Critical transition points between symmetry-broken phases are usually characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that iteratively traces out the large-momentum modes, this well-known fact can easily break down in non-Hermitian systems under open boundary conditions. Based on non-Hermitian Su-Schrieffer-Heeger-type models, we propose a RG scheme based on real-space decimation. We provide concrete examples and an analytic proof to show that the real-space scheme always respects the critical points under RG transformations. We investigate the correlation length of order parameters in the vicinity of critical points. Its divergence and scaling behavior remain intact under the real-space decimation, indicating that our method can be successfully applied to study the critical phenomena in non-Hermitian systems. These results suggest that the real-space RG method will find versatile applications in interacting non-Hermitian quantum systems.

We suggest an easily configurable dynamical method of creating a periodic quasi-2D plasmonic lattice in a metal film by temperature induced variation of the dielectric permittivity. The temperature variations in turn are controlled by two pairs of perpendicular pump beams irradiating the metal surface. By varying the incident angles of the beams one can control the effective spatial periods of the lattice while the erasure time is given by the pulse duration raging from pico- to nanoseconds. We show that the modulation effect is most prominent in the imaginary part of the metal dielectric function and thus the obtained plasmonic crystal is fully dissipative. We also demonstrate that such crystal displays reduced absorption at the Brillouin zone boundary and calculate the transmission as a function of the transient contrast of the lattice.

Heat-assisted magnetic recording (HAMR) technology represents the most promising candidate to replace the current perpendicular recording paradigm to achieve higher storage densities. To better understand HAMR dynamics in granular media we need to describe accurately the magnetization dynamics up to temperatures close to the Curie point. To this end we propose a multiscale approach based on the Landau-Lifshitz-Bloch (LLB) equation of motion parametrized using atomistic calculations. The LLB formalism describes the magnetization dynamics at finite temperature and allows us to efficiently simulate large system sizes and long time scales. Atomistic simulations provide the required temperature dependent input quantities for the LLB equation, such as the equilibrium magnetization and the anisotropy and can be used to capture the detailed magnetization dynamics. The multiscale approach makes it possible to overcome the computational limitations of atomistic models in dealing with large systems, such as a recording track, while incorporating the basic physics of the HAMR process. We investigate the magnetization dynamics of a single FePt grain as a function of the properties of the temperature profile and applied field and test the LLB results against atomistic calculations. Our results prove the appropriateness and potential of the approach proposed here where the granular model is able to reproduce the atomistic simulations and capture the main properties of a HAMR medium.

Magnetic skyrmions are quasiparticle configurations in a magnetic film that can act as information carrying bits for ultrasmall, all-electronic nonvolatile memory. The skyrmions can be nucleated and driven by spin-orbit torque from a current driven in a heavy metal underlayer. Along its gyrotropic path, a Magnus force can cause a skyrmion to be annihilated at the boundaries. By combining interfacial and bulk Dzyaloshinskii-Moriya interactions (DMIs), for instance by using a B20 material on top of a heavy metal layer with high spin-orbit coupling, it is possible to engineer a hybrid skyrmion that will travel parallel to the racetrack with zero Magnus force. We show that by using a spatially varying interfacial DMI, a hybrid skyrmion will automatically self-focus onto such a track as its domain angle evolves along the path. Furthermore, using a gate driven voltage controlled magnetic anisotropy, we can control the trajectory of the hybrid skyrmion and its eventual convergence path and lane selection in a racetrack geometry.

We report on the experimental investigation of the perpendicular magnetic anisotropy in $\mathrm{Pt}/{[\mathrm{Co}/\mathrm{Ni}]}_{\mathrm{N}}/\mathrm{Ir}$ multilayers. Broadband ferromagnetic resonance (FMR) and polar angle dependent FMR measurements reveal the presence of a strong fourth-order contribution to the perpendicular anisotropy. By numerically solving the Smit-Beljers relation, we are able to fit the polar angle dependence of the resonance field and extract both the second and fourth-order anisotropy constants. While this model provides a qualitative description for all samples, we note that, for samples near or in the easy cone state of the phase diagram, systematic deviations emerge in the polar angle dependent data. The exchange stiffness of the multilayers is found to be lower than the weighted average of the exchange stiffness reported for Co and Ni in the literature. We find that the effective Gilbert damping scales with the inverse multilayer thickness, indicating a significant interfacial contribution to the damping process.

$\mathrm{Tm}{\mathrm{B}}_4$ is an anisotropic, metallic magnetic system with geometrical frustration of the Shastry-Sutherland type. Here an experimental study of the magnetocaloric effect (MCE) in Lu-doped $\mathrm{T}{\mathrm{m}}_{1-x}\mathrm{L}{\mathrm{u}}_x{\mathrm{B}}_4$ ($x=0.06$, 0.30), evaluated from the temperature dependence of heat capacity and magnetization curves at 2 K, is presented. The results are described within a theoretical model based on an extended Ising Hamiltonian which considers interactions up to the fourth-next-nearest neighbors. Model parameters were optimized to achieve the best match to the experimental results over the whole range of $\mathrm{L}{\mathrm{u}}^{3+}$ ion concentrations. After optimization a good quantitative agreement with the adiabatic temperature change and a good qualitative agreement with magnetization curves is obtained. Our study shows that the efficiency of the MCE can be tuned by dilution with nonmagnetic Lu ions. The theoretical model developed could be used to design new magnetocaloric materials.

Transition-metal dichalcogenides (TMDCs) stand out with their high chemical stability and the possibility to incorporate a wide range of atoms and molecules between the layers. The behavior of conduction electrons in such $3d$-metal-inserted materials is closely related to their magnetic properties and can be sensitively controlled by external magnetic fields. Here, we study the magnetotransport properties of Mn-inserted $\mathrm{Nb}{\mathrm{S}}_2, {\mathrm{Mn}}_{1/4}\mathrm{Nb}{\mathrm{S}}_2$, demonstrating a complex behavior of the magnetoresistance and of the ordinary and anomalous Hall resistivity. Application of high pressure as tuning parameter leads to the drastic changes of the magnetotransport properties of ${\mathrm{Mn}}_{1/4}\mathrm{Nb}{\mathrm{S}}_2$ exhibiting large negative magnetoresistance up to $-65\%$ at 7.1 GPa. First-principles electronic structure calculations indicate a pressure-induced transition from a ferromagnetic to antiferromagnetic state. Theoretical calculations accounting for the finite temperature magnetic properties suggest a field-induced metamagnetic ferromagnetic-antiferromagnetic transition as an origin of the large negative magnetoresistance. These results inspire the development of materials for spintronic applications based on $3d$-element-inserted TMDCs with a well controllable metamagnetic transition.

The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field for the ferromagnetic and antiferromagnetic cases. While for the limiting case of the isotropic long-range XY model we can extract the elementary one-quasiparticle dispersion analytically and calculate two-quasiparticle excitation energies quantitatively in a numerical fashion, for the long-range Ising limit as well as in the intermediate regime we use perturbative continuous unitary transformations on white graphs in combination with classical Monte Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit. This enables us to determine the quantum-critical breakdown of the high-field polarized phase by analyzing the gap closing including associated critical exponents and multiplicative logarithmic corrections. In addition, for the ferromagnetic isotropic XY model we determined the critical exponents $z$ and $\nu$ analytically by a bosonic quantum-field theory.

Strain-stress relationships for physical properties are of interest for heteroepitaxial material systems, where strain and stress are inherent due to thermal expansion and lattice mismatch. We report linear perturbation theory strain and stress relationships for optical phonon modes in monoclinic crystals for strain and stress situations which maintain the monoclinic symmetry of the crystal. By using symmetry group analysis and phonon frequencies obtained under various deformation scenarios from density-functional perturbation theory calculations on $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, we obtain four strain and four stress potential parameters for each phonon mode. We demonstrate that these parameters are sufficient to describe the frequency shift of the modes regardless of the stress or strain pattern which maintain the monoclinic symmetry of the crystal. The deformation potentials can be used together with experimentally determined phonon frequency parameters from Raman or infrared spectroscopy to evaluate the state of strain or stress of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, for example, in epitaxial heterostructures.

We develop a continuum dislocation description of twist and stretch moiré superlattices in two-dimensional material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints and that minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer and a Peierls-Nabarro-like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moiré superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori and while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Å. Several applications of our model are shown, including predicting the variation of structure with twist angle and describing dislocation line tension and junction energies.

We report the detailed analysis of specific heat $[C_P\left(T\right)]$ and ac susceptibility for magnetically frustrated ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{CoNbO}}_6$ $(x=0–1)$ double perovskites to understand low-temperature complex magnetic interactions and their evolution with $x$. Interestingly, the observed Schottky anomaly in the $x⩽0.4$ samples shifts gradually toward higher temperatures with magnetic field as well as $x$, and the analysis reveals the persistence of the discrete energy states in these samples resulting from the spin-orbit coupling and octahedral distortion. Moreover, the extracted values of the Landé $g$ factor indicate the existence of high-spin state ${\mathrm{Co}}^{3+}$ ions energetically close to a nonmagnetic low-spin state. The specific-heat data show the $\lambda$-type anomaly for the $x⩾0.6$ samples due to evolution of the long-range antiferromagnetic ordering. Our analysis of low-temperature $C_P\left(T\right)$ data for the $x⩾0.6$ samples demonstrates the 3D isotropic Heisenberg antiferromagnetic (AFM) interactions and the temperature-induced second-order AFM-paramagnetic phase transition. More interestingly, we demonstrate the presence of the free ${\mathrm{Co}}^{2+}$-like Kramers doublet ground state in the $x=1$ sample. Further, the ac susceptibility and time evolution of the magnetization data reveal the low-temperature cluster-glass-like behavior in the $x=0–0.4$ samples, where spin-spin correlation strength decreases with $x$.

We introduce a generalization of the Fredkin spin chain with tunable three-body interactions expressed in terms of conventional spin-half operators. Of the model's two free parameters, one controls the preference for Ising antiferromagnetism and the other controls the strength of quantum fluctuations. In this formulation, the so-called $t$-deformed model (an exactly solvable, frustration-free Hamiltonian) lives on a unit circle centered on the origin of the phase diagram. The circle demarcates the boundary between ferromagnetic order inside and various antiferromagnetic phases outside. Throughout most of the nonferromagnetic parts of the phase diagram, the ground state has Dyck word form: i.e., all contributing spin configurations exhibit perfect matching and nesting of spin up and spin down. The exceptions are two regions in which Dyck word mismatches are energetically favorable. We remark that in those regions the energy level spacing can be exponentially small in the system size. It is also the case that exact diagonalization reveals a highly idiosyncratic energy spectrum, presumably because the hard spin twist at the chain ends induces strong incommensurability effects on the bulk system when the chain length is small. As a convergence check, we benchmark our DMRG results to near-double-precision floating-point accuracy against analytical results at exactly solvable points and against exact diagonalization results for small system sizes across the entire parameter space.

The origin of the large magnetoresistance (MR) peak induced by the metamagnetic transition (MMT) in ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ has attracted extensive attention, but still remains puzzling. Here we performed systematic magnetotransport and torque magnetometry measurements of ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ nanosheets, and found surprisingly that the MR peak, together with the MMT, shifts dramatically toward low magnetic field with the decrease of thickness. Meanwhile, the Hall coefficient shows clearly a sign change near the MR peak position, indicating a magnetic field induced change of band topology. Combined with the theoretical calculation, we argue that the nature of the MR peak in ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is associated with the so-called Lifshitz transition due to van Hove singularity, which is closer to the Fermi level in thinner nanosheets.

We employ the Hartree-Fock approximation to identify the magnetic ground state of the Hubbard model on a frustrated square lattice. We investigate the phase diagram as a function of the Coulomb repulsion's strength $U$, and the ratio $t^{\prime }/t$ between the nearest- and next-nearest-neighbor hoppings $t$ and $t^{\prime }$. At half-filling and for a sufficiently large $U$, an antiferromagnetic chiral spin density wave order with nonzero spin chirality emerges as the ground state in a wide regime of the phase diagram near $t^{\prime }/t=1/\sqrt{2}$, where the Fermi surface is well nested for both $(\pi ,\pi )$ and $(\pi ,0)/(0,\pi )$ wave vectors. This triple-$\mathbf{Q}$ chiral phase is sandwiched by a single-$\mathbf{Q}$ Néel phase and a double-$\mathbf{Q}$ coplanar spin-vortex crystal phase, at smaller and larger $t^{\prime }/t$, respectively. The energy spectrum in the chiral spin density wave phase consists of four pairs of degenerate bands. These give rise to two pairs of Dirac cones with the same chirality at the point $(\frac{\pi }{2},\frac{\pi }{2})$ of the Brillouin zone. We demonstrate that the application of a diagonal strain induces a $d_{xy}$-wave next-nearest-neighbor hopping which, in turn, opens gaps in the two Dirac cones with opposite masses. As a result, four pairs of well-separated topologically nontrivial bands emerge, and each pair of those contributes with a Chern number $\pm 1$. At half-filling, this leads to a zero total Chern number and renders the topologically nontrivial properties observable only in the ac response regime. Instead, we show that at $\frac{3}{4}$ filling, the triple-$\mathbf{Q}$ chiral phase yields a Chern insulator exhibiting the quantum anomalous Hall effect.

We study the topological crystalline insulator phase protected by the glide symmetry, which is characterized by the $Z_2$ topological number. In the present paper, we derive a formula for the $Z_2$ topological invariant protected by glide symmetry in a nonprimitive lattice from that in a primitive lattice. We establish a formula for the glide-$Z_2$ invariant for the space group No. $\mathit{9}$ with glide symmetry in the base-centered lattice by folding the Brillouin zone into that of the primitive lattice where the formula for the glide-$Z_2$ invariant is known. The formula is written in terms of integrals of the Berry curvatures and Berry phases in the $k$ space. We also derive a formula of the glide-$Z_2$ invariant when the inversion symmetry is added, and the space group becomes $\mathit{15}$. This reduces the formula into the Fu-Kane-like formula, expressed in terms of the irreducible representations at high-symmetry points in $k$ space. We also construct these topological invariants by the layer-construction approach, and the results completely agree with those from the $k$-space approach.

Results are presented for the dynamics of an almost strong edge mode which is the quasistable Majorana edge mode occurring in nonintegrable spin chains. The dynamics of the edge mode is studied using exact diagonalization, and compared with time evolution with respect to an effective semi-infinite model in Krylov space obtained from the recursion method. The effective Krylov Hamiltonian is found to resemble a spatially inhomogeneous Su-Schrieffer-Heeger model where the hopping amplitude increases linearly with distance into the bulk, typical of thermalizing systems, but also has a staggered or dimerized structure superimposed on it. The nonperturbatively long lifetime of the edge mode is shown to be due to this staggered structure which diminishes the effectiveness of the linearly growing hopping amplitude. On taking the continuum limit of the Krylov Hamiltonian, the edge mode is found to be equivalent to the quasistable mode of a Dirac Hamiltonian on a half line, with a mass which is nonzero over a finite distance, before terminating into a gapless metallic bulk. The analytic estimates are found to be in good agreement with the numerically obtained lifetimes of the edge mode.

Two-dimensional materials with atomic thickness usually possess superior tunability by surface adsorption than their bulk counterparts, showing great promise for novel nanotechnologies. In layered transition-metal dichalcogenide $\mathrm{Ir}{\mathrm{Te}}_2$ there exhibits complex structural distortions induced by charge ordering, resulting in difficulties for the applications of its corresponding monolayer material. Here, using first-principles calculations, we demonstrate that depositing Na on the surface of the $\mathrm{Ir}{\mathrm{Te}}_2$ monolayer can suppress the structural distortion to form a stable $\mathrm{NaIrT}{\mathrm{e}}_2$ sheet. It naturally breaks the inversion symmetry to enable a Rashba-type spin splitting for potential spintronic applications. In addition, the introduced empty Na $s$ band and the valence band of the $\mathrm{Ir}{\mathrm{Te}}_2$ monolayer can be inverted by the application of a perpendicular electric field, achieving a quantum phase transition from normal to topological insulator. Such an electric field-controlled topological phase transition is promising for the realization of topological field-effect transistors. These findings not only provide a feasible approach to stabilizing the $\mathrm{Ir}{\mathrm{Te}}_2$ monolayer, but also broaden its applications in spintronics and low-dissipation topoelectronics.

Electrical control of the orbital degrees of freedom is an important area of research in the emerging field of “orbitronics.” Orbital gyrotropic magnetoelectric effect (OGME) is the generation of an orbital magnetization in a nonmagnetic metal by an applied electric field. Here, we show that strain induces a large GME in the monolayer $\mathrm{Nb}{X}_2$ $(X=\mathrm{S}, \mathrm{Se})$ normal to the plane, primarily driven by the orbital moments of the Bloch bands as opposed to the conventional spin magnetization, without any need for spin-orbit coupling. The key physics is captured within an effective two-band valley-orbital model and it is shown to be driven by three key ingredients: the intrinsic valley orbital moment, broken $C_{3z}$ symmetry, and strain-induced Fermi surface changes. The effect can be furthermore switched by changing the strain condition, with potential for future device applications.

Based on density-functional theory calculations and symmetry analysis, topological Dirac semimetals (DSMs) and exotic hourglass surface states are predicted in stacked hydrogenated stanene and plumbene [Xenes ($X$ = Sn and Pb)]. Two types of topologically nontrivial DSMs are predicted in the hydrogenated Xene crystals, with the two most stable stacking patterns, respectively. The Dirac points in SnH are found occurring along the three- or sixfold (screw) rotation axes due to the inversion of the Sn $5s$ ($5p_z$) and Sn $5p_{x,y}$ bands. The unique Fermi arcs are observed on the surfaces parallel to the rotation axes in the crystals. Very specially, the nonsymmorphic symmetry of a glide-mirror plane in the hydrogenated Xene crystals gives rise to exotic hourglass surface states which can lead to a giant value of spin-Hall conductivity and make the crystals be ideal systems applied in prospective dissipationless spintronics. The topological nature of the both types of the DSMs is identified by the calculations of the ${\mathrm{Z}}_2$ indexes. Phase transitions from topologically nontrivial DSM states to normal insulators (NIs) or to other types of DSMs are also investigated. Our work provides an ideal material platform for carrying out DSMs and a comprehensive study for understanding how DSMs evolve from two-dimensional NIs or quantum spin Hall materials.