The magnetic hedgehog lattice (HL) is a noncoplanar magnetic texture with a periodic array of magnetic monopoles and anti-monopoles. Despite phenomenological and numerical studies thus far, there remain open issues on the microscopic origin, especially with respect to the recent experimental findings of two different types of HLs even at zero magnetic field. Here, we study the stability of the HLs for an effective spin model with long-range interactions arising from itinerant nature of electrons. By variational calculations and simulated annealing, we find that the HLs are stabilized in the ground state at zero magnetic field by the synergetic effect of the anti-symmetric exchange interactions generated by the spin-orbit coupling and the multiple-spin interactions generated by the spin-charge coupling. We also clarify the phase diagram in the magnetic fields, which includes topological phase transitions with pair annihilation of the monopoles and anti-monopoles depending on the field directions.
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 pair…
Multiple-$Q$ magnetic states often induce nontrivial topological spin textures, such as a skyrmion and a hedgehog. We theoretically investigate yet another multiple-$Q$ state with topological defects, a meron-antimeron crystal (MAX), represented by a periodic array of the meron and antimeron with a half-integer skyrmion number. Performing simulated annealing for an effective spin model of noncentrosymmetric itinerant magnets on a triangular lattice, we show that rectangular-shaped and triangular-shaped MAXs are stabilized by the interplay between the biquadratic interaction arising from the sp…
Superpositions of spin helices can yield topological spin textures, such as two-dimensional vortices and skyrmions, and three-dimensional hedgehogs. Their topological nature and spatial dimensionality depend on the number and relative directions of the constituent helices. This allows mutual transformation between the topological spin textures by controlling the spatial anisotropy. Here we theoretically study the effect of anisotropy in the magnetic interactions for an effective spin model for chiral magnetic metals. By variational calculations for both cases with triple and quadruple superpos…
We describe the phenomenon of optical activity of noncentrosymmetric metals in their normal and superconducting states. The found conductivity tensor contains the linear in wave vector off diagonal part responsible for the natural optical activity. Its value is expressed through the ratio of light frequency to the band splitting due to the spin-orbit interaction. The Kerr rotation of polarization of light reflected from the metal surface is calculated. In the additional file "Erratum" I've pointed out the sign error in arXiv:1001.2113 ( PRB v.81, 094525 (2010)) that leads to the wrong statemen…
In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this paper, we develop an electron hydrodynamic theory for noncentrosymmetric metals, where a novel class of electron fluids is realized by lowering crystal symmetries and the resulting geometrical effects. The obtained hydrodynamic equation suggests a nontrivial analogy between electron fluids in noncentrosymmetric metals and chiral fluids in vacuum, and predicts novel hydrodynamic tr…
We present ab initio density-functional study of the noncentrosymmetric B20-type phase of RhGe, which is not found in nature and can be synthesized only at extreme pressures and temperatures. The structural, thermodynamic, electronic, lattice-dynamical, and transport properties of B20-RhGe are calculated, and their evolution with increasing pressure is traced. The temperature dependence of the charge and heat transport properties is evaluated within the semi-classical Boltzmann approach. Using the quasi-harmonic approximation, we determine the range of pressures and temperatures, in which B20-…
Materials containing multiple topological characteristics become more exotic when combined with noncentrosymmetric crystal structures and unusual magnetic phases such as the compensated half-metal state, which is gapped in one spin direction and conducting in the other. First principles calculations reveal these multiple topological features in the compensated half-metal Cr$_2$CoAl having neither time-reversal nor inversion symmetries. In the absence of (minor) spin-orbit coupling (SOC), there are (1) a total of twelve pairs of magnetic Weyl points, (2) three distinct sets of triple nodal poin…
The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond-alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, J1'/J1. A qua…
We present magnetization, specific heat, resistivity, and Hall effect measurements on the cubic B20 phase of MnGe and CoGe and compare to measurements of isostructural FeGe and electronic structure calculations. In MnGe, we observe a transition to a magnetic state at $T_c=275$ K as identified by a sharp peak in the ac magnetic susceptibility, as well as second phase transition at lower temperature that becomes apparent only at finite magnetic field. We discover two phase transitions in the specific heat at temperatures much below the Curie temperature one of which we associate with changes to …
The failure of spatial inversion symmetry in noncentrosymmetric materials introduces two different types of spin-independent and spin-dependent electron hopping. The spin-dependent term can be translated into a quasi-spin-orbit coupling and may affect the electronic structure. In the locally noncentrosymmetric crystals, the presence of a sublattice degree of freedom generates a distinction between the inter- and intra-sublattice hopping integrals. The spin-dependent part of the former (latter), which is even (odd) under parity, is called symmetric (antisymmetric) quasi-spin-orbit coupling. Her…
Transition metal boride Ru$_7$B$_3$ was found to be a noncentrosymmetric superconductor with $T_{C}$ equal to 3.3 K. Superconducting and normal state properties of Ru$_7$B$_3$ were determined by a self-consistent analysis through resistivity($ρ_{xx}$ and $ρ_{xy}$), specific heat, lower critical field measurement and electronic band structure calculation. It is found that Ru$_7$B$_3$ belongs to an s-wave dominated single band superconductor with energy gap 0.5 meV and could be categorized into type II superconductor with weak electron-phonon coupling. Unusual 'kink' feature is clearly observed …
Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their st…
Understanding and control of spin degrees of freedom on the surfaces of topological materials are key to future applications as well as for realizing novel physics such as the axion electrodynamics associated with time-reversal (TR) symmetry breaking on the surface. We experimentally demonstrate magnetically induced spin reorientation phenomena simultaneous with a Dirac-metal to gapped-insulator transition on the surfaces of manganese-doped Bi2Se3 thin films. The resulting electronic groundstate exhibits unique hedgehog-like spin textures at low energies, which directly demonstrate the mechani…
We report on a microscopic study of the noncentrosymmetric superconductor W$_3$Al$_2$C (with $T_c$ = 7.6 K), mostly by means of $^{27}$Al- and $^{13}$C nuclear magnetic resonance (NMR). Since in this material the density of states at the Fermi level is dominated by the tungsten's 5$d$ orbitals, we expect a sizeable spin-orbit coupling (SOC) effect. The normal-state electronic properties of W$_3$Al$_2$C resemble those of a standard metal, but with a Korringa product $1/(T_{1}T)$ significantly smaller than that of metallic Al, reflecting the marginal role played by $s$-electrons. In the supercon…
Even if Weyl semimetals are characterized by quasiparticles with well-defined chirality, exploiting this experimentally is severely hampered by Weyl lattice-fermions coming in pairs with opposite chirality, typically causing the net chirality picked up by experimental probes to vanish. Here we show this issue can be circumvented in a controlled manner when both time-reversal- and inversion- symmetry are broken. To this end, we investigate chirality-disbalance in the carbide family RMC$_2$ (R a rare-earth and M a transition metal), showing several members to be Weyl semimetals. Using the noncen…
SrAuSi$_3$ is a noncentrosymmetric superconductor (NCS) with $T_c$ = 1.54 K, which to date has been studied only via macroscopic techniques. By combining nuclear magnetic resonance (NMR) and muon-spin rotation ($μ$SR) measurements we investigate both the normal and the superconducting phase of SrAuSi$_3$ at a local level. In the normal phase, our data indicate a standard metallic behavior with weak electron correlations and a Korringa constant $S_\mathrm{exp} = 1.31 \times 10^{-5}$ sK. The latter, twice the theoretical value, can be justified by the Moriya theory of exchange enhancement. In th…
Stimulated by recent studies of quantum phases with broken local inversion symmetry, we study the magnetoelectric effect in locally noncentrosymmetric metals. We consider three-dimensional (3D) coupled zigzag chains and demonstrate that the antiferromagnetic moment is induced by the electric current through a staggered antisymmetric spin-orbit coupling. This current-induced magnetism is much larger than that in globally noncentrosymmetric metals. We provide an intuitive understanding of the current-induced antiferromagnetic moment by showing the inverse magnetoelectric effect, that is, the fer…
We study magnetic textures realized in noncentrosymmetric Kondo lattice models, in which localized magnetic moments weakly interact with itinerant electrons subject to Rashba and Dresselhaus spin-orbit couplings. By virtue of state-of-the-art numerical simulations as well as variational calculations, we uncover versatile multiple-$Q$ orderings under zero magnetic field, which are found to originate in the instabilities of the Fermi surface whose spin degeneracy is lifted by the spin-orbit couplings. In the case with equally-strong Rashba and Dresselhaus spin-orbit couplings, which is known to …
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…
Analogous to the Hall effect, the Nernst effect is the generation of a transverse voltage due to a temperature gradient in the presence of a perpendicular magnetic field. The Nernst effect has promise for thermoelectric applications and as a probe of electronic structure. In magnetic materials, a so-called anomalous Nernst effect (ANE) is possible in zero magnetic field. Here we report a colossal ANE reaching 23 $μ$V/K in the ferromagnetic metal UCo$_{0.8}$Ru$_{0.2}$Al. Uranium's $5f$ electrons provide strong electronic correlations that lead to narrow bands, which are a known route to produci…
We report a comprehensive study of the noncentrosymmetric superconductor Mo$_3$P. Its bulk superconductivity, with $T_c = 5.5$ K, was characterized via electrical resistivity, magnetization, and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation/relaxation ($μ$SR) and nuclear magnetic resonance (NMR) techniques. In the normal state, NMR relaxation data indicate an almost ideal metallic behavior, confirmed by band-structure calculations, which suggest a relatively high electron density of states, dominated by the Mo $4d$-orbi…
We systematically investigate the normal and superconducting properties of non-centrosymmetric Re$_{6}$Zr using magnetization, heat capacity, and electrical resistivity measurements. Resistivity measurements indicate Re$_{6}$Zr has poor metallic behavior and is dominated by disorder. Re$_6$Zr undergoes a superconducting transition at $T_{\mathrm{c}} = \left(6.75\pm0.05\right)$ K. Magnetization measurements give a lower critical field, $μ_{0}H_{\mathrm{c1}} = \left(10.3 \pm 0.1\right)$ mT. The Werthamer-Helfand-Hohenberg model is used to approximate the upper critical field $μ_{0}H_{\mathrm{c2}…
We develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar and general non-coplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by th…
Photovoltaic effect, e.g., solar cells, converts light into DC electric current. This phenomenon takes place in various setups such as in noncentrosymmetric crystals and semiconductor pn junctions. Recently, we proposed a theory for producing DC spin current in magnets using electromagnetic waves, i.e., the spin-current counterpart of the solar cells. Our calculation shows that the nonlinear conductivity for the spin current is nonzero in a variety of noncentrosymmetric magnets, implying that the phenomenon is ubiquitous in inversion-asymmetric materials with magnetic excitations. Intuitively,…
Fermi liquid theory provides a remarkably powerful framework for the description of the conduction electrons in metals and their ordering phenomena, such as superconductivity, ferromagnetism, and spin- and charge-density-wave order. A different class of ordering phenomena of great interest concerns spin configurations that are topologically protected, that is, their topology can be destroyed only by forcing the average magnetization locally to zero. Examples of such configurations are hedgehogs (points at which all spins are either pointing inwards or outwards) or vortices. A central question …
Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates
Natural faculty of Science, Langson college of education（朗山师范学院自然科学系）；Department of Theoretical Physics, VNUHCM-University of Science（越南国立大学胡志明市理工大学理论物理系）；Institute of Research and Development, Duy Tan University（戴南大学研发院）；Faculty of Natural Sciences, Duy Tan University（戴南大学自然科学学院）
The synthesis and crystallographic and physical properties of polycrystalline EuNiGe3 are reported. EuNiGe3 crystallizes in the noncentrosymmetric body-centered tetragonal BaNiSn3-type structure. The physical property data consistently demonstrate that this is a metallic system in which Eu spins S = 7/2 order antiferromagnetically at a temperature TN = 13.6 K. Magnetic susceptibility chi data for T > TN indicate that the Eu atoms have spin 7/2 with g = 2, that the Ni atoms are nonmagnetic, and that the dominant interactions between the Eu spins are ferromagnetic. Thus we propose that EuNiGe3 h…
