Strong Spin-orbit Coupling Limit Research Articles

Interplay between Carrier Polarization, Spin-Orbit Coupling and Exchange Field on Anomalous Hall Conductivity in the Presence of Magnetic Impurity in Mn Doped GaAs

We develop a model Hamiltonian to treat anomalous Hall conductivity in dilute magnetic semiconductor (DMS) of type (III, Mn, V) considering the impurity potentials (potential due to interaction of spin of carriers with localized spin of dopant (Mn) and coulomb like potential). Using equation of motion in Green function together with Quantum Kubo-formula of conductivity, the anomalous Hall conductivity is calculated as function of spin-orbit coupling, exchange field and carrier polarization. The calculated result shows that at low impurity concentration, the interplay between spin polarization of carriers, spin-orbit coupling and exchange fields is crucial for existence of anomalous Hall conductivity. The monotonic increment of anomalous Hall conductivity with exchange field is observed for strong spin-orbit coupling limit. In weak spin-orbit coupling limit, the magnitude of anomalous Hall conductivity increases parabolically with the spin-orbit coupling. Our results provide an important basis for understanding the interplay between the spin polarization, spin-orbit coupling, and exchange field on anomalous Hall conductivity at low impurity concentration. The findings are also a key step to realize dissipationless quantum transport without external magnetic field.

Emergent SU(4) Symmetry in α-ZrCl_{3} and Crystalline Spin-Orbital Liquids.

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

Role of spin-orbit coupling in the Kugel-Khomskii model on the honeycomb lattice

We study the effective spin-orbital model for honeycomb-layered transition metal compounds, applying the second-order perturbation theory to the three-orbital Hubbard model with the anisotropic hoppings. This model is reduced to the Kitaev model in the strong spin-orbit coupling limit. Combining the cluster mean-field approximations with the exact diagonalization, we treat the Kugel-Khomskii type superexchange interaction and spin-orbit coupling on an equal footing to discuss ground-state properties. We find that a zigzag ordered state is realized in the model within nearest-neighbor interactions. We clarify how the ordered state competes with the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit. Thermodynamic properties are also addressed. The present work should provide another route to account for the Kitaev-based magnetic properties in candidate materials.

Pentavalent iridium pyrochlore Cd2Ir2O7 : A prototype material system for competing crystalline field and spin-orbit coupling

A new pyrochlore oxide $\mathrm{C}{\mathrm{d}}_{2}\mathrm{I}{\mathrm{r}}_{2}{\mathrm{O}}_{7}$ with an $\mathrm{I}{\mathrm{r}}^{5+}$ charge state was prepared by high-pressure techniques. Although strong spin-orbit coupling (SOC) dominates the electronic states in most iridates so that a SOC-Mott state is proposed in $\mathrm{S}{\mathrm{r}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ in the assumption of an undistorted $\mathrm{Ir}{\mathrm{O}}_{6}$ octahedral crystalline field, the strongly distorted one in the current $\mathrm{C}{\mathrm{d}}_{2}\mathrm{I}{\mathrm{r}}_{2}{\mathrm{O}}_{7}$ exhibits a competing interaction with the SOC. Unexpected from a strong SOC limit, $\mathrm{C}{\mathrm{d}}_{2}\mathrm{I}{\mathrm{r}}_{2}{\mathrm{O}}_{7}$ deviates from a nonmagnetic and insulating $J=0$ ground state. It displays short-range ferromagnetic correlations and metallic electrical transport properties. First-principles calculations well reproduce the experimental observation, revealing the large mixture between the ${j}_{\mathrm{eff}}=1/2$ and ${j}_{\mathrm{eff}}=3/2$ bands near the Fermi surface due to the significant distortion of $\mathrm{Ir}{\mathrm{O}}_{6}$ octahedra. This work sheds light on the critical role of a noncubic crystalline field in electronic properties which has been ignored in past studies of $5d$-electron systems.

Gauge-invariant theory of quasiparticle and condensate dynamics in response to terahertz optical pulses in superconducting semiconductor quantum wells. II. ( s+p )-wave superconductivity in the strong spin-orbit coupling limit

We investigate the optical response to the THz pulses in the s-wave and ($s$+$p$)-wave superconducting semiconductor quantum wells by using the gauge-invariant optical Bloch equations, in which the gauge structure in the superconductivity is explicitly retained. By using the gauge transformation, not only can the microscopic description for the quasiparticle dynamics be realized, but also the dynamics of the condensate is included, with the superfluid velocity and the effective chemical potential naturally incorporated. We reveal that the superfluid velocity itself can contribute to the pump of quasiparticles (pump effect), with its rate of change acting as the drive field to drive the quasiparticles (drive effect). Specifically, the drive effect can contribute to the formation of the blocking region for the quasiparticle, which directly suppresses the anomalous correlation of the Cooper pairs. We find that both the pump and drive effects contribute to the oscillations of the Higgs mode with twice the frequency of the optical field. However, it is shown that the contribution from the drive effect to the excitation of Higgs mode is dominant as long as the driven superconducting momentum is less than the Fermi momentum. This is in contrast to the conclusion from the Liouville or Bloch equations in the literature, in which the drive effect on the anomalous correlation is overlooked with only the pump effect considered.Furthermore, in the gauge-invariant optical Bloch equations, the charge neutrality condition is {\em consistently} considered based on the two-component model for the charge, in which the charge imbalance of quasiparticles can cause the fluctuation of the effective chemical potential. ......

Ground-state phase diagram in the Kugel-Khomskii model with finite spin-orbit interactions

We study ground-state properties in the Kugel-Khomskii model on the two-dimensional honeycomb lattice. Using the cluster mean-field approximations, we deal with the exchange and spin-orbit couplings on an equal footing. We then discuss the stability of the ferromagnetically ordered states against the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit.

Fragile singlet ground-state magnetism in the pyrochlore osmatesR2Os2O7(R=Yand Ho)

The singlet ground state magnetism in pyrochlore osmates Y$_2$Os$_2$O$_7$ and Ho$_2$Os$_2$O$_7$ is studied by DC and AC susceptibility, specific heat, and neutron powder diffraction measurements. Despite the expected non-magnetic singlet in the strong spin-orbit coupling (SOC) limit for Os$^{4+}$ ($5d^4$), Y$_2$Os$_2$O$_7$ exhibits a spin-glass (SG) ground state below 4 K with weak magnetism, suggesting possible proximity to a quantum phase transition between the non-magnetic state in the strong SOC limit and the magnetic state in the strong superexchange limit. Ho$_2$Os$_2$O$_7$ has the same structural distortion as occurs in Y$_2$Os$_2$O$_7$. However, the Os sublattice in Ho$_2$Os$_2$O$_7$ shows long-range magnetic ordering below 36\,K. The sharp difference of the magnetic ground state between Y$_2$Os$_2$O$_7$ and Ho$_2$Os$_2$O$_7$ signals the singlet ground state magnetism in $R_2$Os$_2$O$_7$ is fragile and can be disturbed by the weak $4f-5d$ interactions.

Multi-step shot noise spectrum induced by a local large spin**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504210, 11504211, 11504212, 11274207, 11274208, 11174115, and 11325417), the Key Program of the Ministry of Education of China (Grant No. 212018), the Scientific and Technological Project of Shanxi Province, China (Grant No. 2015031002-2), the Natural Science Foundation of Shanxi Province, China (Grant Nos. 2013011007-2 and 2013021010-5), and the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi Province, China.

We use non-equilibrium Green’s function method to analyze the shot noise spectrum of artificial single molecular magnets (ASMM) model in the strong spin–orbit coupling limit in sequential tunneling regime, mainly focusing on the effects of local large spin. In the linear response regime, the shot noise shows 2S + 1 peaks and is strongly spin-dependent. In the nonlinear response regime, one can observe 2S + 1 steps in shot noise and Fano factor. In these steps one can see the significant enhancement effect due to the spin-dependent multi-channel process of local large spin, which reduces electron correlations.

Odd-parity triplet superconducting phase in multiorbital materials with a strong spin-orbit coupling: application to doped Sr₂IrO₄.

We explore possible superconducting states in t(2g) multiorbital correlated electron systems with strong spin-orbit coupling (SOC). In order to study such systems in a controlled manner, we employ large-scale dynamical mean-field theory (DMFT) simulations with the hybridization expansion continuous-time quantum Monte Carlo (CTQMC) impurity solver. To determine the pairing symmetry, we go beyond the local DMFT formalism using parquet equations to introduce the momentum dependence in the two-particle vertex and correlation functions. In the strong SOC limit, a singlet, d-wave pairing state in the electron-doped side of the phase diagram is observed at weak Hund's coupling, which is triggered by antiferromagnetic fluctuations. When the Hund's coupling is comparable to SOC, a twofold degenerate, triplet p-wave pairing state with relatively high transition temperature emerges in the hole-doped side of the phase diagram, which is associated with enhanced charge fluctuations. Experimental implications to doped Sr2IrO4 are discussed.

Unfrozen spin effect in a composite 1D topological superconductor

The spin of Majorana fermions (MF) is nearly frozen by the applied magnetic field in a composite 1D topological superconductor due to the weak spin-orbit coupling (SOC). In this work, we address theoretically the strong SOC limit and weak-magnetic-field effect, under which the spin degree of freedom of MFs is reactivated and dependent on the wire direction. The quantized zero-energy conductance peak in a bent N/S wire junction can be severely suppressed. The MF phase is significantly modified due to the spin noncollinearity and the fusion of MFs is independent of the wire direction, which is opposite to the strong-magnetic-field case. It is also found that the spatial distribution of an MF could be heavily affected by the wire direction. The findings are helpful to identify and braid MFs in the 1D wire network.

Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom

Combining tight-binding models and first principles calculations, we investigate the quantum anomalous Hall (QAH) effect induced by intrinsic spin-orbit coupling (SOC) in buckled honeycomb lattice with sp orbitals in an external exchange field. Detailed analysis reveals that nontrivial topological properties can arise utilizing not only spin but also orbital degrees of freedom in the strong SOC limit, when the bands acquire non-zero Chern numbers upon undergoing the so-called orbital purification. As a prototype of a buckled honeycomb lattice with strong SOC we choose the Bi(111) bilayer, analyzing its topological properties in detail. In particular, we show the emergence of several QAH phases upon spin exchange of the Chern numbers as a function of SOC strength and magnitude of the exchange field. Interestingly, we observe that in one of such phases, namely, in the quantum spin Chern insulator phase, the quantized charge and spin Hall conductivities co-exist. We consider the possibility of tuning the SOC strength in Bi bilayer via alloying with isoelectronic Sb, and speculate that exotic properties could be expected in such an alloyed system owing to the competition of the topological properties of its constituents. Finally, we demonstrate that 3d dopants can be used to induce a sizeable exchange field in Bi(111) bilayer, resulting in non-trivial Chern insulator properties.

BCS-BEC crossover at finite temperature in spin-orbit-coupled Fermi gases

By adopting a $T$-matrix-based method within the ${G}_{0}G$ approximation for the pair susceptibility, we study the effects of the pairing fluctuation on the three-dimensional spin-orbit-coupled Fermi gases at finite temperature. The critical temperatures of the superfluid to normal phase transition are determined for three different types of spin-orbit coupling (SOC): (1) the extreme oblate (EO) or Rashba SOC, (2) the extreme prolate or equal Rashba-Dresselhaus SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence of the critical temperature signals a crossover from BCS to BEC state; at strong SOC limit, the critical temperature recovers those of ideal BEC of rashbons. The pairing fluctuation induces a pseudogap in the fermionic excitation spectrum in both superfluid and normal phases. We find that, for EO- and S-type SOC, even at weak coupling, sufficiently strong SOC can induce sizable pseudogap. Our research suggests that the spin-orbit-coupled Fermi gases may open new means to the study of the pseudogap formation in fermionic systems.

NMR Chemical Shift in an Electronic State with Arbitrary Degeneracy

We present a theory of nuclear magnetic resonance shielding tensors for electronic states with arbitrary degeneracy. The shieldings are here expressed in terms of generalized Zeeman (g((k))) and hyperfine (A((k))) tensors, of all ranks k allowed by the size of degeneracy. Contrary to recent proposals [T. O. Pennanen and J. Vaara, Phys. Rev. Lett. 100, 133002 (2008)], our theory is valid in the strong spin-orbit coupling limit. Ab initio calculations for the fourfold degenerate Γ(8) ground state of lanthanide-doped fluorite crystals CaF(2):Ln (Ln=Pr(2+), Nd(3+), Sm(3+), and Dy(3+)) show that previously neglected contributions can account for more than 50% of the paramagnetic shift.

Spin–orbital locking, emergent pseudo-spin and magnetic order in honeycomb lattice iridates

The nature of the effective spin Hamiltonian and magnetic order in the honeycomb iridates is explored by considering a trigonal crystal field effect and spin–orbit (SO) coupling. Starting from a Hubbard model, an effective spin Hamiltonian is derived in terms of an emergent pseudo-spin-1/2 moment in the limit of large trigonal distortions and SO coupling. The present pseudo-spins arise from a spin–orbital locking and are different from the jeff = 1/2 moments that are obtained when the SO coupling dominates and trigonal distortions are neglected. The resulting spin Hamiltonian is anisotropic and frustrated by further neighbour interactions. Mean-field theory suggests a ground state with four-sublattice zigzag magnetic order in a parameter regime that can be relevant to the honeycomb iridate compound Na2IrO3, where a similar magnetic ground state has recently been observed. Various properties of the phase, the spin-wave spectrum and experimental consequences are discussed. The present approach contrasts with the recent proposals to understand iridate compounds starting from the strong SO coupling limit and neglecting non-cubic lattice distortions.

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models

We study the magnetic interactions in Mott-Hubbard systems with partially filled t_{2g} levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr2IrO4.

Electrical generation of spin in crystals with reduced symmetry

We propose a simple way of evaluating the bulk spin generation of an arbitrary crystal with a known band structure in the strong spin-orbit coupling limit. We show that, in the presence of an electric field, there exists an intrinsic torque term which gives rise to a nonzero spin generation rate. Using methods similar to those of recent experiments which measure spin polarization in semiconductors, this spin generation rate should be experimentally observable. The wide applicability of this effect is emphasized by explicit consideration of a range of examples: bulk wurtzite and strained zincblende (n-GaAs) lattices, as well as quantum well heterojunction systems.

Mixed-parity superconductivity in centrosymmetric crystals

A weak-coupling formalism for superconducting states possessing both singlet (even parity) and triplet (odd parity) components of the order parameter in centrosymmetric crystals is developed. It is shown that the quasiparticle energy spectrum may be non-degenerate even if the triplet component is unitary. The superconducting gap of a mixed-parity state may have line nodes in the strong spin-orbit coupling limit. The pseudospin carried by the superconducting electrons is calculated, from which follows a prediction of a kink anomaly in the temperature dependence of muon spin relaxation rate. The anomaly occurs at the phase boundary between the bare triplet and mixed-parity states. The stability of mixed-parity states is discussed within Ginzburg-Landau theory. The results may have immediate application to the superconducting series Pr(Os,Ru)4Sb12.

Orbital and spin contributions to thegtensors in metal nanoparticles

We present a theoretical study of the mesoscopic fluctuations of $g$-tensors in a metal nanoparticle. The calculations were performed using a semi-realistic tight-binding model, which contains both spin and orbital contributions to the $g$-tensors. The results depend on the product of the spin-orbit scattering time $\tau_{\textrm{\small so}}$ and the mean-level spacing $\delta$, but are otherwise weakly affected by the specific shape of a {\it generic} nanoparticle. We find that the spin contribution to the $g$-tensors agrees with Random Matrix Theory (RMT) predictions. On the other hand, in the strong spin-orbit coupling limit $\delta \tau_{\textrm{\small so}}/\hbar \to 0$, the orbital contribution depends crucially on the space character of the quasi-particle wavefunctions: it levels off at a small value for states of $d$ character but is strongly enhanced for states of $sp$ character. Our numerical results demonstrate that when orbital coupling to the field is included, RMT predictions overestimate the typical $g$-factor of orbitals that have dominant $d$-character. This finding points to a possible source of the puzzling discrepancy between theory and experiment.

Rotation-Electronic Deperturbation Analysis of the 4f 6s Configurational States of CeO

Rotation-electronic interactions between states of the 4 f 6s configuration of CeO, mediated by the operator -B(R)(Ĵ+·Ĵ−a + Ĵ−·Ĵ+a), have been calculated. Second-order perturbation theory was used to account for the effect of heterogeneous interactions on the rotation constants within a single configuration. Eigenvectors from a ligand field theory calculation were used to evaluate these interactions. The results demonstrate the capability of the ligand field model to predict electronic-rotational interactions, and they illustrate the value of these interactions for uncovering the atomic-ion quantum numbers that are not readily determined for molecules in the strong spin-orbit coupling limit [Hund′s case (c)].

Anisotropic exchange and superconductivity in UPt3.

In this paper an anisotropic exchange interaction is derived and separately fit to high- and low-frequency magnetic neutron scattering data of ${\mathrm{UPt}}_{3}$. This information is used to construct a superconducting pair potential in the strong spin-orbit coupling limit. Solutions of the gap equations show that both high- and low-frequency fluctuations support an ${A}_{1u}$ order parameter, which differ in their vector orientation. Implications of these results in relation to the unique phase diagram ${\mathrm{UPt}}_{3}$ will be discussed.