Chiral symmetry provides the symmetry protection for a large class of topological edge states. It exists in non-Hermitian systems as well, and the same anticommutation relation between the Hamiltonian and a linear chiral operator, i.e., $\{H,\mathrm{\Pi }\}=0$, now warrants a symmetric spectrum about the origin of the complex energy plane. Utilizing two general approaches to identify and generate chiral symmetry, we first show that its symmetry operator in non-Hermitian systems can go beyond simple spatial transformations such as parity or rotation and include imaginary gauge transformations in a systematic way. Furthermore, we reveal hidden non-Hermitian chiral symmetry and its associated particle-hole symmetry, where their operators take unfamiliar forms due to the presence of energy nonconserving elements. Finally, our implementation of non-Hermitian chiral symmetry in a topological lattice leads to an edge state with “folded” localization, where its tail is reflected by the opposite edge and resides on a separate sublattice.

Polarization relaxation fundamentally determines the speed, energy consumption, and functionality of ferroelectric materials and devices, which is considered as the core aspect of ferroelectric-based applications and attracts considerable attention. The relaxation time, describing the temporal characteristics of polarization relaxation, has been reported to vary from subpicoseconds to hundreds of nanoseconds in ferroelectrics, and the microscopic picture is still an open question. In this paper, starting from atomistic models for ferroelectrics, a generalized Langevin equation is proposed to describe the dynamical behaviors of polarization at the mesoscale or macroscale. On one hand, through the artificial construction of adiabatic processes, it is derived that the relaxation time is connected with the lifetimes of the phonon modes involved in a many-body ferroelectric system, bridging the thermodynamics of polarization with the dissipation behavior of the phonon modes at the microscale. On the other hand, the relaxation time is then linked to the kinetic coefficient used in the time-dependent Ginzburg-Landau equation, for the polarization evolution on the meso- or macroscale. Furthermore, based on driven Brownian motion, we propose a theoretical model of the dependence of the polarization switching time with an applied external electric field on a ferroelectric monodomain system. The prediction of the switching time is found to agree well with the dynamical simulation data, which verifies the applicability and reliability of the physical picture of the relaxation time clarified in the current work. Our discussion of the physical picture of the polarization relaxation time provides useful ideas for the development of multiscale modeling method for ferroelectrics.

The high-field magnetic properties and magnetic order of the gem mineral green dioptase ${\mathrm{Cu}}_6\left[{\mathrm{Si}}_6{\mathrm{O}}_{18}\right]·6{\mathrm{H}}_2\mathrm{O}$ have been studied by means of single-crystal neutron diffraction in magnetic fields up to 21 T and magnetization measurements up to 30 T. In zero field, the ${\mathrm{Cu}}^{2+}$ moments in the antiferromagnetic chains are oriented along the $c$ axis with a small off-axis tilt. For a field applied parallel to the $c$ axis, the magnetization shows a spin-flop-like transition at $B^{*}=12.2$ T at 1.5 K. Neutron diffraction experiments show a smooth behavior in the intensities of the magnetic reflections without any change in the periodicity of the magnetic structure. Bulk and microscopic observations are well described by a model of ferromagnetically coupled antiferromagnetic $XXZ$ spin-$\frac{1}{2}$ chains, taking into account a change of the local easy-axis direction. We demonstrate that the magnetic structure evolves smoothly from a deformed Néel state at low fields to a deformed spin-flop state in a high field via a strong crossover around $B^{*}$. The results are generalized for different values of interchain coupling and spin anisotropy.

We present a detailed ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) study of the molecular rotation in the compound $[\mathrm{Cu}{\left(\mathrm{pz}\right)}_2{(2-\mathrm{HOpy})}_2]{\left({\mathrm{PF}}_6\right)}_2$, where $\mathrm{pz}={\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2$ and $2-\mathrm{HOpy}={\mathrm{C}}_5{\mathrm{H}}_4\mathrm{NHO}$. Here, a freezing of the ${\mathrm{PF}}_6$ rotation modes is revealed by several steplike increases of the temperature-dependent second spectral moment, with accompanying broad peaks of the longitudinal and transverse nuclear spin-relaxation rates. An analysis based on the Bloembergen-Purcell-Pound (BPP) theory quantifies the related activation energies as $E_a/k_B=250$ and 1400 K. Further, the anisotropy of the second spectral moment of the ${}^{31}\mathrm{P}$ absorption line was calculated for the rigid lattice, as well as in the presence of several sets of ${\mathrm{PF}}_6$ reorientation modes, and is in excellent agreement with the experimental data. Whereas the anisotropy of the frequency shift and enhancement of nuclear spin-relaxation rates is driven by the molecular rotation with respect to the dipole fields stemming from the Cu ions, the second spectral moment is determined by the intramolecular interaction of nuclear ${}^{19}\mathrm{F}$ and ${}^{31}\mathrm{P}$ moments in the presence of the distinct rotation modes.

It has been recently proven that new types of bulk local order can ensue due to frustrated boundary condition, that is, periodic boundary conditions with an odd number of lattice sites and antiferromagnetic interactions. For the quantum XY chain in zero external fields, the usual antiferromagnetic order has been found to be replaced either by a mesoscopic ferromagnet or by an incommensurate AFM order. In this work we examine the resilience of these new types of orders against a defect that breaks the translational symmetry of the model. We find that, while a ferromagnetic defect restores the traditional, staggered order, an AFM one stabilizes the incommensurate order. The robustness of the frustrated order to certain kinds of defects paves the way for its experimental observability.

Spin wave emission and propagation in magnonic waveguides represent a highly promising alternative for beyond-CMOS computing. It is therefore all the more important to fully understand the underlying physics of the emission process. Here, we use time-resolved scanning transmission x-ray microscopy to directly image the formation process of the globally excited local emission of spin waves in a permalloy waveguide at the nanoscale. Thereby, we observe spin wave emission from the corner of the waveguide as well as from a local oscillation of a domain-wall-like structure within the waveguide. Additionally, an isofrequency contour analysis is used to fully explain the origin of quasicylindrical spin wave excitation from the corner and its concurrent nonreflection and nonrefraction at the domain interface. This study is complemented by micromagnetic simulations which perfectly fit the experimental findings. Thus, we clarify the fundamental question of the emission mechanisms in magnonic waveguides which lay the basis for future magnonic operations.

Temperature-dependent dynamical spin correlations, which can be readily accessed via a variety of experimental techniques, hold the potential of offering a unique fingerprint of quantum spin liquids and other intriguing dynamical states. In this work we present an in-depth study of the temperature-dependent dynamical spin structure factor $S(\mathbf{q},\omega )$ of the antiferromagnetic (AFM) Heisenberg spin-1/2 model on the kagome lattice with additional Dzyaloshinskii-Moriya (DM) interactions. Using the finite-temperature Lanczos method on lattices with up to $N=30$ sites we find that even without DM interactions, chiral low-energy spin fluctuations of the ${120}^{\circ }$ AFM order parameter dominate the dynamical response. This leads to a nontrivial frequency dependence of $S(\mathbf{q},\omega )$ and the appearance of a pronounced low-frequency mode at the M point of the extended Brillouin zone. Adding an out-of-plane DM interactions $D^z$ gives rise to an anisotropic dynamical response, a softening of in-plane spin fluctuations, and, ultimately, the onset of a coplanar AFM ground-state order at $D^z>0.1J$. Our results are in very good agreement with existing inelastic neutron scattering and temperature-dependent NMR spin-lattice relaxation rate $(1/T_1)$ data on the paradigmatic kagome AFM compound herbertsmithite, where the effect of its small $D^z$ on the dynamical spin correlations is shown to be rather small, as well as with $1/T_1$ data on the novel kagome AFM compound ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Cl}}_3$, where its substantial $D^z\approx 0.25J$ interaction is found to strongly affect its spin dynamics.

We present longitudinal-field muon-spin relaxation (LF $\mu \mathrm{SR}$) measurements on two systems that stabilize a skyrmion lattice (SkL): ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$, and ${\mathrm{Co}}_x{\mathrm{Zn}}_y{\mathrm{Mn}}_{20-x-y}$ for $(x,y)=(10,10)$, (8, 9), and (8, 8). We find that the SkL phase of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ exhibits emergent dynamic behavior at megahertz frequencies, likely due to collective excitations, allowing the SkL to be identified from the $\mu \mathrm{SR}$ response. From measurements following different cooling protocols and calculations of the muon stopping site, we suggest that the metastable SkL is not the majority phase throughout the bulk of this material at the fields and temperatures where it is often observed. The dynamics of bulk ${\mathrm{Co}}_8{\mathrm{Zn}}_9{\mathrm{Mn}}_3$ are well described by $\simeq 2$ GHz excitations that reduce in frequency near the critical temperature, while in ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ we observe similar behavior over a wide range of temperatures, implying that dynamics of this kind persist beyond the SkL phase.

A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular momentum between the lattice and the spin systems is achieved by a phenomenological coupling term representing the spin-orbit interaction. The characteristic spectra of the spin and phonon systems are analyzed for different coupling strength and temperatures. The spin spectral density shows magnon modes together with the uncorrelated noise induced by the coupling to the lattice. The effective damping parameter is investigated showing an increase with both coupling strength and temperature. The model paves the way to understanding magnetic relaxation processes beyond the phenomenological approach of the Gilbert damping and the dynamics of the energy transfer between lattice and spins.

We investigate the crystal structure, magnetic properties, and crystalline electric field of tetragonal, $I{4}_1/amd, \mathrm{Na}\mathrm{Ce}{\mathrm{O}}_2$. In this compound, ${\mathrm{Ce}}^{3+}$ ions form a tetragonally elongated diamond lattice coupled by antiferromagnetic interactions (${\mathrm{\Theta }}_{\mathrm{CW}}=-7.69$ K) that magnetically order below $T_N=3.18$ K. The ${\mathrm{Ce}}^{3+}J=5/2$ crystalline electric field-split multiplet is studied via inelastic neutron scattering to parametrize a $J_{\mathrm{eff}}=1/2$ ground state doublet composed of states possessing mixed $|m_z\rangle$ character. Neutron powder diffraction data reveal the onset of $A$-type antiferromagnetism with $\mu =0.57\left(2\right){\mu }_B$ moments aligned along the $c$ axis. The magnetic structure is consistent with the expectations of a frustrated Heisenberg $J_1-J_2$ model on the elongated diamond lattice with effective exchange values $J_1>4J_2$ and $J_1>0$.

We find numerically skyrmionic textures with skyrmion number $Q=0$ in ferromagnets with the Dzyaloshinskii-Moriya interaction, perpendicular anisotropy, and the magnetostatic field. These have a skyrmion part and an antiskyrmion part, and they may be called chiral droplets. They are stable in an infinite film as well as in disk-shaped magnetic elements. Droplets are found in films for values of the parameters close to the transition from the ferromagnetic to the spiral phase. Under spin-transfer torque, they move in the direction of the spin flow and behave as solitary waves of Newtonian character, in stark contrast to the Hall dynamics of the standard $Q=1$ skyrmion.

In this study, spin transport was directly compared in two types of copper oxides: The first is antiferromagnetic CuO, in which ${\mathrm{Cu}}^{2+}$ has one unpaired spin in the $3d$ orbital; the second is diamagnetic ${\mathrm{Cu}}_2\mathrm{O}$ with a ${\mathrm{Cu}}^{+}$ ion having a fully filled $3d$ orbital. The results indicate that CuO exhibits good spin conductivity, whereas ${\mathrm{Cu}}_2\mathrm{O}$ is a spin insulator. This indicates that possessing unpaired spins may be an important characteristic of good spin conductors and that copper oxides may have the potential to be spin manipulators.

Anomalous transport measurements have recently been observed through a wide doping range in the cuprates. Motivated by this, we investigate the effects of a state that shares many features consistent with those of the pseudogap, the mixed triplet-singlet $d$-density wave state, and examine whether its presence could help explain these observations. For a sufficiently doped system Li and Lee (arXiv:1905.04248.) showed that that these density wave states produce a nonzero thermal Hall effect. Through the effect that density waves have on the localized spins of a square lattice in a magnetically ordered phase, we find that the mixed triplet-singlet $d$-density wave state induces stable Dzyaloshinskii-Moriya (DM) interactions among the localized spins in the presence of an external magnetic field. As similar antisymmetric exchange couplings have yielded nonzero thermal Hall contributions, we examine this induced DM interaction by applying Holstein-Primakoff (HP) transformations to study the resulting magnon excitations of the spin models for both antiferromagnetic and ferromagnetic backgrounds, relevant to the near-half-filling and heavily overdoped regimes, respectively. Furthermore, because the triplet-singlet $d$-density wave is experimentally challenging to detect directly, we discuss the magnetic signatures that this state can possibly induce away from the pseudogap regime. We calculate the magnon dispersion for ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ and find that the density wave induces a weak $d_{x^2-y^2}$ anisotropy; upon calculating the non-Abelian Berry curvature for this magnon branch, we show explicitly that the magnon contribution to ${\kappa }_{xy}$ is zero. Finally, we calculate corrections to the magnetic ground state energy, spin canting angles, and the spin-wave dispersion due to the topological density wave for ferromagnetic backgrounds. We find that terms linear in the HP bosons can affect the critical behavior, a point previously overlooked in the literature.

We report a theoretical overview of the magnetic domain wall behavior under an electric current in infinitely long nanotubes with azimuthal magnetization, combining the one-dimensional analytic model and micromagnetic simulations. We highlight effects that, besides spin-transfer torques already largely understood in flat strips, arise specifically in the tubular geometry: the Œrsted field and curvature-induced magnetic anisotropy resulting both from the exchange interaction and material growth. Depending on both the geometry of the tube and the strength of the azimuthal anisotropy, Bloch or Néel walls arise at rest, resulting in two regimes of motion largely dominated by either spin-transfer torques or the Œrsted field. We determine the Walker breakdown current in all cases, and highlight the most suitable parameters to achieve high domain wall speed.

It is interesting to ask whether electron interaction can turn a topologically trivial superconductor into a nontrivial one without the presence of spin-orbital coupling. In this paper we solve a correlated $s$-wave superconducting model exactly. The variation of the fermion number parity of the superconducting ground state as a function of the electron interaction is calculated, and the topological phase diagram is obtained. Topological $s$-wave superconducting states are revealed in the doped Mott insulators, which is further confirmed by the numerical investigation of the topological boundary zero mode.

Palladium hydride alloys are superconductors and hydrogen storage materials. One synthesis route is compression of Pd to high pressure in a hydrogen-rich environment. Here we report the evolution of the unit cell volume of ${\mathrm{PdH}}_x$ synthesized by compressing Pd in a pure ${\mathrm{H}}_2$ medium to pressures from 0.2 to 8 GPa in a diamond anvil cell at room temperature. The volume of the face-centered cubic unit cell changes nonmonotonically with pressure, increasing upon compression from 0.2 to 1 GPa and decreasing upon compression from 1 to 8 GPa. Volume is reversible upon decompression and is independent of whether the sample was heated to 600 K at low pressure ($P<2$ GPa). The x-ray diffraction data show no evidence for a phase transition between 0.2 and 8 GPa. The volume maximum at 1 GPa must be caused by progressive hydrogenation from 0 to 1 GPa. Assuming a pressure-volume-composition equation of state derived from previously published data, the [H]:[Pd] ratio in this study increases to a maximum value of $x=1\pm 0.02$ at $2\pm 0.5$ GPa and remains stable upon further compression to and from 8 GPa. These results add to a mounting body of evidence that ${\mathrm{PdH}}_{1\pm \epsilon }$ is in thermodynamic equilibrium with pure ${\mathrm{H}}_2$ at room temperature from 2 GPa to at least 8 GPa. The simplest interpretation is that H atoms occupy all octahedral sites and no tetrahedral sites in face-centered cubic ${\mathrm{PdH}}_{1.0}$.

We study mechanisms of vortex nucleation in ${\mathrm{Nb}}_3\mathrm{Sn}$ superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy imaging and energy dispersive spectroscopy of some ${\mathrm{Nb}}_3\mathrm{Sn}$ cavities show Sn segregation at grain boundaries in ${\mathrm{Nb}}_3\mathrm{Sn}$ with Sn concentration as high as $\sim 35$ at. % and widths $\sim 3$ nm in chemical composition. Using ab initio calculations, we estimate the effect excess tin has on the local superconducting properties of the material. We model Sn segregation as a lowering of the local critical temperature. We then use time-dependent Ginzburg-Landau theory to understand the role of segregation on magnetic vortex nucleation. Our simulations indicate that the grain boundaries act as both nucleation sites for vortex penetration and pinning sites for vortices after nucleation. Depending on the magnitude of the applied field, vortices may remain pinned in the grain boundary or penetrate the grain itself. We estimate the superconducting losses due to vortices filling grain boundaries and compare with observed performance degradation with higher magnetic fields. We estimate that the quality factor may decrease by an order of magnitude $({10}^{10} \mathrm{to} {10}^9)$ at typical operating fields if 0.03% of the grain boundaries actively nucleate vortices. We additionally estimate the volume that would need to be filled with vortices to match experimental observations of cavity heating.

Previously, based on a phenomenological model, it was proposed that the higher-order topological superconductivity can be realized in a heterostructure with a two-dimensional topological insulator and a high-temperature superconductor. The Majorana bound states naturally emerge at the corners of the system. Here starting from a microscopic model, we restudy this system theoretically. The symmetries of the quasiparticle energy spectra are significantly different from those previously obtained. In the momentum space, the fourfold rotational symmetry of the quasiparticle spectra is broken. For a cylinder geometry, the zero-energy edge states may appear, but they are localized at one boundary. For the finite-size system with open boundaries, the Majorana bound states emerge only at parts of the system corners. All of the asymmetrical results can be understood well by exploring the pairing order parameter and the anomalous Green's function.

In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator, whose eigenequation can be solved by an algorithm of variational uniform matrix product states. Using the singularities of the entanglement entropy, we accurately determine the complete phase diagram of this model. Both the integer vortex-antivortex binding and half-integer vortex-antivortex binding phases are separated from the disordered phase by the usual Berezinskii-Kosterlitz-Thouless (BKT) transitions, while a continuous topological phase transition exists between two different vortex binding phases, exhibiting a logarithmic divergence of the specific heat and exponential divergence of the spin correlation length. A hybrid BKT and Ising universality class of topological phase transition is thus established. We further prove that three phase transition lines meet at a multicritical point from which a deconfinement crossover line extends into the disordered phase.