We present time-resolved high-energy x-ray diffraction, time-resolved hard-x-ray photoelectron spectroscopy (tr-HAXPES), and time-resolved grazing incidence small-angle x-ray scattering (tr-GISAXS) data of the reactive molecular beam epitaxy of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ ultrathin films on various substrates. Reciprocal space maps are recorded during the deposition of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ on ${\mathrm{SrTiO}}_3\left(001\right)$, MgO(001), and NiO/MgO(001) in order to observe the thickness-dependent evolution of Bragg reflections sensitive to the octahedral and tetrahedral sublattices of the inverse spinel structure of ${\mathrm{Fe}}_3{\mathrm{O}}_4$. Rock salt and spinel-exclusive reflections appear at different thicknesses, revealing that first, the iron oxide film grows with ${\mathrm{Fe}}_{1-\delta }\mathrm{O}$ rock salt structure with exclusive occupation of octahedral lattice sites. After reaching a film thickness of $1.1\mathrm{nm}$, further growth of the iron oxide film proceeds in the inverse spinel structure, with both octahedral and tetrahedral lattice sites being occupied. In addition, iron oxide on ${\mathrm{SrTiO}}_3\left(001\right)$ initially grows with none of these structures. Here, the formation of the rock salt structure starts when reaching a film thickness of $1.5\mathrm{nm}$. This is confirmed by tr-HAXPES data obtained during growth of iron oxide on ${\mathrm{SrTiO}}_3\left(001\right)$, which demonstrate an excess of ${\mathrm{Fe}}^{2+}$ cations compared to ${\mathrm{Fe}}_3{\mathrm{O}}_4$ in growing films thinner than $3.2\mathrm{nm}$. This rock salt phase only appears during growth and vanishes after the supply of the Fe molecular beam is stopped. Thus, it can be concluded that the rock salt structure of the interlayer is a property of the dynamic growth process while the film is still exposed to oxygen. The tr-GISAXS data link these structural results to an island growth mode of the first 2–3 nm on both MgO(001) and ${\mathrm{SrTiO}}_3\left(001\right)$ substrates.

The recent rise of material platforms combining magnetism and two-dimensionality of mobile carriers reveals a diverse spectrum of spin-orbit phenomena and stimulates its ongoing theoretical discussions. In this paper, we use the density matrix approach to provide a unified description of subtle microscopic effects governing the electron gas spin behavior in the clean limit upon electric perturbations in two-dimensional magnets with strong spin-orbit coupling. We discuss that an inhomogeneity of electrostatic potential generally leads to the electron gas spin tilting with the subsequent formation of equilibrium skyrmionlike spin textures and demonstrate that several microscopic mechanisms of two-dimensional electron gas (2DEG) spin response are equally important for this effect. We analyze the dynamics of 2DEG spin upon an oscillating electric field with a specific focus on the emergent electric dipole spin resonance. We address the resonant enhancement of magneto-optical phenomena from the spin precession equation perspective and discuss it in terms of the resonant spin generation. We also clarify the connection of both static and dynamic spin phenomena arising in response to a scalar perturbation with the electronic band Berry curvature.

This paper discusses the combined effects of optical excitation power, interface roughness, lattice temperature, and applied magnetic fields on the spin coherence of excitonic states in GaAs/AlGaAs multiple quantum wells. For low optical powers, at lattice temperatures between 4 and 50 K, the scattering with acoustic phonons and short-range interactions appear as the main decoherence mechanisms. Statistical fluctuations of the band gap, however, become also relevant in this regime and we were able to deconvolute them from the decoherence contributions. The circularly polarized magneto-photoluminescence unveils a nonmonotonic tuning of the coherence for one of the spin components at low magnetic fields. This effect has been ascribed to the competition between short-range interactions and spin-flip scattering, modulated by the momentum relaxation time.

Little is known about the role of weak interlayer coupling in the second harmonic generation (SHG) effects of two-dimensional van der Waals (vdW) systems. In this paper, taking homobilayer $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{S}}_2$ and heterobilayer $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{Se}}_2$ as typical examples, we have systemically investigated their SHG susceptibilities ${\chi }^{\left(2\right)}$ as a function of interlayer hopping strength ($t_{\mathrm{int}}$) using first-principles calculations. For the ${\chi }_{yyy}^{\left(2\right)}\left(0;0,0\right)$ of both $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{Se}}_2$, although the increase of $t_{\mathrm{int}}$ can increase the intensities of interlayer optical transitions (IOT), the increased band repulsion around the Γ point can eventually decrease their ${\chi }_{yyy}^{\left(2\right)}\left(0;0,0\right)$ values; the larger the $t_{\mathrm{int}}$, the smaller the ${\chi }_{yyy}^{\left(2\right)}\left(0;0,0\right)$. For the $|{\chi }_{yyy}^{\left(2\right)}\left(-2\omega ;\omega ,\omega \right)|$ spectra of $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{Se}}_2$ in the low photon-energy region, opposite to the $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{S}}_2$, their peak values are very sensitive to the variable $t_{\mathrm{int}}$, due to the strong $t_{\mathrm{int}}$-dependent IOT dominating in the band edge; the larger the $t_{\mathrm{int}}$, the larger the $|{\chi }_{yyy}^{\left(2\right)}\left(-2\omega ;\omega ,\omega \right)|$. For the $|{\chi }_{yyy}^{\left(2\right)}\left(-2\omega ;\omega ,\omega \right)|$ of $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{S}}_2$ in the high photon-energy region, comparing to the $\mathrm{Mo}{\mathrm{S}}_2/\mathrm{Mo}{\mathrm{Se}}_2$, their peak values will decrease in a much more noticeable way as the $t_{\mathrm{int}}$ increases, due to the larger reduction of band-nesting effect. Our study not only can successfully explain the puzzling experimental observations for the different SHG responses in different bilayer transition metal dichalcogenides under variable $t_{\mathrm{int}}$, but also may provide a general understanding for designing controllable the SHG effects in the vdW systems.

We investigate the connections between current-induced spin-orbit torques and unidirectional magnetoresistance (UMR) by performing second harmonic longitudinal resistance measurements on Co/Pt bilayer with magnetic-field ${\mu }_{0}H$ up to 10 T and temperature $T$ down to 2 K. The fieldlike torque $h_{\mathrm{FL}}$ changes sign with varying Co thickness $t_{\mathrm{Co}}$, which indicates that competing mechanisms, i.e., the spin Hall effect (SHE) and the inverse spin galvanic effect (iSGE), are responsible for the generation of $h_{\mathrm{FL}}$. The sign of $h_{\mathrm{FL}}$ coincides with the sign of UMR induced by spin-dependent scattering. However, the dampinglike torque $h_{\mathrm{DL}}$ is proportional to the inverse Co thickness, with no sign reversal for all measured temperatures and $t_{\mathrm{Co}}$, indicating that $h_{\mathrm{DL}}$ originates solely from the SHE. The generation of $h_{\mathrm{DL}}$ via iSGE can be further excluded because of the observation of an $H$-linear dependence of UMR, which, in turn, indicates the negligible exchange coupling between spin accumulation and ferromagnetic metal.

Understanding of the intimate cross coupling between electric and magnetic degrees of freedom in solids usually requires sophisticated models and time-consuming calculation methods. Instead of macroscopic symmetry analysis, we present a simple but general approach to explore the microscopic mechanism of magnetoelectric (ME) effects in magnetic ordered materials based on local spin and lattice symmetry analysis. Our method is successfully applied to ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and orthorhombic $R\mathrm{Mn}{\mathrm{O}}_3$ with linear and quadratic ME effects, respectively. We revealed all the possible microscopic origins of every nonzero ME coefficient that cannot be easily fulfilled by other theoretical methods. Moreover, the contribution from each mechanism can be located down to specific spins or spin pairs. Our theoretical approach is capable of providing a detailed guide on exploring rich spin-induced magnetoelectrics with strong ME effects.

Interlayer transport in high-$T_C$ cuprates is mediated by superconducting tunneling across the ${\mathrm{CuO}}_2$ planes. For this reason, the terahertz frequency optical response is dominated by one or more Josephson plasma resonances and becomes highly nonlinear at fields for which the tunneling supercurrents approach their critical value $I_C$. These large terahertz nonlinearities are in fact a hallmark of superconducting transport. Surprisingly, however, they have been documented in ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x\mathrm{Cu}{\mathrm{O}}_4$ (LBCO) also above $T_C$ for doping values near $x=\frac{1}{8}$ and interpreted as an indication of superfluidity in the stripe phase. Here, electric-field-induced second harmonic is used to study the dynamics of time-dependent interlayer voltages when LBCO is driven with large-amplitude terahertz pulses, in search of other characteristic signatures of Josephson tunneling in the normal state. We show that this method is sensitive to the voltage anomalies associated with 2π Josephson phase slips, which near $x=\frac{1}{8}$ are observed both below and above $T_C$. These results document a regime of nonlinear transport that shares features of fluctuating stripes and superconducting phase dynamics.

Elemental rhenium exhibiting type-II superconductivity has been previously reported to break time-reversal symmetry in the superconducting state. We have investigated an arc-melted sample of rhenium exhibiting type-I superconductivity. Low-temperature zero-field muon-spin relaxation measurements indicate that time-reversal symmetry is preserved in the superconducting state. Muon diffusion is observed, which is due to quantum mechanical tunneling between interstitial sites. The normal state behavior is characterized by the conduction electrons screening the muons and thermal broadening, and is typical for a metal. Energy asymmetries between muon trapping sites and the superconducting energy gap also characterize the superconducting state behavior.

The layered metal phosphorous trisulfide ${\mathrm{FePS}}_3$ is reported to be a Mott insulator at ambient conditions and to undergo structural and insulator-metal phase transitions under pressure. However, the character of the resulting metallic states has not been understood clearly so far. Here, we theoretically study the phase transitions of ${\mathrm{FePS}}_3$ using first-principles methods based on density functional theory and embedded dynamical mean field theory. We find that the Mott transition in ${\mathrm{FePS}}_3$ can be orbital selective, with $t_{2g}$ states undergoing a correlation-induced insulator-to-metal transition while $e_g$ states remain gapped. We show that this orbital-selective Mott phase, which occurs only when nonhydrostatic pressure is used, is a bad metal (or non-Fermi liquid) with large fluctuating moments due to Hund's coupling. Further application of pressure increases the crystal-field splitting and converts the system to a conventional Fermi liquid with low-spin configurations dominant. Our results show that ${\mathrm{FePS}}_3$ is an example of a system that realizes an orbital-selective Mott phase, allowing tuning between correlated and uncorrelated metallic properties in an accessible pressure range ($\le 18$ GPa).

Based on the density functional theory, we examine the origin of ferromagnetism in the Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ using different types of response theories. We argue that the magnetism of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ has a dual nature and bears certain aspects of both itineracy and localization. On the one hand, the magnetism is soft, where the local magnetic moments strongly depend on temperature and the angles formed by these moments at different Co sites of the kagome lattice, as expected for itinerant magnets. On the other hand, the picture of localized spins still remains adequate for the description of the local stability of the ferromagnetic (FM) order with respect to the transversal spin fluctuations. For the latter purposes, we employ two approaches, which provide quite different pictures for interatomic exchange interactions: the regular magnetic force theorem and a formally exact theory based on the calculation of the inverse response function. The exact theory predicts ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ to be a three-dimensional ferromagnet with the strongest interaction operating between next-nearest neighbors in the adjacent kagome planes. The ligand states are found to play a very important role by additionally stabilizing the FM order. When the local moments decrease, the interplane interactions sharply decrease, first causing the FM order to become quasi-two-dimensional, and then making it unstable with respect to the spin-spiral order propagating perpendicular to the kagome plane. The latter instability is partly contributed by the states at the Fermi surface and may be relevant to the magnetic behavior of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ near the Curie temperature. Peculiarities of the half-metallic ferromagnetism in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ are also discussed.

We show that in cubic crystals with anisotropic impurity centers the sum of squares of the magnetic resonance [electron paramagnetic resonance (EPR)] frequencies is invariant with respect to the magnetic field direction. The connection between such an invariant and the $g$-tensor components of the impurity is derived for different types of centers. The established regularity is confirmed experimentally for the spin-noise spectra of a cubic $\mathrm{Ca}{\mathrm{F}}_2-{\mathrm{Nd}}^{3+}$ crystal. We show how this property of the EPR spectra can be efficiently used for the assignment of paramagnetic centers in cubic crystals.

In the presence of certain symmetries, three-dimensional Dirac semimetals can harbor not only surface Fermi arcs, but also surface Dirac cones. Motivated by the experimental observation of rotation-symmetry-protected Dirac semimetal states in iron-based superconductors, we investigate the potential intrinsic topological phases in a $C_{4z}$-rotational invariant superconducting Dirac semimetal with $s_{\pm }$-wave pairing. When the normal state harbors only surface Fermi arcs on the side surfaces, we find that an interesting gapped superconducting state with a quartet of Bogoliubov-Dirac cones on each side surface can be realized, even though the first-order topology of its bulk is trivial. When the normal state simultaneously harbors surface Fermi arcs and surface Dirac cones, we find that a second-order time-reversal invariant topological superconductor with helical Majorana hinge states can be realized. The criteria for these two distinct topological phases have a simple geometric interpretation in terms of three characteristic surfaces in momentum space. By reducing the bulk material to a thin film normal to the axis of rotation symmetry, we further find that a two-dimensional first-order time-reversal invariant topological superconductor can be realized if the inversion symmetry is broken by applying a gate voltage. Our work reveals that diverse topological superconducting phases and types of Majorana modes can be realized in superconducting Dirac semimetals.

In contrast to electron (fermion) systems, topological phases of charge neutral bosons have been poorly understood despite recent extensive research on insulating magnets. The most important unresolved issue is how the inevitable interbosonic interactions influence the topological properties. It has been proposed that the quantum magnet $\mathrm{Sr}{\mathrm{Cu}}_2{\left({\mathrm{BO}}_3\right)}_2$ with an exact ground state serves as an ideal platform for this investigation, as the system is expected to be a magnetic analog of a Chern insulator with electrons replaced by bosonic magnetic excitations (triplons). Here, in order to examine topologically protected triplon chiral edge modes in $\mathrm{Sr}{\mathrm{Cu}}_2{\left({\mathrm{BO}}_3\right)}_2$, we measured and calculated the thermal Hall conductivity ${\kappa }_{xy}$. Our calculations show that the sign of ${\kappa }_{xy}$ is negative, which is opposite to the previous calculations, and its magnitude is $2\pi$ times smaller. No discernible ${\kappa }_{xy}$ was observed, and its values are at most 20–30% of our calculations if present. This implies that even relatively weak interparticle interactions seriously influence the topological transport properties at finite temperatures. These findings demonstrate that, in contrast to fermionic cases, the picture of noninteracting topological quasiparticles cannot be naively applied to bosonic systems, calling special attention to the interpretation of the topological bosonic excitations reported for various insulating magnets.

The conformal field theory (CFT) approach to Kondo problems, originally developed by Affleck and Ludwig (AL), has greatly advanced the fundamental knowledge of Kondo physics. The CFT approach to Kondo impurities is based on a necessary approximation, i.e., the linearization of the low-lying excitations in a narrow energy window about the Fermi surface. This treatment works well in normal metal baths but encounters fundamental difficulties in systems with Fermi points and high-order dispersion relations. Prominent examples of such systems are the recently proposed topological semimetals with emergent higher-order fermions. Here, we develop a new CFT technique that yields exact solutions to the Kondo problems in higher-order fermion systems. Our approach does not require any linearization of the low-lying excitations, and more importantly, it rigorously bosonizes the entire energy spectrum of the higher-order fermions. Therefore it provides a more solid theoretical base for evaluating the thermodynamic quantities at finite temperatures. Our work significantly broadens the scope of CFT techniques and brings about unprecedented applications beyond the reach of conventional methods.

High-quality thin films of the topological insulator ${\left({\mathrm{Bi}}_{0.4}{\mathrm{Sb}}_{0.6}\right)}_2{\mathrm{Te}}_3$ have been deposited on $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ (111) by molecular beam epitaxy. Their electronic structure was investigated by in situ angle-resolved photoemission spectroscopy and in situ scanning tunneling spectroscopy. The experimental results reveal striking similarities with relativistic ab initio tight-binding calculations. We find that ultrathin slabs of the three-dimensional topological insulator ${\left({\mathrm{Bi}}_{0.4}{\mathrm{Sb}}_{0.6}\right)}_2{\mathrm{Te}}_3$ display topological surface states, surface states with large weight on the outermost Te atomic layer, and dispersive bulk energy levels that are quantized. We observe that the bandwidth of the bulk levels is strongly reduced. These bunched bulk states as well as the surface states give rise to strong peaks in the local density of states.

We report on the far-field photoluminescence intensity distribution of interlayer excitons in ${\mathrm{MoSe}}_2\text{−}{\mathrm{WSe}}_2$ heterostacks as measured by back focal plane imaging in the temperature range between 1.7 and 20 K. By comparing the data with an analytical model describing the dipolar emission pattern in a dielectric environment, we are able to obtain the relative contributions of the in- and out-of-plane transition dipole moments associated to the interlayer exciton photon emission. We determine the transition dipole moments for all observed interlayer exciton transitions to be $(99\pm 1)\%$ in plane for R- and H-type stacking, independent of the excitation power and therefore the density of the exciton ensemble in the experimentally examined range. Finally, we discuss the limitations of the presented measurement technique to observe correlation effects in exciton ensembles.

One big achievement in modern condensed matter physics is the recognition of the importance of various band geometric quantities in physical effects. As prominent examples, Berry curvature and the Berry curvature dipole are connected to the linear and the second-order Hall effects, respectively. Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. Based on the extended semiclassical formalism, we develop a theory for the third-order charge transport and derive explicit formulas for the third-order conductivity. Our theory is applied to the two-dimensional (2D) Dirac model to investigate the essential features of the BCP and the third-order Hall response. We further demonstrate the combination of our theory with the first-principles calculations to study a concrete material system, the monolayer FeSe. Our work establishes a foundation for the study of third-order transport effects, and reveals the third-order Hall effect as a tool for characterizing a large class of materials and for probing the BCP in band structure.

We study the zero-temperature phase diagrams of Majorana-Hubbard models with $\mathrm{SO}(N$) symmetry on two-dimensional honeycomb and $\pi$-flux square lattices, using mean-field and renormalization group approaches. The models can be understood as real counterparts of the $\mathrm{SU}(N$) Hubbard-Heisenberg models and may be realized in Abrikosov vortex phases of topological superconductors, or in fractionalized phases of strongly frustrated spin-orbital magnets. In the weakly interacting limit, the models feature stable and fully symmetric Majorana semimetal phases. Increasing the interaction strength beyond a finite threshold for large $N$, we find a direct transition towards dimerized phases, which can be understood as staggered valence bond solid orders, in which part of the lattice symmetry is spontaneously broken and the Majorana fermions acquire a mass gap. For small to intermediate $N$, on the other hand, phases with spontaneously broken $\mathrm{SO}(N$) symmetry, which can be understood as generalized Néel antiferromagnets, may be stabilized. These antiferromagnetic phases feature fully gapped fermion spectra for even $N$, but gapless Majorana modes for odd $N$. While the transitions between Majorana semimetal and dimerized phases are strongly first order, the transitions between Majorana semimetal and antiferromagnetic phases are continuous for small $N\le 3$ and weakly first order for intermediate $N\ge 4$. The weakly first-order nature of the latter transitions arises from fixed-point annihilation in the corresponding effective field theory, which contains a real symmetric tensorial order parameter coupled to the gapless Majorana degrees of freedom, realizing interesting examples of fluctuation-induced first-order transitions.

We investigate experimentally and theoretically the temporal evolution of the spin of the conduction band electron and that of the valence band heavy hole, both confined in the same semiconductor quantum dot. We use all-optical pulse techniques to perform complete tomographic measurements of the spin as a function of time after its initialization and study the total spin purity (coherence), measured here. In the important limit of a weak externally applied magnetic field, comparable in strength to the Overhauser field due to fluctuations in the surrounding nuclei spins, the measured spin purity performs complex temporal oscillations. We use a central-spin model encompassing the spin' s Zeeman and the hyperfine interactions to reproduce the measured results quantitatively. Our studies are essential for designing and optimizing quantum-dot-spin-based entangled multiphoton sources that set stringent limitations on the magnitude of the externally applied field.