$1T\text{−}{\mathrm{TaSe}}_2$ is a prototypical charge density wave (CDW) material for which electron-phonon coupling and associated lattice distortion play an important role in driving and stabilizing the CDW phase. Here, we investigate the lattice dynamics of bulk $1T\text{−}{\mathrm{TaSe}}_2$ using angle-resolved ultralow wavenumber Raman spectroscopy down to 10 ${\mathrm{cm}}^{-1}$. Our high-resolution spectra allow us to identify at least 27 Raman-active modes in the commensurate (CCDW) phase. Contrary to other layered materials, we do not find evidence of interlayer breathing or shear modes, suggestive of $AA$ stacking in the bulk, or sufficiently weak interlayer coupling. Polarization dependence of the mode intensities allows assignment of their symmetry, which is supported by first-principles calculations of the phonons for the bulk structure using density functional theory. A detailed temperature dependence in the range $T=80$–500 K allows us to identify soft modes associated with the CDW superlattice. Upon entering the incommensurate (ICCDW) phase above 473 K, we observe a dramatic loss of resolution of all modes, and significant linewidth broadening associated with a reduced phonon lifetime as the charge-order becomes incommensurate with the lattice.

We predict the presence of minority magnons in monolayer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ using first-principles calculations. Minority magnons constitute a new type of collective magnetic excitation which increase the magnetic moment—contrary to ordinary (majority) magnons which lower it—giving rise to spin-raising poles in the dynamic susceptibility ${\chi }^{-+}\left(\omega \right)$. The presence of such quasiparticles is made possible by the nontrivial ferromagnetic band structure of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. We calculate the susceptibility using time-dependent density functional theory and perform a detailed mode analysis, which allows us to identify and investigate individual magnon modes as well as the Stoner excitations that constitute the many-body spectrum. The analysis reveals a plethora of both majority and minority excitations, which in addition to the main magnon branches include satellite, valley, and spin-inversion magnons thanks to the electron itinerancy of the system. Crucially, the analysis allows us to separate peaks of a coherent collective nature from those of mixed magnon/Stoner nature. To this end, we predict that the lowest energy minority magnon mode of monolayer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ indeed constitutes a coherent collective quasiparticle at long wavelengths and introduce a simplistic Gaussian model for the observed minority magnon enhancement. The underlying physics is in no way restricted to ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, and minority magnons are thus expected to be observable in other complex ferromagnetic materials as well.

The well-established delocalization-localization (DL) transition in Hermitian Aubry-André-Harper (AAH) lattices with incommensurate on-site potentials provides a compelling illustration of the subtle localized behavior of eigenstates. Our study extends the Anderson localization (AL) threshold to the non-Hermitian scenario by focusing on an AAH lattice that incorporates both dissipative couplings and loss modulations, demonstrating that the DL transition behaviors observed in Hermitian quasicrystals represent merely special cases of this broader phenomenon. We rigorously confirm the validity of the generalized AL threshold by observing the remarkable consistency between the numerical mean inverse participation ratio and the analytical Lyapunov exponent. Meanwhile, we investigate the impact of dissipative couplings and system size on the DL transition. Moreover, we propose a novel scheme for constructing dissipatively coupled AAH lattices, which involves cavity fields weakly coupled to engineered resonators. Our work significantly advances the understanding of AL by extending its threshold from Hermitian to non-Hermitian systems, demonstrating their compatibility and the promising possibilities for exploring criticality in non-Hermitian quasiperiodic lattices.

We investigate the fragility of quantum information in a topologically ordered state, namely, the ground state of a weakly Zeeman perturbed honeycomb Kitaev model under unitary (Hamiltonian) evolution interrupted by random local projective measurements of the spins, using the tripartite mutual information $\gamma$—equivalent to the topological entanglement entropy for topologically ordered states—as a measure. Our findings show that in the steady state, $\gamma$ remains significant up to high measurement rates per site $r$ comparable to the Kitaev coupling scale when the initial state has Ising topological order (ITO), beyond which it degrades with increasing $r.$ We contrast this with the Abelian $Z_2$ topologically ordered ground state in the toric code regime of the Kitaev model with the same energy per site, which has garnered greater attention in the literature of fault-tolerant quantum computation. We observe that $\gamma$ in the toric code regime of the Kitaev model collapses rapidly beyond very small values of $r.$ Further, we also find that at high measurement rates, while topological order is lost, certain observables leave distinct signatures of the initial quantum state, thus providing a diagnostic of the topological order.

We investigate the bulk-boundary correspondence for massless Dirac fermions in $\alpha \text{−}{T}_3$ lattice where the Berry phase can be continuously tuned from $\pi$ (graphene) to 0 ($T_3$ or dice lattice) without modifying the energy dispersion. The topological origin of edge states is revealed by the unitary transformation of the Hamiltonian, which maps an $\alpha \text{−}{T}_3$ zigzag ribbon (ZR) onto a stub Su-Schrieffer-Heeger (SSH) chain. In the Majorana representation of the eigenstates, the topological invariant is manifested by the azimuthal winding number on the Bloch sphere. Particularly, $T_3$ ZR exemplifies a topologically nontrivial system with zero Berry phase. Contrary to conventional topological insulators, the gap closing in the corresponding stub SSH chain is not accompanied by a topological phase transition.

We investigate theoretically magnetoentropic signatures of the crystal phase of magnetic skyrmions of various kinds, commonly appearing in two dimensions, viz., Néel, Bloch, and antiskyrmions. Using Monte Carlo calculations based on spin Hamiltonians, we obtain magnetic entropy change $\mathrm{\Delta }{S}_m$ in the presence of three different types of Dzyaloshinskii-Moriya interactions responsible for these skyrmions. The phase mapping of $\mathrm{\Delta }{S}_m$ using skyrmion counting number $N_{sk}$ in temperature-magnetic field plane reveals fluctuation-dominated weak first-order transition in the precursor phase of the skyrmions, and a sign change in $\mathrm{\Delta }{S}_m$ when the system enters into the skyrmion crystal phase—in agreement with recent experimental findings. We also find that the fractional entropy change in going from a ferromagnetic phase to the skyrmion crystal phase is much larger compared to the conventional route of a paramagnetic phase to a ferromagnetic phase, used for the purpose of magnetic cooling. The magnetoentropic signatures of the different types of skyrmion crystals are found to be similar. Our results indicate that the skyrmion crystals exhibit enhanced cooling efficiency and have the potential to upgrade the existing magnetic cooling methods.

We report the magnetic and electrical transport properties of the single crystals of ${\mathrm{Pr}}_3{\mathrm{HfBi}}_5, {\mathrm{Nd}}_3{\mathrm{HfBi}}_5$, and ${\mathrm{Sm}}_3{\mathrm{HfBi}}_5$, three Hf-based bismuth compounds in the quasi-one-dimensional ${\mathrm{Ln}}_3{M\mathrm{Pn}}_5$ ($\mathit{Ln}$ = lanthanide; $M=\mathrm{Mg}$, transition metal; $\mathit{Pn}$ = pnictide) family. All the three materials exhibit antiferromagnetic transition and strong magnetic anisotropy. The metamagnetic transitions, identified as 1/3 and 1/6 fractional magnetization phases, have been revealed in the distorted kagome lattice plane of ${\mathrm{Pr}}_3{\mathrm{HfBi}}_5$ and ${\mathrm{Nd}}_3{\mathrm{HfBi}}_5$. Accompanied by the emergence of fractional magnetization phases, the transverse magnetoresistance (MR) of ${\mathrm{Pr}}_3{\mathrm{HfBi}}_5$ and ${\mathrm{Nd}}_3{\mathrm{HfBi}}_5$ decreases sharply, leading to the formation of large negative MR. However, the metamagnetic transition and negative MR are absent in ${\mathrm{Sm}}_3{\mathrm{HfBi}}_5$. In addition, the magnetic phase diagrams of ${\mathrm{Pr}}_3{\mathrm{HfBi}}_5, {\mathrm{Nd}}_3{\mathrm{HfBi}}_5$, and ${\mathrm{Sm}}_3{\mathrm{HfBi}}_5$ have been constructed. Our study not only provides detailed transport properties of these three materials, but also indicates the potential of the Hf-based ${\mathrm{Ln}}_3{M\mathrm{Pn}}_5$ materials in exploring magnetic frustration related interesting physical phenomena.

The investigation of magnetic textures with noncoplanar ordering in bulk chiral magnets and thin-film heterostructures is a focal point in condensed matter physics due to the rich physical phenomena associated with topologically nontrivial states and low-energy excitations. Challenges arise in visually capturing the anisotropy of these textures, including the well-studied skyrmions. A prudent approach involves the examination of magnetotransport through the study of topological Hall effect. However, in this paper, we utilized a less-explored planar Hall measurement configuration to examine the spin-canted state of a Heisenberg ferromagnetic insulator europium sulfide (EuS) in ${\mathrm{Bi}}_2{(\mathrm{Se},\mathrm{Te})}_3/\mathrm{EuS}$ bilayer devices. Our observation of planar Hall anisotropy, substantiated by theoretical investigations, thus far provides evidence for the existence of an unconventional magnetic phase in interfacial EuS, such as the elongated skyrmions, opening up promising avenues in the development of next-generation topological spintronic devices.

The Hall coefficient $R_{\mathrm{H}}$ as a function of temperature for ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ (PCCO) at $x=0.17$ shows two sign changes between 0 and $300\mathrm{K}$ that can be explained qualitatively using the two-carrier model. Using this two-carrier model, one predicts the presence of a nonlinear $B^3$ contribution to the Hall resistivity ${\rho }_{yx}$ that should be easily observed when the linear coefficient $R_{\mathrm{H}}$ is approaching zero. We present the measurement of this nonlinear Hall resistivity for overdoped PCCO thin films at $x=0.18$. We show that this weak nonlinear term persists at all temperatures despite being dominated by the linear term ($R_{\mathrm{H}}B$). It is strongly temperature dependent and, analyzing it with the two-carrier model, we conclude that the density of electron carriers is larger than the hole density, but that the hole mobility is larger than that of the electrons. This nonlinear Hall resistivity should be observable for similar materials for which $R_{\mathrm{H}}\left(T\right)$ goes through sign reversals as does overdoped PCCO.

The recent discovery of high-$T_c$ superconductivity near 80 K in the bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has attracted widespread attention. The prerequisite to understanding the unconventional superconductivity in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ is the determination of the electronic properties, such as the band structure and possible correlation effect. Here, we report a set of data on single-particle tunneling measurements on ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ single crystals at ambient pressure. A gaplike feature was observed in the tunneling spectra at low energies around the Fermi energy. The spectrum looks roughly symmetric with gap edges at about $+98$ and $-92$ meV. We attribute this gaplike feature to two alternative origins: either reflecting the bonding and antibonding bands derived from the Ni-$3d_{z^2}$ orbital, or a mixed contribution from a density wave gap and these two bands. Meanwhile, a finite density of states remains even in the gapped region, which is thought to be the vestige contribution of the $\mathrm{Ni}\text{−}3d_{x^2-y^2}$ orbital. Furthermore, it is found that the density of states is suppressed in a wide energy range with a sharp rise at about $\pm 1.4$ eV, indicating a general correlation effect. Theoretical calculations give partial consistency with the experimental observations. Our results provide important information to understand the electronic states of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ at ambient pressure.

We develop a microscopic theory of ac Josephson effect in superconducting junctions described by an arbitrary scattering matrix that may include magnetic effects. In the limit of constant in time bias voltage $V$ applied to the junction we derive a formally exact current-phase relation (CPR) that is manifestly $2\pi$ periodic in the Josephson phase $\phi$ in full accordance with general principles. Our result unambiguously argues against the idea of the so-called “fractional ac Josephson effect” admitting $4\pi$ periodic in $\phi$ CPR. We also demonstrate that at any nonzero $V$ quantum dynamics of Andreev bound states becomes non-Hermitian, which signals their instability, thus making any “quasi-equilibrium” description of ac Josephson effect unreliable. We specifically address the limit of highly transparent junctions with magnetic scattering where—along with super- and excess current terms—at small $V$ we also recover a nontrivial $2\pi$-periodic dissipative current with the amplitude ${\propto \left|V\right|}^{1/3}$.

Monolayer molybdenum disulfide $\left({\mathrm{MoS}}_2\right)$ under strain has many interesting properties and possible applications in technology. A recent experimental study examined the effect of strain on the band gap of monolayer ${\mathrm{MoS}}_2$ on a mildly curved graphite surface, reporting that under biaxial strain with a Poisson's ratio of 0.44, the band gap decreases at a rate of 400 meV/% strain. In this paper, we performed density functional theory calculations for a free-standing ${\mathrm{MoS}}_2$ monolayer, using the generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE), the Heyd-Scuseria-Ernzerhof screened hybrid functional HSE06, and many-body perturbation theory with the $GW$ approximation using PBE wave functions $(G_0{W}_0@\mathrm{PBE})$. For the unstrained monolayer, we found a standard level of agreement for the band gap between theory and experiment. For biaxial strain at the experimental Poisson's ratio, we found that the band gap decreases at rates of 63 meV/% strain (PBE), 73 meV/% strain (HSE06), and 43 meV/% strain $(G_0{W}_0@\mathrm{PBE})$, which are significantly smaller than the experimental rate. We also found that PBE predicts a similarly smaller rate (90 meV/% strain) for a different Poisson's ratio of 0.25. Spin-orbit correction has little effect on the gap or its strain dependence. The strong disagreement between theory and experiment may reflect an unexpectedly strong effect of the substrate on the strain dependence of the gap. Additionally, we observed a transition from a direct to an indirect band gap under strain, and (under an equal biaxial strain of 10%) a semiconductor-to-metal transition, consistent with previous theoretical work.

We study nonequilibrium quantum dynamics of spin chains by employing principal component analysis on data sets of wave function snapshots and examine how information propagates within these data sets. The quantities we employ are derived from the spectrum of the sample second moment matrix, built directly from data sets. Our investigations on several interacting spin chains featuring distinct spin or energy transport reveal that the growth of data information spreading follows the same dynamical exponents as that of the underlying quantum transport of spin or energy. Specifically, our approach enables an easy, data-driven, and, importantly, interpretable diagnostic to track energy transport with a limited number of samples, which is usually challenging without any assumption on the Hamiltonian form. These observations are obtained at a modest finite-size and evolution time, which aligns with experimental and numerical constraints. Our framework directly applies to experimental quantum simulator data sets of dynamics in higher-dimensional systems, where classical simulation methods usually face significant limitations and apply equally to both near- and far-from-equilibrium quenches.

We have investigated the magnetic properties and mapped out the phase diagram of the honeycomb magnet ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ with Co $3d^7$ in out-of-plane magnetic fields. This material has previously been proposed to show nearest-neighbor Kitaev interactions between Co spins and maybe even Kitaev quantum spin liquid behavior in high fields. At 0.01 T, we observe a thermal phase transition at $T_{\text{N}}=27\mathrm{K}$, transitioning from a paramagnetic state to a canonical ferrimagnetic state. Upon increasing the magnetic field, a spin-floplike phase transition occurred before saturation of $\mathit{J}=1/2$ between 10 K and $T_{\text{N}}$. Below 10 K, a peak-dip-peak structure emerges between 10 and 17 T in the magnetic susceptibility ($dM/dH$) before the magnetic saturation, reminiscent of magnetization plateau behavior. The measurement of the magnetocaloric effect also shows dip-peak-dip behavior in this field range. Our data can be explained by an XXZ model with a single ion anisotropy and possibly small Kitaev and $\mathrm{\Gamma }$ exchange interactions. We also determined the magnetization saturation field that helps constrain the energy scale of the exchange interactions.

We report the transport, thermodynamic, and magnetic properties of stoichiometric single-crystalline ${\mathrm{Ce}}_5{\mathrm{CoGe}}_2$ by measuring the electrical resistivity, specific heat, DC magnetization, and AC susceptibility. ${\mathrm{Ce}}_5{\mathrm{CoGe}}_2$ crystallizes in an orthorhombic structure with space group $Pnma$, and undergoes a long-range ferromagnetic (FM) transition at $T_{\mathrm{C}}=10.9$ K, showing a strong magnetic anisotropy at low temperature with an easy $a$ axis. Furthermore, the AC susceptibility exhibits a single cusp with a clear frequency dependence. Detailed analysis suggests that a cluster-type spin glass (SG) state appears below the freezing temperature $T_{\mathrm{f}}=10.9\left(1\right)$ K in ${\mathrm{Ce}}_5{\mathrm{CoGe}}_2$, which is identical to $T_{\mathrm{C}}$ within error bar. These findings suggest the coexistence of FM order and frustrated glassy magnetic components below $T_{\mathrm{C}}$ in ${\mathrm{Ce}}_5{\mathrm{CoGe}}_2$.

Co-Fe Prussian blue analog (PBA) complex possesses various spin configurations and discrete energy levels with different types of spin localizations, making it suitable for the exploration of spin manipulation and logic functionality towards the molecular spintronics applications. In this paper, we perform an ab initio investigation on the electronic structure, spin localization, ultrafast optical-driven spin dynamics, and the possible spin logic functionality of this structure. The results show that within the calculated energy window of the many-body electronic states, spin-crossover and spin-transfer scenarios, driven by specific well-tailored laser, can be both achieved reversibly in subpicoseconds with high fidelities. Among them, a multifunctional dynamical process that simultaneously includes spin transfer, spin-crossover, and charge transfer is found. In addition, the potential of applying the same laser to drive different kinds of spin dynamics is indicated. Towards the device applications, the Pauli and Hadamard quantum logic gates and the half-adder functionality are further elaborately constructed based on the achieved spin scenarios. Our results suggest the present structure is quite promising in novel high-performance single-molecular devices and advanced spin logic processing from the viewpoints of both scientific research and technological applications, and thus propel the development of future molecular spintronic devices and quantum information technology.

The interplay of magnetic correlations, crystal electric field interactions, and spin-orbit coupling in low-dimensional frustrated magnets fosters novel ground states with unusual excitations. Here, we report the magnetic properties and crystal electric field (CEF) scheme of a rare-earth-based square-lattice antiferromagnet ${\mathrm{NdKNaNbO}}_5$ investigated via magnetization, specific heat, electron spin resonance (ESR), and inelastic neutron scattering (INS) experiments. The low-temperature Curie-Weiss temperature ${\theta }_{\mathrm{CW}}\simeq -0.6$ K implies net antiferromagnetic interactions between the ${\mathrm{Nd}}^{3+}$ ions. Two broad maxima are observed in the low-temperature specific heat data in magnetic fields, indicating multilevel Schottky anomalies because of the effect of CEF. No magnetic long-range order is detected down to 0.4 K. The CEF excitations of Kramers' ion ${\mathrm{Nd}}^{3+}$ ($J=9/2$) probed via INS experiments evince dispersionless excitations characterizing the transitions among the CEF energy levels. The fit of the INS spectra enabled the mapping of the CEF Hamiltonian and the energy eigenvalues of the Kramers' doublets. The simulation using the obtained CEF parameters reproduces the broad maxima in specific heat in zero field as well as in different applied fields. The significant contribution from $J_z=\pm 1/2$ state to the wave function of the ground-state doublet indicates the role of strong quantum fluctuations at low temperatures. The magnetic ground state is found to be a Kramers' doublet with effective spin $J_{\mathrm{eff}}=1/2$ at low temperatures.

We report magnetic susceptibility, high-field magnetization, muon spin relaxation, and electron spin resonance measurements of the breathing pyrochlore antiferromagnets ${\mathrm{LiGa}}_{1-x}{\mathrm{In}}_x{\mathrm{Cr}}_4{\mathrm{O}}_8$ ($x=0.2$, 0.5). Unlike the previously proposed spin-glass-like phase for $0.1<x<0.75$, we find no signature for spin glassiness and phase segregation in both the $x=0.2$ and 0.5 compounds. Instead, we identify a two-step magnetic transition with a partial spin freezing at $T^{*}=12\mathrm{K}$ ($x=0.2$) and 9 K ($x=0.5$) followed by quasistatic order at $T_{\text{m}}=6\mathrm{K}$ ($x=0.2$) and 3 K for ($x=0.5$). In addition, for $T_{\text{m}}<T<T^{*}$, we observe evidence of a competition between fast and slow spin dynamics, suggesting a thermal and temporal distribution of spin correlations. Our findings underscore the possibility of realizing novel magnetic phases by tuning bond alternation and introducing bond disorder through chemical substitution.