Antisymmetric Spin-orbit Interaction Research Articles

Microscopic mechanism for intrinsic nonlinear anomalous Hall conductivity in noncollinear antiferromagnetic metals

We theoretically investigate an intrinsic nonlinear anomalous Hall effect (INAHE) in space-time ($\mathcal{PT}$) symmetric antiferromagnetic metals. The INAHE is characterized by an asymmetric and nondissipative part of the second-order electric conductivity tensor in the clean limit in contrast to the Drude-type symmetric conductivity tensor with dissipation. By introducing a multipole description, we show that the emergence of the INAHE is due to active odd-parity magnetic quadrupoles or magnetic toroidal dipoles under magnetic orderings. In order to clarify the microscopic origin of the INAHE, we specifically consider a fundamental tight-binding model of a three-dimensional tetragonal system. We demonstrate that the INAHE arises from the effective coupling between magnetic ordering and antisymmetric spin-orbit interaction. We also discuss essential electron hopping paths driving the INAHE.

Analysis of model-parameter dependences on the second-order nonlinear conductivity in PT -symmetric collinear antiferromagnetic metals with magnetic toroidal moment on zigzag chains

A magnetic toroidal moment is a fundamental electronic degree of freedom in the absence of both spatial inversion and time-reversal symmetries and gives rise to novel multiferroic and transport properties. We elucidate essential model parameters of the nonlinear transport in the space-time ($\mathcal{PT}$) symmetric collinear antiferromagnetic metals accompanying a magnetic toroidal moment. By analyzing the longitudinal and transverse components of the second-order nonlinear conductivity on a two-dimensionally stacked zigzag chain based on the nonlinear Kubo formula, we show that an effective coupling between the magnetic toroidal moment and the antisymmetric spin-orbit interaction is an essential source of the nonlinear conductivity. Moreover, we find that the nonreciprocal longitudinal current and nonlinear transverse current in a multi-band system are largely enhanced just below the transition temperature of the antiferromagnetic ordering. We also discuss the relevance of the nonlinear conductivity to the linear magnetoelectric coefficient and conductivity. Our result serves as a guide for exploring microscopic essence and clarifying the parameter dependence of the nonlinear conductive phenomena in ferrotoroidal metals.

Chirality-Induced Spin Polarization over Macroscopic Distances in Chiral Disilicide Crystals.

A spin-polarized state is examined under charge current at room temperature without magnetic fields in chiral disilicide crystals NbSi_{2} and TaSi_{2}. We found that a long-range spin transport occurs over ten micrometers in these inorganic crystals. A distribution of crystalline grains of different handedness is obtained via location-sensitive electrical transport measurements. The sum rule holds in the conversion coefficient in the current-voltage characteristics. A diamagnetic nature of the crystals supports that the spin polarization is not due to localized electron spins but due to itinerant electron spins. A large difference in the strength of antisymmetric spin-orbit interaction associated with 4d electrons in Nb and 5d ones in Ta is oppositely correlated with that of the spin polarization. A robust protection of the spin polarization occurs over long distances in chiral crystals.

Observation of Nonlinear Spin-Charge Conversion in the Thin Film of Nominally Centrosymmetric Dirac Semimetal SrIrO_{3} at Room Temperature.

Spin-charge conversion via spin-orbit interaction is one of the core concepts in the current spintronics research. The efficiency of the interconversion between charge and spin current is estimated based on Berry curvature of Bloch wave function in the linear-response regime. Beyond the linear regime, nonlinear spin-charge conversion in the higher-order electric field terms has recently been demonstrated in noncentrosymmetric materials with nontrivial spin texture in the momentum space. Here, we report the observation of the nonlinear charge-spin conversion in a nominally centrosymmetric oxide material SrIrO_{3} by breaking inversion symmetry at the interface. A large second-order magnetoelectric coefficient is observed at room temperature because of the antisymmetric spin-orbit interaction at the interface of Dirac semimetallic bands, which is subject to the symmetry constraint of the substrates. Our study suggests that nonlinear spin-charge conversion can be induced in many materials with strong spin-orbit interaction at the interface by breaking the local inversion symmetry to give rise to spin splitting in otherwise spin degenerate systems.

Orbital crossing in spin-split Fermi surfaces and anisotropic effective mass of the noncentrosymmetric heavy-fermion paramagnet UPt5

We report the single-crystal growth of the noncentrosymmetric cubic heavy-fermion paramagnet ${\mathrm{UPt}}_{5}$ and comparative Fermi surface studies of de Haas-van Alphen (dHvA) experiments and theoretical band calculations. We also present the results of single-crystal x-ray diffraction, electrical resistivity, heat capacity, and magnetization measurements using single crystals of ${\mathrm{UPt}}_{5}$. The dHvA experiments reveal nearly spherical split hole Fermi surfaces and largely split electron Fermi surfaces, which are in agreement with the results of a band-structure calculation. The largely split electron Fermi surfaces may be understood through the antisymmetric spin-orbit interaction derived from U-$5f$ and Pt-$5d$ electrons. We explain the observed unexpected dHvA frequencies quasiquantitatively based on orbital crossing using the coupled network analysis in the split hole Fermi surface pair. Furthermore, the temperature dependence of the dHvA amplitude reveals enhanced cyclotron effective masses of up to $29{m}_{0}$ and a peculiar anisotropic effective mass in the paramagnetic cubic heavy-fermion ${\mathrm{UPt}}_{5}$.

Real spin and pseudospin topologies in the noncentrosymmetric topological nodal-line semimetal CaAgAs

We present the topology of spin-split Fermi surface of CaAgAs as determined by de Haas-van Alphen (dHvA) effect measurements combined with ab initio calculations. We have determined the torus-shaped nodal-line Fermi surface from the dHvA oscillations of $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ orbits. The former orbit encircles the nodal line, while the latter does not. Nevertheless, a nontrivial Berry phase is found for both orbits. The nontrivial phase of $\ensuremath{\beta}$ arises from the orbital characters, which can be expressed as a pseudospin rotating around the nodal line. On the other hand, the phase of $\ensuremath{\gamma}$ is attributed to the vortex of real spin texture induced by an antisymmetric spin-orbit interaction. Our result demonstrates that both the real spin and pseudospin textures are indispensable in interpreting the electronic topology in noncentrosymmetric nodal-line semimetals.

Splitting Fermi Surfaces and Heavy Electronic States in Non-Centrosymmetric U3Ni3Sn4

We report the single-crystal growth of the non-centrosymmetric paramagnet U3Ni3Sn4 by the Bridgman method and the Fermi surface properties detected by de Haas-van Alphen (dHvA) experiments. We have also investigated single-crystal U3Ni3Sn4 by single-crystal X-ray diffraction, magnetization, electrical resistivity, and heat capacity measurements. The angular dependence of the dHvA frequencies reveals many closed Fermi surfaces, which are nearly spherical in topology. The experimental results are in good agreement with local density approximation (LDA) band structure calculations based on the 5f-itinerant model. The band structure calculation predicts many Fermi surfaces, mostly with spherical shape, derived from 12 bands crossing the Fermi energy. To our knowledge, the splitting of Fermi surfaces due to the non-centrosymmetric crystal in 5f-electron systems is experimentally detected for the first time. The temperature dependence of the dHvA amplitude reveals a large cyclotron effective mass of up to 35m0, indicating the heavy electronic state of U3Ni3Sn4 due to the proximity of the quantum critical point. From the field dependence of the dHvA amplitude, a mean free path of conduction electrons of up to 1950A is detected, reflecting the good quality of the grown crystal. The small splitting energy related to the antisymmetric spin-orbit interaction is most likely due to the large cyclotron effective mass.

DHvA Effect Reveals Asymmetric Spin Orbit Interaction and Spin Texture of Fermi Surface

The precise de Haas–van Alphen (dHvA) experiments on the non-centrosymmetric cubic compound Yb4Sb3 clarified the anomalous spin character based on the antisymmetric spin orbit interaction.

Antisymmetric Spin–Orbit Coupling Effect on Kondo-Induced Electric Polarization in a Triangular Triple Quantum Dot

We study the local antisymmetric spin-orbit (ASO) coupling effect on spin, orbital, and charge degrees of freedom for the Kondo effect in a triangular triple quantum dot (TTQD). Here, one of the three QDs is coupled to a metallic lead through electron tunneling, and a local electric polarization is induced by the Kondo effect. The ASO interaction is introduced in the other two coupled QDs on the opposite side of the lead. Generally, the ASO coupling effect is very weak and not easily detectable, but it essentially causes spin and charge reconfigurations in the TTQD through the Kondo effect. Using an extended Anderson model for the TTQD Kondo system, we elucidate that the ASO coupling gives rise to a considerable reduction of the emergent electric polarization, as a consequence of the parity mixing of molecular orbitals in the triangular loop as well as the spin-up and spin-down coupling of local electrons. The latter leads to a local diamagnetic susceptibility owing to the ASO coupled spins. We also show that the Kondo-induced electric polarization can be controlled by the ASO coupling as well as by the magnetic flux penetrating through the TTQD.

Appropriate conditions to realize a p -wave superfluid state starting from a spin-orbit-coupled s -wave superfluid Fermi gas

We theoretically investigate a spin-orbit coupled $s$-wave superfluid Fermi gas, to examine the time evolution of the system, after an $s$-wave pairing interaction is replaced by a $p$-wave one at $t=0$. In our recent paper, we proposed that this manipulation may realize a $p$-wave superfluid Fermi gas, because the $p$-wave pair amplitude that is induced in the $s$-wave superfluid state by a parity-broken antisymmetric spin-orbit interaction gives a non-vanishing $p$-wave superfluid order parameter, immediately after the $p$-wave interaction is turned on. In this paper, using a time-dependent Bogoliubov-de Gennes theory, we assess this idea under various conditions with respect to the $s$-wave and $p$-wave interaction strengths, as well as the spin-orbit coupling strength. From these, we clarify that the momentum distribution of Fermi atoms in the initial $s$-wave state ($t<0$) is a key to produce a large $p$-wave superfluid order parameter. Since the realization of a $p$-wave superfluid state is one of the most exciting and difficult challenges in cold Fermi gas physics, our results may provide a possible way to accomplish this.

Mechanical properties of non-centrosymmetric CePt3Si and CePt3B

Elastic moduli, hardness (both at room temperature) and thermal expansion (4.2–670 K) have been experimentally determined for polycrystalline CePt3Si and its prototype compound CePt3B as well as for single-crystalline CePt3Si. Resonant ultrasound spectroscopy was used to determine elastic properties (Young’s modulus E and Poisson’s ratio ν) via the eigenfrequencies of the sample and the knowledge of sample mass and dimensions. Bulk and shear moduli were calculated from E and ν, and the respective Debye temperatures were derived. In addition, ab initio DFT calculations were carried out for both compounds. A comparison of parameters evaluated from DFT with those of experiments revealed, in general, satisfactory agreement. Positive and negative thermal expansion values obtained from CePt3Si single crystal data are fairly well explained in terms of the crystalline electric field model, using CEF parameters derived recently from inelastic neutron scattering. DFT calculations, in addition, demonstrate that the atomic vibrations keep almost unaffected by the antisymmetric spin–orbit coupling present in systems with crystal structures having no inversion symmetry. This is opposite to electronic properties, where the antisymmetric spin–orbit interaction has shown to distinctly influence features like the superconducting condensate of CePt3Si.

Spin-Triplet Pairing Induced by Spin-Singlet Interactions in Noncentrosymmetric Superconductors

In noncentrosymmetric superconductors, we examine the effect of the difference between the intraband and interband interactions, which becomes more important when the band splitting increases. We define the difference ΔVμ between their coupling constants, i.e., that between the intraband and interband hopping energies of intraband Cooper pairs. Here, the subscript μ of ΔVμ indicates that the interactions scatter the spin-singlet and spin-triplet pairs when μ = 0 and μ = 1,2,3, respectively. It is shown that the strong antisymmetric spin–orbit interaction reverses the target spin parity of the interaction: it converts the spin-singlet and spin-triplet interactions represented by ΔV0 and ΔVμ>0 into effective spin-triplet and spin-singlet pairing interactions, respectively. Hence, for example, triplet pairing can be induced solely by the singlet interaction ΔV0. We name the pairing symmetry of the system after that of the intraband Cooper pair wave function, but with an odd-parity phase factor excluded. The ...

Rashbon Bound States Associated with a Spherical Spin–Orbit Coupling in an Ultracold Fermi Gas with an s-Wave Interaction

We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin-orbit interaction, $H_{\rm so}=\lambda{\bf p}\cdot{\bf \sigma}$ (where ${\bf \sigma}=(\sigma_x,\sigma_y,\sigma_z)$ are Pauli matrices). Extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR) to include this spin-orbit coupling, we determine the superfluid phase transition temperature $T_{\rm c}$, as functions of the strength of a pairing interaction $U_s$, as well as the spin-orbit coupling strength $\lambda$. Evaluating poles of the NSR particle-particle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the $U_{s}$-$\lambda$ phase diagram. Since the antisymmetric spin-orbit interaction $H_{\rm so}$ breaks the inversion symmetry of the system, rashbon bound states naturally have, not only a spin-singlet and even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus, our results would be also useful for the study of this parity mixing effect in the BCS-BEC crossover regime of a spin-orbit coupled Fermi gas.

Proposed method to realize thep-wave superfluid state using ans-wave superfluid Fermi gas with a synthetic spin-orbit interaction

We theoretically propose an idea to reach the $p$-wave superfluid phase in an ultracold Fermi gas. The key of our idea is that the pairing symmetry of a Fermi superfluid is fully dominated by the symmetry of the superfluid order parameter, which is essentially given by the product of a pair amplitude and a pairing interaction. Noting this, in our proposal, we first prepare a $p$-wave pair amplitude by, not using a $p$-wave interaction, but using the phenomenon that a $p$-wave pair amplitude is induced in an $s$-wave superfluid Fermi gas with antisymmetric spin-orbit interaction. In this case, although the system is still in the $s$-wave superfluid state with the $s$-wave superfluid order parameter, when one suddenly replaces the $s$-wave interaction by an appropriate $p$-wave one (which is possible in cold Fermi gases by using a Feshbach resonance technique), the product of the $p$-wave interaction and the $p$-wave pair amplitude that has already been prepared in the spin-orbit coupled $s$-wave superfluid state immediately gives a finite $p$-wave superfluid order parameter. Thus, at least just after this manipulation, the system is in the $p$-wave superfluid state, being characterized by the artificially produced $p$-wave superfluid parameter. In this paper, to assess our idea, we evaluate the $p$-wave pair amplitude in a spin-orbit coupled $s$-wave superfluid Fermi gas at $T=0$. We determine the region where a large $p$-wave pair amplitude is obtained in the phase diagram with respect to the strengths of the $s$-wave pairing interaction and the spin-orbit coupling. We also discuss the accessibility of this optimal region on the viewpoint of the superfluid phase transition temperature. Since the achievement of a $p$-wave superfluid Fermi gas is one of the most crucial issues in cold atom physics, our proposal would be useful for this exciting challenge.

De Haas–van Alphen Effect in Rh2Ga9and Ir2Ga9without Inversion Symmetry in the Crystal Structure and Related Compounds T2Al9(T: Co, Rh, Ir) with Inversion Symmetry

We succeeded in growing high-quality single crystals of Rh2Ga9 and Ir2Ga9 with the non-centrosymmetric (distorted Co2Al9-type) monoclinic structure by the Ga-self flux method, and carried out the de Haas–van Alphen (dHvA) experiments. The Fermi surface is found to be split into two different Fermi surfaces, reflecting the non-centrosymmetric crystal structure. A magnitude of the antisymmetric spin–orbit interaction or a splitting energy between the two Fermi surfaces are determined to be 56 K for dHvA branch α and 45 K for branch β in Rh2Ga9, where these dHvA branches correspond to main Fermi surfaces. The present splitting values are compared with 290 and 130 K in Ir2Ga9, respectively. The splitting energy is found to be larger in the Ir-5d conduction electrons than in the Rh-4d conduction electrons. The split dHvA branches in Rh2Ga9 and Ir2Ga9 are also compared with the single dHvA branch in Co2Al9, Rh2Al9, and Ir2Al9 with inversion symmetry in the crystal structure.

Renormalization Effect of the Antisymmetric Spin–Orbit Interaction through Spin Fluctuations

The theoretical research shows that when a noncentrosymmetric metal is close to the magnetic critical point in the phase diagram, its Fermi surface is deformed by the critical spin fluctuations through the antisymmetric component of self-energy.

Chiral-Structure-Driven Split Fermi Surface Properties in TaSi2, NbSi2, and VSi2

We carried out de Haas–van Alphen (dHvA) experiments for TaSi2, NbSi2, and VSi2 with the hexagonal chiral structure, and compared them with the results of energy band calculations. The Fermi surface is found to be split into two different Fermi surfaces, reflecting the non-centrosymmetric crystal structure. A magnitude of the antisymmetric spin–orbit interaction or a splitting energy between the two Fermi surfaces is determined to be 493 K for dHvA branch α (α′) and 564 K for branch β (β′), where these dHvA branches correspond to main Fermi surfaces. The present splitting values are compared with 209 and 244 K in NbSi2, and 19 and 39 K in VSi2, respectively. The splitting energy is found to be larger in the Ta-5d conduction electrons than those with the Nb-4d and V-3d conduction electrons.

Dynamical axion in topological superconductors and superfluids

We consider dynamical axion phenomena in topological superconductors and superfluids in three spatial dimensions in terms of the gravitoelectromagnetic topological action, in which the axion field couples with mechanical rotation under finite temperature gradient. The dynamical axion is induced by relative phase fluctuations between topological and s-wave superconducting orders. We show that an antisymmetric spin-orbit interaction which induces parity-mixing of Cooper pairs enlarges the parameter region in which the dynamical axion fluctuation appears as a low-energy excitation. We propose that the dynamical axion increases the moment of inertia, and in the case of ac mechanical rotation, i.e. a shaking motion with a finite frequency $\omega$, as $\omega$ approaches the dynamical axion fluctuation mass, the observation of this effect becomes feasible.

Chiral Crystal Structure and Split Fermi Surface Properties in TaSi2

We carried out a de Haas–van Alphen (dHvA) experiment in TaSi2 with the hexagonal chiral structure, together with an energy band calculation. The Fermi surface is found to be split into two different Fermi surfaces, reflecting the non-centrosymmetric crystal structure. The magnitude of the antisymmetric spin–orbit interaction or the splitting energy between the two Fermi surfaces is determined to be 493 K for dHvA branch α (α'), 564 K for branch β (β'), and 617 K for branch γ (γ'), where these dHvA branches correspond to the main Fermi surfaces. The present splitting values are compared with 19, 39, and 110 K, respectively, observed in a similar compound, VSi2. The splitting energy is found to be larger in Ta-\(5d\) conduction electrons than in V-\(3d\) conduction electrons. Furthermore, we found a magnetic breakthrough effect for branches γ (γ') and α (α'), of which the circulating orbits are separate but are nearly degenerate in three and two regions, respectively.

Split Fermi Surface Properties of VSi2without Mirror Planes in the Chiral Crystal Structure

VSi2 is hexagonal in the crystal structure, and the basal plane stacks along the [0001] direction. Interestingly, each plane is rotated by 60\circ relative to the neighboring one. Therefore, there exist no mirror planes in this chiral structure. We carried out a de Haas–van Alphen (dHvA) experiment and clarified the Fermi surface properties. Each dHvA branch was found to be split into two branches on the basis of the antisymmetric spin–orbit interaction. The magnitude of the antisymmetric spin–orbit interaction in this chiral structure was determined for the first time to be 19 K for dHvA branch α (dHvA frequency \(F = 7.9 \times 10^{7}\) Oe and cyclotron mass \(m^{*}_{\text{c}} = 1.6\) \(m_{0}\)), 39 K for branch β (\(F = 4.1 \times 10^{7}\) Oe and \(m^{*}_{\text{c}} = 3.4\) \(m_{0}\)), and 110 K for branch γ (\(F = 1.8 \times 10^{7}\) Oe and \(m^{*}_{\text{c}} = 2.3\) \(m_{0}\)). These dHvA branches correspond to the main Fermi surfaces, which are well explained by the results of the energy band calculations based on the full potential linear augmented plane wave (FLAPW) method. The present values are mainly due to the V-\(3d\) conduction electrons.