Higher-order topological insulators (HOTIs) or multipole insulators, hosting peculiar corner states, were discovered [Benalcazar et al., Science 357, 61 (2017) and Schindler et al., Sci. Adv. 4, eaat0346 (2018)]. It was independently discovered [Hasimoto et al., Phys. Rev. B 95, 165443 (2017)] that continuum five-dimensional (5D) Weyl semimetals generically host the corner states, and so do four-dimensional (4D) class A and three-dimensional (3D) class AIII topological insulators. In this paper we further confirm that the 5D Weyl semimetals, upon dimensional reduction, lead to universal higher-order topology. First we explain a discrete symmetry protecting the 5D Weyl semimetals, and describe dimensional reductions of the 5D Weyl semimetals to the popular HOTIs in the continuum limit. We calculate the topological charge carried by edge states of the 5D Weyl semimetal, for the most generic boundary condition. The topological charge is a Dirac monopole, which can also be seen from that edge Hamiltonians, are always of the form of a 3D Weyl semimetal. This edge topology leads to the edge-of-edge states, or the corner states, generically, suggesting that the 5D Weyl semimetal is thought of as a physical structural origin of corner states in HOTIs. In addition, we explicitly calculate a nested Wilson loop of the 5D Weyl semimetal and find that the topological structure is identical to that of a Wilson loop of a Dirac monopole.

We investigate the automatic differentiation of dominant eigensolver where only a small proportion of eigenvalues and corresponding eigenvectors are obtained. Back-propagation through the dominant eigensolver involves solving certain low-rank linear systems without direct access to the full spectrum of the problem. Furthermore, the backward pass can be conveniently differentiated again, which implies that in principle one can obtain arbitrarily higher-order derivatives of the dominant eigendecomposition process. These results allow for the construction of an efficient dominant eigensolver primitive, which has wide applications in quantum physics. As a demonstration, we compute second-order derivative of the ground-state energy and fidelity susceptibility of one-dimensional transverse-field Ising model through the exact diagonalization approach. We also calculate the ground-state energy of the same model in the thermodynamic limit by performing gradient-based optimization of uniform matrix product states. By programming these computational tasks in a fully differentiable way, one can efficiently handle the dominant eigendecomposition of very large matrices while still sharing various advantages of differentiable programming paradigm, notably, the generic nature of the implementation and free of tedious human efforts of deriving gradients analytically.

We show that new silicon crystalline phases, observed in the experiment with the laser-induced microexplosions in silicon crystals [Rapp et al., Nat. Commun. 6, 7555 (2015)], are all superstructures of a disordered high-symmetry phase with $Ia\overline{3}d$ cubic space group, as well as known for many years phases $bc8$ (Si-III) and $r8$ (Si-XII). The physics of this phenomenon is rather nontrivial: The $bc8$-like superstructures appear as regularly ordered patterns of switchable atomic strings, preserving everywhere the energetically favorable tetrahedral coordination of silicon atoms. The variety of superstructures arises because each string can be switched between two states independently of the others. An infinite family of different phases can be obtained this way and a number of them are considered here in detail. In addition to the known $bc8$, $bt8$, and $r8$ crystals, 128 tetrahedral structures with 16 (6 phases), 24 (22 phases), and 32 (100 phases) atoms per primitive cell are generated and studied; most of them are new ones. For the coarse-grain description of the structures with two possible states of switchable strings, the black/white (switched/nonswitched) Shubnikov symmetry groups have been used. An ab initio relaxation of the atomic positions and lattice parameters shows that all the considered phases are metastable and have higher density and energy relative to the $bc8$ phase at the ambient pressure. A possible scenario for appearance of those phases from the high-temperature amorphous phase is discussed.

The electronic state of layered three-dimensional topological insulators at high pressure is a compelling but a puzzling hot topic. The open question is the structural origins for the pressure-induced novel physics of electronic topological transition (ETT), topological superconductivity, and Majorana fermions in the same isostructural $R\text{−}3m$ phase. Here, we report a combined investigation on the local structure and bulk electronic state of topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ using x-ray diffraction, high quality x-ray absorption fine-structure spectroscopies both at the $\mathrm{Bi}{L}_3$ edge and at the Se K edge, and first-principles theoretical calculations. We have found three pressure-induced distinct intermediate states in the isostructural rhombohedral phase of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. The bulk electronic structure of the $R\text{−}3m$ phase was calculated based on the experimental structure. The corresponding distinct electronic states provide the origins of ETT at ∼3 GPa and the metallization at 7–9.5 GPa in the $R\text{−}3m$ phase of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. Our results demonstrate that the local structure plays a critical role in the electronic states of topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$.

The phonons of wurtzite and zinc blende GaAs were calculated at simultaneously elevated temperature and pressure, and elastic constants were calculated as functions of pressure. Pressure caused instabilities of shorter-wavelength transverse acoustic modes in both wurtzite and zinc blende GaAs, causing them to fall to zero at 18 and 20 GPa, respectively. The Born stability criteria, which depend on elastic constants and only long wavelength phonons, therefore overestimated the pressure needed to induce instability at 0 K. At elevated temperatures, explicit anharmonicity pushes the onset of instability to higher pressures in both wurtzite and zinc blende GaAs. Phonon linewidth and densities of states data showed that the quasiharmonic approximation failed to account for temperature-induced phonon frequency shifts, and the quasiharmonic approximation became less reliable at elevated pressure. In general, the number of three-phonon processes increased with pressure, thereby increasing the temperature-driven broadening of phonon spectral lineshapes.

We demonstrate spin-orbit torque (SOT) switching of amorphous CoTb single-layer films with perpendicular magnetic anisotropy (PMA). The switching sustains even the film thickness is above 10 nm, where the critical switching current density stays almost constant. Without the need of overcoming the strong interfacial Dzyaloshinskii-Moriya interaction caused by the heavy metal, a quite low assistant field of ∼20 Oe is sufficient to realize the full switching. The SOT effective field decreases and undergoes a sign change with the decrease of the Tb concentration, implying that a combination of the spin Hall effect from both Co and Tb as well as an asymmetric spin current absorption accounts for the SOT switching mechanism. Our findings advance the use of magnetic materials with bulk PMA for energy-efficient and thermally stable nonvolatile memories, and add a different dimension for understanding the ordering and asymmetry in amorphous thin films.

We perform thermodynamic and inelastic neutron scattering (INS) measurements to study the lattice dynamics (phonons) of a cubic collinear antiferromagnet ${\mathrm{Cu}}_3{\mathrm{TeO}}_6$ which hosts topological spin excitations (magnons). While the specific heat and thermal conductivity results show that the thermal transport is dominated by phonons, the deviation of the thermal conductivity from a pure phononic model indicates that there is a strong coupling between magnons and phonons. In the INS measurements, we find a mode in the excitation spectra at 4.5 K, which exhibits a slight downward dispersion around the Brillouin zone center. This mode disappears above the Néel temperature and thus cannot be a phonon. Furthermore, the dispersion is distinct from that of a magnon. Instead, it can be explained by the magnon-polaron mode, collective excitations resulting from the hybridization between magnons and phonons. We consider the suppression of the thermal conductivity and emergence of the magnon-polaron mode to be evidence for magnon-phonon coupling in ${\mathrm{Cu}}_3{\mathrm{TeO}}_6$.

The fluctuations of the magnetic order parameter, or longitudinal spin excitations, are investigated theoretically in the ferromagnetic Fe and Ni as well as in the antiferromagnetic phase of the pnictide superconductor FeSe. The charge and spin dynamics of these systems is described by evaluating the generalized charge and spin density response function calculated from first-principles linear response time-dependent density functional theory within adiabatic local spin density approximation. We observe that the formally noninteracting Kohn-Sham system features strong coupling between the magnetization and charge dynamics in the longitudinal channel and that the coupling is effectively removed upon the inclusion of the Coulomb interaction in the charge channel and the resulting appearance of plasmons. The longitudinal spin fluctuations acquire a collective character without the emergence of the Goldstone boson, similar to the case of paramagnon excitations in nonmagnetic metals like Pd. In ferromagnetic Fe and Ni the longitudinal spin dynamics is governed by interactions between low-energy intraband electron-hole pairs while in quasi-two-dimensional antiferromagnet FeSe it is dominated by the interband transitions with energies of the order of exchange splitting. In the later material, the collective longitudinal magnetization fluctuations feature well-defined energies and long lifetimes for small momenta and appear below the particle-hole continuum. The modes become strongly Landau damped for growing wave vectors. We relate our theoretical findings to existing experimental spinpolarized electron energy loss spectroscopy results. In bulk bcc Fe, the longitudinal magnetic modes appear above the typical energies of transverse spin-waves, have energies comparable with the Stoner spin-flip excitation continuum and are order of magnitude less energetic than the charge dynamics.

We investigate the ultrafast magnetization dynamics of individual nanomagnets resonantly excited by surface acoustic waves (SAWs) generated nonlocally by nonmagnetic phononic gratings. Using a time-resolved magneto-optic Kerr effect microscope, we report the dependence of the magnetoelastic resonance on SAW wavelength and nanomagnet size. Our measurements show that the precession amplitude of single nanomagnets increases monotonically and nonlinearly with decreasing sample size. In addition, for nanomagnets below a critical size we find that the oscillation amplitude increases with SAW frequency. Field-swept measurements of the magnetization dynamics reveal that the damping of the magnetoelastic resonance also decreases with the size of the magnet, ultimately reaching a minimum value determined by the Gilbert damping. This work shows that acoustically driven spin dynamics possess favorable scaling characteristics, which supports the notion that efficient, high-frequency (10–100 GHz) nanoscale straintronic devices limited only by $\alpha$ are feasible.

Molybdenum ditelluride (${\mathrm{MoTe}}_2$) is attracting considerable interest since it is the archetypal type-II Weyl semimetal and a candidate for topological superconductivity. We investigate the superconducting phase diagram of two ${\mathrm{MoTe}}_2$ polymorphs using the ab initio anisotropic Migdal-Eliashberg theory, and we show that the superconducting dome originates from the synergistic contribution of the density of states at the Fermi level and the transverse acoustic Te modes in the $1T^{\prime }$ phase. We find that the electron and hole pockets carry trivial $s$-wave order parameters of slightly different magnitude, reminiscent of a two-gap structure as suggested by recent experiments. We suggest that a possible route for enhancing the superconducting critical temperature, and realizing $s_{+-}$ pairing, in the $T_d$ phase is to exploit its nontrivial band topology via electron doping.

Sodium is the most abundant alkali-metal element and has one of the simplest electronic structures of any metal. At ambient conditions, sodium forms a body-centered-cubic lattice. However, during cooling, it undergoes a partial martensitic phase transition to a complex mixture of rhombohedral polytypes commencing from 36 K. Although the Fermi surface (FS) of bcc sodium has been extensively studied, not much attention has been given to the FS of the martensite structure. Here we report results for the Fermi surface and quantum oscillation (QO) frequencies of several energetically favorable crystal structures of Na at low temperature from first-principles calculations. Interestingly we find that despite drastic differences in the crystal structures of the candidate low-temperature phases of sodium, for all these phases the strongest quantum oscillation peak is centered at 28 kT. Our theoretical results are accompanied by experimental data of QO on a multigrain sodium sample at $T=0.3$ K and $B_{\max }=18$ T exhibiting a sharp peak at 28 kT, independent of the sample orientation. The persistence of this peak even in the presence of the structural transitions has an implication for using the quantum oscillations of polycrystalline sodium for high magnetic field calibration.

The localization landscape [M. Filoche and S. Mayboroda, Proc. Natl. Acad. Sci. USA 109, 14761 (2012)] gives direct access to the localization of bottom-of-band eigenstates in noninteracting disordered systems. We generalize this approach to eigenstates at arbitrary energies in systems with or without internal degrees of freedom by introducing a modified ${\mathcal{L}}^2$ landscape, and we demonstrate its accuracy in a variety of archetypal models of Anderson localization in one and two dimensions. This ${\mathcal{L}}^2$-landscape function can be efficiently computed using hierarchical methods that allow evaluating the diagonal of a well-chosen Green's function. We compare our approach to other landscape methods, bringing insights on their strengths and limitations. Our approach is general and can in principle be applied to both studies of topological Anderson transitions and many-body localization.

We report on the nonequilibrium monopole dynamics in the classical spin ice ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ detected by means of high-resolution magnetostriction measurements. Significant lattice changes occur at the transition from the kagome-ice to the saturated-ice phase, visible in the longitudinal and transverse magnetostriction. A hysteresis opening at temperatures below $0.6\mathrm{K}$ suggests a first-order transition between the kagome and saturated state. Extremely slow lattice relaxations, triggered by changes of the magnetic field, were observed. These lattice-relaxation effects result from nonequilibrium monopole formation or annihilation processes. The relaxation times extracted from our experiment are in good agreement with theoretical predictions with decay constants of the order of $10{}^4$ s at $0.3\mathrm{K}$.

The compounds $A_2\mathrm{C}{\mathrm{u}}_3\mathrm{O}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_3$ $(A=\mathrm{Na},\mathrm{K})$ are characterized by copper hexamers that are weakly coupled to realize antiferromagnetic order below $T_N\approx 3\mathrm{K}$. They constitute quantum spin systems with $S=1$ triplet ground states. We investigated the energy-level splittings of the copper hexamers by inelastic neutron scattering experiments covering the entire range of the magnetic excitation spectra. The observed transitions are governed by very unusual selection rules that we ascribe to the underlying spin-coupling topology. This is rationalized by model calculations that allow an unambiguous interpretation of the magnetic excitations concerning both the peak assignments and the nature of the spin-coupling parameters.

Spin pumping from ferromagnetic Fe into antiferromagnetic CoO across a Ag spacer layer was studied using ferromagnetic resonance (FMR) in Py/CoO/Ag/Fe/Ag(001). The thin Py film on top of CoO permits an alignment of the CoO Néel vector through field cooling in two otherwise equivalent [110] and $\left[1\overline{1}0\right]$ crystalline axes which are parallel and perpendicular to the Fe magnetization direction, respectively. Fe FMR linewidth is measured as a function of Ag thickness in 10–20-GHz frequency range and in 180–330 K temperature range. We find that there exists an anisotropy in the Fe FMR damping for parallel and perpendicular alignment of the Fe and CoO spins. However, such anisotropic damping exists only at thin Ag thickness where there exists a magnetic interlayer coupling between Fe and CoO, and vanishes at thick Ag thickness where the interlayer coupling becomes negligible but permitting spin-current transmission into CoO. Our result indicates the absence of anisotropic spin current for parallel and perpendicular alignment of the Fe and CoO spin axes.

We investigate a microscopic origin of nonreciprocal magnons that is distinct from the Dzyaloshinskii-Moriya interaction in a honeycomb antiferromagnet. The key ingredient is a symmetric anisotropic exchange interaction depending on the bond direction, which results in valley-type nonreciprocal magnon excitations under staggered antiferromagnetic ordering. Furthermore, we find that this type of nonreciprocal magnon exhibits a peculiar magnetic-field response; the nonreciprocal direction can be manipulated by the in-plane rotating magnetic field. The obtained results can be accounted for by the emergence of magnetic toroidal multipoles.

The change in vortex ensemble in ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{0.67}{\mathrm{P}}_{0.33}\right)}_2$, an isovalently doped iron-based superconductor (IBS), is studied through global magnetization measurements and single vortex imaging before and after 6 MeV proton irradiation. The field dependence of the critical current density ($J_{\mathrm{c}}$) is analyzed through the strong pinning model, with which the pristine sample is consistent. After the irradiation, the $J_{\mathrm{c}}$ aberrates from the strong pinning field dependence of $B^{-5/8}$ and evolves to a weaker $B^{-1/3}$ dependence with an anomalous two-step behavior creating a cusplike feature. The cusp coincides with the field of the local minima in the normalized relaxation rate ($S$), manifested by increased pinning due to increased intervortex interactions followed by fast vortex dynamics caused by flux activation at higher fields. Furthermore, single vortex imaging reveals that while long-range triangular correlation of the Abrikosov vortex lattice is observed in pristine samples, irradiated samples exhibit a highly disordered glassy vortex state which is more densely packed with increased pinning force. These artificial defects incorporated via proton irradiation have the same pinning effect as Co doping which not only shifts the pinning force to a higher degree but also broadens its distribution, in contrast to P doping which only broadens the pinning distribution without inducing a shift. All in all, through this investigation, we provide a systematic understanding of the pinning behavior in ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{0.67}{\mathrm{P}}_{0.33}\right)}_2$ through carefully controlling the defects in the system.