We present a systematic analysis of our ability to tune chiral Dzyaloshinskii-Moriya interaction (DMI) in compensated ferrimagnetic $\mathrm{Pt}/\mathrm{GdCo}/{\text{Pt}}_{1-x}{\text{W}}_x$ trilayers by cap layer composition. Using first-principles calculations, we show that the DMI increases rapidly for only $\sim 10$% W and saturates thereafter, in agreement with experiments. The calculated DMI shows a spread in values around the experimental mean, depending on the atomic configuration of the cap layer interface. The saturation is attributed to the vanishing of spin-orbit coupling energy at the cap layer and the simultaneous constancy at the bottom interface. Additionally, we predict the DMI in $\mathrm{Pt}/\mathrm{GdCo}/X$ $(X=\text{Ta},\text{W},\text{Ir})$ and find that W in the cap layer favors a higher DMI than Ta and Ir that can be attributed to the difference in $d$-band overlap around the Fermi level. Our results open up exciting combinatorial possibilities for controlling the DMI in ferrimagnets towards nucleating and manipulating ultrasmall high-speed skyrmions.

In situ synchrotron x-ray diffraction was conducted on polycrystalline ${\mathrm{DyPO}}_4$ to elucidate the details of the pressure-induced transition from the xenotime polymorph to the monazite polymorph. We used three different pressure-transmitting media (neon, a 16:3:1 methanol-ethanol-water mixture, and potassium chloride) to investigate the effect of hydrostaticity on the phase behavior. Specifically, our data clearly show a hydrostatic onset pressure of the xenotime-monazite transition of 9.1 GPa, considerably lower than the 15.3 GPa previously determined by Raman spectroscopy. Based on (quasi)hydrostatic data taken in a neon environment, third-order Birch-Murnaghan equation-of-state fits give a xenotime bulk modulus of 144 GPa and a monazite bulk modulus of 180 GPa (both with pressure derivatives of 4.0). Structural data and axial compressibilities show that ${\mathrm{DyPO}}_4$ is sensitive to shear and has an anisotropic response to pressure. More highly deviatoric conditions cause the onset of the transition to shift to pressures at least as low as 7.0 GPa. We attribute early transition to shear-induced distortion of the ${\mathrm{PO}}_4$ tetrahedra. Our characterization of the high-pressure behavior of ${\mathrm{DyPO}}_4$ under variable hydrostaticity is critical for advancing rare earth orthophosphate fiber coating applications in ceramic matrix composites and may inform future tailoring of phase composition for controlled shear and pressure applications.

The structural complexities of the lead-free piezoelectric system $\left(1\text{−}x\right){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}{\mathrm{TiO}}_3\text{−}x{\mathrm{BaTiO}}_3$ (NBT-BT) continues to pose challenge regarding understanding the mechanisms underlying several interesting phenomena. Issues like (i) whether thermal depoling across compositions is triggered by a structural transformation event or not, (ii) what causes the average Cc structure to partially transform to $R3c$ at $x\sim 0.03$ in unpoled specimens, (iii) what makes complete depoling of the compositions $0.03\le x\le 0.05$ occur in a considerably small temperature interval as compared to those for $x<0.03$, (iv) what makes the $R3c$-$P4bm$ transition temperature $\left(T_2\right)$ abruptly become smaller than the depolarization temperature $\left(T_d\right)$ at $x=0.06$, etc., have remain unresolved. Here, we offer structural insights on these issues by carrying out a detailed investigation using a set of complementary tools involving temperature-dependent x-ray powder diffraction, neutron powder diffraction, dielectric, ferroelectric, piezoelectric, and thermally induced depoling current measurements. We show that onset of thermal depoling in NBT $(x=0)$ well below its depolarization temperature is caused by abrupt reduction of intrinsic polarization in the ferroelectric $R3c$ phase, triggered by the appearance of the $P4bm$ phase. Our study suggests that partial conversion of the Cc average structure to $R3c$ in unpoled NBT-BT at $x\sim 0.03$ (more precisely in the range $0.03\le x\le 0.05$) is catalyzed by the appearance of $P4bm$ phase. The overlap of $T_d$ and $T_2$ for this composition range is correlated with the collapse of the tetragonality of the $P4bm$ phase and significantly reduced kinetic barrier associated with the $R3c\to P4bm$ transformation. We show that the abrupt crossover between $T_d$ and $T_2$ at $x=0.06$ is due to takeover of the thermal depoling process by an emergent tetragonal $\left(P4mm\right)$-like ferroelectric distortion. We present updated phase diagrams of poled and unpoled specimens which highlight all the subtle details needed to explain the temperature-dependent properties of this complex piezoelectric alloy system.

${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ is the first material in which antiskyrmions have been observed in ultrathin single-crystalline specimens. While bulk crystals exhibit fractal patterns of purely ferromagnetic domain ordering at room temperature, ultrathin ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ lamellae clearly show antiskyrmion lattices with lattice spacings up to several $\mu \mathrm{m}$. In the paper presented here, we systematically investigate the thickness region from 400 nm to 10 $\mu \mathrm{m}$ using $100\times 100\mu {\mathrm{m}}^2$ wide ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ plates, and identify the critical thickness-to-width aspect ratio ${\alpha }_0=0.044$ for the ferromagnetic fractal domain to the noncollinear texture phase transition. Additionally, we also explore these noncollinear magnetic textures below the critical aspect ratio ${\alpha }_0$ above and below the spin-reorientation transition temperature $T_{\mathrm{SR}}$ while applying variable external magnetic fields. What we find is a strong hysteresis for the occurrence of an antiskyrmion lattice, since the antiskyrmions preferentially nucleate by pinching them off from helical stripes in the transition to the field polarized state.

We investigate phase transitions of a geometrically frustrated polar magnet ${\mathrm{CaBaCo}}_4{\mathrm{O}}_7$, which exhibits the largest magnetoelectric (ME) effect in multiferroic compounds reported so far. Measurements of magnetization, sound velocity, and neutron diffraction of single crystals reveal an antiferromagnetic phase between the ferrimagnetic transition temperature $T_{\mathrm{C}}\sim 60$ $\mathrm{K}$ and $T^{*}\sim 69$ $\mathrm{K}$. In the antiferromagnetic phase, the ordered Co moments on the triangular layers remain nearly disordered. We demonstrate that a large electric-polarization change emerges upon the antiferromagnetic-to-ferrimagnetic transition. The large ME coupling can be attributed to the exchange striction.

Single-crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice ${\mathrm{Tb}}_2{\mathrm{Ir}}_3{\mathrm{Ga}}_9$. While the $Rln2$ magnetic contribution to the low-temperature entropy indicates a $J_{\mathrm{eff}}=1/2$ moment for the lowest-energy crystal-field doublet, the ${\mathrm{Tb}}^{3+}$ ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyaloshinskii-Moriya interactions, the Tb moments in the $ab$ plane are slightly canted towards $\mathbf{b}$ with a canted moment of 1.22 ${\mu }_{\mathrm{B}}$ per formula unit. A minimal $xxz$ spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high-symmetry directions and the field dependence of the magnetization along the three crystallographic axes. Long-range magnetic interactions for both in-plane and out-of-plane couplings up to the second nearest neighbors are needed to account for the observed static and dynamic properties. The $z$ component of the exchange interactions between Tb moments is larger than the $x$ and $y$ components. This compound also exhibits bond-dependent exchange with negligible nearest-neighbor exchange coupling between moments parallel and perpendicular to the $4f$ orbitals. Despite the $J_{\mathrm{eff}}=1/2$ moments, the spin Hamiltonian is denominated by a large in-plane anisotropy $K_z\sim -1\mathrm{meV}$. DFT calculations confirm the antiferromagnetic ground state and the substantial interplane coupling at larger Tb-Tb distances.

We investigate the emergence of ferromagnetism in the two-dimensional metal halide $\mathrm{Co}{\mathrm{Br}}_2$, with a special focus on the role of electronic correlations. The calculated phonon spectrum shows that the system is thermodynamically stable, unlike other Co halides. We apply two well-known methods for the estimation of the Curie temperature. First, we do density-functional theory $+U$ calculations to calculate exchange couplings, which are subsequently used in a classical Monte Carlo simulation of the resulting Ising spin model. The transition temperature calculated in this way is of the order of 100 K but shows a strong dependence on the choice of interaction parameters. Second, we apply dynamical mean-field theory to calculate the correlated electronic structure and estimate the transition temperature. This results in a similar estimate for a noticeable transition temperature of approximately 100 K, but without the strong dependence on the interaction parameters. The effect of electron-electron interactions are strongly orbital selective, with only moderate correlations in the three low-lying orbitals (one doublet plus one singlet) and strong correlations in the doublet at higher energy. This can be traced back to the electronic occupation in DMFT, with five electrons in the three low-lying orbitals and two electrons in the high-energy doublet, making the latter one half filled. Nevertheless, the overall spectral gap is governed by the small gap originating from the low-lying doublet+singlet orbitals, which changes very weakly with interaction $U$. In that sense, the system is close to a Mott metal-to-insulator transition, which was shown previously to be a hot spot for strong magnetism.

We write down and analyze a model demonstrating the co-existence of conventional symmetry-breaking order and symmetry-protected topological (SPT) order in the one-dimensional chain. When appropriately generalized to a model on a graph, the SPT and symmetry-breaking orders exist for each individual loop, or cycle, of the graph. It arises as a consequence of the kind of “global” symmetry operator responsible for SPT and the local-order parameter defining the Ginzburg-Landau order, both of which exist in our model and commute with the Hamiltonian. The anti-commuting character of these two-order parameters is responsible for the ground state degeneracy (GSD). As such operators and their anti-commuting relations can be defined for each independent loop, the GSD grows exponentially with the first Betti number for a graph.

Nodal line semimetals have lately aroused much experimental and theoretical interest, with their gap closing along unconventional trajectories in the three-dimensional Brillouin zone. These trajectories or nodal lines can close into loops and trace out intricate knotted or linked configurations with complicated topologies. In this paper, we investigate the semiclassical optical response of two nodal loops in linked, unlinked, and touching configurations, focusing particularly on the interplay of response anisotropy and nonlinearity. We provide a geometric picture that unifies these aspects and sheds light on the effects of nodal topology and geometry. Based on a model abstracted from generic multi-nodal-loop scenarios, both with or without linkages, our findings will be applicable for a large class of nodal semimetal materials with multiple nodal lines or loops.

Hydrostatic pressure response of $\mathrm{LaAu}{\mathrm{Sb}}_2$ charge density wave (CDW) system is investigated using electrical transport, x-ray diffraction (XRD), and density-functional theory (DFT). Resistivity data at ambient pressure evidence a clear CDW transition at 83 K. X-ray diffraction at ambient pressure reveals that in plane and out of plane axes show opposite behavior with decreasing temperature, in particular, out of plane $c$ axis develops a distinct change at ∼250 K, much above the observed CDW transition at 83 K. The CDW transition shifts to low temperature with increasing pressure. Our resistivity data indicate a complete suppression of the CDW transition at ∼3.6 GPa. High-pressure XRD revealed a change from the linear trend for the out of plane ($c$) and the in plane ($a$) lattice parameters for pressure above 3.8 GPa. With compression, DFT indicated an anomaly in the c/a ratio around 8 GPa. The calculated electronic structure also indicated minor changes in the band structure in this pressure range. In addition, high-pressure DFT structural investigations reveal the $\mathrm{LaAu}{\mathrm{Sb}}_2$ system to be stable up to pressures as high as 150 GPa.

Electron-electron interactions are intrinsically long ranged, but many models of strongly interacting electrons only take short-ranged interactions into account. Here, we present results of atomistic calculations including both long-ranged and short-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene and demonstrate that qualitatively different results are obtained when long-ranged interactions are neglected. In particular, we use Hartree theory augmented with Hubbard interactions and calculate the interacting spin susceptibility at a range of doping levels and twist angles near the first magic angle to identify the dominant magnetic instabilities. At the magic angle, mostly antiferromagnetic order is found, while ferromagnetism dominates at other twist angles. Moreover, long-ranged interactions significantly increase the twist angle window in which strong correlation phenomena can be expected. These findings are in good agreement with available experimental data.

The non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems depicts the exponential localization of eigenstates at the system's boundaries. It has led to a number of counterintuitive phenomena and challenged our understanding of bulk-boundary correspondence in topological systems. This work aims to investigate how the NHSE localization and topological localization of in-gap edge states compete with each other, with several representative static and periodically driven 1D models, whose topological properties are protected by different symmetries. The emerging insight is that at critical system parameters, even topologically protected edge states can be perfectly delocalized. In particular, it is discovered that this intriguing delocalization occurs if the real spectrum of the system's edge states falls on the same system's complex spectral loop obtained under the periodic boundary condition. We have also performed sample numerical simulation to show that such delocalized topological edge states can be safely reconstructed from time-evolving states. One particular application of delocalized topological edge states in assisting adiabatic edge state pumping is also computationally demonstrated.

Band structures are intrinsically influenced by the mode interaction in waveguide array, which can support many intriguing phenomena such as negative refraction, on-chip lensing, and quantum-analog dynamics like Bloch oscillation and topological interface transportation. Multiple branches of band may emerge due to the comprehensive mode interactions associated with high-order photonic modes supported in high refractive index dielectric waveguide. Furthermore, the number of photonic modes confined in a high-index waveguide is determined by both the width and working frequency. Hence, the mode interaction and resultant band structure can be effectively tuned by the frequency. As such, a diversity of equifrequency contours could be generated and modulated among a wide frequency range, which, however, remains largely unexplored. Here, we present several frequency-determined beam dynamics in a composite ternary plasmonic-dielectric waveguide array, including collimation effect, angle-dependent beam branching/multibranching, conicallike beam diffraction. Based on the evolution of the band structure, photonic Zitterbewegung effect and Klein tunneling can also be observed. In contrast to the coherent coupling between symmetric and antisymmetric modes that gives rise to the photonic Zitterbewegung effect, we show that three-mode coherent coupling in the ternary system can yield a superimposed extreme oscillation of the beam. This represents an extension of the general Zitterbewegung effect in photonic system. Additionally, the Klein tunneling sandwiched in two types of artificial waveguide arrays with different Dirac points is demonstrated, and approximately unimpeded penetration is exhibited. The configurations discussed here can be readily implemented in on-chip systems for a variety of potential applications including wave routing, selectively directional coupling, and multiplexing.

$2M-{\mathrm{WS}}_2$ is a newly discovered superconductor with a rather high critical transition temperature $(T_c=8.8\mathrm{K})$ and topological surface states. Recently Majorana bound states were observed in magnetic vortices of this material. Thus uncovering the flux dynamics of the magnetic vortices is essential to further promote the physical understanding and its practical application in topological quantum computation. Here we report an in-depth investigation on this issue by the temperature- and field-dependent electric transport measurements. The magnitudes of activation energy under both field orientations are rather low, revealing a weak pinning strength of the flux in the present system. Moreover, clear anisotropic thermally activated flux-flow behaviors are revealed. Under the in-plane field ($H\parallel bc$), the activation energy $U$ shows a $(1-T/T_c)H^{-\alpha }$ dependence indicating the three-dimensional feature, while under the out-of-plane field $(H\perp bc)$, $U$ is proportional to $(1-T/T_c)lnH$, which suggests a two-dimensional liquid state for the vortices.

Magnets with frustration often show accidental degeneracies, characterized by a large classical ground-state space (CGSS). Quantum fluctuations may “select” one of these ground states—a phenomenon labeled “order by (quantum) disorder” in literature. In this article, we examine the mechanism(s) by which such state selection takes place. We argue that a magnet, at low energies, maps to a particle moving on the CGSS. State selection corresponds to localization of the particle at a certain point on this space. We distinguish two mechanisms that can bring about localization. In the first, quantum fluctuations generate a potential on the CGSS space. If the potential has a deep enough minimum, then the particle localizes in its vicinity. We denote this as “order by potential” (ObP). In the second scenario, the particle localizes at a self-intersection point due to bound-state formation—a consequence of geometry and quantum interference. Following recent studies by the present authors, we denote this scenario as “order by singularity” (ObS). In either case, localization leads to an energy gap between the ground state(s) and higher-energy states. This pseudo-Goldstone gap behaves differently in the two mechanisms, scaling differently with the spin length. We place our discussion within the context of the one-dimensional spin-$S$ Kitaev model. We map out its CGSS which grows systematically with increasing system size. It resembles a network where the number of nodes increases exponentially. In addition, the number of wires that cross at each node also grows exponentially. This self-intersecting structure leads to ObS, with the low-energy physics determined by a small subset of the CGSS, consisting of “Cartesian” states. A contrasting picture emerges when an additional XY antiferromagnetic coupling is introduced. The CGSS simplifies dramatically, taking the form of a circle. Spin wave fluctuations generate a potential on this space, giving rise to state selection by ObP under certain conditions. Apart from contrasting ObS and ObP, we discuss the possibility of ObS in macroscopic magnets.

We present out-of-plane dielectric and magnetodielectric measurements of single-crystalline $\alpha \text{−}{\mathrm{RuCl}}_3$ with various degrees of stacking faults. A frequency-dependent, but field-independent, dielectric anomaly appears at $T_A(f=100\mathrm{kHz})\sim 4$ K once both magnetic transitions at $T_{N1}\sim 7$ K and $T_{N2}\sim 14$ K set in. The observed dielectric anomaly is attributed to the emergence of possible local electric polarizations whose inversion symmetry is broken by inhomogeneously distributed stacking faults. A field-induced intermediate phase is only observed when a magnetic field is applied perpendicular to the Ru-Ru bonds for samples with minimal stacking faults. Less pronounced in-plane anisotropy is found in samples with a sizable contribution from stacking imperfections. Our findings suggest that dielectric measurement is a sensitive probe in detecting the structural and magnetic properties, which may be a promising tool, especially in studying $\alpha \text{−}{\mathrm{RuCl}}_3$ thin-film devices. Moreover, the stacking details of ${\mathrm{RuCl}}_3$ layers strongly affect the ground state both in the magnetic and electric channels. Such a fragile ground state against stacking faults needs to be overcome for realistic applications utilizing the magnetic and/or electric properties of Kitaev-based physics in $\alpha \text{−}{\mathrm{RuCl}}_3$.

$\left({\mathrm{K}}_x{\mathrm{Na}}_{1-x}\right){\mathrm{NbO}}_3$ (KNN) and its solid solutions are considered as potential alternatives to traditional Pb-based piezoelectric materials. Recent investigations indicated that the local structure in KNN is much more complex than its long-range average structure. Here, we have undertaken a systematic investigation of the temperature-dependent evolution of local and average structures of KNN5 $[\left({\mathrm{K}}_x{\mathrm{Na}}_{1-x}\right){\mathrm{NbO}}_3,x=0.5]$ using time of flight neutron scattering. Rietveld analysis of neutron diffraction patterns indicated that the average structure of KNN5 changes from monoclinic to tetragonal to cubic upon heating from 100 to 773 K. In contrast, analysis of neutron pair distribution function (PDF) indicated that the local structure stays monoclinic within the above temperature range. Based on comparative analysis of local and average structures, it is proposed that the average structural phase transitions in KNN5 are partly derived from a local ordering of the polar units, which are correlated over a length of 10 ∼ 15 Å. A clear indication of order-disorder type transition at 473 K is evident from the temperature-dependent PDF patterns. Additionally, based on local structural analysis, it is shown that large electrical polarization in KNN5 can be attributed to displacements of both A-site and B-site atoms. These structural insights may help in further optimization of electrical properties of Pb-free KNN piezoceramics.