We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in $3d$ ferromagnetic metals [Fe, Co, permalloy $({\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$; Py), and Ni] by varying their resistivities and temperature. At low temperatures where the phonon scattering is negligible, the skew scattering coefficients of the SHE and AHE in Py are related to its spin polarization. However, this simple relation breaks down for Py at higher temperatures as well as for the other ferromagnetic metals at any temperature. We find that, in general, the relation between the SHE and AHE is more complex, with the temperature dependence of the SHE being much stronger than that of AHE.

We compute the ratio of the pairing gap $\mathrm{\Delta }$ at $T=0$ and $T_c$ for a set of quantum-critical models in which the pairing interaction is mediated by a gapless boson with local susceptibility $\chi \left(\mathrm{\Omega }\right)\propto 1/{\left|\mathrm{\Omega }\right|}^{\gamma }$ (the $\gamma$ model). The limit $\gamma =0+$ $\left[\chi \right(\mathrm{\Omega })=log\left|\mathrm{\Omega }\right|]$ describes color superconductivity, and models with $\gamma >0$ describe superconductivity in a metal at the onset of charge or spin order. The ratio $2\mathrm{\Delta }/T_c$ has been recently computed numerically for $0<\gamma <2$ within Eliashberg theory and was found to increase with increasing $\gamma$ [T.-H. Lee et al., Phys. Rev. Lett. 121, 187003 (2018)]. We argue that the origin of the increase is the divergence of $2\mathrm{\Delta }/T_c$ at $\gamma =3$. We obtain an approximate analytical formula for $2\mathrm{\Delta }/T_c$ for $\gamma \le 3$ and show that it agrees well with the numerics. We also consider in detail the opposite limit of small $\gamma$. Here we obtain the explicit expressions for $T_c$ and $\mathrm{\Delta }$, including numerical prefactors. We show that these prefactors depend on fermionic self-energy in a rather nontrivial way. The ratio $2\mathrm{\Delta }/T_c$ approaches the BCS value 3.53 at $\gamma \to 0$.

We show that the behavior of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors near a surface is considerably different from the usual case. The order parameter of the FF state is strongly deformed near the surface, which leads to a number of unusual features in the linear magnetic response, such as “antiscreening” or “overscreening” of the applied field. In a fully isotropic FF case, the Meissner effect is still present, despite the vanishing of the transverse superfluid density in the bulk. We also calculate the surface critical field $H_{c3}$, which exhibits a peculiar temperature dependence.

We consider spin angular momentum density in inhomogeneous acoustic fields: evanescent waves and surface waves at interfaces with negative-density metamaterials. Despite being purely longitudinal (curl-free), acoustic waves possess intrinsic vector properties described by the velocity field. Motivated by the recent description and observation of the spin properties in elastic and acoustic waves, we compare these properties with their well-known electromagnetic counterparts. Surprisingly, both the transverse spin of evanescent waves and the parameters of surface waves are very similar in electromagnetism and acoustics. We also briefly analyze the important role of dispersion in the description of the energy and spin densities in acoustic metamaterials.

We study the relaxation of long chains of magnetic nanoparticles (MNPs). In spite of the simplicity of this system, there is no theoretical framework for this basic assembly. Using the two-level approximation for energy, we perform first-principles calculations and kinetic Monte Carlo (kMC) simulations to obtain the effective relaxation time ${\tau }_N^{}$ of the chain by incorporating the effects of dipole-dipole interactions and anisotropy axes orientation of the MNPs. For analytical tractability, we consider the case when all easy-axis and initial magnetic moments make an angle $\alpha$ with the chain axis. In the absence of dipolar interactions, the relaxation is governed, as expected, by the usual Néel relaxation time ${\tau }_N^0$. In the presence of interactions, the magnetic relaxation curve is always perfectly fitted by an exponentially decaying function. The dipolar field induces antiferromagnetic or ferromagnetic interactions between the moments: depending on $\alpha$ values, this induces a fastening of relaxation time $\left({\tau }_N^{}<{\tau }_N^0\right)$ or a slowing down $\left({\tau }_N^{}>{\tau }_N^0\right)$. The analytical determination of ${\tau }_N^{}$ is nontrivial, but we have obtained an approximate form that is confirmed by kMC simulations. Finally, it is shown that the equilibrium state is comprised of short-lived ferromagnetic and antiferromagnetic domains, the size of which increases with the dipolar strength. We believe that the above conclusions can be drawn for chains with more complicated structures exhibiting bends, curls, and intersections in higher dimensions. Our study is relevant in the context of applications such as magnetic recording, digital data processing, and magnetic hyperthermia, in which long chains of MNPs are ubiquitous.

We describe here a type of magnetoresistance that takes place in naturally layered and outstanding ordered single phase manganites that may be mediated by magnon excitation. In particular, we show the effect for the Ruddlesden-Popper compound, $\mathrm{LaS}{\mathrm{r}}_2\mathrm{M}{\mathrm{n}}_2{\mathrm{O}}_7$ synthesized by ceramic method. This material exhibits, besides the conventional colossal magnetoresistance, another type of magnetoresistance at low temperature, associated with breaking of the A-type antiferromagnetic coupling of Mn-containing planes. Excitation of magnons or application of a magnetic field breaks this antiparallel alignment so that some electrons, initially confined on the planes, become itinerant along the interplain directions through a double exchange mechanism, giving rise to resistance variations of the order of ∼60% for polycrystalline samples. The effect described here might be present in other types of manganites exhibiting a natural layered structure, opening up the possibility of developing magnetoresistive devices based on antiferromagnetic oxide materials without requiring artificial multilayered structures.

We study in-plane lateral heterostructures of commensurate transition-metal dichalcogenides, such as ${\mathrm{MoS}}_2\text{−}{\mathrm{WS}}_2$ and ${\mathrm{MoSe}}_2\text{−}{\mathrm{WSe}}_2$, and find interfacial and edge states that are highly localized to these regions of the heterostructure. These are one-dimensional (1D) in nature, lying within the band gap of the bulk structure and exhibiting complex orbital and spin structure. We describe such heteroribbons with a three-orbital tight-binding model that uses first principles and experimental parameters as input, allowing us to model realistic systems. Analytical modeling for the 1D interfacial bands results in long-range hoppings due to the hybridization along the interface, with strong spin-orbit couplings. We further explore the Ruderman-Kittel-Kasuya-Yosida indirect interaction between magnetic impurities located at the interface. The unusual features of the interface states result in effective long-range exchange noncollinear interactions between impurities. These results suggest that transition-metal dichalcogenide interfaces could serve as stable, tunable 1D platform with unique properties for possible use in exploring Majorana fermions, plasma excitations, and spintronics applications.

Complete expressions of the thermal-expansion coefficient $\alpha$ and the Grüneisen parameter $\mathrm{\Gamma }$ are derived on the basis of the self-consistent renormalization (SCR) theory. By considering the zero point as well as thermal spin fluctuation under the stationary condition, the specific heat for each class of the magnetic quantum critical point (QCP) specified by the dynamical exponent $z=3$ [feorromagnetism (FM)] and $z=2$ [antiferromagnetism (AFM)] and the spatial dimension $(d=3$ and 2) is shown to be expressed as $C_V=C_{\mathrm{a}}-C_{\mathrm{b}}$, where $C_{\mathrm{a}}$ is dominant at low temperatures, reproducing the past SCR criticality endorsed by the renormalization group theory. Starting from the explicit form of the entropy and using the Maxwell relation, $\alpha ={\alpha }_{\mathrm{a}}+{\alpha }_{\mathrm{b}}$ (with ${\alpha }_{\mathrm{a}}$ and ${\alpha }_{\mathrm{b}}$ being related to $C_{\mathrm{a}}$ and $C_{\mathrm{b}}$, respectively) is derived, which is proven to be equivalent to $\alpha$ derived from the free energy. The temperature-dependent coefficient found to exist in ${\alpha }_{\mathrm{b}}$, which is dominant at low temperatures, contributes to the crossover from the quantum-critical regime to the Curie-Weiss regime. For sufficiently low temperatures, the thermal-expansion coefficient at the QCP behaves as $\alpha \approx {\alpha }_{\mathrm{b}}\sim T^{1/3}$ (3D FM), $T^{1/2}$ (3D AFM), $-lnT$ (2D FM), and $-ln(-lnT)/ln\left(-\frac{T}{lnT}\right)$ (2D AFM). Based on these correctly calculated $C_V$ and $\alpha$, Grüneisen parameter $\mathrm{\Gamma }={\mathrm{\Gamma }}_{\mathrm{a}}+{\mathrm{\Gamma }}_{\mathrm{b}}$ is derived, where ${\mathrm{\Gamma }}_{\mathrm{a}}$ and ${\mathrm{\Gamma }}_{\mathrm{b}}$ contain ${\alpha }_{\mathrm{a}}$ and ${\alpha }_{\mathrm{b}}$, respectively. The inverse susceptibility (renormalized by the mode-mode coupling of spin fluctuations) coupled to the volume $V$ in ${\mathrm{\Gamma }}_{\mathrm{b}}$ gives rise to the divergence of $\mathrm{\Gamma }$ at the QCP for each class even though the characteristic energy scale of spin fluctuation $T_0$ is finite at the QCP, which gives a finite contribution in ${\mathrm{\Gamma }}_{\mathrm{a}}=-\frac{V}{T_0}{\left(\frac{\partial T_0}{\partial V}\right)}_{T=0}$. For $T\ll T_0$, the Grüneisen parameter at the QCP behaves as $\mathrm{\Gamma }\approx {\mathrm{\Gamma }}_{\mathrm{b}}\sim -T^{-2/3}/lnT$ (3D FM), $T^{-1/2}/(\mathrm{const}.-T^{1/2})$ (3D AFM), $-T^{-2/3}lnT$ (2D FM), and $ln(-lnT)/\left[TlnTln\left(-\frac{T}{lnT}\right)\right]$ (2D AFM). General properties of $\alpha$ and $\mathrm{\Gamma }$ including their signs as well as the relation to $T_0$ and the Kondo temperature in temperature-pressure phase diagrams of Ce- and Yb-based heavy electron systems are discussed.

Terahertz conductivity spectra of charges moving ballistically in one-, two-, and three-dimensional infinitely deep rectangular potential wells were investigated theoretically using semiclassical and quantum Kubo formulas. The conductivity spectrum of a degenerate electron gas in these nanostructures exhibits a series of geometrical resonances. These further couple with plasmon resonances occurring in isolated structures: qualitatively different interaction regimes are found in one-, two-, and three-dimensional nanostructures. In contrast, the response of a nondegenerate electron gas smears into a single broad band due to the excessive spectral broadening caused by the wide distribution of charge velocities.

The two-dimensional conducting interfaces in ${\mathrm{SrTiO}}_3$-based systems are known to show a variety of coexisting and competing phenomena in a complex phase space. Magnetoresistance measurements, which are typically used to extract information about the various interactions in these systems, must be interpreted with care, since multiple interactions can contribute to the resistivity in a given range of magnetic field and temperature. Here we review all the phenomena that can contribute to transport in ${\mathrm{SrTiO}}_3$-based conducting interfaces at low temperatures. We apply this understanding to the perpendicular magnetoresistance data of the high-mobility system of (111) oriented $\left({\mathrm{La}}_{0.3}{\mathrm{Sr}}_{0.7}\right)\left({\mathrm{Al}}_{0.65}{\mathrm{Ta}}_{0.35}\right){\mathrm{O}}_3/\mathrm{STO}$ heterostructures, and find an excess negative magnetoresistance contribution which cannot be explained by weak localization alone. We argue that contributions from magnetic scattering as well as electron-electron interactions, combined with weak localization/antilocalization, can provide a possible explanation for the observed magnetoresistance.

It is known that the field-induced spin-density-wave (FISDW) phases are experimentally observed in the quasi-one-dimensional (Q1D) organic conductors with chemical formula ${\left(\mathrm{TMTSF}\right)}_2\mathrm{X}$ ($\mathrm{X}={\mathrm{PF}}_6$, ${\mathrm{ClO}}_4$, etc.) and some others in moderate magnetic fields. From a theoretical point of view, they appear as a result of “one dimensionalization” of the Q1D electron spectra due to the orbital electron effect in a magnetic field. We predict that the novel FISDW phases with different physical meaning have to appear in inclined high magnetic fields in Q1D conductors as a result of combination of the spin-splitting and orbital electron effects. We suggest performing the corresponding experiments in the ${\left(\mathrm{TMTSF}\right)}_2\mathrm{X}$ materials.

In this Rapid Communication, we present the order of the phonon modes and the appearance of the reststrahlen bands for monoclinic symmetry materials with polar lattice vibrations. Phonon modes occur in associated pairs of transverse and longitudinal optical modes, and pairs either belong to inner or outer phonon modes. Inner modes are nested within outer modes. Outer modes cause polarization-dependent reststrahlen bands. Inner modes cause polarization-independent reststrahlen bands. The directional limiting frequencies within the Born-Huang approach are bound to within outer mode frequency regions not occupied by inner mode pairs. Hence, an unusual phonon mode order can occur where both lower-frequency as well as upper-frequency limits for the directional modes can be both transverse and/or longitudinal modes. We exemplify our findings using experimental data for the recently unraveled case of monoclinic symmetry $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ [Phys. Rev. B 93, 125209 (2016)] and demonstrate excellent agreement with results from density functional theory calculations.

We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band, its Bloch wave function possesses immovable discontinuities generated by the band-crossing with other bands, and thus the vector bundle associated with the flat band cannot be defined. This singularity precludes the compact localized states from forming a complete set spanning the flat band. Once the degeneracy at the band crossing point is lifted, the singular flat band becomes dispersive and can acquire a finite Chern number in general, suggesting a new route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave function of a nonsingular flat band has no singularity, and thus forms a vector bundle. A nonsingular flat band can be completely isolated from other bands while preserving the perfect flatness. All one-dimensional flat bands belong to the nonsingular class. We show that a singular flat band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a flat band model Hamiltonian in which one can freely design its singular or nonsingular nature. Finally, we propose a general formula for the compact localized state spanning the flat band, which can be easily implemented in numerics and offer a basis set useful in analyzing correlation effects in flat bands.

A combination of the density functional theory and the single-site dynamical mean-field theory is employed to study the pressure dependence of the electronic structure for cubic phase californium. We predict that its $5f$ electrons could undergo an orbital-selective localized-itinerant transition under moderate pressure. The volume contraction causes remarkable charge redistribution and valence fluctuation behaviors, which are the driving forces of the divalent-trivalent transition. Additionally, we find that the angular momentum coupling mechanism is hardly affected by pressure. The $5f$ orbital occupancy is well described by the intermediate-coupling scheme.

Carbon nanotubes are one-dimensional nanoscale systems with strongly pronounced chirality-dependent optical properties with multiple excitonic transitions. We investigate the high-energy $G$ mode of semiconducting single-walled nanotubes of different chiralities at first excitonic transition by applying resonant Raman spectroscopy. The $G$ mode intensity dependence on excitation energy yielded asymmetric resonance Raman profiles similar to ones we reported for the second excitonic transition. We find the scattering efficiency to be strongest at the incoming Raman resonance. Still, the degree of asymmetry is different for the first and second transitions and the first transition profiles provide a narrower line shape due to longer exciton lifetimes. The overall scattering efficiency is up to a factor of 25 times more intense at first excitonic transition, compared to the second transition. The fifth-order perturbation theory, with implemented phonon scattering pathways between excitonic states, excellently reproduced experimental data.

Bismuth titanate, ${\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12}$ (BiT), is a complex layered ferroelectric material that is composed of three perovskitelike units and one fluoritelike unit stacked alternatively along the transverse direction. The ground-state crystal structure is monoclinic with the spontaneous polarization ($\sim 50\mu \mathrm{C}/\mathrm{c}{\mathrm{m}}^2$) along the plane. BiT typically grows along the $c$ direction in thin-film form, and having the polarization vector aligned with the growth orientation can be beneficial for several potential device applications. It is well known that judicious doping of ferroelectrics is an effective method in adjusting the magnitude and the orientation of the spontaneous polarization. Here, we show using first-principles density-functional theory and a detailed phonon analysis that Bi atoms in the fluoritelike layers have significantly more impact on the magnitude and orientation of the spontaneous polarization vector as compared to the perovskitelike layer. The low-energy hard-phonon modes are characterized by fluoritelike layers experiencing transverse displacements and large changes in Born effective charges on Bi atoms. Thus, the breaking of symmetry caused by doping of Bi sites within the fluoritelike layer leads to the formation of uncancelled permanent dipole moments along the transverse direction. This provides an opportunity for doping the Bi site in the fluoritelike layer. Isovalent dopants P, As, and Sb were studied. P is found to be most effective in the reorientation of the spontaneous polarization. It leads to a threefold enhancement of the out-of-plane component of polarization and to a commensurate rotation of the spontaneous polarization vector by 36.2° towards the transverse direction.

Ab initio molecular dynamics simulations were performed to analyze changes in the structure and dynamics of molten Pb along the melting line for pressures ranging from ambient to 70 GPa. Common neighbor analysis reveals a local structural order of the underlying crystalline phase at the corresponding pressure, which increasingly competes with the existing icosahedral local order with pressure. Obtained dispersions of longitudinal and transverse collective excitations contain two branches of transverse modes for all pressures. Analysis of the pressure dependence of observed two-peak structure of the Fourier spectra of velocity autocorrelation functions allowed us to identify their peak locations with the frequencies of nonpropagating transverse branches in the second pseudo-Brillouin zone.

We study the bulk and edge properties of a driven Kitaev chain, where the driving is performed as instantaneous quenches of the on-site energies. We identify three periodic driving regimes: low period, which is equivalent to a static model, with renormalized parameters obtained from the Baker-Campbell-Hausdorff (BCH) expansion; intermediate period, where the first order BCH expansion breaks down; and high period when the quasienergy gap at $\omega /2$ closes. We investigate the dynamical localization properties for the case of quasiperiodic potential driving as a function of its amplitude and the pairing strength, obtaining regimes with extended, critical, and localized bulk states, if the driving is performed at high frequencies. In these we characterize wave-packet propagation, obtaining ballistic, subdiffusive, and absence of spreading, respectively. In the intermediate period regime, we find an additional region in the phase diagram with a mobility edge between critical and localized states. Furthermore, we investigate the stability of these phases under time aperiodicity on the drivings, observing that the system eventually thermalizes: It results in featureless random states which can be described by the symmetry of the Hamiltonian. In a system with open edges, we find that both Majorana and fermionic localized edge modes can be engineered with a spatially quasiperiodic potential, in similarity with the case of homogeneous on-site energies. Besides, we demonstrate the possibility of creating multiple Majorana 0 and $\pi$ modes in a driven setting, even if the underlying static Hamiltonian is in its trivial phase. Lastly, we study the robustness of the Majorana modes against the aperiodicity in the driving period, showing that the ones created via quasiperiodic potential are more robust to the decoherence. Moreover, we find an example where a Majorana mode displays high robustness, provided that it is chosen from a special point in the topological region.

We present an ab initio study of the spin-transfer torque in Fe/MgO/FePt/Fe magnetic tunnel junctions. We consider an FePt film with a thickness up to six unit cells, either in direct contact with the MgO spacer or with an intercalated ultrathin Fe seed layer. We find that in the FePt layer the torque is not attenuated as strongly as in the case of pure Fe. Moreover, in FePt the torque alternates sign at the Fe and Pt atomic planes throughout the stack for all FePt thicknesses considered. Finally, when Fe is intercalated between MgO and $L{1}_0$ FePt, the torque is sharply attenuated, and it is transferred to FePt only for an Fe seed layer that is less than two atomic planes thick. We attribute these features to the different spatial profiles of the exchange and correlation field and the induced nonequilibrium spin accumulation. The calculated tunneling magnetoresistance of the Fe/MgO/FePt/Fe junctions studied is enhanced with respect to the one of Fe/MgO/Fe, while it is reduced with Fe intercalation. Our work shows that $L{1}_0$ FePt junctions can be promising candidates for current-operated magnetic devices and that the magnetic texture at the atomic scale has an important effect on the spin-transfer torque.