We study spin torques induced by Rashba spin-orbit coupling in two-dimensional ferromagnets under the good-metal condition ${\epsilon }_F\tau /\hslash \gg 1$ (${\epsilon }_F$ the Fermi energy, $\tau$ the electron lifetime) by employing the Kubo formula. We find that in the presence of spin-dependent disorder the Rashba torque changes greatly as the system evolves out of the weak-disorder limit where $\hslash /\tau$ is much smaller than any intrinsic energy scale characterizing the multiband structure. The antidamping-like component of Rashba torque can be comparable to and larger than the field-like one out of the weak-disorder limit. The semiclassical Boltzmann theory produces the same results as microscopic linear response calculations only in the weak-disorder limit. Our analysis indicates that rich behaviors of various nonequilibrium phenomena beyond the Boltzmann theory may also be present even when ${\epsilon }_F\tau /\hslash \gg 1$ in multiband systems where ${\epsilon }_F$ is not the unique intrinsic energy scale.

A two-dimensional electron gas interacting with an external periodic potential attracts attention as a designable artificial material to explore topological phases. Here, to introduce a periodic potential into a Shockley state, superstructures of CO molecules have been fabricated on a Cu(111) surface by atom manipulation with a low-temperature scanning tunneling microscope. Local electronic states have been investigated in relation to specific locations on the CO triangular lattice. All tunneling spectra of the lattice exhibit a reduction at the bottom energy of the surface-state band, which reflects absorption of surface-state electrons into the bulk. For an ($8\times 8$) CO structure, spectra measured at positions corresponding to two equivalent triangular sublattices of artificial graphene have different features near the Fermi level. This sublattice site dependence is not observed for a ($6\times 6$) structure. First-principles calculations for a ($4\times 4$) structure have reproduced the local density of states that depend on the sublattice sites. These results can be understood that coupling between the surface state and the bulk is strengthened via scattering by the adsorbates, and that the external periodic potential is perturbed by the second layer of the Cu(111) substrate. The periodicity of the external potential appears to be the key parameter which dominates the equivalence of pseudospin states in the artificial graphene.

Elucidating the details of electron-phonon coupling in semiconductors and insulators is a topic of pivotal interest, as it governs the transport mechanisms and is responsible for various phenomena such as spectral-weight transfers to phonon sidebands and self-trapping. Here, we investigate the influence of the electron-phonon interaction on the excitonic peaks of rutile ${\mathrm{TiO}}_2$, revealing a strong anisotropic polarization dependence with increasing temperature, namely, an anomalous blue shift for light polarized along the $a$ axis and a conventional red shift for light polarized along the $c$ axis. By employing many-body perturbation theory, we identify two terms in the electron-phonon interaction Hamiltonian that contribute to the anomalous blue shift of the $a$-axis exciton. Our approach paves the way to a complete ab initio treatment of the electron-phonon interaction and of its influence on the optical spectra of polar materials.

The XXZ model on a square lattice in the presence of a transverse magnetic field is studied within the spin-wave theory to investigate the resulting canted antiferromagnet. The small- and large-field regimes are probed separately both for easy-axis and easy-plane scenarios which reveal an unentangled factorized ground state at an intermediate value of the field. Goldstone modes are obtained for the field-free XY antiferromagnet as well as for the isotropic antiferromagnet with field up to its saturation value. Moreover, for an easy-plane anisotropy, we find that there exists a nonzero field, where magnon degeneracy appears as a result of restoration of a U(1) sublattice symmetry and that, across that field, there occurs a magnon band crossing. For completeness, we then obtain the system phase diagram for $S=1/2$ via large-scale quantum Monte Carlo simulations using the stochastic series expansion technique. Our numerical method is based on a quantization of spin along the direction of the applied magnetic field and does not suffer from a sign problem, unlike comparable algorithms based on a spin quantization along the axis of anisotropy. With this formalism, we are also able to obtain powder averages of the transverse and longitudinal magnetizations, which may be useful for understanding experimental measurements on polycrystalline samples.

We compare the two-dimensional (2D) plasmon dispersion relations for monolayer graphene when the sample is doped with carriers in the conduction band and the temperature $T$ is zero with the case when the temperature is finite and there is no doping. Additionally, we have obtained the plasmon excitations when there is doping at finite temperature. The results were obtained in the random-phase approximation which employs energy electronic bands calculated using ab initio density functional theory. We found that in the undoped case the finite temperature results in appearance in the low-energy region of a 2D plasmon which is absent for the $T=0$ case. Its energy is gradually increased with increasing $T$. It is accompanied by expansion in the momentum range where this mode is observed as well. The 2D plasmon dispersion in the $\mathrm{\Gamma }M$ direction may differ in substantial ways from that along the $\mathrm{\Gamma }K$ direction at sufficiently high temperature and doping concentrations. Moreover, at temperatures exceeding $\approx 300$ meV a second mode emerges along the $\mathrm{\Gamma }K$ direction at lower energies like it occurs at a doping level exceeding $\approx 300$ meV. Once the temperature exceeds $\approx 0.75$ eV this mode ceases to exist whereas the 2D plasmon exists as a well-defined collective excitation up to $T=1.5\mathrm{eV}$, a maximal temperature investigated in this work.

We study transport across $p-n$ junctions of gapped two-dimensional semi-Dirac materials: nodal semimetals whose energy bands disperse quadratically and linearly along distinct crystal axes. The resulting electronic properties—relevant to materials such as ${\mathrm{TiO}}_2/{\mathrm{VO}}_2$ multilayers and $\alpha$-(BEDT-TTF)${}_2{\mathrm{I}}_3$ salts—continuously interpolate between those of mono- and bilayer graphene as a function of propagation angle. We demonstrate that tunneling across the junction depends on the orientation of the tunnel barrier relative to the crystalline axes, leading to strongly nonmonotonic current-voltage characteristics, including negative differential conductance in some regimes. In multivalley systems, these features provide a natural route to engineering valley-selective transport.

The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in second-order structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e., the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally, we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe.

The lattice thermal conductivity of ${\mathrm{Cu}}_2\mathrm{O}$ was studied using ab initio density functional methods. The performance of generalized gradient approximation (GGA), GGA-PBE, and PBE0 exchange-correlation functionals was compared for various electronic and phonon-related properties. The $3d$ transition metal oxides such as ${\mathrm{Cu}}_2\mathrm{O}$ are known to be a challenging case for pure GGA functionals, and in comparison to the GGA-PBE the PBE0 hybrid functional clearly improves the description of both electronic and phonon-related properties. The most striking difference is found in the lattice thermal conductivity, where the GGA underestimates it as much as 40% in comparison to experiments, while the difference between the experiment and the PBE0 hybrid functional is only a few percent.

We experimentally investigate the influence of a driven, dynamic vortex magnetization state on an individual nitrogen-vacancy (NV) spin in diamond. The vortex core can be translated within the ferromagnet using an applied magnetic field, allowing us to map out the spatial dependence of the interaction. The vortex displacement is determined using magneto-optical microscopy, while the vortex's influence on the spin is probed using optically detected magnetic resonance to measure the Rabi oscillation frequency between spin levels. We find that the close proximity of the vortex core to the NV (within about 200 nm) leads to more than an order of magnitude enhancement of the Rabi frequency. The NV/vortex interaction differs significantly for transitions to the $m_s=+1$ and $m_s=-1$ spin states, which we attribute to the chiral nature of the vortex state dynamics. We compare the results with micromagnetic simulations and a simple analytical model to shed light on the mechanisms behind the observed effects.

Magnetic exchange stiffness in TM/MgO(001) [transition metal (TM) = Fe, Co, and Ni] is investigated by means of the first-principles full-potential linearized augmented plane wave method. We find that while the exchange stiffness constants are positive (ferromagnetic) in all considered systems, there are negative energy orbital contributions to the exchange stiffness preferring antiferromagnetic alignment. The different contributions can be explained simply in terms of bandwidth narrowing of the $d_{xz}$ band arising from an introduction of spin canting on neighboring TM atoms along the $x$ direction. This scenario reflects well the stability of the $d$ bands, especially in the cases of Fe/MgO and Co/MgO, on going from the ferromagnetic state towards the spin spiral states, and the exchange stiffness constant may be determined by the position of the Fermi level. As for the Ni/MgO system, we find that the exchange stiffness constant is much smaller than in the other two cases due to the almost full occupation of the relevant $d$ orbitals. When this mechanism which is associated with the bandwidth narrowing is applied to investigate the effect of external field on the exchange stiffness, we find that in both Fe/MgO and Co/MgO, the application of positive field increases the exchange stiffness due to the modification of the TM-O atomic distance.

We report angular-dependent spin-wave spectroscopy on kagome artificial spin ice made of large arrays of interconnected ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ nanobars. Spectra taken in saturated and disordered states exhibit a series of resonances with characteristic in-plane angular dependencies. Micromagnetic simulations allow us to interpret characteristic resonances of a two-step magnetization reversal of the nanomagnets. The dynamic properties are consistent with topological defects that are provoked via a magnetic field applied at specific angles. Simulations that we performed on previously investigated kagome artificial spin ice consisting of isolated nanobars show characteristic discrepancies in the spin-wave modes which we explain by the absence of vertices.

A Josephson spin valve is a ferromagnetic spin valve sandwiched between two superconducting electrodes. It has been predicted theoretically that such a device may exhibit a long-range proximity effect due to generation of unconventional odd-frequency spin-triplet and long-range spin-singlet components of the supercurrent. In this work we present a comprehensive numerical analysis of Josephson spin-valve characteristics. Our analysis is based on micromagnetic simulations for Ni-based spin valves. The supercurrent through the spin valve depends on shapes and sizes of components, the magnetic domain structure, and the flux quantization. For very small monodomain spin valves, the triplet current is manifested by a dissimilar double maximum in the magnetic field dependence of the critical current $I_c\left(H\right)$. However, this feature is washed away in larger devices due to appearance of domains and flux quantization. The only remaining signature of the triplet current in this case are beatings in $I_c\left(H\right)$ with a half-flux quantum periodicity. The complexity of the device can make it difficult to identify the spin-triplet supercurrent without a detailed knowledge of the spin-valve state. However, we argue that unambiguous conclusions can be made from a systematic analysis of size, thickness, and shape dependencies of the Josephson spin-valve characteristics.

Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed.

Based on first-principles band-structure calculations, we predict that an inversion-breaking, stoichiometric single crystal ${\mathrm{NbIrTe}}_4$ is a Weyl semimetal candidate. Without spin-orbit coupling (SOC), we find that there are only eight Weyl points in the $k_z=0$ plane. The separation between Weyl points of opposite chiralities is determined by the magnitude of the band inversion. When considering the SOC, ${\mathrm{NbIrTe}}_4$ hosts 16 Weyl points in the whole Brillouin zone. Actually, there are only three irreducible Weyl points and two of them are type-II Weyl points. Finally, the surface-state Fermi arc structures on (001) surface are also obtained. The results on the surface correspond with the properties in the bulk.

The spin Peltier effect (SPE), heat-current generation due to spin-current injection, in various metal (Pt, W, and Au single layers and Pt/Cu bilayer)/ferrimagnetic insulator [yttrium-iron-garnet (YIG)] junction systems has been investigated by means of a lock-in thermography (LIT) method. The SPE is excited by a spin current across the metal/YIG interface, which is generated by applying a charge current to the metallic layer via the spin Hall effect. The LIT method enables the thermal imaging of the SPE free from the Joule-heating contribution. Importantly, we observed spin-current-induced temperature modulation not only in the Pt/YIG and W/YIG systems, but also in the Au/YIG and Pt/Cu/YIG systems, excluding the possible contamination by anomalous Ettingshausen effects due to proximity-induced ferromagnetism near the metal/YIG interface. As demonstrated in our previous study, the SPE signals are confined only in the vicinity of the metal/YIG interface; we buttress this conclusion by reducing a spatial blur due to thermal diffusion in an infrared-emission layer on the sample surface used for the LIT measurements. We also found that the YIG-thickness dependence of the SPE is similar to that of the spin Seebeck effect measured in the same Pt/YIG sample, implying the reciprocal relation between them.

A rather unique feature of the two-dimensional electron gas formed at the interface between the two insulators ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ is to host both gate-tunable superconductivity and strong spin-orbit coupling. In the present work, we use the disorder generated by Cr substitution of Al atoms in ${\mathrm{LaAlO}}_3$ as a tool to explore the nature of superconductivity and spin-orbit coupling in these interfaces. We analyze the transport properties of three different samples whose only relevant difference is their elastic scattering time ${\tau }_e$. A reduction of the superconducting $T_c$ is observed with Cr doping consistent with an increase of electron-electron interaction in the presence of disorder. In addition, the evolution of spin-orbit coupling with gate voltage and Cr doping evidences a Dyakonov-Perel mechanism of spin relaxation (${\tau }_{\mathrm{SO}}\propto {\tau }_e^{-1}$) in the presence of a Rashba-type spin-orbit interaction.

We investigate the degeneracy of the superconducting vortex matter ground state by directly visualizing the vortex configurations in a kagome lattice of elongated antidots via scanning Hall probe microscopy. The observed vortex patterns, at specific applied magnetic fields, are in good agreement with the configurations obtained using time-dependent Ginzburg-Landau simulations. Both results indicate that the long-range interaction in this nanostructured superconductor is unable to lift the degeneracy between different vortex states and the pattern formation is mainly ruled by the nearest-neighbor interaction. This simplification makes it possible to identify a set of simple rules characterizing the vortex configurations. We demonstrate that these rules can explain both the observed vortex distributions and the magnetic-field-dependent degree of degeneracy.