We investigate how the critical driving amplitude at the Floquet many-body localized (MBL) to ergodic phase transition differs between smooth and nonsmooth drives. To this end, we numerically study a disordered spin-1/2 chain which is periodically driven by a sine or square-wave drive over a wide range of driving frequencies. In both cases the critical driving amplitude increases monotonically with the frequency, and at large frequencies it is identical for the two drives. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while that of the sinusoidal drive is almost constant over a wide frequency range. By analyzing the density of drive-induced resonances we conclude that this difference is due to resonances induced by the higher harmonics which are present (absent) in the Fourier spectrum of the square-wave (sine) drive. Furthermore, we suggest a numerically efficient method for estimating the frequency dependence of the critical driving amplitudes for different drives which is based on calculating the density of drive-induced resonances. We conclude that delocalization occurs once the density of drive-induced resonances reaches a critical value determined only by the static system.

The perovskite ${\mathrm{SrRuO}}_3$ is a prototypical itinerant ferromagnet which allows interface engineering of its electronic and magnetic properties. We report the synthesis and investigation of atomically flat artificial multilayers of ${\mathrm{SrRuO}}_3$ with the spin-orbit semimetal ${\mathrm{SrIrO}}_3$ in combination with band-structure calculations with a Hubbard $U$ term and topological analysis. The latter reveal an electronic reconstruction and emergence of flat Ru-$4{\mathrm{d}}_{xz}$ bands near the interface, ferromagnetic interlayer coupling, and a negative Berry-curvature contribution to the anomalous Hall effect. We analyze the Hall effect and magnetoresistance measurements as a function of the field angle from an out-of-plane towards an in-plane orientation (either parallel or perpendicular to the current direction) by a two-channel model. The magnetic easy direction is tilted by about ${20}^{\circ }$ from the sample normal for low magnetic fields, rotating towards the out-of-plane direction by increasing fields. Fully strained epitaxial growth enables a strong anisotropy of magnetoresistance. An additional Hall effect contribution, not accounted for by the two-channel model, is compatible with stable skyrmions only up to a critical angle of roughly ${45}^{\circ }$ from the sample normal. Within about ${20}^{\circ }$ from the thin film plane an additional peaklike contribution to the Hall effect suggests the formation of a nontrivial spin structure.

We develop a generic all-inductive procedure to measure the band structure of spin waves in a magnetic thin stripe. In contrast to existing techniques, our method works even if several spin wave branches coexist in the investigated frequency interval, provided that the branches possess sufficiently different group velocities. We first measure the microwave scattering matrix of a network composed of distant antennas inductively coupled to the spin wave bath of the magnetic film. After a mathematical transformation to the time domain to get the transmission impulse response, the different spin wave branches are viewed as wave packets that reach successively the receiving antenna after different travel times. In analogy with time-of-flight spectroscopy, the wave packets are then separated by time gating. The time-gated responses are used to recalculate the contribution of each spin wave branch to the frequency domain scattering matrix. The dispersion relation of each branch stems from the absolute phase of the time-gated transmission parameter. The spin-wave wave vector can be determined unambiguously if the results for several propagation distances are combined, so as to get the dispersion relations.

CuO, known to be multiferroic (MF) from $T_L=213\mathrm{K}$ to $T_N=230\mathrm{K}$ at ambient pressure, has been the subject of debates about its ability to exhibit multiferroicity at room temperature (RT) under high hydrostatic pressure. Here we address this question based on theoretical and experimental investigations. The influence of hydrostatic pressure on $T_L$ and $T_N$ has been estimated from ab initio calculations combined with classical Monte-Carlo simulations and a quasi-1D antiferromagnetic analytical model. From the experimental side, electric permittivity anomalies related to ferroelectric transitions have been followed with dielectric measurements on single crystals up to 6.1 GPa. We show that the temperature $T_N$ below which the MF state forms increases with pressure linearly to higher pressure that hitherto supposed, and indeed based on our calculations, should exceed RT above about 20 GPa.

We investigate the origin of the experimentally observed varying current-frequency nonlinearity of the propagating spin wave mode in nanocontact spin torque oscillators. Nominally identical devices with 100 nm diameter are characterized by electrical microwave measurements and show large variation in the generated frequency as a function of drive current. This quantitative and qualitative device-to-device variation is described in terms of continuous and discontinuous nonlinear transitions between linear current intervals. The thin-film grain microstructure in our samples is determined using atomic force and scanning electron microscopy to be on the scale of 30 nm. Micromagnetic simulations show that the reflection of spin waves against the grain boundaries results in standing wave resonance configurations. For a simulated device with a single artificial grain, the frequency increases linearly with the drive current until the decreased wavelength eventually forces another spin wave antinode to be formed. This transition results in a discontinuous step in the frequency versus current relation. Simulations of complete, randomly generated grain microstructures additionally shows continuous nonlinearity and a resulting device-to-device variation in frequency that is similar to the experimental levels. The impact of temperature from 4 to 300 K on the resonance mode-transition nonlinearity and frequency noise is investigated using simulations and it is found that the peak levels of the spectral linewidth as a function of drive current agree quantitatively with typical levels found in experiments at room temperature. The impact of the grain microstructure on the localized oscillation modes is also investigated.

The spin Hall effect in a heavy metal thin film allows to probe the magnetic properties of an adjacent magnetic insulator via magnetotransport measurements. Here, we investigate the magnetoresistive response of yttrium iron garnet/platinum heterostructures from room temperature to beyond the Curie temperature $T_{\mathrm{C}}\approx 560\mathrm{K}$ of the ferrimagnetic insulator. We find that the amplitude of the (local) spin Hall magnetoresistance decreases monotonically from $300\mathrm{K}$ towards $T_{\mathrm{C}}$, mimicking the evolution of the saturation magnetization of yttrium iron garnet. Interestingly, the spin Hall magnetoresistance vanishes around $500\mathrm{K}$, well below $T_{\mathrm{C}}$, which we attribute to the formation of a parasitic interface layer by interdiffusion. We confirm the presence of such an interface region with Fe and Pt intermixing by transmission electron microscopy and spatially resolved energy dispersive x-ray analysis. Around room temperature the nonlocal magnon-mediated magnetoresistance exhibits a power law scaling $T^{\alpha }$ with $\alpha \sim 3/2$, as already reported. The exponent decreases gradually to $\alpha \sim 1/2$ at around $420\mathrm{K}$, before the nonlocal magnetoresistance vanishes rapidly at a similar temperature as the spin Hall magnetoresistance. We attribute the reduced $\alpha$ at high temperatures to the increasing thermal magnon population which leads to enhanced scattering of the nonequilibrium magnon population and a reduced magnon diffusion length. Finally, we find a magnetic field independent offset voltage in the nonlocal signal for $T>470\mathrm{K}$, which we associate with electronic leakage currents through the normally insulating yttrium iron garnet film. Indeed, this nonlocal offset voltage is thermally activated with an energy close to the band gap.

We studied effects of tilted magnetocrystalline anisotropy on the magnetic domains in a bubble-hosting magnet ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$. With increasing the in-plane uniaxial magnetocrystalline anisotropy, the magnetic ground state in ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ thin plates changes from disordered stripe domains to stripe domains with preferred orientation. Through transport of intensity equation analysis, we further characterized the transition from skyrmion bubbles to biskyrmionlike configurations with increase in the tilted in-plane magnetocrystalline anisotropy when an out-of-plane magnetic field was applied. In addition, differential phase contrast scanning transmission electron microscopy (DPC-STEM) observations and micromagnetic simulations were carried out to confirm that the biskyrmionlike configurations were type-II bubbles. We show that, in addition tilting a magnetic field to induce misalignment between the magnetic field and the easy magnetization axis, tilting the uniaxial magnetic anisotropy can also be used to stabilize type-II bubbles. Our results also indicate DPC-STEM can help to distinguish between type-II bubbles and biskyrmions.

The paramagnetic Curie temperature ${\theta }_{\mathrm{p}}$ is a concept that describes the magnetic ordering temperature in the well-established Curie-Weiss law. Despite the successful explanations of the magnetic behavior, the anisotropy is not usually considered. Although anisotropic ${\theta }_{\mathrm{p}}$ has been reported for several layered antiferromagnetic or ferrimagnetic materials owing to the orientation-dependent exchange, in ferromagnetic systems, ${\theta }_{\mathrm{p}}$ was thought to be almost isotropic for decades, and the occasionally reported small difference has remained unexplained. In this paper, we experimentally report the anisotropic magnetization, critical temperature, and paramagnetic Curie temperature in highly anisotropic magnetic ${\mathrm{Rh}}_2\mathrm{CoSb}$ caused by a large magnetocrystalline anisotropy. The saturation magnetization along the $c$ axis is 25% larger than that along the $a$ axis. The critical temperature and paramagnetic Curie temperature along the $c$ axis are 6 and 15 K higher than those along the $a$ axis, respectively, as deduced from the Arrott plots and inverse susceptibility. A simple modification of the Curie-Weiss law was made to calculate the anisotropic ${\theta }_{\mathrm{p}}$, which well explains not only ${\mathrm{Rh}}_2\mathrm{CoSb}$, but also many other previously reported ferromagnetic materials.

Based on the two-fluid model of helium II, a theory is proposed to explain the recently observed temperature dependence of the zero-phonon line (ZPL) in the optical spectra of Dy atoms in superfluid helium. According to this theory, the main reason for the observed dependence is the temperature redistribution of the normal and superfluid components of the liquid helium. It is also found that due to the Archimedes' principle, the linear vibronic interaction with long-wave phonons in the liquid phase is singularly enhanced. This enhancement, in turn, leads to a finite broadening of the ZPL of the superfluid component and a linear temperature dependence of the ZPL width of the normal component. The proposed theory allows us to explain the experimental results.

Inspired by the rich physical properties of IV-VI compounds, we choose polycrystalline ${\mathrm{Pb}}_{0.99}{\mathrm{Cr}}_{0.01}\mathrm{Se}$ to investigate its structural, vibrational, and electrical transport properties under pressure up to 50 GPa. The structural transitions from the $B1$ to $Pnma$ phase and then to the $B2$ phase in this sample are verified by the x-ray diffraction and Raman scattering measurements. The formation of the intermediate phase is suggested to be mediated by Peierls distortion, and the broad hump in the temperature-dependent resistivity in the intermediate phase gives further evidence of this phenomenon. When the material evolves into the $B2$ phase, superconductivity is observed to emerge, accompanied by suppressing the broad hump of resistivity at intermediate temperatures. Meanwhile, Hall coefficient measurements indicate that the carrier type changes during the structural transitions. These results suggest that the superconductivity in the $B2$ phase for this material is originated by “melting” the Peierls lattice distortion. By extending the present findings to other similar IV-VI semiconductors, we propose that all group IV-VI compounds could exhibit superconductivity in their $B2$ phase due to the lattice melting at high pressures.

The winding number has been widely used as an invariant for diagnosing topological phases in one-dimensional chiral-symmetric systems. We put forward a real-space representation for the winding number. Remarkably, our method reproduces an exactly quantized winding number even in the presence of disorders that break translation symmetry but preserve chiral symmetry. We prove that our real-space representation of the winding number, the winding number defined through the twisted boundary condition, and the real-space winding number derived previously [Phys. Rev. Lett. 113, 046802 (2014)], are equivalent in the thermodynamic limit at half-filling. Our method also works for the case of filling less than one half, where the winding number is not necessarily quantized. Around the disorder-induced topological phase transition, the real-space winding number has large fluctuations for different disordered samples, however, its average over an ensemble of disorder samples may well identify the topological phase transition. Besides, we show that our real-space winding number can be expressed as a Bott index, which has been used to represent the Chern number for two-dimensional systems.

We study the role of nonperturbative phonon scattering in strongly anharmonic materials having ultralow lattice thermal conductivity with unusual temperature dependence. We take ${\mathrm{Tl}}_3{\mathrm{VSe}}_4$ as an example and investigate its lattice dynamics using perturbation theory (PT) up to the fourth order and molecular dynamics (MD) with a machine-learning potential. We find distinct differences of phonon linewidth between PT and MD in the whole Brillouin zone. The comparison between the theoretical phonon linewidths and experiments suggests that PT severely underestimates the phonon scatterings, even when the fourth-order anharmonicity is included. Moreover, we extend our calculations to higher temperatures and evaluate the two-channel thermal conductivity based on the unified theory developed by Simoncelli et al. [Nat. Phys. 15, 809 (2019)]. We find a crucial coherence contribution to the total thermal conductivity at high temperatures. Our results pave the path for future studies of phonon properties and lattice thermal conductivities of strongly anharmonic crystals beyond the conventional PT realm.

Quenching a quantum system involves three basic ingredients: the initial phase, the postquench target phase, and quantum dynamics, which may carry the information of the former two. Here we propose a dynamical theory, based on an interaction quench, to characterize both the equilibrium symmetry-breaking order and topological phases by nonequilibrium correlated quantum dynamics. We illustrate the theory with the Haldane-Hubbard model, which is quenched from an initial correlated magnetic phase to a topologically nontrivial regime. We show that the quench dynamics exhibit profound universal behaviors on the so-called band-inversion surfaces (BISs), from which both the topological phase in the weakly interacting regime and the correlated magnetic phase in the strongly interacting regime can be extracted. In particular, the topology is characterized by dynamical topological patterns emerging on BISs, which are robust against interaction-induced dephasing and heating; the symmetry-breaking order can be read out from a universal dynamical scaling behavior, which is valid beyond the mean-field theory. This work uncovers the first paradigm of nonequilibrium characterization of equilibrium symmetry-breaking and topological phases.

We perform calculations with the $\mathrm{DFT}+U$ approach for the three Cr trihalides $\mathrm{Cr}{\mathrm{I}}_3, \mathrm{Cr}{\mathrm{Br}}_3$, and $\mathrm{Cr}{\mathrm{Cl}}_3$ with the aim to determine magnetic exchange interactions and magnetic ordering temperatures. A comprehensive investigation is carried out to assess the role of the Hubbard parameter $U$ as well as of the schemes used to correct for the double counting (DC) of the Coulomb interaction. For the bilayer systems, both with low-temperature (LT) or high-temperature (HT) stacking, magnetic exchange parameters and ordering temperatures are calculated within the random-phase approximation for spin waves. Our results show that the most commonly used DC scheme, the “fully localized limit” (FLL) of $\mathrm{DFT}+U$, erroneously favors ferromagnetic coupling between the layers of a bilayer structure, and yields Curie temperatures in excess of the experimental values. With the help of a perturbative model for superexchange, we are able to trace the source of this error back to the too small band gap in the majority spin channel in the FLL calculations. In contrast, when using the “around-mean-field” (AMF) DC scheme and a realistic value of $U=1.7$ eV for the Cr-$3d$ orbitals, we find that the magnetic interlayer coupling is antiferromagnetic (AFM) in all three materials, in agreement with recent experiments for ${\mathrm{CrI}}_3$. We calculate the antiferromagnetic ordering temperature for both LT and HT stacking to be 22 K and 29 K for bilayer ${\mathrm{CrI}}_3$. Thus, according to our calculations, the AFM order can be observed independently of the crystal structure of the film, while the LT structure remains to be the ground state. Bilayer ${\mathrm{CrBr}}_3$ films are predicted to have a Néel temperature similar to that of ${\mathrm{CrI}}_3$, whereas the ${\mathrm{CrCl}}_3$ films prefer antiparallel in-plane magnetization.

$\mathrm{Rb}\mathrm{Fe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$ is one of the best physical examples of a quasi-two-dimensional easy-plane triangular-lattice antiferromagnet. Although the magnetic phase diagram of this material has been well-studied, there are discrepancies in the literature concerning the number of magnetic phases, as well as the nature of the phase transitions. By performing ultrasound velocity measurements, we have obtained a detailed phase diagram with magnetic fields parallel and perpendicular to the triangular layers. The order of the phase transitions was found to be consistent with previous theoretical studies of generic two-dimensional triangular antiferromagnets. To support our experimental findings, we present a phenomenological model that includes biquadratic and next-nearest-neighbor interplane interactions. This model is sufficient to reproduce the phase diagram at low temperatures, and the next-nearest-neighbor interactions are shown to stabilize the incommensurate phases ($\mathbb{Y}$ and $\mathbb{V}$). Furthermore, the model provides insight regarding the magnetic ordering along the $\widehat{c}$-axis in the magnetic plateau phase, suggesting that period 3 is established whenever the next-nearest-neighbor superexchange interactions are unequal. In the systems in which these interactions are expected to be equal, the model predicts degeneracy between period 2 and period 3 structures, at the classical level.

Quantum states of a skyrmion in a two-dimensional antiferromagnetic lattice are obtained by quantizing the scaling parameter of Belavin-Polyakov model. Skyrmion classical collapse due to violation of the translational invariance of the continuous spin-field model by the lattice is replaced in quantum mechanics by transitions between discrete energy levels of the skyrmion. Rates of transitions due to emission of magnons are computed. Ways of detecting quantization of skyrmion states are discussed.

We present an experimental study of vortex dynamics in magnetic nanocontacts based on pseudo spin valves comprising the ${\mathrm{Co}}_2\mathrm{MnGe}$ Heusler compound. The films were grown by molecular beam epitaxy, where precise stoichiometry control and tailored stacking order allowed us to define the bottom ferromagnetic layer as the reference layer, with minimal coupling between the free and reference layers. 20-nm diameter nanocontacts were fabricated using a nanoindentation technique, leading to self-sustained gyration of the vortex generated by spin-transfer torques above a certain current threshold. By combining frequency- and time-domain measurements, we show that different types of spin-transfer induced dynamics related to different modes associated to the magnetic vortex configuration can be observed, such as mode hopping, mode coexistence, and mode extinction appearing in addition to the usual gyration mode.

In this paper, we investigate the ground-state phase diagram of the $S=1/2$ Heisenberg-$\mathrm{\Gamma }$ model on a honeycomb lattice by dimer series expansion and exact diagonalization. We focus on the effects of the anisotropy of the interactions; by tuning the coupling constants, the system changes between the isolated dimer and the spin-chain models. We find that, in the spin-chain limit, there are three kinds of states: A Tomonaga-Luttinger liquid and two magnetically long-range-ordered states. All three states become two-dimensional long-range-ordered states by the infinitesimal interchain interaction except for the case where the Heisenberg interaction is much weaker than the off-diagonal symmetric $\left(\mathrm{\Gamma }\right)$ interaction. Starting from the isolated dimer limit, a triplet dimer phase survives up to the isotropically interacting system in a large part of the phase diagram where the Heisenberg and $\mathrm{\Gamma }$ interactions are ferromagnetic and antiferromagnetic, respectively. Otherwise, a phase transition to a magnetically ordered phase occurs before the interaction becomes isotropic. This indicates that the quantum spin liquid proposed in the $\mathrm{\Gamma }$ model [A. Catuneanu et al., npj Quantum Mater. 3, 23 (2018)] is unstable against the anisotropy of the interactions.

The valleys in hexagonal two-dimensional systems with broken inversion symmetry carry an intrinsic orbital magnetic moment. Despite this, such systems possess zero net magnetization unless additional symmetries are broken since the contributions from both valleys cancel. A nonzero net magnetization can be induced through applying both uniaxial strain to break the rotational symmetry of the lattice and an in-plane electric field to break time-reversal symmetry owing to the resulting current. This creates a magnetoelectric effect whose strength is characterized by a magnetoelectric susceptibility, which describes the induced magnetization per unit applied in-plane electric field. Here, we predict the strength of this magnetoelectric susceptibility for Bernal-stacked bilayer graphene as a function of the magnitude and direction of strain, the chemical potential, and the interlayer electric field. We estimate that an orbital magnetization of $\sim 5400{\mu }_{\text{B}}/\mu {\text{m}}^2$ can be achieved for 1% uniaxial strain and a $10-\mu \mathrm{A}$ bias current, which is almost three orders of magnitude larger than previously probed experimentally in strained monolayer ${\mathrm{MoS}}_2$. We also identify regimes in which the magnetoelectric susceptibility switches sign not only upon reversal of the interlayer electric field, but also in response to small changes in the carrier density. Taking advantage of this reversibility, we further show that it is experimentally feasible to probe the effect using scanning magnetometry.