Rare-earth (RE) transition-metal (TM) thin films have exhibited great promise for spintronic applications; however, the variation of their magnetic properties with composition and thickness has yet to be adequately quantified. In this paper, we investigate the atomic magnetic moments of few-nanometer-thick GdCo and TbCo via x-ray magnetic circular dichroism and find a significant decrease in both RE and Co average moments with increasing RE concentration, consistent with a local Co environment model description. We observe a shift in compensation composition to higher RE concentrations as the thickness of GdCo and TbCo films decreases $<10$ nm. Based on the dependence of the saturation magnetization $\left(M_s\right)$ on temperature and thickness, we posit the existence of an intrinsic unalloyed RE dead layer at room temperature that reduces the effective RE concentration in the remaining alloyed region, resulting in significant, nonzero $M_s$ in thin films at higher RE concentrations than is observed in thick films. We demonstrate a simple model for RE-TM films that accurately describes $M_s$ as a function of both RE content and film thickness. In addition, the atomic $g$ factors of GdCo and TbCo are found to vary significantly with RE concentration, largely deviating from their elemental values over the bulk of composition space.

A superfluid spontaneously breaks the usual $U\left(1\right)$ symmetry because of condensation. In this article, we illustrate six linearly independent families of emergent $U\left(1\right)$ symmetries that naturally appear in infrared limits in a broad class of generic gapless topological superfluids (that either belong to a stable phase or are quantum critical). In gapless states we have considered, emergent $U\left(1\right)$ symmetry groups are embedded in a $Spin\left(4\right)=SU\left(2\right)\otimes SU\left(2\right)$ group that double covers (and algebraically is isomorphic to) an $SO\left(4\right)$ group. All $U\left(1\right)$ charges associated with symmetries are further invariant under an $SU\left(2\right)$ spin group or an equivalent of it but always break preexisting higher space-time Lorentz symmetry of the $SO(3,1)$ group. Emergent $U\left(1\right)$ symmetries can be further spontaneously broken only if interactions are strong enough and resultant strong-coupling states become fully gapped. However, if states remain gapless, emergent $U\left(1\right)$ symmetries are always present, despite that these states may exhibit much lower space-time symmetries compared to their weakly interacting gapless Lorentz symmetric counterparts. In the limit of our interests, we have identified all possible gapless real fermions with or without Lorentz symmetries and find that they all display emergent $U\left(1\right)$ symmetries in the infrared limit. We argue emergent $U\left(1\right)$ symmetries are intrinsic in a broad class of interacting gapless superfluid or superconducting states and are typically well defined in high dimensions where there are infrared stable fixed points dictating emergent properties.

A self-consistent stochastic model of domain structure formation in a uniaxial ferroelectric, quenched from a high-temperature paraelectric phase to a low-temperature ferroelectric phase, is developed with an account of the applied electric field and the feedback effect via local depolarization fields. Both polarization and field components are considered as Gauss random variables. A system of integrodifferential equations for correlation functions of all involved variables is derived and solved analytically and numerically. Phase diagram in terms of the average value and dispersion of polarization reveals different possible equilibrium states and available final single-domain and multidomain states. The time-dependent evolution of the average polarization and dispersion discloses a bifurcation behavior and the temperature-dependent value of the electric field, deciding between the single-domain and multidomain final states, which can be interpreted as the coercive field. Analytical and numerical results for the time-dependent correlation length and correlation functions exhibit plausible agreement with available experimental data.

Scrambling is the delocalization of quantum information over a many-body system and underlies all quantum-chaotic dynamics. We employ discrete quantum cellular automata as classically simulable toy models of scrambling. We observe that these automata break ergodicity, i.e., they exhibit quantum scarring. We also find that the time scale of scrambling rises with the local Hilbert-space dimension and obeys a specific combinatorial pattern. We then show that scarring is mostly suppressed in a semiclassical limit, demonstrating that semiclassical-chaotic systems are more ergodic.

The chiral magnetic soliton, a topological kinklike spin texture, has significant applications in spintronic components. In this work, a crossover of critical behavior is found in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_2$, a chiral magnetic soliton host with the highest $T_C$ to date. Angular-dependent magnetization reveals that ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_2$ exhibits an easy orientation within the isotropic $ab$ plane, but displays anisotropy with the $c$ axis. By using a modified iterative method, two distinct sets of critical exponents, including ${\beta }_{-}=0.3190\left(1\right)$ and ${\gamma }_{-}=1.263\left(8\right)$ for $T\le T_C$, and ${\beta }_{+}=0.3475\left(2\right)$ and ${\gamma }_{+}=1.385\left(5\right)$ for $T\ge T_C$, are acquired on both sides of the transition. Analysis of the exponents indicates a crossover of the magnetic interaction from a three-dimensional Ising type below $T_C$ to a three-dimensional Heisenberg type above $T_C$, implying nontrivial magnetism in this system. Based on universality scaling, a detailed $H-T$ phase diagram around $T_C$ is constructed for $H\perp c$. The crossover of the critical behavior in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_2$ is peculiar to chiral magnetic soliton hosts, suggesting that the three-dimensional magnetic coupling is replaced by a one-dimensional one in the chiral magnetic soliton phase via a phase transition.

A relationship between evolution of the long-range magnetic order, crystal structure, and lattice distortions in $\mathrm{LaMn}{\mathrm{O}}_3$ was studied by a combination of neutron diffraction and Raman spectroscopy at high pressures up to 39 and 50 GPa, respectively, covering the temperature range 5 to 290 K. The Raman spectra reveal a gradual structural phase transformation evolving in the pressure range of 4 to 17 GPa, caused by a modification of the Jahn-Teller (JT) lattice distortions from the static cooperative character to the local one. A presence of residual JT-distorted regions associated with the initial phase is detected up to 32 GPa, where the insulator-metal transition occurs. At higher pressure, the local JT distortions also vanish completely at further compression up to 50 GPa. In the neutron diffraction data, a strong suppression of the A-type antiferromagnetic (AFM) phase is observed over the pressure region of the phase transformation. This is accompanied by a noticeable reduction in magnitude of the $Q_2$ and $Q_3$ JT local modes. The effective ordered magnetic manganese moment is reduced about twice at pressures up to 14 GPa. At higher pressures up to 30 GPa, residual regions of the A-type AFM phase coexist with the magnetically disordered phase. In the range 30 to 39 GPa, i.e., during the pressure-induced insulator-metal transition, these regions disappear and, finally, the magnetically disordered metallic phase becomes the only ground state. The possible models of the insulator-metal transition in $\mathrm{LaMn}{\mathrm{O}}_3$ are analyzed.

We present a high-field study of the strongly anisotropic easy-plane square lattice $S=2$ quantum magnet ${\mathrm{Ba}}_2{\mathrm{FeSi}}_2{\mathrm{O}}_7$. This compound is a rare high-spin antiferromagnetic system with very strong easy-plane anisotropy, such that the interplay between spin level crossings and antiferromagnetic order can be studied. We observe a magnetic field-induced spin level crossing occurring within an ordered state. This spin level crossing appears to preserve the magnetic symmetry while producing a nonmonotonic dependence of the order parameter magnitude. The resulting temperature–magnetic field phase diagram exhibits two dome-shaped regions of magnetic order overlapping around 30 T. The ground state of the lower-field dome is predominantly a linear combination of $|S^z=0\rangle$ and $|S^z=1\rangle$ states, while the ground state of the higher-field dome can be approximated by a linear combination of $|S^z=1\rangle$ and $|S^z=2\rangle$ states. At 30 T, where the spin levels cross, the magnetization exhibits a slanted plateau, the magnetocaloric effect shows a broad hump, and the electric polarization shows a weak slope change. We determined the detailed magnetic phase boundaries and the spin level crossings using measurements of magnetization, electric polarization, and the magnetocaloric effect in pulsed magnetic fields to 60 T. We calculate these properties using a mean-field theory based on direct products of SU(5) coherent states and find good agreement. Finally, we measure and calculate the magnetically induced electric polarization that reflects magnetic ordering and spin level crossings. This multiferroic behavior provides another avenue for detecting phase boundaries and symmetry changes.

A Josephson junction laser is realized when a microwave cavity is driven by a voltage-biased Josephson junction. Through the ac Josephson effect, a dc voltage generates a periodic drive that acts on the cavity and generates interactions between its modes. A sufficiently strong drive enables processes that downconvert a drive resonant with a high harmonic into photons at the cavity fundamental frequency, breaking the discrete time translation symmetry set by the Josephson frequency. Using a classical model, we determine when and how this transition occurs as a function of the bias voltage and the number of cavity modes. We find that certain combinations of mode number and voltage tend to facilitate the transition which emerges via an instability within a subset of the modes. Despite the complexity of the system, there are cases in which the critical drive strength can be obtained analytically.

We propose and benchmark a modified time-evolving block decimation algorithm that uses a truncation scheme based on the QR decomposition instead of the singular value decomposition (SVD). The modification reduces the scaling with the dimension of the physical Hilbert space $d$ from $d^3$ down to $d^2$. Moreover, the QR decomposition has a lower computational complexity than the SVD and allows for highly efficient implementations on GPU hardware. In a benchmark simulation of a global quench in a quantum clock model, we observe a speedup of up to three orders of magnitude comparing QR and SVD based updates on an A100 GPU.

We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires and propose topological markers directly measurable from ground-state correlation functions. These quantities remain powerful tools in the presence of couplings and interactions. We show with the density matrix renormalization group that the double critical Ising (DCI) phase of two interacting Kitaev chains is a fractional topological phase with gapless Majorana modes in the bulk, and a one-half topological invariant per wire. Using both numerics and quantum field theoretical methods, we show that the phase diagram remains stable in the presence of an interwire hopping amplitude $t_{\perp }$ at length scales below $\sim 1/t_{\perp }$. A large interwire hopping amplitude results in the emergence of two integer topological phases, stable also at large interactions. They host one edge mode per boundary shared between both wires. At large interactions, the two wires are described by Mott physics, with the $t_{\perp }$ hopping amplitude resulting in a paramagnetic order.

We study induced pairing between two identical fermions mediated by an attractively interacting quantum impurity in two-dimensional systems. Based on a stochastic variational method (SVM), we investigate the influence of confinement and finite interaction range effects on the mass ratio beyond which the ground state of the quantum three-body problem undergoes a transition from a composite bosonic trimer to an unbound dimer-fermion state. We find that confinement as well as a finite interaction range can greatly enhance trimer stability, bringing it within reach of experimental implementations such as found in ultracold atom systems. In the context of solid-state physics, our solution of the confined three-body problem shows that exciton-mediated interactions can become so dominant that they can even overcome detrimental Coulomb repulsion between electrons in atomically-thin semiconductors. Our paper thus paves the way towards a universal understanding of boson-induced pairing across various fermionic systems at finite density, and opens perspectives towards realizing unexplored forms of electron pairing beyond the conventional paradigm of Cooper pair formation.

We develop a theoretical approach that makes it possible to analyze the role of multipole contributions in the scattering spectra of arbitrarily shaped magnetic particles with the relative permittivity and permeability given in a general tensor-valued form. The method for calculating the exact multipole moments with the inclusion of induced electric polarization and magnetization is suggested and explicitly applied for dipole and quadrupole terms. The final expressions for the dipole and quadrupole moments are obtained in such a form that they can be easily implemented in numerical solvers. Successful verification of the analytical expressions for multipole moments and the multipole decomposition of the scattered field and scattering cross section is provided by comparing the results obtained for differently shaped magnetic particles using the analytical Mie theory, numerical discrete dipole approximation, and comsol multiphysics software. As a particular example, the manifestation of the Faraday effect for fields scattered by a ferrite sphere is discussed in the framework of the multipole decomposition method with the derived magnetization terms. Accounting for the magnetic properties of particles in the multipole analysis of the electromagnetic scattering significantly expands the method's capabilities for studying and modeling metamaterial properties in the spectral ranges where natural materials can have a relative permeability different from unity.

We perform a theoretical and numerical study of the optical properties of both direct and inverse three-dimensional (3D) chiral woodpile structures and a corresponding chiral Bragg stack, also known as a Reusch pile. We compute transmission spectra in the helical direction for finite crystals and photonic band structures, where we ensure the effective index of all structures to be the same. We find that both 3D structures show dual-band circular dichroism, where light with a particular circular polarization state—either left- or right-handed—reveals a broad stop band with major attenuation, whereas the other polarization state is transmitted nearly unimpeded. We observe such gaps in different frequency ranges with alternating handedness. The appearance of the circular-polarized gaps is successfully interpreted with a physical model wherein the circular polarization either corotates or counterrotates with the chiral structure, thereby effectively leading to a spatially dependent or a constant refractive index, and thus to the presence or absence of a gap. We find that the presence or absence of circularly polarized gaps is tuned by the transverse periods perpendicular to the chiral axis in both the 3D direct and inverse chiral woodpile crystal structures. The tunability of circular dichroism may find applications as on-chip sensors for circularly polarized light and in the on-chip detection of chiral molecules.

A Rayleigh-type surface acoustic wave (SAW) is used in various fields as classical and quantum information carriers because of its surface localization, high electrical controllability, and low propagation loss. Coupling and hybridization between the SAW and other physical systems such as magnetization, electron charge, and electron spin are the recent focuses in phononics and spintronics. A precise measurement of the surface wave amplitude is often necessary to discuss the coupling strengths. However, there are only a few such measurement techniques and they generally require a rather complex analysis. Here we develop and demonstrate a straightforward measurement technique that can quantitatively characterize the SAW. The technique optically detects the surface waving due to the coherently driven SAW by the optical path modulation. Furthermore, when the measurement system operates in the shot-noise-limited regime, the surface slope and displacement at the optical spot can be deduced from the optical path modulation signal. Our demonstrated technique will be an important tool for SAW-related research.

A lattice mismatch between Van der Waals layers produces a moiré pattern and a subsequent electron band reconstruction. When the bilayer is charged, the sliding motion of one layer with respect to the other produces electric pumping. Here I discuss the reciprocal process: that a voltage bias produces a layer-shear mechanical force. The effect is deduced from the lowest-order correction to the mechanical action by the coupling with electrons in an external field. In twisted bilayer graphene the new mechanical force is shown to be perpendicular to the applied field (due to ${\mathrm{C}}_2$ symmetries exchanging the layers) and proportional to the charge density measured from neutrality. This is strictly true when the chemical potential is within a gap opened by the moiré potential due to a topological quantization, and approximately true when the chemical potential crosses the flat bands in a model including the self-consistent Hartree interaction. In a mechanical device the effect should be manifested as an apparent enhancement of the friction between layers when the system is charged. Depinning fields for the sliding motion of the layers are estimated in the order of ${\mathcal{E}}_c\sim$ kV/cm around the magic angle.

It is rarely reported that collinear antiferromagnetic (AFM) metals can exhibit the anomalous Hall effect (AHE). In this Letter, based on symmetry analysis and the first-principles electronic structure calculations, we predict that two existing collinear antiferromagnets ${\mathrm{Nb}}_2{\mathrm{FeB}}_2$ and ${\mathrm{Ta}}_2{\mathrm{FeB}}_2$, whose Néel temperatures are above room temperature, have a very large AHE with anomalous Hall conductance (AHC) $-100$ and $-54{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$, respectively. We further complete the symmetry requirements for realizing the AHE in collinear antiferromagnetism.

Alloying a material and hence segregating solutes to grain boundaries is one way to tailor a material to the demands of its application. Direct observation of solute segregation is necessary to understand how the interfacial properties are altered. In this study, we investigate the atomic structure of a high-angle grain boundary both in pure copper and upon silver segregation by aberration-corrected scanning transmission electron microscopy and spectroscopy. We further correlate the experiments to atomistic simulations to quantify the local solute excess and its impact on grain boundary properties. We observe that the grain boundary structure remains intact upon silver segregation and up to five different positions within a structural unit serve as segregation sites. By combining the atomic-resolution observation with atomistic modeling, we are able to quantify the local silver concentration and elucidate the underlying segregation mechanism.

The equations of state and band-gap closures for $\mathrm{Pb}{\mathrm{Cl}}_2$ and $\mathrm{Sn}{\mathrm{Cl}}_2$ were studied using both experimental and theoretical methods. We measured the volume of both materials to a maximum pressure of 70 GPa using synchrotron-based angle-dispersive powder x-ray diffraction. The lattice parameters for both compounds showed anomalous changes between 16–32 GPa, providing evidence of a phase transition from the cotunnite structure to the related ${\mathrm{Co}}_2\mathrm{Si}$ structure, in contrast to the postcotunnite structure as previously suggested. First-principles calculations confirm this finding and predict a second phase transition to a ${\mathrm{Co}}_2\text{Si-like}$ structure between 75– 110 GPa in $\mathrm{Pb}{\mathrm{Cl}}_2$ and 60–75 GPa in $\mathrm{Sn}{\mathrm{Cl}}_2$. Band gaps were measured under compression to ∼70 GPa for $\mathrm{Pb}{\mathrm{Cl}}_2$ and ∼66 GPa for $\mathrm{Sn}{\mathrm{Cl}}_2$ and calculated up to 200 GPa for $\mathrm{Pb}{\mathrm{Cl}}_2$ and 120 GPa for $\mathrm{Sn}{\mathrm{Cl}}_2$. We find an excellent agreement between our experimental and theoretical results when using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional, which suggests that this functional could reliably be used to calculate the band gap of similar $A{X}_2$ compounds. Experimental and calculated band-gap results show discontinuous decreases in the band gap corresponding to phase changes to higher-coordinated crystal structures, giving insight into the relationship between interatomic geometry and metallicity.

Phase-space representations are a family of methods for dynamics of both bosonic and fermionic systems, that work by mapping the system's density matrix to a quasiprobability density and the Liouville-von Neumann equation of the Hamiltonian to a corresponding density differential equation for the probability. We investigate here the accuracy and the computational efficiency of one approximate phase-space representation, called the fermionic truncated Wigner approximation (fTWA), applied to the Fermi-Hubbard model. On a many-body 2D system, with hopping strength and Coulomb $U$ tuned to represent the electronic structure of graphene, the method is found to be able to capture the time evolution of first-order (site occupation) and second-order (correlation functions) moments significantly better than the mean-field, Hartree-Fock method. The fTWA was also compared to results from the exact diagonalization method for smaller systems, and in general the agreement was found to be good. The fully parallel computational requirement of fTWA scales in the same order as the Hartree-Fock method, and the largest system considered here contained 198 lattice sites.

The quantum many-body interactions in one-dimensional spin-$\frac{1}{2}$ systems are subject to Tomonaga-Luttinger liquid (TLL) physics, which predict an array of multiparticle excitations that form continua in momentum-energy space. Here we use inelastic neutron spectroscopy to study the TLL spin dynamics in ${\mathrm{SrCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$, a compound which contains weakly coupled spin-$\frac{1}{2}$ chains of Co atoms, at 0.05 K and in a longitudinal magnetic field up to 9.0 T. The measurements were performed above 3.9 T, where the ground-state Néel antiferromagnetic (AFM) order is completely suppressed and the multiparticle excitations are exclusively of the TLL type. In this region and below 7.0 T, the longitudinal TLL mode—psinon/antipsinon (P/AP)—is unexpectedly well described by a damped harmonic oscillator (DHO) while approaching the zone center defining the static spin-spin correlations. A non-DHO-type, continuumlike signal is seen at higher fields, but deviations from the ideal one-dimensional TLL still remain. This change in the P/AP mode coincides with the phase transition between the longitudinal spin density wave (LSDW) and transverse AFM order. Inside the LSDW state, the DHO-type P/AP spectral weight increases and the linewidth broadens as the magnetic order parameter decreases. These results reveal the impact of three-dimensional magnetic order on the TLL spin dynamics; they call for beyond-mean-field treatment for the interchain exchange interactions.