Structural, electronic, and magnetic properties of modified cubic spinel compound ${\mathrm{LiNi}}_{0.5}{\mathrm{Mn}}_{1.5}{\mathrm{O}}_4$ are studied via x-ray diffraction, resistivity, dc and ac magnetization, heat capacity, neutron diffraction, ${}^7\mathrm{Li}$ nuclear magnetic resonance, magnetocaloric effect, magnetic relaxation, and magnetic memory effect experiments. We stabilized this compound in a cubic structure with space group $P{4}_{3}32$. It exhibits semiconducting character with an electronic band gap of $\mathrm{\Delta }/k_{\mathrm{B}}\simeq 0.4$ eV. The interaction within each ${\mathrm{Mn}}^{4+}$ and ${\mathrm{Ni}}^{2+}$ sublattice and between ${\mathrm{Mn}}^{4+}$ and ${\mathrm{Ni}}^{2+}$ sublattices is found to be ferromagnetic (FM) and antiferromagnetic (AFM), respectively. This leads to the onset of a ferrimagnetic transition at $T_{\mathrm{C}}\simeq 125$ K. The reduced values of frustration parameter ($f$) and ordered moments reflect magnetic frustration due to competing FM and AFM interactions. From the ${}^7\mathrm{Li}$ nuclear magnetic resonance shift vs susceptibility plot, the average hyperfine coupling between ${}^7\mathrm{Li}$ nuclei and ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Mn}}^{4+}$ spins is calculated to be $\sim 672.4$ Oe/${\mu }_{\mathrm{B}}$. A detailed critical behavior study is done in the vicinity of $T_{\mathrm{C}}$ using modified-Arrott plot, Kouvel-Fisher plot, and universal scaling of magnetization isotherms. The magnetic phase transition is found to be second order in nature and the estimated critical exponents correspond to the three-dimensional XY universality class. A large magnetocaloric effect is observed with a maximum value of isothermal change in entropy $\mathrm{\Delta }{S}_m\simeq -11.3$ J/Kg K and a maximum relative cooling power of $\text{RCP}\simeq 604$ J/Kg for 9 T magnetic field change. The imaginary part of the ac susceptibility depicts a strong frequency-dependent hump at $T=T_{\mathrm{f}2}$ well below the blocking temperature $T_{\mathrm{b}}\simeq 120$ K. The Arrhenius behavior of frequency dependent $T_{\mathrm{f}2}$ and the absence of zero-field-cooled memory confirm the existence of superparamagnetism in the ferrimagnetically ordered state.

An approach to account for the effect of thermal lattice vibrations when calculating exchange coupling parameters is presented on the basis of the Korringa-Kohn-Rostoker Green function method making use of the alloy analogy model. Using several representative systems, it is shown that depending on the material the effect of thermal lattice vibrations can have a significant impact on the isotropic exchange as well as the Dzyaloshinskii-Moriya interactions (DMI). This should lead in turn to an additional contribution to the temperature dependence of the magnetic properties of solids, which cannot be neglected in the general case. As an example, we discuss such an influence on the critical temperature of various magnetic phase transitions. In particular, in the case of skyrmion hosting materials, a strong impact of lattice vibrations on the DMI is an additional source for the temperature dependent skyrmion size and stability, which should be taken into consideration. The present approach gives also access to features of magnetic properties that are associated with static atomic displacements as, for example, in random high-entropy alloys.

Noncentrosymmetric superconductors have sparked significant research interests due to their exciting properties, such as the admixture of spin-singlet and spin-triplet pairing. Here we report on the muon spin rotation and relaxation and thermodynamic measurements on the noncentrosymmetric superconductor ${\mathrm{La}}_7{\mathrm{Rh}}_3$, which show an isotropic superconducting gap but also spontaneous time-reversal-symmetry breaking occurring at the onset of superconductivity. We show that our results pose severe constraints on any microscopic theory of superconductivity in this system. A symmetry analysis identifies ground states compatible with time-reversal-symmetry breaking, and the resulting gap functions are discussed. Furthermore, general energetic considerations indicate the relevance of electron-electron interactions for the pairing mechanism, in accordance with hints of spin fluctuations revealed in susceptibility measurements.

We have studied the intrinsic spin Hall conductivity of $3d$ transition metal ferromagnets using first-principles calculations. We find the spin Hall conductivity of bcc Fe and fcc Ni, prototypes of ferromagnetic systems, depends on the direction of magnetization. The spin Hall conductivity of electrons with their spin orientation orthogonal to the magnetization are found to be larger than that when the two are parallel. For example, the former can be more than four times larger than the latter in bcc Fe. Such a difference arises due to the anisotropy of the spin current operator in the spinor space: Its expectation value with the Bloch states depends on the relative angle between the conduction electron spin and the magnetization. A simple analytical form is developed to describe the relation between the spinor states, with respect to the magnetization direction, and the Berry and spin Berry curvatures. The model can account for the characteristics found in the calculations. These results show that ferromagnets can be used to generate spin current and its magnitude can be controlled by the magnetization direction.

We propose an efficient microscopic design procedure of electronic band structures having intrinsic spin and momentum dependences in spin-orbit-coupling free antiferromagnets. Our bottom-up design approach to creating desired spin-split and reshaped electronic band structures could result in further findings of practical spin-orbit-coupling free materials exhibiting a giant spin-dependent and/or nonreciprocal transport, magnetoelectric and elastic responses, and so on, as a consequence of such band structures. We establish a systematic guideline to construct symmetric/antisymmetric spin-split and antisymmetrically deformed spin-independent band structures in spin-orbit-coupling free systems by using two polar multipole degrees of freedom, i.e., electric and magnetic toroidal multipoles. The two polar multipoles constitute a complete set and describe arbitrary degrees of freedom in the hopping Hamiltonian, whose onsite and offsite degrees of freedom in a cluster are described as the so-called cluster and bond multipoles, respectively, and another degree of freedom connecting between clusters is expressed as momentum multipoles. By using these multipole descriptions, we elucidate simple microscopic conditions to realize intrinsic band deformations in magnetically ordered states: The symmetric spin splitting is realized in collinear magnets when cluster and bond multipoles contain the same symmetry of multipoles. The antisymmetric spin splitting occurs in noncollinear antiferromagnets when a bond-type magnetic toroidal multipole is present. Furthermore, the antisymmetric band deformation with spin degeneracy is realized in noncoplanar antiferromagnets. We exemplify three lattice systems formed by a triangle unit, triangular, kagome, and breathing kagome structures, to demonstrate the band deformations under the magnetic ordering. On the basis of the proposed procedure, we list up various candidate materials showing intrinsic band deformations in accordance with MAGNDATA, magnetic structures database.

Rare-earth polyhydrides formed under pressure are promising conventional superconductors, with the critical temperature $T_c$ in compressed ${\mathrm{LaH}}_{10}$ almost reaching room temperature. Here, we report a systematic computational investigation of the structural and superconducting properties of rare-earth (RE) polyhydrides formed under pressure across the whole lanthanide series. Analyses of the electronic and dynamical properties and electron-phonon coupling interaction for the most hydrogen-rich hydrides ${\mathrm{REH}}_n$ ($n=8,9,10$) that can be stabilized below 400 GPa show that enhanced $T_c$ correlates with a high density of H $s$ states and low number of RE $f$ states at the Fermi level. In addition to previously predicted and measured ${\mathrm{LaH}}_{10}$ and ${\mathrm{CeH}}_9$, we suggest ${\mathrm{YbH}}_{10}$ and ${\mathrm{LuH}}_8$ as additional potential high-$T_c$ superconducters. They form a “second island” of high-$T_c$ superconductivity amongst the late lanthanide polyhydrides, with an estimated $T_c$ of 102 K for ${\mathrm{YbH}}_{10}$ at 250 GPa.

We study theoretically many-body properties of magic-angle twisted bilayer graphene for different doping levels. Our investigation is focused on the emergence, stability, and manifestations of nematicity of the ordered low-temperature electronic state. It is known that, at vanishing interactions, the low-energy spectrum of the system studied consists of four almost-flat almost-degenerate bands. Electron-electron repulsion lifts this degeneracy. To account for such an interaction effect, a numerical mean-field theory is used. Assuming that the ground state has spin-density-wave-like order, we introduce a multicomponent order parameter describing spin magnetization. Our simulations show that the order-parameter structure depends on the doping level. In particular, doping away from the charge-neutrality point reduces the rotational symmetry of the ordered state, indicating the appearance of an electron nematic state. Manifestations of the nematicity can be observed in the spatial distribution of the spin magnetization within a moiré cell, as well as in the single-electron band structure. The nematicity is the strongest at half-filling (two extra electrons or holes per supercell). We argue that nematic symmetry breaking is a robust feature of the system ground state, stable against model parameter variations. Specifically, it is shown that, away from the charge-neutrality point, it persists for all three parametrizations of the interlayer hopping amplitudes discussed in the paper. Obtained theoretical results are consistent with the available experimental data.

Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems), entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, we introduce a simple model for fermions moving in the deconfined phase of a ${\mathbb{Z}}_2$ gauge theory by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code permits us to tune the ground state between an orthogonal metal and an orthogonal semimetal in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a diagrammatic technique, we are able to explore physics beyond the integrable point to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit, thus providing an important link between quantum materials and quantum information theory.

We show that chiral co-propagating Luttinger liquid edge modes can be created and tuned by shining high-frequency, (time-reversal breaking) circularly polarized light, normal to the layers. The one-dimensional chiral modes can be localized either at the edge of the system or at a domain-wall created when different portions of the graphene sheet are irradiated by oppositely polarized light; the number of such modes depends on the mismatch of Chern numbers across the boundary or domain wall. These modes, under a high-frequency drive, essentially have a static charge distribution and form a chiral Luttinger liquid under Coulomb interaction, which can be tuned by means of the driving parameters. We also note that unlike the Luttinger liquids created by electrostatic confinement in bilayer graphene, here there is no back-scattering, and hence our wires along the edge or domain wall are stable to disorder.

Symmetry is fundamental to topological phases. In the presence of a gauge field, spatial symmetries will be projectively represented, which may alter their algebraic structure and generate novel physics. We show that the ${\mathbb{Z}}_2$ projectively represented translational symmetry operators adopt a distinct anticommutation relation. As a result, each energy band is twofold degenerate, and carries a varying spinor structure for translation operators in momentum space, which cannot be flattened globally. Moreover, combined with other internal or external symmetries, they give rise to exotic band topologies. Particularly, with the inherent time-reversal symmetry, a single fourfold Dirac point must be enforced at the Brillouin zone corner. By breaking one primitive translation, the Dirac semimetal is shifted into a special topological insulator phase, where the edge bands have a Möbius twist. Our work opens an arena of research for exploring topological phases protected by projectively represented space groups.

In this work, we report nuclear magnetic resonance (NMR) combined with density functional theory studies of the transition metal dichalcogenide ${\mathrm{ZrTe}}_2$. The measured NMR shift anisotropy reveals a quasi-two-dimensional behavior connected to a topological nodal line close to the Fermi level. With the magnetic field perpendicular to the ${\mathrm{ZrTe}}_2$ layers, the measured shift can be well-fitted by a combination of enhanced diamagnetism and spin shift due to high-mobility Dirac electrons. The spin-lattice relaxation rates with external field both parallel and perpendicular to the layers at low temperatures match the expected behavior associated with extended orbital hyperfine interaction due to quasi-two-dimensional Dirac carriers. In addition, calculated band structures also show clear evidence for the existence of a nodal line in ${\mathrm{ZrTe}}_2$ between $\mathrm{\Gamma }$ and $A$. For intermediate temperatures, there is a sharp reduction in spin-lattice relaxation rate that can be explained as due to a reduced lifetime for these carriers, which matches the reported large change in mobility in the same temperature range. Above 200 K, the local orbital contribution starts to dominate in an orbital relaxation mechanism revealing the mixture of atomic functions.

The dynamics of exciton recombination and spin relaxation in thin (Ga,Al)(Sb,As)/AlAs quantum wells (QWs) with indirect band gap are studied. The band alignment in these QWs is identified as type I. The exciton recombination time exceeds hundreds of microseconds, while the spin relaxation times of the electron and the heavy hole in an exciton do not exceed hundreds of nanoseconds. The heavy-hole longitudinal $g$ factor is determined to be $+2.5$. Despite the long exciton lifetimes, the photoluminescence circular polarization degree induced by a magnetic field is unexpectedly small and does not exceed $25\%$.

We study the dynamical stability of two-dimensional (2D) metals from Li to Pb in the periodic table. Using a first-principles approach, we calculate the phonon band structure of 2D metals that have planar hexagonal (HX), buckled honeycomb (bHC), and buckled square (bSQ) lattice structures. The bHC and bSQ are dynamically stable structures for most transition metals, whereas the HX and bHC are dynamically stable structures for alkali earth and noble metals. Thin films thicker than bHC and bSQ are dynamically stable for group 5 elements and indium. We demonstrate that the trend in the dynamical stability of 2D metals is correlated with that of three-dimensional (3D) metals. This provides design principles of ordered alloys: 2D metals are building blocks for constructing 3D alloys, where the similarity regarding the dynamical stability of different 2D metals is important for creating dynamically stable alloys.

Inside a three-dimensional strong topological insulator, a tube with $h/2e$ magnetic flux carries a pair of protected one-dimensional linear fermionic modes. This phenomenon is known as the “wormhole effect.” In this work, we find that the wormhole effect, as a unique degree of freedom, introduces exotic transport phenomena and thus manipulates the transport properties of topological insulators. Our numerical results demonstrate that the transport properties of a double-wormhole system can be manipulated by the wormhole interference. Specifically, the conductance and local density of states both oscillate with the Fermi energy due to the interference between the wormholes. Furthermore, by studying the multiwormhole systems, we find that the number of wormholes can also modulate the differential conductance through a ${\mathbb{Z}}_2$ mechanism. Finally, we propose two types of topological devices in real applications, the “wormhole switch” device and the “traversable wormhole” device, which can be finely tuned by controlling the wormhole degree of freedom.

Complex structured intermetallic compounds often show brittleness at ambient temperature or under high strain rate deformation, but ductility at elevated temperature or low strain rate deformation. The change of dislocation behavior plays a decisive role in the brittle-to-ductile transition. Here, dislocations are studied in a hexagonal structured Laves-phase intermetallic compound with aberration-corrected scanning transmission electron microscopy after quasistatic compression at high temperature or high-speed impact at room temperature. Different slip mechanisms are resolved for the prismatic dislocations. Under the high-temperature compression, a shuffle mechanism assisted by diffusion mediates the dislocation motion to form planar defects strictly following the topologically close-packing rules. In contrast, under the high-speed room-temperature impact, the prismatic dislocations prefer to glide on undulated planes that comprise small facets with high atom density.

Using linear-response density functional calculations we study how the soft modes at both the zone center and the zone boundary are influenced by charge doping in cubic $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$. We find (i) upon the electron doping of $n=-0.5$ per unit cell, the soft-mode frequency at zone-center $\mathrm{\Gamma }$ becomes considerably lower than that at the zone-boundary $R$, showing that electron doping may turn antiferroelectric $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ into ferroelectric. (ii) On the other hand, when the hole is doped into $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$, the soft mode at $R$ or $M$ remains to be the lowest in frequency, and therefore antiferroelectric instability is robust and persists after hole doping. Since hole doping makes $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ metallic, the coexistence of metallicity and antiferroelectricity demonstrates the feasibility of metallic antiferroelectricity. (iii) Electron doping and hole doping are revealed to impact the atom-atom interaction very differently. The origin responsible for these charge-doping phenomena is provided.

We study the superconducting proximity effect in inhomogeneous systems in which a disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We self-consistently compute the local superconducting order parameters in the real-space Bogoliubov–de Gennes framework for three cases, namely, when states are (i) extended, (ii) localized, or (iii) critical. The results show that the spatial decay of the superconducting order parameter as one moves away from the normal-superconductor interface is power law in cases (i) and (iii), stretched exponential in case (ii). In the quasicrystalline case, we observe self-similarity in the spatial modulation of the proximity-induced superconducting order parameter. To characterize fluctuations, which are large in these systems, we study the distribution functions of the order parameter at the center of the normal region. These are Gaussian functions of the variable [case (i)] or of its logarithm [cases (ii) and (iii)]. We give arguments to explain the characteristics of the distributions and their scaling with system size for each of the three cases.

The lifetime of antiskyrmions at room temperature in an Mn–Pt–Sn tetragonal Heusler material has been calculated using an atomic scale representation including nearly a million spins. The evaluation of the pre-exponential factor in the Arrhenius rate expression for this large system is made possible by implementation of harmonic transition state theory that avoids evaluation of the eigenvalues of the Hessian matrix. The parameter values in the extended Heisenberg Hamiltonian, including anisotropic Dzyaloshinskii-Moriya interaction, are chosen to reproduce experimental observations [Nayak et al., Nature (London) 548, 561 (2017)], in particular, the 150-nm diameter. The calculated results are consistent with the long lifetime observed in the laboratory and this exceptional stability of the antiskyrmions is found to result from large activation energy for collapse due to strong exchange coupling while the pre-exponential factor in the Arrhenius expression for the lifetime is found to have a typical magnitude of ${10}^{-12}$ s, despite the large number of spins. The long lifetime is, therefore, found to result from energetic effects rather than entropic effects in this system.

The features of spin and charge transport in conductive helimagnets, which are due to the action of an inhomogeneous exchange magnetic field on the spin of conduction electrons, are theoretically studied. The interaction between the spin of moving particles and an inhomogeneous external magnetic field was first recorded in the famous Stern-Gerlach experiment that investigated the quantum nature of spin. In the present paper, we have demonstrated that two physical effects—the electrical magnetochiral effect (EMChE) and the kinetic magnetoelectric effect (KMEE)—can be explained through the interaction of the spins of itinerant electrons in chiral helimagnets with spatially inhomogeneous effective magnetic field of exchange origin. All parameters of the EMChE and KMEE are presented in terms of both the characteristic frequencies of spin relaxation of conduction electrons in a helimagnet and the frequencies of their Larmor precession in external and internal exchange fields. It has been shown that the effective frequency of conduction-electron spin relaxation in a helimagnet contains three components: (i) the rate of spin-lattice relaxation caused by spin-orbit scattering of conduction electrons by defects of the crystal lattice, (ii) the rate of change in the average spin of electrons due to their “diffusion” escape from a region with a given direction of the average spin to a region with a different direction of spin density, and (iii) the contribution of the Larmor precession of the spins of electrons moving in the helimagnet's exchange field that assigns the precession axis altering its direction in space. The peculiarities of the EMChE and KMEE that substantially depend on the ratio of the above-listed spin relaxation rates and the angular frequencies of electron precession are described. The numerical estimates performed show that the mechanism of generating EMChE provides the effect magnitude sufficient to be experimentally detected in metallic helimagnets. The frequency regions of spin relaxation and spin precession are determined to observe a giant electrical magnetochiral effect and resonant behavior of the chiral magnetoresistance. We have called the appropriate effect “magnetochiral kinetic resonance” (MChKR). The physical nature of MChKR is elucidated. The latter arises due to the coincidence of the Larmor precession frequency of an electron in the effective field and the phase change frequency of the helicoidal exchange field acting on the electron moving along the helicoid's axis with a speed equal to that of the electron flow. We have demonstrated how the experimental studies of the KMEE can be used to directly determine the chirality of helimagnets.