Several rare-earth transition-metal ferrimagnetic systems exhibit all-optical magnetization switching upon excitation with a femtosecond laser pulse. Although this phenomenon is very promising for future optomagnetic data storage applications, the role of nonlocal spin transport in these systems is scarcely understood. Using Co/Gd and Co/Tb bilayers, we isolate the contribution of the rare-earth materials to the generated spin currents by using the precessional dynamics they excite in an adjacent ferromagnetic layer as a probe. By measuring terahertz (THz) standing spin-waves as well as GHz homogeneous precessional modes, we probe both the high- and low-frequency components of these spin currents. The low-frequency homogeneous mode indicates a significant contribution of Gd to the spin current but not from Tb, consistent with the difficulty in achieving all-optical switching in Tb-containing systems. Measurements on the THz frequency spin waves reveal the inability of the rare-earth generated spin currents to excite dynamics at the subpicosecond timescale. We present modeling efforts using the $s-d$ model, which effectively reproduces our results and allows us to explain the behavior in terms of the temporal profile of the spin current.

We evaluate the zero-point renormalization (ZPR) due to electron-phonon interactions of 28 solids using the projector-augmented-wave (PAW) method. The calculations cover diamond, many zincblende semiconductors, rock-salt and wurtzite oxides, as well as silicate and titania. Particular care is taken to include long-range electrostatic interactions via a generalized Fröhlich model. The data are compared to recent calculations [Miglio et al., npj Comput. Mater. 6, 167 (2020)] and generally very good agreement is found. We discuss in detail the evaluation of the electron-phonon matrix elements within the PAW method. We show that two distinct versions can be obtained depending on when the atomic derivatives are taken. If the PAW transformation is applied before taking derivatives with respect to the ionic positions, then equations similar to the ones conventionally used in pseudopotential codes are obtained. If the PAW transformation is used after taking the derivatives, then the full-potential spirit is largely maintained. We show that both variants yield very similar ZPRs for selected materials when the rigid-ion approximation is employed. In practice, we find, however, that the pseudoversion converges more rapidly with respect to the number of included unoccupied states.

We present dielectric, polarization, resistivity, specific-heat, and magnetic susceptibility data on single crystals of the lacunar spinels ${\mathrm{GaNb}}_4{\mathrm{Se}}_8$ and ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$, tetrahedral cluster-based materials with substantial spin-orbit coupling. We concentrate on the possible occurrence of antipolar order in these compounds, as previously reported for the isoelectronic ${\mathrm{GaNb}}_4{\mathrm{S}}_8$, where spin-orbit coupling plays a less important role. Our broadband dielectric-spectroscopy investigations reveal clear anomalies of the intrinsic dielectric constant at the magnetostructural transitions in both systems that are in accord with the expectations for antipolar transitions. A similar anomaly is also observed at the cubic-cubic transition of the Nb compound leading to an intermediate phase. Similar to other polar and antipolar lacunar spinels, we find indications for dipolar relaxation dynamics at low temperatures. Polarization measurements on ${\mathrm{GaNb}}_4{\mathrm{Se}}_8$ reveal weak ferroelectric ordering below the magnetostructural transition, either superimposed to antipolar order or emerging at structural domain walls. The temperature-dependent dc resistivity evidences essentially thermally activated charge transport with different activation energies in the different phases. A huge steplike increase of the resistivity at the magnetostructural transition of the Ta compound points to a fundamental change in the electronic structure or the mechanism of the charge transport. At low temperatures, charge transport is governed by in-gap impurity states, as also invoked to explain the resistive switching in these compounds.

We describe a mechanism for order fractionalization in a two-dimensional Kondo lattice model, in which electrons interact with a gapless spin liquid of Majorana fermions described by the Yao-Lee model. When the Kondo coupling to the conduction electrons exceeds a critical value, the model develops a superconducting instability into a state with a a spinor order parameter with charge $e$ and spin $S=\frac{1}{2}$. The broken symmetry state develops a gapless Majorana Dirac cone in the bulk. By including an appropriate gauge string, we can show that the charge $e$, spinorial order develops off-diagonal long-range order that allows electrons to coherently tunnel arbitrarily long distances through the spin liquid.

Here, using the ultrafast optical pump-probe spectroscopy, we have studied the quasiparticle dynamics in the type-II Dirac semimetal ${\mathrm{NiTe}}_2$. Anomalous dynamic optical responses are detected around a critical temperature $T^{*}$ ($\sim 60$ K), which is also evidenced by the transport experiment. In specific, our results reveal a phonon-assisted electron-hole recombination process showing an anomaly at $T^{*}\simeq 60$ K. We discover an unusual phonon renormalization behavior, manifested by the $T$-dependent phonon energy and lifetime exhibiting anomalies at $T^{*}$. We unveil that the observed anomalous $T$-dependencies can be attributed to the sudden shift of the phonon mode involved in the recombination, which originates from the abrupt change of electronic structure near the Fermi surface. These findings can provide deeper insight into the nonequilibrium carrier and lattice properties in the topological materials.

Resonant soft-x-ray reflectivity and vibrating sample magnetometry have been used to characterize field driven and spin orbit torque driven magnetization reversal in a CoFeTaB/Pt bilayer. Reversal of the magnetization occurs either along the applied field direction or perpendicular to the current flow direction. Magnetometry results show that field driven (current driven) coercivities are reduced by application of a current (field) highlighting the roles played by the two external parameters. In the current switching case, it is demonstrated with soft-x-ray hysteresis loops that only the layers near the interface with Pt switch, possibly highlighting the role of proximity effects of the magnetized Pt. We show how magnetization reversal perpendicular to the beam results in hysteresis behavior in the reflected intensity that is dependent on the magnetization but independent of the helicity of the circular polarization of the incident beam.

The disappearance of a charge-density-wave (CDW) transition in $\mathrm{Lu}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_2\mathrm{In}$ is thought to be closely linked to a maximum of the superconducting transition temperature in the system. We studied the superstructure and the phonon softening in $\mathrm{Lu}{\left({\mathrm{Pt}}_{0.5}{\mathrm{Pd}}_{0.5}\right)}_2\mathrm{In}$ by means of neutron and high-resolution inelastic x-ray scattering. A full phonon softening at ${\mathit{q}}_{\mathrm{CDW}}=\left(0.50.50\right)$ with the appearance of superstructure peaks could be clearly identified. This supports the CDW transition to be a continuous transition. The large tail of the superstructure intensity above the CDW transition indicates the importance of critical fluctuations. In general, the observed phonon dispersion relations are quite similar to those predicted by theoretical calculations. However, the softening occurs in a much narrower momentum range than predicted.

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin states encoded by random RBMs with independent and identically distributed complex Gaussian weights. By mapping the computation of ensemble-averaged quantities to statistical mechanics models, we are able to investigate the parameter space of the RBM ensemble in the thermodynamic limit. We discover qualitatively distinct wave functions by varying RBM parameters, which correspond to distinct phases in the equivalent statistical mechanics model. Notably, there is a regime in which the typical RBM states have near-maximal entanglement entropy in the thermodynamic limit, similar to that of Haar-random states. However, these states generically exhibit nonergodic behavior in the Ising basis, and do not form quantum state designs, making them distinguishable from Haar-random states.

The synthesis and characterization of the vanadium-based kagome metal $\mathrm{Tb}\mathrm{V}{}_6\mathrm{Sn}{}_6$ is presented. X-ray measurements confirm that this material forms with the same crystal structure type as the recently investigated kagome metals $\mathrm{Gd}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$, with space group symmetry $P6/mmm$. A signature of a phase transition at 4.1 K is observed in heat capacity, resistivity, and magnetic susceptibility measurements, and both resistivity and magnetization measurements exhibit hysteresis in magnetic field. Furthermore, a strikingly large anisotropy in the magnetic susceptibility was observed, with the $c$-axis susceptibility roughly 75 times the $ab$ plane susceptibility at 5 K. This is highly suggestive of uniaxial ferromagnetism, and the large size of $9.4{\mu }_b/\mathrm{f}.\mathrm{u}.$ indicates the ${\mathrm{Tb}}^{3+}4f$ electronic moments cooperatively align perpendicular to the V kagome lattice plane. The entropy at the phase transition is nearly $R$ ln(2), indicating that the crystalline electric field ground state of the ${\mathrm{Tb}}^{3+}$ ion is a doublet, and therefore the sublattice of $4f$ electrons in this material can be shown to map at low temperatures to the Ising model in a $D_{6h}$ symmetry environment. Hall measurements at temperatures from 300 to 1.7 K can be described by two-band carrier transport at temperatures below around 150 K, with a large increase in both hole and electron mobilities, similar to $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$, and an anomalous Hall effect is seen below the ordering temperature. Angle-resolved photoemission measurements above the magnetic ordering temperature reveal typical kagome dispersions. Our study presents $\mathrm{Tb}\mathrm{V}{}_6\mathrm{Sn}{}_6$ as an interesting system where Ising ferromagnetism coexists with nontrivial electronic states emerging from a kagome lattice.

The tetragonal intermetallic compound ${\mathrm{EuAl}}_4$ hosts an exciting variety of low-temperature phases. In addition to a charge density wave below 140 K, four ordered magnetic phases are observed below 15.4 K in zero field. Recently, a skyrmion phase was proposed based on Hall effect measurements under a $c$-axis magnetic field. We present a detailed investigation of the phase transitions in ${\mathrm{EuAl}}_4$ under $c$-axis magnetic field. Our dilatometry, heat-capacity, DC magnetometry, AC magnetic susceptibility, and resonant ultrasound spectroscopy measurements reveal three magnetic phase transitions not previously reported. The first key result is a detailed $\mathit{H}\parallel \left[001\right]$ magnetic phase diagram mapping the seven phases we observe. Second, we identify a high-field phase, phase VII, which directly corresponds to the region were skyrmions have been previously suggested. Our results provide guidance for future studies exploring the complex magnetic interactions and spin structures in ${\mathrm{EuAl}}_4$.

The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard model, while the nature of the state is under debate. Using the density matrix renormalization group with $\mathrm{SU}{\left(2\right)}_{\mathrm{spin}}\otimes \mathrm{U}{\left(1\right)}_{\mathrm{charge}}$ symmetries implemented, we study the triangular-lattice Hubbard model defined on the long cylinder geometry up to circumference $W=6$. A gapped quantum spin liquid, with on-site interaction $9\lesssim U/t\lesssim 10.75$, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length $L$ increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.

${\mathrm{BaCuSi}}_2{\mathrm{O}}_6$ is a quasi-two-dimensional (2D) quantum antiferromagnet containing three different types of stacked, square-lattice bilayer hosting spin-1/2 dimers. Although this compound has been studied extensively over the last two decades, the critical applied magnetic field required to close the dimer spin gap and induce magnetic order, which exceeds 23 T, has to date precluded any kind of neutron scattering investigation. However, the HFM/EXED instrument at the Helmholtz-Zentrum Berlin made this possible at magnetic fields up to 25.9 T. Thus we have used HFM/EXED to investigate the field-induced ordered phase, in particular to look for quasi-2D physics arising from the layered structure and from the different bilayer types. From neutron diffraction data, we determined the global dependence of the magnetic order parameter on both magnetic field and temperature, finding a form consistent with 3D quantum critical scaling; from this we deduce that the quasi-2D interactions and nonuniform layering of ${\mathrm{BaCuSi}}_2{\mathrm{O}}_6$ are not anisotropic enough to induce hallmarks of 2D physics. From neutron spectroscopy data, we measured the dispersion of the strongly Zeeman-split magnetic excitations, finding good agreement with the zero-field interaction parameters of ${\mathrm{BaCuSi}}_2{\mathrm{O}}_6$. We conclude that HFM/EXED allowed a significant extension in the application of neutron scattering techniques to the field range above 20 T and in particular opened previously unavailable possibilities in the study of field-induced magnetic quantum phase transitions.

The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter ${\varphi }_0$. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the $38.2^{\circ }$ configuration may be within experimentally observable energy scales. We identify the first magic angle for any ${\varphi }_0$ at a condition similar to that of the BM model. At this angle, the lowest two moiré bands at charge neutrality become flat except near the ${\mathit{\Gamma }}_M$ point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at ${\varphi }_0=\pm \pi /2$ where many moiré bands around charge neutrality (often 8 or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and $p_x$, $p_y$ 2-orbital honeycomb lattice tight-binding models.

We develop a unified theoretical framework encompassing one-body and many-body forms of self-interaction. We find an analytic expression for both the one-body and the many-body self-interaction energies, and quantitatively connect the two expressions through the dielectric constant. The two forms of self-interaction are found to coincide in the absence of electron screening. This analysis confers superiority to the notion of many-body self-interaction over the notion of one-body self-interaction. Next, we develop a semilocal density functional scheme that addresses the many-body self-interaction of polarons, thereby overcoming the limitations of standard density functional theory. Polaron localization is achieved through the addition of a weak local potential in the Kohn-Sham Hamiltonian that enforces the piece-wise linearity of the total energy upon partial electron occupation. Our method equivalently applies to electron and hole polarons and does not require any constraint on the wave functions during the self-consistent optimization. The implementation of this scheme does not produce any computational overhead compared to standard semilocal calculations and achieves fast convergence. This approach results in polaron properties, including the atomic geometry, the electron density, and the formation energy, which are close to those achieved with a hybrid functional that similarly satisfies the piece-wise linearity condition. This suggests that addressing the many-body self-interaction results in a polaron description that is robust with respect to the functional adopted. We illustrate our approach through applications to the electron polaron in ${\mathrm{BiVO}}_4$, the hole polaron in MgO, and the hole trapped at the Al impurity in $\alpha -{\mathrm{SiO}}_2$.

In this work we analyze the nonequilibrium transport through a quantum impurity (quantum dot or molecule) attached to ferromagnetic leads by using a hybrid numerical renormalization group–time-dependent density matrix renormalization group thermofield quench approach. For this, we study the bias dependence of the differential conductance through the system, which shows a finite zero-bias peak, characteristic of the Kondo resonance and reminiscent of the equilibrium local density of states. In the nonequilibrium settings, the resonance in the differential conductance is also found to decrease with increasing the lead spin polarization. The latter induces an effective exchange field that lifts the spin degeneracy of the dot level. Therefore, as we demonstrate, the Kondo resonance can be restored by counteracting the exchange field with a finite external magnetic field applied to the system. Finally, we investigate the influence of temperature on the nonequilibrium conductance, focusing on the split Kondo resonance. Our work thus provides an accurate quantitative description of the spin-resolved transport properties relevant for quantum dots and molecules embedded in magnetic tunnel junctions.

One of the outstanding questions in the study of twisted bilayer graphene—from both experimental and theoretical points of view—is the nature of its superconducting phase. In this paper we perform a comprehensive synthesis of existing experiments, and argue that experimental constraints are strong enough to allow the structure of the superconducting order parameter to be nearly uniquely determined. In particular, we argue that the order parameter is nodal, and is formed from an admixture of spin-singlet and spin-triplet Cooper pairs. This argument is made on phenomenological grounds, without committing to any particular microscopic model of the superconductor. Existing data is insufficient to determine the orbital parity of the order parameter, which could be either $p$ wave or $d$ wave. We propose a way in which the measurement of Andreev edge states can be used to distinguish between the two.

Since the discovery of topological insulators a great deal of research effort has been devoted to magnetic topological materials, in which nontrivial spin properties can be controlled by magnetic fields, culminating in a wealth of fundamental phenomena and possible applications. The main focus was on ferromagnetic materials that can host Weyl fermions and therefore spin-textured Fermi arcs. The recent discovery of Fermi arcs and new magnetic band splitting in the antiferromagnet (AFM) NdBi has opened up new avenues for exploration. Here we show that these uncharted effects are not restricted to this specific compound, but also emerge in CeBi and NdSb when they undergo paramagnetic to AFM transition. Our data show that the Fermi arcs in NdSb have twofold symmetry, leading to strong anisotropy that may enhance effects of spin textures on transport properties. Our findings thus demonstrate that the RBi and RSb series are materials that host magnetic Fermi arcs and may be a potential platform for modern spintronics.

Using small-angle neutron scattering, we have investigated higher-order peaks in the skyrmion-lattice phase of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ in which two different skyrmion lattices, SkX1 and SkX2, are known to form. For each skyrmion-lattice phase, we observed two sets of symmetrically inequivalent peaks at the higher-order-reflection positions with the indices $\left(110\right)$ and $\left(200\right)$. Under the condition where the SkX1 and SkX2 coexist, we confirmed the absence of the scattering at $\mathbf{Q}$ positions combining reflections from the two phases, indicating a significantly weak double-scattering component. Detailed analysis of the peak profile as well as the temperature and magnetic-field dependence of the peak intensity also supports the intrinsic higher-order modulation rather than the parasitic double scattering. The two higher-order modulations show contrasting magnetic-field dependence; the former $\left(110\right)$ increases as the field is increased, whereas the latter $\left(200\right)$ decreases. This indicates that, in ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$, skyrmions are weakly distorted, and the distortion is field dependent in a way that the dominant higher-order modulation switches from $\left(110\right)$ to $\left(200\right)$ under the field. Monte Carlo simulations under sweeping external magnetic field qualitatively reproduce the observed magnetic-field dependence and suggests that the higher-order modulations correspond to the superlattices of weak swirlings appearing in the middle of the original triangular-latticed skyrmions.

When superconductivity is suppressed by high magnetic fields in ${\mathrm{La}}_{2-\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{CuO}}_4$, striped antiferromagnetic (AFM) order becomes the magnetic ground state of the entire pseudogap regime, up to its end at the doping $p^{*}$ [Frachet, Vinograd et al., Nat. Phys. 16, 1064 (2020)]. Glass-like freezing of this state is detected in ${}^{139}\mathrm{La}$ NMR measurements of the spin-lattice relaxation rate $T_1^{-1}$. Here, we present a quantitative analysis of $T_1^{-1}$ data in the hole-doping range $p=x=0.12-0.171$, based on the Bloembergen-Purcell-Pound (BPP) theory, modified to include statistical distribution of parameters arising from strong spatial inhomogeneity. We observe spin fluctuations to slow down at temperatures $T$ near the onset of static charge order and, overall, the effect of the field $B$ may be seen as equivalent to strengthening stripe order by approaching $p=0.12$ doping. In details, however, our analysis reveals significant departure from usual field-induced magnetic transitions. The continuous growth of the amplitude of the fluctuating moment with increasing $B$ suggests a nearly-critical state in the $B\to 0$ limit, with very weak quasistatic moments possibly confined in small areas like vortex cores. Further, the nucleation of spin order in the vortex cores is shown to account quantitatively for both the value and the $p$ dependence of a field scale characterizing bulk spin freezing. The correlation time of the fluctuating moment appears to depend exponentially on $B/T$ (over the investigated range). This explains the timescale dependence of various experimental manifestations, including why, for transport measurements, the AFM moments may be considered static over a considerable range of $B$ and $T$. These results make the high-field magnetic ground state up to $p^{*}$ an integral part of the discussion on putative quantum criticality.

In ferromagnetic multilayers, a single laser pulse with a fluence above an optical nucleation threshold can create magnetic skyrmions, which are randomly distributed over the area of the laser spot. However, in order to study the dynamics of skyrmions and for their application in future data technology, a controllable localization of the skyrmion nucleation sites is crucial. Here, it is demonstrated that patterned reflective masks behind a thin magnetic film can be designed to locally tailor the optical excitation amplitudes reached, leading to spatially controlled skyrmion nucleation on the nanometer scale. Using x-ray microscopy, the influence of nanopatterned backside aluminum masks on the optical excitation is studied in two sample geometries with varying layer sequence of substrate and magnetic Co/Pt multilayer. Surprisingly, the masks' effect on suppressing or enhancing skyrmion nucleation reverses when changing this sequence. Moreover, optical near-field enhancements additionally affect the spatial arrangement of the nucleated skyrmions. Simulations of the spatial modulation of the laser excitation and the following heat transfer across the interfaces in the two sample geometries are employed to explain these observations. The results demonstrate a reliable approach to add nanometer-scale spatial control to optically induced magnetization processes on ultrafast timescales.