Heusler ferromagnets based on Co are important materials for spintronics. This is due to the exceptional combinations of high Curie temperature and strong spin polarization, including half-metallicity, found in some of these. We investigate the full Heusler compounds, ${\mathrm{Co}}_2\mathrm{TiSi}$, ${\mathrm{Co}}_2\mathrm{MnSi}$, and ${\mathrm{Co}}_2\mathrm{FeSi}$ using first principles calculations. ${\mathrm{Co}}_2\mathrm{TiSi}$ and ${\mathrm{Co}}_2\mathrm{MnSi}$ are half metals, while ${\mathrm{Co}}_2\mathrm{FeSi}$ is not. The trends in the Curie temperatures are reproduced by the calculated spin wave dispersions. Remarkably, ${\mathrm{Co}}_2\mathrm{TiSi}$ is a very itinerant magnet but ${\mathrm{Co}}_2\mathrm{FeSi}$ and ${\mathrm{Co}}_2\mathrm{MnSi}$ show local moment behavior regarding the Fe and Mn, while retaining the itinerancy of the Co magnetism. These materials can therefore be described as itinerant systems with embedded local moment atoms. This provides an explanation for their exceptional behavior. Our results do not support the half-metallic character proposed for ${\mathrm{Co}}_2\mathrm{FeSi}$, but they are consistent with a higher Curie temperature relative to the Mn compound. The density of states and transport spin polarizations ${\mathrm{Co}}_2\mathrm{FeSi}$ have opposite signs. Importantly, although there is a large minority spin density of states at the Fermi level, leading to a low density of states spin polarization, we find a very strong transport spin polarization in ${\mathrm{Co}}_2\mathrm{FeSi}$. This, combined with the large moment, cubic structure, and high Curie temperature supports the further investigation of ${\mathrm{Co}}_2\mathrm{FeSi}$ for spintronic applications that make use of the transport spin polarization.

Integrating topologically stabilized magnetic textures such as skyrmions as nanoscale information carriers into future technologies requires the reliable control by electric currents. Here, we uncover that the relevant skyrmion Hall effect, which describes the deflection of moving skyrmions from the current flow direction, acquires important corrections owing to anisotropic spin-orbit torques that alter the dynamics of topological spin structures. Thereby, we propose a viable means for manipulating the current-induced motion of skyrmions and antiskyrmions. Based on these insights, we demonstrate by first-principles calculations and symmetry arguments that the motion of spin textures can be tailored by materials design in magnetic multilayers of Ir/Co/Pt and Au/Co/Pt. Our work advances the understanding of the current-induced dynamics of these magnetic textures, which underlies a plethora of memory and logic applications.

We present results of a multimethod investigation of the polar antiferromagnets $\mathrm{N}{\mathrm{i}}_2\mathrm{CoTe}{\mathrm{O}}_6$ and $\mathrm{NiC}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$, inspired by the colossal magnetoelectric effect present in $\mathrm{N}{\mathrm{i}}_3\mathrm{Te}{\mathrm{O}}_6$. Both compounds crystalize in the same polar space group $R3$ as $\mathrm{N}{\mathrm{i}}_3\mathrm{Te}{\mathrm{O}}_6$, preserving the crystal symmetry at least from room temperature down to 2 K. $\mathrm{N}{\mathrm{i}}_2\mathrm{CoTe}{\mathrm{O}}_6$ and $\mathrm{NiC}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$ undergo antiferromagnetic phase transitions at $T_{\mathrm{N}}=55$ and 52 K, and spin-flop transitions at an external magnetic field of approximately 8 and 4 T, respectively. Both compounds present an incommensurate antiferromagnetic helical structure with spins lying in the $ab$ plane, in contrast to the collinear one along the $c$ axis in $\mathrm{N}{\mathrm{i}}_3\mathrm{Te}{\mathrm{O}}_6$. Moreover, dielectric anomalies are observed at their antiferromagnetic phase transitions, suggesting a magnetoelectric behavior. Spin and lattice dynamics studies by a combination of infrared, Raman, and terahertz spectroscopies were performed. Below $T_{\mathrm{N}}$, in both $\mathrm{N}{\mathrm{i}}_2\mathrm{CoTe}{\mathrm{O}}_6$ and $\mathrm{NiC}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$, low-frequency spin excitations extremely sensitive to external magnetic field were observed. At least one of these magnons was simultaneously seen in Raman and THz spectra of both compounds, therefore we propose to assign them to electromagnons.

We study the finite-temperature Fermi-liquid to non-Fermi-liquid crossover in the two-dimensional Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where by comparing the single-particle self-energy and the two-particle spin susceptibility we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behavior that is itself characterized by a long, but finite, correlation length scale which we extract. We compute the single-particle self-energy, and the charge/spin susceptibilities for the entire doping range at relatively high temperature, and also for the half-filled weak-coupling case at relatively low temperatures. We perform fluctuation diagnostics to decompose the single-particle self-energy into scattering $q$-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of $t^{\prime }$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.

Low-dimensional semiconducting ferromagnets have attracted considerable attention due to their promising applications as nanosize spintronics. However, realizing robust ferromagnetic couplings that can survive at high temperature is restrained by two decisive factors: superexchange couplings and anisotropy. Despite widely explored low-dimensional anisotropy, strengthening superexchange couplings has rarely been investigated. Here, we found that ligands with lower electronegativity can strengthen ferromagnetic superexchange couplings and further proposed the ligand modulation strategy to enhance the Curie temperature of low-dimensional ferromagnets. Based on the metallic $\mathrm{Cr}{X}_2$ ($X$ = S, Se, Te) family, substituting ligand atoms by halides can form stable semiconducting phase as CrSeCl, CrSeBr and CrTeBr. It is interesting to discover that, the nearest ferromagnetic superexchange couplings can be strengthened when substituting ligands from S to Se and Te. Such evolution originates from the enhanced electron hopping integral and reduced energy intervals between $d$ and $p$ orbitals, while the competing second nearest antiferromagnetic couplings are also benefitted due to delocalized $p-p$ interactions. Finally, ligand modulation strategy is applied in other ferromagnetic monolayers, further verifying our theory and providing a fundamental understanding on controlling superexchange couplings in low dimension.

We study the superconducting instability in disordered noncentrosymmetric monolayers with intrinsic Ising spin-orbit coupling (SOC) subjected to an in-plane Zeeman magnetic field. The pairing interaction contains the channels allowed by crystal symmetry, such that, in general, the pairing state is a mixture of singlet and triplet Cooper pairs. The joint action of the SOC and Zeeman field selects a specific in-plane $\mathbf{d}$-vector triplet component to couple with the singlets, which gains robustness against disorder through the coupling. The out-of-plane $\mathbf{d}$-vector component, that in the clean case is immune to both the Zeeman field and SOC, is obliterated by a very small impurity scattering rate. We formulate the quasiclassical theory of Ising superconductors and solve the linearized Eilenberger equations to obtain the pair-breaking equations that determine the Zeeman field: temperature dependence of the continuous superconducting transition. Our discussion emphasizes how the Zeeman field, SOC, and disorder affect the different superconducting order parameters, and we show how the spin fields inevitably induce odd-frequency pairing correlations.

Topological phases have recently witnessed rapid progress in non-Hermitian systems. Here we study a one-dimensional non-Hermitian Aubry-André-Harper (AAH) model with imaginary periodic or quasiperiodic modulations. We demonstrate that the non-Hermitian off-diagonal AAH models can host zero-energy modes at the edges. In contrast to the Hermitian case, the zero-energy mode can be localized only at one edge. Such a topological phase corresponds to the existence of a quarter winding number defined by eigenenergy in momentum space. We further find the coexistence of a zero-energy mode located only at one edge and topological nonzero-energy edge modes characterized by a generalized Bott index. In the incommensurate case, a topological non-Hermitian quasicrystal is predicted where all bulk states and two topological edge states are localized at one edge. Such topological edge modes are protected by the generalized Bott index. Finally, we propose an experimental scheme to realize these non-Hermitian models in electric circuits. Our findings add another direction for exploring topological properties in Aubry-André-Harper models.

Identifying unconventional quantum phase transitions is one of the most fundamental subjects in quantum physics. To this end, critical exponents in disorder-driven quantum phase transitions in Weyl semimetals and symmetry-protected topological phases have been extensively studied in recent years. In this Rapid Communication, we provide precise critical exponent of the Anderson metal-insulator transition in three-dimensional (3D) orthogonal class with particle-hole symmetry, class CI, as $\nu =1.16\pm 0.02$. We further study disorder-driven quantum phase transitions in the 3D nodal line Dirac semimetal model, which belongs to class BDI, and estimate the critical exponent as $\nu =0.80\pm 0.02$. From a comparison of the exponents, we conclude that a disorder-driven reentrant insulator-metal transition from the topological insulator phase in the class BDI to the metal phase belongs to the same universality class as the Anderson transition in the 3D class BDI. We also argue that small disorder drives the nodal line Dirac semimetal in the clean limit to the metal.

We investigate the Sn composition dependence of the Yb valence and local magnetization in ${\mathrm{YbMn}}_6{\mathrm{Ge}}_{6-x}{\mathrm{Sn}}_x$ ($4.25\le x\le 5.80$) using x-ray absorption spectroscopy (XANES) and x-ray magnetic circular dichroism at the Yb $L_3$ edge. In these materials, where Mn is ferromagnetically ordered, we observe a decrease of the Yb valence upon reducing the chemical pressure by Sn doping and a suppression of the Yb magnetic moment for strongly hybridized $4f$ states ($\nu \sim 2.77$). In the vicinity of the Yb magnetic instability ($x_c\sim 5.23$), a remarkably sharp peak is observed in the composition dependence of the valence and magnetic moment at low temperature, which is reminiscent of enhanced valence and magnetic susceptibilities predicted by recent theories on unconventional quantum criticality. This anomaly is also present in the room-temperature XANES signal, suggesting that rare-earth intermetallics with a magnetized $3d$ sublattice form a distinct group of heavy-fermion metals where the high energy of the exchange interactions can bring quantum criticality up to high temperature.

We report on the Dzyaloshinskii-Moriya (DMI) interaction at the interface between a ferromagnet and an oxide. We demonstrate experimentally that oxides can give rise to DMI. By comparison of systems comprised of $\mathrm{Pt}/\mathrm{C}{\mathrm{o}}_{90}\mathrm{F}{\mathrm{e}}_{10}$/oxide and $\mathrm{Cu}/\mathrm{C}{\mathrm{o}}_{90}\mathrm{F}{\mathrm{e}}_{10}$/oxide, we also show how oxidation of one interface can enhance and add to the total DMI of that generated by the Pt interface. This is due to the fact that the DMI on both interfaces promotes left-handed chirality. Finally, by use of ferromagnetic resonance spectroscopy, we show that the DMI and the spectroscopic splitting factor, which is a measure of the orbital momentum, are correlated. This indicates the importance of hybridization and charge transfer at the oxide interface for the DMI.

Rashba spin-orbit torque derived from the broken inversion symmetry at ferromagnet/heavy metal interfaces has potential application in spintronic devices. In the conventional description of the precessional and damping components of the Rashba spin-orbit torque in magnetization textures, the decomposition coefficients are assumed to be independent of the topology of the underlying structure. Contrary to this common wisdom, for Schrödinger electrons trespassing ballistically across a magnetic domain wall, we found that the decomposition coefficient of the damping component is determined by the topology of the domain wall. The resultant damping Rashba spin-orbit torque is protected by the topology of the underlying magnetic domain wall and robust against small deviations from the ideal domain-wall profile. Our identification of a topological damping Rashba spin-orbit torque component in magnetic domain walls will help one to understand experiments on current-driven domain-wall motion in ferromagnet/heavy metal systems with broken inversion symmetry and to facilitate its utilization in innovative device designs.

In order to provide a comprehensive theoretical description of ${\mathrm{MgSiO}}_3$ at extreme conditions, we combine results from path integral Monte Carlo and density functional molecular dynamics simulations and generate a consistent equation of state for this material. We consider a wide range of temperature and density conditions from ${10}^4$ to ${10}^8\mathrm{K}$ and from 0.321 to 64.2 $\mathrm{g}{\mathrm{cm}}^{-3}$ (0.1- to 20-fold the ambient density). We study how the L and K shell electrons are ionized with increasing temperature and pressure. We derive the shock Hugoniot curve and compare with experimental results. Our Hugoniot curve is in good agreement with the experiments, and we predict a broad compression maximum that is dominated by the K shell ionization of all three nuclei while the peak compression ratio of 4.70 is obtained when the Si and Mg nuclei are ionized. Finally we analyze the heat capacity and structural properties of the liquid.

Using density functional calculations, we present a comprehensive study of the electronic and magnetic properties of the quantum spin chain materials ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ and ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Br}}_2$. With the first-principles linear response method, we calculate the magnetic exchange parameters, and the theoretical values are in a quantitatively good agreement with experiments. Depending on the signs and magnitudes of the interchain magnetic exchange interactions, we find that the magnetic order of ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Br}}_2$ along the $b$ axis is antiferromagnetic, while ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ has strong frustration along the $b$ axis. Based on the obtained magnetic exchange parameters, we successfully reproduce the experimental spin-wave dispersion. We also calculate Dzyaloshinskii-Moriya interactions, which are found to dominate in these compounds compared to the interchain magnetic exchange interactions. Finally, we obtain the phase diagram for these two materials using Monte Carlo simulations. Our results are consistent with previous experiments, giving a complete explanation of the magnetic structure.

Polarized Raman scattering in magnetoelectric ${\mathrm{LiNiPO}}_4$ shows a sharp resonant peak at 37 ${\mathrm{cm}}^{-1}$ in the magnetically ordered phase, originating from a one-magnon excitation of ${\mathrm{Ni}}^{2+}S=1$ localized moments at the zone center. Also, a broad component with maximum intensity at $\sim 65{\mathrm{cm}}^{-1}$ is observed and successfully modeled in terms of light scattering from two-magnon excitations within the framework of the Fleury-Loudon theory using five relevant exchange parameters, providing an independent experimental confirmation of their values previously obtained with inelastic neutron scattering data in this material. An additional peak at 58 ${\mathrm{cm}}^{-1}$, already reported in previous works, shows no detectable Zeeman splitting for magnetic fields up to 6 T along the crystallographic a and c directions, excluding one-magnon scattering as a possible assignment for this peak. The possible nature of this excitation is discussed.

Examination of an annular system of underdamped Josephson junctions in the presence of external radiation showed that the ability of the system to lock with some external radiation was determined not only by the number but also by the type of rotating excitations (fluxons or antifluxons). Shapiro steps can be observed in the current-voltage characteristic only in the system with trapped fluxons or in the system with fluxon-antifluxon pairs. If the trapped fluxons circulate simultaneously with fluxon-antifluxon pairs, there are no Shapiro steps regardless of the amplitude or frequency of the applied external radiation.

Each unit cell in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ contains a pair of two-dimensional ${\mathrm{CuO}}_2$ layers. While the crystal structure is globally inversion symmetric, the individual layers are not. This leads, necessarily, to a nonvanishing Rashba spin-orbit coupling (SOC) in the ${\mathrm{CuO}}_2$ layers, with opposite signs of the coupling constant in each layer. These so-called Rashba bilayers generate hidden spin textures, with a vanishing net spin at each $\mathbf{k}$ point in the Brillouin zone, but nonvanishing spin textures in each layer separately. Here, we trace the microscopic origin of the Rashba splitting through the orbital structure of the ${\mathrm{CuO}}_2$ conduction bands, obtain a generic three-orbital model Hamiltonian, and show that the magnitude of the spin-splitting predicted by density functional theory is $\sim 10$ meV.

We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a cnot gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.

We utilize Langevin molecular dynamics simulations to study dynamical critical behavior of magnetic flux lines near the depinning transition in type-II superconductors subject to randomly distributed attractive point defects. We employ a coarse-grained elastic line Hamiltonian for the mutually repulsive vortices and purely relaxational kinetics. In order to infer the stationary-state critical exponents for the continuous nonequilibrium depinning transition at zero temperature $T=0$ and at the critical driving current density $j_c$, we explore two-parameter scaling laws for the flux lines' gyration radius and mean velocity as functions of the two relevant scaling fields $T$ and $j-j_c$. We also investigate critical aging scaling for the two-time height auto-correlation function in the early-time nonequilibrium relaxation regime to independently measure critical exponents. We provide numerical exponent values for the distinct universality classes of noninteracting and repulsive vortices.

Chiral topological superconductors are expected to appear as intermediate states when a quantum anomalous Hall system is proximity coupled to an $s$-wave superconductor and the magnetization direction is reversed. In this paper, we address the edge state properties of ordinary quantum Hall systems proximity coupled to $s$-wave superconductors, accounting explicitly for Landau quantization. We find that the appearance of topological superconducting phases with an odd number of Majorana edge modes is dependent on the structure of the system's vortex lattice. More precisely, vortex lattices containing odd number of superconducting flux quanta per unit cell, always support an even number of chiral edge channels and are therefore adiabatically connected to normal quantum Hall insulators. We discuss strategies to engineer chiral topological superconductivity in proximity-coupled quantum Hall systems by manipulating vortex-lattice structure.