ordered states can exhibit AHE. In the $d^2$ case, $C$-type AFM states give rise to dc AHE in metals and optical (finite-$ω$) AHE in insulators accompanying orbital ordering, while in the $d^3$ case, a $G$-type AFM insulating state supports the optical AHE. By resolving the components in the spin patterns compatible with the space group symmetry, we specify the collinear AFM component to be responsible for the AHE, rather than the small ferromagnetic component. We discuss the microscopic origin of the AHE: the collinear AFM spin structure produces a nonzero Berry phase from the triangular units of the lattice, activated by the complex orbital mixing terms owing to the GdFeO$_3$-type distortion, and results in the microscopic Lorentz force.

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arXiv2022

Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models

The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin $S=1/2$ moments on a honeycomb lattice. In recent years, the model has been extended to higher $S$ from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general $S$, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-$S$ Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general $S$. We show that, similar to the $S=1/2$ case, the phase diagram for higher $S$ contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing $S$, becoming vanishingly narrow for $S\geq 2$, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search of higher-$S$ Kitaev materials.

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arXiv2022

Magnetic Hedgehog Lattice in a Centrosymmetric Cubic Metal

The hedgehog lattice (HL) is a three-dimensional topological spin texture hosting a periodic array of magnetic monopoles and antimonopoles. It has been studied theoretically for noncentrosymmetric systems with the Dzyaloshinskii-Moriya interaction, but the stability, as well as the magnetic and topological properties, remains elusive in the centrosymmetric case. We here investigate the ground state of an effective spin model with long-range bilinear and biquadratic interactions for a centrosymmetric cubic metal by simulated annealing. We show that our model stabilizes a HL composed of two pairs of left- and right-handed helices, resulting in no net scalar spin chirality, in stark contrast to the noncentrosymmetric case. We find that the HL turns into topologically-trivial conical states in an applied magnetic field. From the detailed analyses of the constituent spin helices, we clarify that the ellipticity and angles of the helical planes change gradually while increasing the magnetic field. We discuss the results in comparison with the experiments for a centrosymmetric cubic metal SrFeO$_3$.

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arXiv2022

Magnetic field-temperature phase diagrams for multiple-$Q$ magnetic orderings: Exact steepest descent approach to long-range interacting spin systems

Multiple-$Q$ magnetic orderings represent magnetic textures composed of superpositions of multiple spin density waves or spin spirals, as represented by skyrmion crystals and hedgehog lattices. Such magnetic orderings have been observed in various magnetic materials in recent years, and attracted enormous attention, especially from the viewpoint of topology and emergent electromagnetic fields originating from noncoplanar magnetic structures. Although they often exhibit successive phase transitions among different multiple-$Q$ states while changing temperature and an external magnetic field, it is not straightforward to elucidate the phase diagrams, mainly due to the lack of concise theoretical tools as well as appropriate microscopic models. Here, we provide a theoretical framework for a class of effective spin models with long-range magnetic interactions mediated by conduction electrons in magnetic metals. Our framework is based on the steepest descent method with a set of self-consistent equations that leads to exact solutions in the thermodynamic limit, and has many advantages over existing methods such as biased variational calculations and numerical Monte Carlo simulations. Applying the framework to the models with instabilities toward triple- and hextuple-$Q$ magnetic orderings, we find that interesting reentrant phase transitions where the multiple-$Q$ phases appear only at finite temperature and/or nonzero magnetic field. Furthermore, we show that the multiple-$Q$ states can be topologically-nontrivial stacked skyrmion crystals or hedgehog lattices, which exhibit large net spin scalar chirality associated with nonzero skyrmion number. The results demonstrate that our framework could be a versatile tool for studying magnetic and topological phase transitions and related quantum phenomena in actual magnetic metals hosting multiple-$Q$ magnetic orderings.

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arXiv2022

Inverse Hamiltonian design by automatic differentiation

An ultimate goal of materials science is to deliver materials with desired properties at will. In the theoretical study, a standard approach consists of constructing a Hamiltonian based on phenomenology or first principles, calculating physical observables, and improving the Hamiltonian through feedback. However, there is also an approach that bypasses such a cumbersome procedure, namely, to obtain an appropriate Hamiltonian directly from the desired properties. Solving the inverse problem has the potential to reach qualitatively different principles, but most research to date has been limited to quantitative determination of parameters within known models. Here, we present a general framework that enables the inverse design of Hamiltonians by optimizing numerous parameters using automatic differentiation. By applying it to the quantum anomalous Hall effect (AHE), we show that our framework can not only rediscover the Haldane model but also automatically generate a new Hamiltonian that exhibits a six-times larger AHE. In addition, the application to the photovoltaic effect (PVE) gives an optimal Hamiltonian for electrons moving on a noncoplanar spin texture, which can generate $\sim 900$~A/m$^2$ under solar radiation. This framework would accelerate materials exploration by establishing unprecedented models and principles beyond human intuition and empirical rules.

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arXiv2022

Feasibility of Kitaev quantum spin liquids in ultracold polar molecules

Ultracold atoms and molecules trapped in optical lattices are expected to serve as simulators of strongly correlated systems and topological states of matter. A fascinating example is to realize the Kitaev quantum spin liquid by using ultracold polar molecules. However, although experimental implementation of the Kitaev-type interaction was proposed, the stability of the Kitaev quantum spin liquid has not been fully investigated thus far. Here we study a quantum spin model with long-range angle-dependent Kitaev-type interactions proposed for the polar molecules, by the pseudofermion functional renormalization group method. We reveal that the ground state is magnetically ordered in both ferromagnetic and antiferromagnetic models regardless of the spatial anisotropy of the interactions, while the isotropic case is most frustrated and closest to the realization of the Kitaev quantum spin liquid. Furthermore, by introducing a cutoff in the interaction range, we clarify how the Kitaev quantum spin liquid is destroyed by the long-range interactions. The results urge us to reconsider the feasibility of the Kitaev quantum spin liquid in ultracold polar molecules.

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arXiv2022

Asymmetric modulation of Majorana excitation spectra and nonreciprocal thermal transport in the Kitaev spin liquid under a staggered magnetic field

We present the theoretical results for the Majorana band structure and thermal transport properties in the Kitaev honeycomb model under a staggered magnetic field in addition to a uniform one. The Majorana band structure is asymmetrically modulated in momentum space, and the valley degree of freedom is activated and controlled by the magnitudes and directions of the uniform and staggered magnetic fields; as a result, the Majorana excitation is either gapped or gapless, the latter of which in general has Majorana Fermi surfaces, in contrast to the point nodes in the absence of the fields. We show that the asymmetric deformation of the Majorana band induces a nonlinear (nonreciprocal) thermal transport, in addition to the linear one. The field dependence of the linear thermal current is correlated with the magnitude of the Majorana gap, while that of the nonlinear thermal current is associated with the asymmetry of the Majorana excitation spectra. We show the estimates of the thermal currents and discuss that the linear response is experimentally measurable, whereas future improvement is required for the observation of the nonlinear one. We also discuss how the thermal currents are modulated by other additional effects of the magnetic field and contributions from conventional magnons, latter of which are expected in heterostructures to realize an internal staggered magnetic field.

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arXiv2022

Spin dynamics in the square-lattice cupola system Ba(TiO)Cu$_4$(PO$_4$)$_4$

We report high-resolution single-crystal inelastic neutron scattering measurements on the spin-1/2 antiferromagnet Ba(TiO)Cu$_4$(PO$_4$)$_4$. This material is formed from layers of four-site \cupola" structures, oriented alternately upwards and downwards, which constitute a rather special realization of two-dimensional (2D) square-lattice magnetism. The strong Dzyaloshinskii-Moriya (DM) interaction within each cupola, or plaquette, unit has a geometry largely unexplored among the numerous studies of magnetic properties in 2D Heisenberg models with spin and spatial anisotropies. We have measured the magnetic excitations at zero field and in fields up to 5 T, finding a complex mode structure with multiple characteristic features that allow us to extract all the relevant magnetic interactions by modelling within the linear spin-wave approximation. We demonstrate that Ba(TiO)Cu$_4$(PO$_4$)$_4$ is a checkerboard system with almost equal intra- and inter-plaquette couplings, in which the intra-plaquette DM interaction is instrumental both in enforcing robust magnetic order and in opening a large gap at the Brillouin-zone center. We place our observations in the perspective of generalized phase diagrams for spin-1/2 square-lattice models and materials, where exploring anisotropies and frustration as routes to quantum disorder remains a frontier research problem.

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arXiv2022

Phase degree of freedom and topology in multiple-$Q$ spin textures

A periodic array of topological spin textures, such as skyrmions and hedgehogs, is called the multiple-$Q$ spin texture, as it is represented by a superposition of multiple spin density waves. Depending on the way of superposition, not only the magnetic but also the topological properties are modified, leading to a variety of quantum transport and optical phenomena caused by the emergent electromagnetic fields through the Berry phase. Among others, the phase degree of freedom of the superposed waves is potentially important for such modifications, but its effect has not been fully elucidated thus far. Here we perform systematic theoretical analyses of magnetic and topological properties of the multiple-$Q$ spin textures with the phase degree of freedom. By introducing a hyperspace with an additional dimension corresponding to the phase degree of freedom, we establish a generic framework to deal with the phase shift in the multiple-$Q$ spin textures. Applying the framework to the two-dimensional 3$Q$ spin textures, we clarify the complete topological phase diagram while changing the phase and magnetization, which depends on the types of the superposed waves. We also study the three-dimensional 4$Q$ spin textures and clarify even richer topological phase diagrams. In particular, we find novel topological phase transitions associated with the previously unidentified Dirac strings on which the hedgehogs and antihedgehogs cause pair creation and fusion. Moreover, we demonstrate that phase shifts are caused by an external magnetic field in both 3$Q$ and 4$Q$ cases by analyzing the numerical data in the previous studies. Our results illuminate the topological aspects of the skyrmion and hedgehog lattices with the phase degree of freedom, which would be extended to other multiple-$Q$ textures and useful for the exploration of topologically nontrivial magnetic phases and exotic quantum phenomena.

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arXiv2021

Spin excitation spectra in helimagnetic states: proper-screw, cycloid, vortex crystal, and hedgehog lattice

We investigate the spin excitation spectra in chiral and polar magnets by the linear spin-wave theory for an effective spin model with symmetric and antisymmetric long-range interactions. In one dimension, we obtain the analytic form of the dynamical spin structure factor for proper-screw and cycloidal helical spin states with uniform twists, which shows a gapless mode with strong intensity at the helical wave number. When introducing spin anisotropy in the symmetric interactions, we numerically show that the stable spin spirals become elliptically anisotropic with nonuniform twists and the spin excitation is gapped. In higher dimensions, we find that similar anisotropy stabilizes multiple-$Q$ spin states, such as vortex crystals and hedgehog lattices. We show that the anisotropy in these states manifests itself in the dynamical spin structure factor: a strong intensity in the transverse components to the wave number appears only when the helical wave vector and the corresponding easy axis are perpendicular to each other. Our findings could be useful not only to identify the spin structure but also to deduce the stabilization mechanism by inelastic neutron scattering measurements.

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arXiv2021

Charge density waves in multiple-$Q$ spin states

Coupling between spin and charge degrees of freedom in electrons is a source of various electronic and magnetic properties of solids. We theoretically study charge density waves induced by the spin-charge coupling in the presence of magnetic orderings in itinerant magnets. By performing a perturbative calculation in the weak-coupling limit of the Kondo lattice model, we derive a useful formula for the relationship between charge and spin density waves, which can be applied to any magnetic orderings, including noncollinear and noncoplanar ones composed of multiple spin density waves called multiple-$Q$ magnetic orderings. We demonstrate the predictive power for single-$Q$ and double-$Q$ states including skyrmion and meron-antimeron crystals on a square lattice, in comparison with the numerical calculations. Moreover, we show that the charge density waves contain richer information than the spin density waves, and are indeed useful in distinguishing the spin textures with similar spin structure factors. We discuss the relation to bond modulation in terms of the kinetic bond energy and the vector spin chirality. We also perform numerical calculations beyond the perturbative regime and find that the charge density waves can be enhanced when the electron filling is commensurate. Furthermore, we investigate the effect of the spin-orbit coupling, which can lead to additional charge density waves owing to effective anisotropic magnetic interactions in momentum space. Our result will provide a way to identify complex magnetic orderings and their origins from the charge modulations.

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arXiv2021

Electrical conductivity in helical and conical magnetic states

We theoretically study the electrical conductivity in a one-dimensional helimagnet whose spin texture changes from helimagnetic to conical magnetic, and to forced ferromagnetic state while increasing the magnetic field along the helical axis. We find that the conductivity in the helimagnetic state at zero field depends on the electron filling and the coefficient of the spin-charge coupling. We also find that the conductivity in the conical magnetic state changes nonlinearly to the applied field, and the magnetoresistance becomes negative and positive depending on the model parameters.

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arXiv2021

Phase shift, ellipticity, angle, and topological number in skyrmion lattices

We theoretically study skyrmion lattices realized in a Kondo lattice model on a triangular lattice, focusing on the phase, ellipticity, and angle of the constituent multiple-$Q$ waves. Analyzing the numerical data obtained in the previous study [Ozawa R, Hayami S and Motome Y 2017 Phys. Rev. Lett. 118 147205], we extract these parameters for the two types of skyrmion lattices with the skyrmion number of $1$ and $2$. We show that the topological transition between the two skyrmion lattices driven by an external magnetic field is accompanied by significant modulations of all three parameters.

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arXiv2021

Determinant-free fermionic wave function using feed-forward neural networks

We propose a general framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. The anticommutation relation for fermions is usually implemented to a variational wave function by the Slater determinant (or Pfaffian), which is a computational bottleneck because of the numerical cost of $O(N^3)$ for $N$ particles. We bypass this bottleneck by explicitly calculating the sign changes associated with particle exchanges in real space and using fully connected neural networks for optimizing the rest parts of the wave function. This reduces the computational cost to $O(N^2)$ or less. We show that the accuracy of the approximation can be improved by optimizing the "variance" of the energy simultaneously with the energy itself. We also find that a reweighting method in Monte Carlo sampling can stabilize the calculation. These improvements can be applied to other approaches based on variational Monte Carlo methods. Moreover, we show that the accuracy can be further improved by using the symmetry of the system, the representative states, and an additional neural network implementing a generalized Gutzwiller-Jastrow factor. We demonstrate the efficiency of the method by applying it to a two-dimensional Hubbard model.

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arXiv2021

Quadratic Optical Responses in a Chiral Magnet

Chiral magnets, which break both spatial inversion and time reversal symmetries, carry a potential for quadratic optical responses. Despite the possibility of enhanced and controlled responses through the magnetic degree of freedom, the systematic understanding remains yet to be developed. We here study nonlinear optical responses in a prototypical chiral magnetic state with a one-dimensional conical order by using the second-order response theory. We show that the photovoltaic effect and the second harmonic generation are induced by asymmetric modulation of the electronic band structure under the conical magnetic order, and the coefficients, including the sign, change drastically depending on the frequency of incident lights, the external magnetic field, and the strength of spin-charge coupling. We find that both effects can be enormously large compared to those in the conventional nonmagnetic materials. Our results would pave the way for next-generation optical electronic devices, such as unconventional solar cells and optical sensors, based on chiral magnets.

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arXiv2021

Electronic and magnetic properties of iridium ilmenites $A$IrO$_3$ ($A=$ Mg, Zn, and Mn)

We theoretically investigate the electronic band structures and magnetic properties of ilmenites with edge-sharing IrO$_6$ honeycomb layers, $A$IrO$_3$ with $A=$ Mg, Zn, and Mn, in comparison with a collinear antiferromagnet MnTiO$_3$. The compounds with $A=$ Mg and Zn were recently reported in Y.~Haraguchi {\it et al.}, Phys. Rev. Materials {\bf 2}, 054411 (2018), while MnIrO$_3$ has not been synthesized yet but the honeycomb stacking structure was elaborated in a superlattice with MnTiO$_3$ in K.~Miura {\it et al.}, Commun. Mater. {\bf 1}, 55 (2020). We find that, in contrast to MnTiO$_3$, where an energy gap opens in the Ti $3d$ bands by antiferromagnetic ordering of the high-spin $S=5/2$ moments, MgIrO$_3$ and ZnIrO$_3$ have a gap in the Ir $5d$ bands under the influence of both spin-orbit coupling and electron correlation. Their electronic structures are similar to those in the spin-orbit coupled Mott insulators with the $j_{\rm eff}=1/2$ pseudospin degree of freedom, as found in monoclinic $A_2$IrO$_3$ with $A=$ Na and Li which have been studied as candidates for the Kitaev spin liquid. Indeed, we find that the effective exchange interactions between the $j_{\rm eff}=1/2$ pseudospins are dominated by the Kitaev-type bond-dependent interaction and the symmetric off-diagonal interactions. On the other hand, for MnIrO$_3$, we show that the local lattice structure is largely deformed, and both Mn $3d$ and Ir $5d$ bands appear near the Fermi level in a complicated manner, which makes the electronic and magnetic properties qualitatively different from MgIrO$_3$ and ZnIrO$_3$. Our results indicate that the IrO$_6$ honeycomb network in the ilmenites $A$IrO$_3$ with $A=$ Mg and Zn would offer a good platform for exotic magnetism by the spin-orbital entangled moments like the Kitaev spin liquid.

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arXiv2021

A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field

The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in the simulations of quantum many-body systems. In this method, the sign problem is alleviated by shifting the integration domain for the auxiliary fields, appearing for example in the conventional determinant quantum Monte Carlo method, from real space to an appropriate manifold in complex space. Here we extend this method to quantum spin models with generic two-spin interactions, by using the Hubbard-Stratonovich transformation to decouple the exchange interactions and the Popov-Fedotov transformation to map the quantum spins to complex fermions. As a demonstration, we apply the method to the Kitaev model in a magnetic field whose ground state is predicted to deliver a topological quantum spin liquid with non-Abelian anyonic excitations. To illustrate how the sign problem is alleviated in this method, we visualize the asymptotic Lefschetz thimbles in complex space, together with the saddle points and the zeros of the fermion determinant. We benchmark our method in the low-temperature region in a magnetic field and show that the sign of the action is recovered considerably and unbiased numerical results are obtained with sufficient precision.

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arXiv2021

Vortex creation and control in the Kitaev spin liquid by local bond modulations

The Kitaev model realizes a quantum spin liquid where the spin excitations are fractionalized into itinerant Majorana fermions and localized $\mathbb{Z}_2$ vortices. Quantum entanglement between the fractional excitations can be utilized for decoherence-free topological quantum computation. Of particular interest is the anyonic statistics realized by braiding the vortex excitations under a magnetic field. Despite the promising potential, the practical methodology for creation and control of the vortex excitations remains elusive thus far. Here we theoretically propose how one can create and move the vortices in the Kitaev spin liquid. We find that the vortices are induced by a local modulation of the exchange interaction; especially, the local Dzyaloshinskii-Moriya (symmetric off-diagonal) interaction can create vortices most efficiently in the (anti)ferromagnetic Kitaev model, as it effectively flips the sign of the Kitaev interaction. We test this idea by performing the {\it ab initio} calculation for a candidate material $α$-RuCl$_3$ through the manipulation of the ligand positions that breaks the inversion symmetry and induces the local Dzyaloshinskii-Moriya interaction. We also demonstrate a braiding of vortices by adiabatically and successively changing the local bond modulations.

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