We show that the computation of formation probabilities (FP's) in the configuration basis and the full counting statistics of observables in quadratic fermionic Hamiltonians are equivalent to the calculation of emptiness formation probability (EFP) in the Hamiltonian with a defect. In particular, we first show that the FP of finding a particular configuration in the ground state is equivalent to the EFP of the ground state of the quadratic Hamiltonian with a defect. Then, we show that the probability of finding a particular value for any quadratic observable is equivalent to a FP problem and ultimately leads to the calculation of EFP in the ground state of a Hamiltonian with a defect. We provide exact determinant formulas for the FP in generic quadratic fermionic Hamiltonians. For applications of our formalism we study the statistics of the number of particles and kinks. Our conclusions can be extended also to quantum spin chains, which can be mapped to free fermions via Jordan-Wigner transformation. In particular, we provide an exact solution to the problem of the transverse field $XY$ chain with a staggered line defect. We also study the distribution of magnetization and kinks in the transverse field $XY$ chain numerically and show how the dual nature of these quantities manifests itself in the distributions.

We measured the temperature-dependent equilibrium vacancy concentration using in situ positron annihilation spectroscopy in order to determine the enthalpy $H_{\text{f}}$ and entropy $S_{\text{f}}$ of vacancy formation in elementary fcc La. The Arrhenius law applied for the data analysis, however, is shown to fail in explaining the unexpected high values for both $S_{\text{f}}$ and $H_{\text{f}}$: in particular $S_{\text{f}}=16\left(2\right)k_{\text{B}}$ is one order of magnitude larger compared to other elemental metals, and the experimental value of $H_{\text{f}}$ is found to be more than three standard deviations off the theoretical one $H_{\text{f}}=1.46\text{eV}$ (our DFT calculation for La at $T=0\text{K}$). A consistent explanation is given beyond the classical Arrhenius approach in terms of a temperature dependence of the vacancy formation entropy with $S_{\text{f}}^{\prime }=0.01119\left(13\right)k_{\text{B}}/\text{K}$ accounting for the anharmonic potential introduced by vacancies.

We use neutron scattering to show that ferromagnetic (FM) phase transition in the two-dimensional (2D) honeycomb lattice ${\mathrm{CrI}}_3$ is a weakly first order transition and controlled by spin-orbit coupling (SOC) induced magnetic anisotropy, instead of magnetic exchange coupling as in a conventional ferromagnet. With increasing temperature, the magnitude of magnetic anisotropy, seen as a spin gap at the Brillouin zone center, decreases in a power law fashion and vanishes at $T_C$, while the in-plane and $c$-axis spin-wave stiffnesses associated with magnetic exchange couplings remain robust at $T_C$. We also compare parameter regimes where spin waves in ${\mathrm{CrI}}_3$ can be described by a Heisenberg Hamiltonian with Dzyaloshinskii-Moriya interaction or a Heisenberg-Kitaev Hamiltonian. These results suggest that the SOC induced magnetic anisotropy plays a dominant role in stabilizing the FM order in single layer 2D van der Waals ferromagnets.

To date the realization of magnetoresistive random access memory (RAM) and magnetoelectric RAM (MeRAM) devices relies primarily on ultrathin ferromagnetic-based (FeCoB/MgO) magnetic tunnel junctions. On the other hand, the Heusler family of intermetallics is considered very promising for spintronic applications. Nevertheless, the voltage controlled magnetic anisotropy (VCMA) in ultrathin Heusler-based magnetic-tunnel junction stacks remains unexplored. Here, using the ferrimagnetic Heusler ${\mathrm{Mn}}_3\mathrm{Ga}$ as a prototype system, we report ab initio calculations of the electric field modulation of magnetism in the $\mathrm{Ir}/{\mathrm{Mn}}_3\mathrm{Ga}$/MgO heterostructure. The trilayer structures with one and three monolayer Ir caps and Mn-Mn termination exhibit large perpendicular magnetic anisotropy in contrast to those with Mn-Ga termination which yield in-plane magnetization orientation. We predict giant VCMA coefficients the magnitude and sign of which depend on both the interface termination and the Ir cap thickness. The underlying atomistic mechanism lies on the electric-field-induced shifts of the spin-orbit coupling energies of the spin-polarized $\mathrm{Ir}/d$ orbitals with different orbital angular momentum symmetries. Our paper paves the way for exploiting the unique magnetic properties of ferrimagnetic Heusler compounds for next generation MeRAM devices.

A continuum model of frustrated ferromagnets is analyzed in detail in the regime of low applied magnetic field, $H_0<1/4$, where the ground state is a spatially varying conical spiral. By changing variables to a corotating spin field, the model is reformulated as a gauged $\sigma$ model in a fixed background gauge, allowing the construction of stable isolated skyrmions, and stable multiskyrmion clusters, which approach the conical ground state at spatial infinity. Due to the spatial anisotropy induced by the ground state, these skyrmions exhibit only discrete symmetries, and are of neither Néel nor Bloch type. These skyrmions are continuously connected to the more familiar solutions in the high-field regime ($H_0>1/4$), acquiring axial symmetry in the limit $H_0\to 1/4$. The propagation of small-amplitude spin waves through the conical ground state is also analyzed and is found to depend strongly on both $H_0$ and the propagation direction relative to the ground state. In contrast to spin waves in the high-field regime ($H_0>1/4$), there is no spectral gap: waves may propagate with any angular frequency.

The identification of deep-level defects that act as detrimental nonradiative recombination centers is critical for optimizing the optoelectronic performance of hybrid perovskites. Although extensive studies have been devoted to revealing the nature of deep-level defects in hybrid perovskites, it is still unclear what defects are responsible for the experimentally observed nonradiative recombination rates. Employing first-principles approaches, we quantitatively show that the iodine interstitial is a dominant nonradiative recombination center in methylammonium-lead iodide. This important insight points to a target for defect engineering in order to further improve the performance of hybrid perovskites.

It is commonly anticipated that an insulating state will collapse in favor of an emergent metallic state at high pressures: The average electron density must increase with pressure, while the electronic bandwidth is expected to broaden and fill the insulating energy band gap. Here we report an unusually stable insulating state that persists up to at least 185 GPa in $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$, the archetypical spin-orbit-driven $J_{\mathrm{eff}}=1/2$ insulator. This study shows that the electrical resistance R of single-crystal $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$ initially decreases with applied pressure P, reaches a minimum in the range 32–38 GPa, then abruptly rises to recover the insulating state with increasing P up to 185 GPa. However, evidence of a saturation of R below 80 K for $P\ge 124\mathrm{GPa}$ GPa raises the possibility of a low-temperature exotic state. Our synchrotron x-ray diffraction and Raman scattering data show the emergence of the rapid increase in R is accompanied by a structural phase transition from the native tetragonal $I{4}_1/acd$ phase to an orthorhombic $Pbca$ phase (with much reduced symmetry) at 40.6 GPa. The clear correspondence of the onset pressures of these two anomalies is key to understanding the stability of the insulating state at megabar pressures: Pressure-induced, structural distortions prevent the expected onset of metallization, despite the sizable volume compression attained at the highest pressure accessed in this study.

The wide application of amorphous materials in solar cells, memristors, and optical sensors has stimulated interest in understanding heat conduction in amorphous systems owing to their thermal management issues. Thermal transport in amorphous materials fundamentally differs from their crystalline counterparts due to the lack of long-range order. Despite great progress in understanding the thermal transport in crystalline materials over the past few decades from both first-principles computations and thermal transport characterizations, details of heat conduction in amorphous systems remain largely unknown. Here, we quantify different types of heat carriers in amorphous silicon using mean free path spectroscopy, with characteristic sizes down to 50 nm. We show that despite its disordered nature, more than half of thermal conductivity is contributed by propagating vibrational waves, which have mean free paths mostly above 100 nm. This provides direct evidence supporting the diversity of heat carriers in amorphous systems; some modes transport heat as propagating waves, while others do not. Our results suggest mean free path spectroscopy is a versatile tool for understanding thermal transport in disordered systems.

Cubic perovskite $\mathrm{BaFe}{\mathrm{O}}_3$ single crystals with stoichiometric oxygen content were successfully grown by a two-step method. With decreasing temperature, the crystal experiences a spin-glassy transition at $T_{\mathrm{SG}}\approx 181\mathrm{K}$, followed by a long-range spiral antiferromagnetic ordering at $T_N\approx 117\mathrm{K}$, and then a third spin transition at $T_N^{\prime }\approx 97\mathrm{K}$, revealing the subtle magnetic competition and interactions. As a result, a smaller magnetic field (∼0.4 T) can induce a metamagnetic transition towards a ferromagnetic state with the saturated magnetic moment about $3.2{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ at 2 K. The easy magnetization axis looks to vary from the direction perpendicular to [111] to the [100] axis. Semiconducting behavior with a small activation energy is observed above $T_{\mathrm{N}}$, whereas the spiral spin ordering changes the electrical transport to be likely half-metallic with considerable negative magnetoresistance effect.

The spinless Falicov-Kimball model exhibits outside the particle-hole symmetric point different stable nonhomogeneous charge orderings. These include the well-known charge stripes and a variety of orderings with phase-separated domains, which can significantly influence the charge transport through the correlated electron system. We show this by investigating a heterostructure in which the Falicov-Kimball model on a finite two-dimensional lattice is located between two noninteracting semi-infinite leads. We use a combination of nonequilibrium Green's function techniques with a sign-problem-free Monte Carlo method for finite temperatures or a simulated annealing technique for the ground state to address steady-state transport through the system. We show that different ground-state phases of the central system can lead to simple metallic-like or insulating charge transport characteristics, but also to more complicated current-voltage dependencies reflecting a multiband character of the transmission function. Interestingly, with increasing temperature, the orderings tend to form transient phases before the system reaches the disordered phase. This leads to nontrivial temperature dependencies of the transmission function and charge current.

High-magnetic-field transport measurements and ab initio calculations on the layered superconductor $\mathrm{TaS}{\mathrm{e}}_3$ have provided evidence for the existence of a three-dimensional strong topological state. Longitudinal magnetotransport measurements up to ∼33 T unveiled striking Shubnikov–de Haas oscillations with two fundamental frequencies at 100 and 175 T corresponding to a nontrivial hole Fermi pocket at the Γ point and a nontrivial electron Fermi pocket at the B point, respectively, in the Brillouin zone. However, calculations revealed one more electron pocket at the B point which was not detected by the magnetotransport measurements, presumably due to the limited carrier momentum relaxation time. Angle-dependent quantum oscillations by rotating the sample with respect to the magnetic field revealed clear changes in the two fundamental frequencies, indicating anisotropic electronic Fermi pockets. The ab initio calculations gave the topological $Z_2$ invariant of (1; 100) and revealed a single Dirac cone on the $(10-1)$ surface at the $\overline{\mathrm{X}}$ point with helical spin texture at a constant energy contour, suggesting a strong topological state. The results demonstrate $\mathrm{TaS}{\mathrm{e}}_3$ as an excellent platform to study the interplay between the topological phase and superconductivity and a promising system for the exploration of topological superconductivity.

Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. Motivated by gaining a better microscopic understanding of the local physics of such $d$-orbital quantum magnets, we carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions. While the rotationally invariant Kanamori interaction in the $t_{2g}$ sector leads to a fivefold degenerate $J=2$ manifold, we find that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J=2$ levels. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation ($\mu \mathrm{SR}$) experiments on cubic $5d^2$ osmate double perovskites ${\mathrm{Ba}}_2{\mathrm{ZnOsO}}_6$, ${\mathrm{Ba}}_2{\mathrm{CaOsO}}_6$, and ${\mathrm{Ba}}_2{\mathrm{MgOsO}}_6$, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the $J=2$ multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate ${\mathrm{Ba}}_2{\mathrm{YReO}}_6$. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of $f$-electron based heavy fermion compounds.

Inelastic neutron scattering (INS) from polycrystalline antiferromagnetic LaMnAsO, LaMnSbO, and BaMnAsF are analyzed using a $J_1\text{−}{J}_2\text{−}{J}_c$ Heisenberg model in the framework of the linear spin-wave theory. All three systems show clear evidence that the nearest- and next-nearest-neighbor interactions within the Mn square lattice layer ($J_1$ and $J_2$) are both antiferromagnetic (AFM). However, for all compounds studied the competing interactions have a ratio of $2J_2/J_1<1$, which favors the square lattice checkerboard AFM structure over the stripe AFM structure. The interplane coupling $J_c$ in all three systems is on the order of $\sim 3\times {10}^{-4}{J}_1$, rendering the magnetic properties of these systems with quasi-two-dimensional character. The substitution of Sb for As significantly lowers the in-plane exchange coupling, which is also reflected in the decrease of the Néel temperature, $T_{\mathrm{N}}$. Although BaMnAsF shares the same MnAs sheets as LaMnAsO, their $J_1$ and $J_2$ values are substantially different. Using density functional theory, we calculate exchange parameters $J_{ij}$ to rationalize the differences among these systems.

Spin-orbit interactions in solids have inspired innovative physics for spin-based technologies. One such example is the persistent spin helix, where spin-orbit interactions from the semiconductor lattice are balanced with those in asymmetric quantum wells, to create long-lived spin textures. Spin transport in the presence of the momentum-dependent spin-orbit interactions lead to Larmor precession and subsequent dephasing that challenges the design of current spin-based information processing devices. We demonstrate that external magnetic fields can be applied to overcome this issue for spin-polarized charge carriers transported by in-plane electric fields. A frame of reference picture is introduced to describe the emergence and dynamics of the polarization-locked spin-wave packet after optical excitation. Applying well-matched magnetic fields maintains the persistent spin-helix profile regardless of whether the frame of reference is in motion or not. Monte Carlo simulations allow this traveling persistent spin-helix concept to be extended to a proposed spin Hall-effect transistor to ease design requirements.

The extremely large magnetoresistance (XMR) effect in nonmagnetic semimetals has attracted intensive attention recently. Here we propose an XMR candidate material SrPd based on first-principles electronic structure calculations in combination with a semiclassical model. The calculated carrier densities in SrPd indicate that there is a good electron-hole compensation, while the calculated intrinsic carrier mobilities are as high as ${10}^5{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$. There are only two doubly degenerate bands crossing the Fermi level for SrPd, thus a semiclassical two-band model is available for describing its transport properties. Accordingly, the magnetoresistance of SrPd under a magnetic field of 4 Tesla is predicted to reach ${10}^5\%$ at low temperature. Furthermore, the calculated topological invariant indicates that SrPd is topologically trivial. Our theoretical studies suggest that SrPd can serve as an ideal platform to examine the charge compensation mechanism of the XMR effect.

The distorted kagome lattice antiferromagnet ${\mathrm{Tb}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$ with a hexagonal structure has the Néel temperature $T_{\mathrm{N}}=22$ K. To clarify the $4f$-electronic state and an influence of electric quadrupoles in ${\mathrm{Tb}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$, ultrasonic measurements on a single-crystalline sample at zero magnetic field and under fields were carried. A characteristic elastic softening of the transverse modulus $C_{66}$ originating from a quadrupole interaction was found. The crystal electric field parameters were determined to reproduce $C_{66}$, magnetic susceptibilities, and magnetization curves. The obtained level scheme is that the ground and first excited states are singlets, despite the existence of both the magnetic transition and the quadrupole interaction, indicating that ${\mathrm{Tb}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$ is a curious compound. The positive sign of the quadrupole-quadrupole coupling constant for $C_{66}$ indicates a ferroquadrupolar-type interaction of the electric quadrupole $O_{xy}$ or $O_2^2$. The anisotropic magnetic field dependencies of $T_{\mathrm{N}}$ in the field along [100] and [001] were also clarified.

The wide variety of complex physical behavior exhibited in transition metal oxides, particularly the perovskites $AB{\mathrm{O}}_3$, makes them a material family of interest in many research areas, but the drastically different electronic structures possible in these oxides raises challenges in describing them accurately within density functional theory (DFT) and related methods. Here, we evaluate the ability of the ACBN0, a recently developed first-principles approach to computing the Hubbard $U$ correction self-consistently, to describe the structural and electronic properties of the first-row transition metal perovskites with $\left(B=\mathrm{V}-\mathrm{Ni}\right)$. ACBN0 performs competitively with hybrid functional approaches such as the Heyd-Scuseria-Ernzerhof functional even when they are optimized empirically, at a fraction of the computational cost. ACBN0 also describes both the structure and band gap of the oxides more accurately than a conventional Hubbard $U$ correction performed by using $U$ values taken from the literature.

In a system with a Dirac-like linear dispersion there are always states that fulfill the resonance condition for electromagnetic radiation of arbitrary frequency $\mathrm{\Omega }$. When a flat band is present, two coexistent kinds of resonant transitions are found. Considering the $\alpha -{\mathcal{T}}_3$ graphene model as a minimal model with a flat band and Dirac cones and describing the dynamics using the interaction picture, we study the band transitions induced by an external electromagnetic field. We find that transitions depend upon the relative angle between the electron momentum and the electromagnetic field wave vector. For parllel incidence, the transitions are found using Floquet theory, while for other angles perturbation theory is used. In all cases, the transition probabilities and the frequencies are found. For the parallel momentum, no symmetry is broken by the field, and light does not change the spectrum, while for some limit special cases of the parameter $\alpha$ or by charge doping, the system behaves as a three-level or two-level Rabi system. All these previous results were compared with numerical simulations. Good agreement was found between both. The obtained results show a rich system in which different kinds of transitions coexist.

A detailed derivation of the Rashba spin-orbit (SO) Hamiltonian for conduction electrons in wurtzite heterostructures is lacking in the literature. Here we derive in a consistent and systematic way such an effective Hamiltonian, valid for quantum wells, wires, and dots with arbitrary confining potentials and external magnetic fields. We start from an $8\times 8$ Kane model accounting for the $s-p_z$ orbital mixing important to wurtzite structures, but absent in zincblende, and apply both quasidegenerate perturbation theory (Löwdin partitioning) and the folding down approach to derive an effective $2\times 2$ Hamiltonian for conduction electrons. For bulk systems, our derivation consistently yields the well-known linear-in-momentum bulk inversion asymmetry (BIA) Rashba-like term, with SO coupling ${\alpha }_{\mathrm{bulk}}^{\mathrm{BIA}}$, entirely following from the $s-p_z$ orbital mixing and in agreement with experiments. We also obtain the correct form of the bulk Dresselhaus term, which is the same as that of the Rashba. However, our calculated bulk Dresselhaus SO parameters $\gamma$ and $b$ are too small. Focusing on wurtzite quantum wells, we perform a self-consistent Poisson-Schrödinger calculation in the Hartree approximation to determine all the relevant SO couplings of the confined effective $2\times 2$ electron Hamiltonian. Our total linear Rashba-type SO Hamiltonian contains a structural inversion asymmetry (SIA) part, modulated by the Hartree, doping, and external gate potentials of the wells, and, in contrast to zincblende structures, a confined Rashba-type contribution induced by the BIA of the underlying wurtzite lattice. Our calculation shows this latter BIA term to be the main contribution to the confined Rashba coupling in wurtzite wells. As a concrete example, we determine the intrasubband (intersubband) Rashba ${\alpha }_{\nu }$ ($\eta$) and linear Dresselhaus ${\beta }_{\nu }$ ($\mathrm{\Gamma }$) SO coupling strengths for GaN/AlGaN single and double wells with one and two occupied subbands ($\nu =1,2$). Since the linear Rashba and the Dresselhaus terms have the same functional form, we can define a total effective SO coupling ${\alpha }_{\nu }^{\mathrm{eff}}={\alpha }_{\nu }+{\beta }_{\nu }$. For the GaN/${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{N}$ single well with one occupied subband we find ${\alpha }_1^{\mathrm{eff}}=7.16$ meV Å, in agreement with weak antilocalization measurements. In the case of two occupied subbands, we observe that the intersubband Rashba $\eta$ is much weaker than the intrasubband coupling ${\alpha }_{\nu }$. For double wells even in the presence of strong built-in electric fields (spontaneous and piezoelectric, crucial in GaN/AlGaN wells), we find a seemingly symmetric potential configuration at which both the Rashba $\eta$ and Dresselhaus $\mathrm{\Gamma }$ intersubband couplings exhibit their highest strengths. On the other hand, we observe that the intrasubband Dresselhaus couplings ${\beta }_1$ and ${\beta }_2$ interchange their values as the gate voltage $V_{\text{g}}$ varies across zero; a similar behavior, though less pronounced, is seen for the Rashba couplings ${\alpha }_1$ and ${\alpha }_2$. We believe our general effective Hamiltonian for electrons in wurtzite heterostructures put forward here, should stimulate additional theoretical works on wurtzite quantum wells, wires, and dots with variously defined geometries and external magnetic fields.

Recently the anomalous Hall effect was predicted as a possible mechanism to produce magnetization-dependent spin current. Here we have applied NiFe/Ru/perpendicular magnetic multilayers and a specific geometry to demonstrate magnetization switching driven by anomalous spin-orbit torque resulting from the bulk anomalous Hall effect. The anomalous spin Hall torque of NiFe is strong enough not only to switch the magnetization of perpendicular Co but also leads to opposite switching chirality compared with the ordinary spin Hall torque. This work confirmed the existence of a strong anomalous spin Hall torque due to anomalous Hall effect, which may lay a foundation to develop spin-orbit torque devices free of heavy metals.