It is well-known that operators of localized spins within a magnetic material satisfy neither fermionic nor bosonic commutation relations. Thus, to construct diagrammatic many-body perturbation theory requiring the Wick theorem, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. However, to make calculations tractable, the square root of operators in the HP transformation is expanded into a Taylor series truncated to some low order. This poses a question on the range of validity of the truncated HP transformation when describing nonequilibrium dynamics of localized spins interacting with each other or with conduction electron spins—a problem frequently encountered in numerous transport phenomena in magnonics and spintronics. Here we apply exact diagonalization techniques to a Hamiltonian of fermions (i.e., electrons) interacting with HP bosons versus a Hamiltonian of fermions interacting with the original localized spin operators to compare their many-body states and one-particle equilibrium and nonequilibrium Green's functions (GFs). We employ as a test bed a one-dimensional quantum Heisenberg ferromagnetic spin-$S$ XXX chain of $N\le 7$ sites, where $S=1$ or $S=5/2$, and the ferromagnet can be made metallic by allowing electrons to hop between the sites while interacting with the localized spins via $sd$ exchange interaction. For these two different versions of the Hamiltonian of this model, we compare the structure of their ground states, time evolution of excited states, spectral functions computed from the retarded GF in equilibrium, and matrix elements of the lesser GF out of equilibrium. Interestingly, magnonic spectral function can be substantially modified by acquiring additional peaks due to quasibound states of electrons and magnons once the interaction between these subsystems is turned on. The Hamiltonian of fermions interacting with HP bosons gives an incorrect ground state and electronic spectral function unless a large number of terms are retained in the truncated HP transformation. Furthermore, tracking the nonequilibrium dynamics of localized spins over longer time intervals requires a progressively larger number of terms in truncated HP transformation, even if a small magnon density is excited initially, but the required number of terms is reduced when interaction with conduction electrons is turned on. Finally, we show that recently proposed [M. Vogl et al., Phys. Rev. Res. 2, 043243 (2020); J. König et al., SciPost Phys. 10, 007 (2021)] resummed HP transformation, where spin operators are expressed as polynomials in bosonic operators, resolves the trouble with truncated HP transformation while allowing us to derive an exact quantum many-body (manifestly Hermitian) Hamiltonian consisting of a finite and fixed number of boson-boson and electron-boson interacting terms.

We investigate the static and ultrafast magneto-optical response of the hexagonal chiral helimagnet ${\mathrm{Cr}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ above and below the helimagnetic ordering temperature. The presence of a magnetic easy plane contained within the crystallographic $ab$ plane is confirmed, while degenerate optical pump-probe experiments reveal significant differences in the dynamic between the parent, $\mathrm{Nb}{\mathrm{S}}_2$, and Cr-intercalated compounds. Time-resolved magneto-optical Kerr effect measurements show a two-step demagnetization process, where an initial, subpicosecond relaxation and subsequent buildup $(\tau >50\mathrm{ps})$ in the demagnetization dynamic scale similarly with increasing pump fluence. Despite theoretical evidence for partial gapping of the minority spin channel, suggestive of possible half-metallicity in ${\mathrm{Cr}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$, such a long demagnetization dynamic likely results from spin-lattice relaxation as opposed to minority state blocking. However, comparison of the two-step demagnetization process in ${\mathrm{Cr}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ with other $3d$ intercalated transition metal dichalcogenides reveals a behavior that is unexpected from conventional spin-lattice relaxation, and may be attributed to the complicated interaction of local moments with itinerant electrons in this material system.

Symmetry lowering at an interface leads to an enhancement of the effect of spin-orbit coupling and to a discontinuity of spin currents passing through the interface. This discontinuity is characterized by a “spin-memory loss” (SML) parameter $\delta$ that has only been determined directly at low temperatures. Although $\delta$ is believed to be significant in experiments involving interfaces between ferromagnetic and nonmagnetic metals, especially heavy metals like Pt, it is more often than not neglected to avoid introducing too many unknown interface parameters in addition to often poorly known bulk parameters like the spin-flip diffusion length $l_{\mathrm{sf}}$. In this work, we calculate $\delta$ along with the interface resistance $A{R}_{\mathrm{I}}$ and the spin-asymmetry parameter $\gamma$ as a function of temperature for $\mathrm{Co}|\mathrm{Pt}$ and $\mathrm{Py}|\mathrm{Pt}$ interfaces where Py is the ferromagnetic ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ alloy, permalloy. We use first-principles scattering theory to calculate the conductance as well as local charge and spin currents, modeling temperature-induced disorder with frozen thermal lattice and, for ferromagnetic materials, spin disorder within the adiabatic approximation. The bulk and interface parameters are extracted from the spin currents using a Valet-Fert model generalized to include SML.

Coulomb interactions strongly influence the spectrum and the wave functions of a few electrons or holes confined in a quantum dot. In particular, when the confinement potential is not too strong, the Coulomb repulsion triggers the formation of a correlated state, the Wigner molecule, where the particles tend to split apart. We show that the anisotropy of the confinement potential strongly enhances the molecularization process and affects the performances of quantum dot systems used as spin qubits. Relying on analytical and numerical solutions of the two-particle problem—both in a simplified single-band approximation and in realistic setups—we highlight the exponential suppression of the singlet-triplet gap with increasing anisotropy. We compare the molecularization effects in different semiconductor materials and discuss how they specifically hamper Pauli spin blockade readout and reduce the exchange interactions in two-qubit gates.

We study the effect of the spin-orbit interaction on heavy holes confined in a double quantum dot in the presence of a magnetic field of arbitrary direction. Rich physics arise as the two hole states of different spin are not only coupled by the spin-orbit interaction but additionally by the effect of site-dependent anisotropic $g$ tensors. It is demonstrated that these effects may counteract in such a way as to cancel the coupling at certain detunings and tilting angles of the magnetic field. This feature may be used in singlet-triplet qubits to avoid leakage errors and implement an electrical spin-orbit switch, suggesting the possibility of task-tailored two-axes control. Additionally, we investigate systems with a strong spin-orbit interaction at weak magnetic fields. By exact diagonalization of the dominant Hamiltonian we find that the magnetic field may be chosen such that the qubit ground state is mixed only within the logical subspace for realistic system parameters, hence reducing leakage errors and providing reliable control over the qubit.

The discovery of two-dimensional (2D) ferroelectrics with switchable out-of-plane polarization such as monolayer $\alpha \text{−}{\mathrm{In}}_2{\mathrm{Se}}_3$ offers a new avenue for ultrathin high-density ferroelectric-based nanoelectronics such as ferroelectric field effect transistors and memristors. The functionality of ferroelectrics depends critically on the dynamics of polarization switching in response to an external electric/stress field. Unlike the switching dynamics in bulk ferroelectrics that have been extensively studied, the mechanisms and dynamics of polarization switching in 2D remain largely unexplored. Molecular dynamics (MD) using classical force fields is a reliable and efficient method for large-scale simulations of dynamical processes with atomic resolution. Here we developed a deep neural network-based force field of monolayer ${\mathrm{In}}_2{\mathrm{Se}}_3$ using a concurrent learning procedure that efficiently updates the first-principles-based training database. The model potential has accuracy comparable with density functional theory (DFT), capable of predicting a range of thermodynamic properties of ${\mathrm{In}}_2{\mathrm{Se}}_3$ polymorphs and lattice dynamics of ferroelectric ${\mathrm{In}}_2{\mathrm{Se}}_3$. Pertinent to the switching dynamics, the model potential also reproduces the DFT kinetic pathways of polarization reversal and ${180}^{\circ }$ domain wall motions. Moreover, isobaric-isothermal ensemble MD simulations predict a temperature-driven $\alpha \to \beta$ phase transition at the single-layer limit, as revealed by both local atomic displacement and Steinhardt's bond orientational order parameter $Q_4$. Our paper paves the way for further research on the dynamics of ferroelectric $\alpha \text{−}{\mathrm{In}}_2{\mathrm{Se}}_3$ and related systems.

Spin relaxation and decoherence is at the heart of spintronics and spin-based quantum information science. Currently, theoretical approaches that can accurately predict spin relaxation of general solids including necessary scattering pathways and are capable of nanosecond to millisecond simulation time are urgently needed. We present a first-principles real-time density-matrix approach based on Lindblad dynamics to simulate ultrafast spin dynamics for general solid-state systems. Through the complete first-principles descriptions of pump, probe, and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent electronic spin-orbit couplings, our method can directly simulate the ultrafast pump-probe measurements for coupled spin and electron dynamics over nanoseconds at any temperatures and doping levels. We first apply this method to a prototypical system GaAs and obtain excellent agreement with experiments. We found that the relative contributions of different scattering mechanisms and phonon modes differ considerably between spin and carrier relaxation processes. In sharp contrast to previous work based on model Hamiltonians, we point out that the electron-electron scattering is negligible at room temperature but becomes dominant at low temperatures for spin relaxation in $n$-type GaAs. We further examine ultrafast dynamics in novel spin-valleytronic materials: monolayer and bilayer ${\mathrm{WSe}}_2$ with realistic defects. We find that spin relaxation is highly sensitive to local symmetry and chemical bonds around defects. For the bilayer ${\mathrm{WSe}}_2$, we identify the scattering pathways in ultrafast dynamics and determine relevant dynamical properties, essential to its utilization of unique spin-valley-layer locking effects. Our work provides a predictive computational platform for spin dynamics in solids, which has potential for designing new materials ideal for spintronics and quantum information technology.

We present an experimental and simulation study of the collective dynamics of liquid ${\mathrm{D}}_2$ in the range of exchanged wave vectors $3\le Q\le 14{\mathrm{nm}}^{-1}$. Neutron Brillouin scattering results for the center-of-mass dynamic structure factor of this moderately quantum fluid are compared, on an absolute scale, with those obtained by three different quantum simulation methods such as ring polymer molecular dynamics and two versions of the Feynman-Kleinert approach. The experimental data can be well described by dynamical models typically used for liquids. Some discrepancies show up both among simulations, and between simulations and experimental data. Such discrepancies are found to mainly concern the damping of the propagating sound modes.

The recent discovery of superconducting interfaces in the $\mathrm{KTa}{\mathrm{O}}_3$ (111)-based heterostructures is intriguing, since a much higher superconducting critical temperature $\left(T_C;\sim 2\mathrm{K}\right)$ is achieved compared to that in the $\mathrm{SrTi}{\mathrm{O}}_3$ heterostructures (∼300 mK). In this paper, we report the superconducting properties of the $\mathrm{EuO}/\mathrm{KTa}{\mathrm{O}}_3$ (111) interface as a function of the interface carrier density ($n_s$). The maximum $T_C$ is observed to be ∼2 K at $n_s\sim 1\times {10}^{14}\mathrm{c}{\mathrm{m}}^{–2}$. In addition we show that the critical current density and the upper critical magnetic field can be effectively tuned by the back gate voltage. Interestingly, the gate dependence of the upper critical magnetic field exhibits a trend opposite to that of $T_C$ in the underdoped region, suggesting a relatively larger Cooper pairing potential.

Time-resolved diffuse scattering experiments have gained increasing attention due to their potential to reveal nonequilibrium dynamics of crystal lattice vibrations with full momentum resolution. Although progress has been made in interpreting experimental data on the basis of one-phonon scattering, understanding the role of individual phonons can be sometimes hindered by multiphonon excitations. In Ref. [M. Zacharias, H. Seiler, F. Caruso, D. Zahn, F. Giustino, P. C. Kelires, and R. Ernstorfer, Phys. Rev. Lett. 127, 207401 (2021)], we have introduced a rigorous approach for the calculation of the all-phonon inelastic scattering intensity of solids from first-principles. In the present work, we describe our implementation in detail and show that multiphonon interactions are captured efficiently by exploiting translational and time-reversal symmetries of the crystal. We demonstrate its predictive power by calculating the scattering patterns of monolayer molybdenum disulfide $\left({\mathrm{MoS}}_2\right)$, bulk ${\mathrm{MoS}}_2$, and black phosphorus (bP), and we obtain excellent agreement with our measurements of thermal electron diffuse scattering. Remarkably, our results show that multiphonon excitations dominate in bP across multiple Brillouin zones, while in ${\mathrm{MoS}}_2$ they play a less pronounced role. We expand our analysis for each system and examine the effect of individual atomic and interatomic vibrational motion on the diffuse scattering signals. We further demonstrate the high-throughput capability of our approach by reporting all-phonon scattering maps of two-dimensional ${\mathrm{MoSe}}_2$, ${\mathrm{WSe}}_2$, ${\mathrm{WS}}_2$, graphene, and ${\mathrm{CdI}}_2$, rationalizing in each case the effect of multiphonon processes. As a side point, we show that the special displacement method reproduces the thermally distorted configuration that generates precisely the all-phonon diffuse pattern. The present methodology opens the way for systematic calculations of the scattering intensity in crystals and the accurate interpretation of static and time-resolved inelastic scattering experiments.

We investigated spin-1/2 hydrogenated titanium (Ti) atoms on MgO using scanning tunneling microscopy (STM) combined with electron spin resonance (ESR) in vector magnetic fields. Rotating external magnetic fields, we observed rather drastic changes in both amplitude and frequency of resonance signals for single Ti atoms. While the variation of ESR amplitudes reflects the effects of the spin polarization of a magnetic tip and local magnetic fields created by the interaction between the tip and Ti, the change of resonance frequencies shows the anisotropy of $g$ values for Ti atoms. Using the Ti atoms at the low-symmetry bridge adsorption site of the MgO lattice allowed for identifying the $g$ values in all three spatial directions. Multiplet calculations confirmed the origin of this anisotropy as the spin-orbit coupling induced effects of crystal. Our results show the capability of single atomic spins as a sensor to probe magnetic surroundings and highlight the precision of ESR-STM to identify the single atom's spin states in a solid-state environment.

A series of recent experiments has demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. [Nature (London) 595, 526 (2021)] studies the behavior of the superconductor in an in-plane magnetic field and an out-of-plane displacement field, finding that the superconductor is unlikely to have purely spin-singlet pairing. This work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, the superconductor undergoes a transition to a distinct field-induced superconducting state. Inspired by these results, we develop an understanding of the superconductivity in TTG using a combination of phenomenological reasoning and microscopic theory. We describe the role that an in-plane field plays in TTG, and we use this understanding to argue that the reentrant transition may be associated with a quantum Lifshitz phase transition, with the high-field phase possessing finite-momentum pairing. We argue that the superconductor is likely to involve a superposition of singlet and triplet pairing, and we describe the structure of the normal state. We also draw lessons for twisted bilayer graphene (TBG), and we explain the differences in the phenomenology with TTG despite their close microscopic relationship. We propose that a singlet-triplet superposition is realized in the TBG superconductor as well, and that the $\nu =-2$ correlated insulator may be a time-reversal protected ${\mathbb{Z}}_2$ topological insulator obtained through spontaneous spin symmetry breaking.

We study mean-field states resulting from the pairing of electrons in time-reversal broken fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps magnetic flux $\mathrm{\Phi }=(p/q){\mathrm{\Phi }}_0$ comparable to the flux quantum ${\mathrm{\Phi }}_0=h/e$. It is established that the dimension and degeneracy of the irreducible representations of the magnetic translation group (MTG) furnished by the charge 2e pairing fields have different properties from those furnished by single-particle Bloch states, and in particular are shown to depend on the parity of the denominator $q$. We explore this symmetry analysis to formulate a Ginzburg-Landau theory describing the thermodynamic properties of Hofstadter superconductors at arbitrary rational flux $\mathrm{\Phi }=(p/q){\mathrm{\Phi }}_0$ in terms of a multicomponent order parameter that describes the finite momentum pairing of electrons across different Fermi surface patches. This phenomenological theory leads to a rich phase diagram characterized by different symmetry breaking patterns of the MTG, which can be interpreted as distinct classes of vortex lattices. A class of ${\mathbb{Z}}_q$-symmetric Hofstadter SCs is identified, in which the MTG breaks down to a ${\mathbb{Z}}_q$ subgroup. We study the topological properties of such ${\mathbb{Z}}_q$-symmetric Hofstadter SCs and show that the parity of the Chern numbers is fixed by the parity of $q$. We identify the conditions for the realization of Bogoliubov Fermi surfaces in the presence of parity and MTG symmetries, establishing a novel topological invariant capturing the existence of such charge-neutral gapless excitations. Our findings, which could bear relevance to the description of re-entrant superconductivity in moiré systems in the Hofstadter regime, establish Hofstadter SC as a fertile setting to explore symmetry broken and topological orders.

The magnetic structure and the multiferroic relaxation dynamics of ${\mathrm{NaFeGe}}_2{\mathrm{O}}_6$ were studied by neutron scattering on single crystals partially utilizing polarization analysis. In addition to the previously reported transitions, the incommensurate spiral ordering of ${\mathrm{Fe}}^{3+}$ moments in the $ac$ plane develops an additional component along the crystallographic $b$ direction below $T\approx 5\mathrm{K}$, which coincides with a lock-in of the incommensurate modulation. The quasistatic control of the spin-spiral handedness, respectively of the vector chirality, by external electric fields proves the invertibility of multiferroic domains down to the lowest temperature. Time-resolved measurements of the multiferroic domain inversion in ${\mathrm{NaFeGe}}_2{\mathrm{O}}_6$ reveal a simple temperature and electric-field dependence of the multiferroic relaxation that is well described by a combined Arrhenius-Merz relation, as it has been observed for ${\mathrm{TbMnO}}_3$. The maximum speed of domain wall motion is comparable to the spin-wave velocity deduced from an analysis of the magnon dispersion.

We show that in anisotropic Fermi liquids where momentum-conserving scattering is much faster than momentum-relaxing scattering processes, local imaging of the electric current flow patterns can cleanly distinguish between ballistic, viscous, and ohmic flow patterns simultaneously (using a single image). We propose using multilayer graphene-based heterostructures, including ABA-trilayer graphene, as a natural experimental platform where an anisotropic ballistic-to-viscous crossover may be visible in near-term experiments. Such experiments could lead to more direct measurements of momentum-conserving scattering lengths in electronic Fermi liquids.

Calculation of conductivity in the Hubbard model is a challenging task. Recent years have seen much progress in this respect and numerically exact solutions are now possible in certain regimes. In this paper we discuss the calculation of conductivity for the square-lattice Hubbard model in the presence of a perpendicular magnetic field, focusing on orbital effects. We present the relevant formalism in all detail and in full generality, and then discuss the simplifications that arise at the level of the dynamical mean field theory (DMFT). We prove that the Kubo bubble preserves gauge and translational invariance, and that in the DMFT the vertex corrections cancel regardless of the magnetic field. We present the DMFT results for the spectral function and both the longitudinal and Hall conductivities in several regimes of parameters. We analyze thoroughly the quantum oscillations of the longitudinal conductivity and identify a high-frequency oscillation component, arising as a combined effect of scattering and temperature, in line with recent experimental observations in moiré systems.

We construct random unitary Gaussian circuits for continuous-variable (CV) systems subject to Gaussian measurements. We show that when the measurement rate is nonzero, the steady-state entanglement entropy saturates to an area-law scaling. This is different from a many-body qubit system, where a generic entanglement transition is widely expected. Due to the unbounded local Hilbert space, the time scale to destroy entanglement is always much shorter than the one to build it, while a balance could be achieved for a finite local Hilbert space. By the same reasoning, the absence of transition should also hold for other nonunitary Gaussian CV dynamics.

We report the magnetic properties of easy-plane antiferromagnetic NiO(111) thin films epitaxially grown on ferromagnetic Fe(110) layers. We find that the magnetic moments in NiO are rotatable within the NiO(111) sample plane and both magnetic anisotropy and orientation of antiferromagnetic NiO spins are determined by the magnetic properties of underlying ferromagnetic Fe layer. Specifically, the magnetic state and anisotropy of antiferromagnetic NiO can be modified by tuning the thickness of Fe, changing the temperature, or applying small external magnetic field.

We studied the field-dependent thermal conductivity ($\kappa$) of ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$, a compound considered as the manifestation of the Kitaev model based on the high-spin $d^7 {\mathrm{Co}}^{2+}$ ions. We found that in-plane magnetic fields beyond a critical value $B_c\approx 10\mathrm{T}$ are able to drastically enhance $\kappa$ at low temperatures, resulting in a double-peak structure of $\kappa \left(T\right)$ that closely resembles the behavior of $\alpha \text{−}{\mathrm{RuCl}}_3$. This result suggests that heat transport in ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ is primarily phononic, and it is strongly affected by scattering from magnetic excitations that are highly tunable by external fields. Interestingly, for magnetic fields $\mathbf{B}\parallel \mathbf{a}$ (i.e., along the zigzag direction of the Co-Co bonds), there is an extended field range which separates the long-range magnetic order for $B\le B_c\approx 10\mathrm{T}$ and the partially spin-polarized gapped high-field phase for $B\gtrsim 12\mathrm{T}$. The low-energy phonon scattering is particularly strong in this field range, consistent with the notion that the system becomes a quantum spin liquid with prominent spin fluctuations down to energies of no more than 2 meV.

Using a time-resolved cathodoluminescence system dedicated to the UV spectral range, we present an estimate of the radiative lifetime of free excitons in hexagonal boron nitride (hBN) at room temperature. This is carried out from a single experiment giving both the absolute luminescence intensity under continuous excitation and the decay time of free excitons in the time domain. The radiative lifetime of indirect excitons in hBN is equal to 27 ns, which is much shorter than in other indirect band gap semiconductors. This is explained by the close proximity of the electron and the hole in the exciton complex, and also by the small energy difference between indirect and direct excitons. The unusually high luminescence efficiency of hBN for an indirect band gap is therefore semiquantitatively understood.