We revisit the numerical problem of computing the high temperature spin stiffness, or Drude weight, $D$ of the spin-$1/2$ $XXZ$ chain using exact diagonalization to systematically analyze its dependence on system symmetries and ensemble. Within the canonical ensemble and for states with zero total magnetization, we find $D$ vanishes exactly due to spin-inversion symmetry for all but the anisotropies ${\tilde{\mathrm{\Delta }}}_{MN}=cos(\pi M/N)$ with $N,M\in {\mathbb{Z}}^{+}$ coprimes and $N>M$, provided system sizes $L\ge 2N$, for which states with different spin-inversion signature become degenerate due to the underlying $s{l}_2$ loop algebra symmetry. All these loop-algebra degenerate states carry finite currents which we conjecture [based on data from the system sizes and anisotropies ${\tilde{\mathrm{\Delta }}}_{MN}$ (with $N<L/2$) available to us] to dominate the grand-canonical ensemble evaluation of $D$ in the thermodynamic limit. Including a magnetic flux not only breaks spin-inversion in the zero magnetization sector but also lifts the loop-algebra degeneracies in all symmetry sectors—this effect is more pertinent at smaller $\mathrm{\Delta }$ due to the larger contributions to $D$ coming from the low-magnetization sectors which are more sensitive to the system's symmetries. Thus we generically find a finite $D$ for fluxed rings and arbitrary $0<\mathrm{\Delta }<1$ in both ensembles. In contrast, at the isotropic point and in the gapped phase ($\mathrm{\Delta }\ge 1$) $D$ is found to vanish in the thermodynamic limit, independent of symmetry or ensemble. Our analysis demonstrates how convergence to the thermodynamic limit within the gapless phase ($\mathrm{\Delta }<1$) may be accelerated and the finite-size anomalies overcome: $D$ extrapolates nicely in the thermodynamic limit to either the recently computed lower bound or the thermodynamic Bethe ansatz result provided both spin inversion is broken and the additional degeneracies at the ${\tilde{\mathrm{\Delta }}}_{MN}$ anisotropies are lifted.

We present a reentrant phase transition in a bridging model between two different topological models: Kitaev and Haldane chains. This model is activated by introducing a bond alternation into the Kitaev chain [A. Y. Kitaev, Phys. Usp. 44, 131 (2001)]. Without the bond alternation, the finite pairing potential induces a topological state defined by the zero-energy Majorana edge mode, while finite bond alternation without the pairing potential makes a different topological state similar to the Haldane state, which is defined by the local Berry phase in the bulk. The topologically ordered state corresponds to the Su-Schrieffer-Heeger state, which is classified as the same symmetry class. We thus find a phase transition between the two topological phases with a reentrant phenomenon, and extend the phase diagram in the plane of the pairing potential and the bond alternation by using three techniques: recursive equation, fidelity, and Pfaffian. In addition, we find that the phase transition is characterized by both the change of the position of Majorana zero-energy modes from one edge to the other edge and the emergence of a string order in the bulk, and that the reentrance is based on a sublattice U(1) rotation. Consequently, our paper and model not only open a direct way to discuss the bulk and edge topologies but demonstrate an example of the reentrant topologies.

Random fields disorder Ising ferromagnets by aligning single spins in the direction of the random field in three space dimensions, or by flipping large ferromagnetic domains at dimensions two and below. While the former requires random fields of typical magnitude similar to the interaction strength, the latter Imry-Ma mechanism only requires infinitesimal random fields. Recently, it has been shown that for dilute anisotropic dipolar systems a third mechanism exists, where the ferromagnetic phase is disordered by finite-size glassy domains at a random field of finite magnitude that is considerably smaller than the typical interaction strength. Using large-scale Monte Carlo simulations and zero-temperature numerical approaches, we show that this mechanism applies to disordered ferromagnets with competing short-range ferromagnetic and antiferromagnetic interactions, suggesting its generality in ferromagnetic systems with competing interactions and an underlying spin-glass phase. A finite-size-scaling analysis of the magnetization distribution suggests that the transition might be first order.

We report an extensive study on the zero field ground state of a powder sample of the pyrochlore ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. A sharp heat capacity anomaly that labels a low temperature phase transition in this material is observed at 280 mK. Neutron diffraction shows that a quasicollinear ferromagnetic order develops below $T_{\mathrm{c}}$ with a magnetic moment of $0.87\left(2\right){\mu }_{\mathrm{B}}$. High resolution inelastic neutron scattering measurements show, below the phase transition temperature, sharp gapped low-lying magnetic excitations coexisting with a remnant quasielastic contribution likely associated with persistent spin fluctuations. Moreover, a broad inelastic continuum of excitations at $\sim 0.6$ meV is observed from the lowest measured temperature up to at least 2.5 K. At 10 K, the continuum has vanished and a broad quasielastic conventional paramagnetic scattering takes place at the observed energy range. Finally, we show that the exchange parameters obtained within the framework of linear spin-wave theory do not accurately describe the observed zero field inelastic neutron scattering data.

Using a two-band double-exchange model with Jahn-Teller lattice distortions and superexchange interactions, supplemented by quenched disorder, at an electron density $n=0.65$, we explicitly demonstrate the coexistence of the $n=1/2$-type $\left(\pi ,\pi \right)$ charge-ordered and the ferromagnetic nanoclusters above the ferromagnetic transition temperature $T_{\mathrm{c}}$ in colossal magnetoresistive (CMR) manganites. The resistivity increases due to the enhancement of the volume fraction of the charge-ordered and the ferromagnetic nanoclusters upon decreasing the temperature down to $T_{\mathrm{c}}$. The ferromagnetic nanoclusters start to grow and merge, and the volume fraction of the charge-ordered nanoclusters decreases below $T_{\mathrm{c}}$, leading to the sharp drop in the resistivity. By applying a small external magnetic field $h$, we show that the resistivity above $T_{\mathrm{c}}$ increases, as compared with the case when $h=0$, a fact that further confirms the coexistence of the charge-ordered and the ferromagnetic nanoclusters. In addition, we show that the volume fraction of the charge-ordered nanoclusters decreases upon increasing the bandwidth, and consequently the resistivity hump diminishes for large bandwidth manganites, in good qualitative agreement with experiments. The obtained insights from our calculations provide a complete pathway to understand the phase competition in CMR manganites.

We report on directly determining the complex permittivity tensor using a method combining a developed light source from a segmented cross undulator of synchrotron radiation and the magneto-optical Kerr effect. The empirical permittivity, which carries the electronic and magnetic information of a material, has element specificity and has perfect confirmation using the quantum-mechanical calculation for itinerant electrons systems. These results help in understanding the interaction of light and matter, and they provide an interesting approach to seek the best materials as optical elements, for example, in extended-ultraviolet lithographic technologies or in state-of-the-art laser technologies.

The high-temperature normal state of the unconventional cuprate superconductors has resistivity linear in temperature $T$, which persists to values well beyond the Mott-Ioffe-Regel upper bound. At low temperatures, within the pseudogap phase, the resistivity is instead quadratic in $T$, as would be expected from Fermi liquid theory. Developing an understanding of these normal phases of the cuprates is crucial to explain the unconventional superconductivity. We present a simple explanation for this behavior, in terms of the umklapp scattering of electrons. This fits within the general picture emerging from functional renormalization group calculations that spurred the Yang-Rice-Zhang ansatz: Umklapp scattering is at the heart of the behavior in the normal phase.

We use scattering theory to study the spatial resolution achievable in vibrational energy loss spectroscopy using a focused beam of high-energy ($\sim 100$ keV) electrons. We first outline a theory for calculating vibrational-spectroscopic images of crystalline or noncrystalline materials at nanometer spatial resolution or better (up to atomic resolution). The electron scattering and the atomic vibrations are treated quantum mechanically. Dipolar scattering from long-wavelength optical vibrations is included. We present calculated atomically resolved vibrational-spectroscopic images of a polar crystalline material (hexagonal boron nitride). For such materials, dipole scattering from long optical vibrations can give rise to a strong background in the images, which has implications for the attainable spatial resolution. We show that an annular collection geometry can significantly reduce the dipole background, thereby reducing the electron dose required to observe atomic-scale contrast.

Extending the notion of symmetry protected topological phases to insulating antiferromagnets (AFs) described in terms of opposite magnetic dipole moments associated with the magnetic $\mathrm{N}\acute{\mathrm{e}}\mathrm{el}$ order, we establish a bosonic counterpart of topological insulators in semiconductors. Making use of the Aharonov-Casher effect, induced by electric field gradients, we propose a magnonic analog of the quantum spin Hall effect (magnonic QSHE) for edge states that carry helical magnons. We show that such up and down magnons form the same Landau levels and perform cyclotron motion with the same frequency but propagate in opposite direction. The insulating AF becomes characterized by a topological ${\mathbb{Z}}_2$ number consisting of the Chern integer associated with each helical magnon edge state. Focusing on the topological Hall phase for magnons, we study bulk magnon effects such as magnonic spin, thermal, Nernst, and Ettinghausen effects, as well as the thermomagnetic properties of helical magnon transport both in topologically trivial and nontrivial bulk AFs and establish the magnonic Wiedemann-Franz law. We show that our predictions are within experimental reach with current device and measurement techniques.

Noncollinear antiferromagnets have recently been attracting considerable interest partly due to recent surprising discoveries of the anomalous Hall effect (AHE) in them and partly because they have promising applications in antiferromagnetic spintronics. Here we study the anomalous Nernst effect (ANE), a phenomenon having the same origin as the AHE, and also the spin Nernst effect (SNE) as well as AHE and the spin Hall effect (SHE) in noncollinear antiferromagnetic ${\mathrm{Mn}}_{3}X$ ($X=\mathrm{Sn}$, Ge, Ga) within the Berry phase formalism based on ab initio relativistic band structure calculations. For comparison, we also calculate the anomalous Nernst conductivity (ANC) and anomalous Hall conductivity (AHC) of ferromagnetic iron as well as the spin Nernst conductivity (SNC) of platinum metal. Remarkably, the calculated ANC at room temperature (300 K) for all three alloys is huge, being 10–40 times larger than that of iron. Moreover, the calculated SNC for ${\mathrm{Mn}}_3\mathrm{Sn}$ and ${\mathrm{Mn}}_3\mathrm{Ga}$ is also larger, being about five times larger than that of platinum. This suggests that these antiferromagnets would be useful materials for thermoelectronic devices and spin caloritronic devices. The calculated ANC of ${\mathrm{Mn}}_3\mathrm{Sn}$ and iron are in reasonably good agreement with the very recent experiments. The calculated SNC of platinum also agrees with the very recent experiments in both sign and magnitude. The calculated thermoelectric and thermomagnetic properties are analyzed in terms of the band structures as well as the energy-dependent AHC, ANC, SNC, and spin Hall conductivity via the Mott relations.

The magnetoelectric effects in the surface states of the three-dimensional (3D) topological insulator (TI) are extremely strong due to the full spin-momentum locking. Here the microscopic theory of S/3D TI bilayer structures in terms of quasiclassical Green's functions is developed. On the basis of the developed formalism it is shown that the DOS in the S/TI bilayer manifests giant magnetoelectric behavior and, as a result, S/3D TI heterostructures can work as nonmagnetic fully electrically controllable spin filters. It is shown that due to the full spin-momentum locking the amplitudes of the odd-frequency singlet and triplet components of the condensate wave function are equal. The same is valid for the even frequency singlet and triplet components. We unveil the connection between the odd-frequency pairing in S/3D TI heterostructures and magnetoelectric effects in the DOS.

The intrinsic magnetic state (ferromagnetic or antiferromagnetic) of ultrathin ${\mathrm{LaMnO}}_3$ films on the most commonly used ${\mathrm{SrTiO}}_3$ substrate is a long-existing question under debate. Either strain effect or nonstoichiometry was argued to be responsible for the experimental ferromagnetism. In a recent experiment [X. R. Wang, C. J. Li, W. M. Lü, T. R. Paudel, D. P. Leusink, M. Hoek, N. Poccia, A. Vailionis, T. Venkatesan, J. M. D. Coey, E. Y. Tsymbal, Ariando, and H. Hilgenkamp, Science 349, 716 (2015)], one more mechanism, namely, the self-doping due to polar discontinuity, was argued to be the driving force of ferromagnetism beyond the critical thickness. Here systematic first-principles calculations have been performed to check these mechanisms in ultrathin ${\mathrm{LaMnO}}_3$ films as well as superlattices. Starting from the very precise descriptions of both ${\mathrm{LaMnO}}_3$ and ${\mathrm{SrTiO}}_3$, it is found that the compressive strain is the dominant force for the appearance of ferromagnetism, while the open surface with oxygen vacancies leads to the suppression of ferromagnetism. Within ${\mathrm{LaMnO}}_3$ layers, the charge reconstructions involve many competitive factors and certainly go beyond the intuitive polar catastrophe model established for ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures. Our paper not only explains the long-term puzzle regarding the magnetism of ultrathin ${\mathrm{LaMnO}}_3$ films but also sheds light on how to overcome the notorious magnetic dead layer in ultrathin manganites.

Spin liquids are exotic quantum states characterized by the existence of fractional and deconfined quasiparticle excitations, referred to as spinons and visons. Their fractional nature establishes topological properties such as a protected ground-state degeneracy. This work investigates spin-orbit coupled spin liquids where, additionally, topology enters via nontrivial band structures of the spinons. We revisit the ${\mathbb{Z}}_2$ spin-liquid phases that have recently been identified in a projective symmetry-group analysis on the square lattice when spin-rotation symmetry is maximally lifted [J. Reuther et al., Phys. Rev. B 90, 174417 (2014)]. We find that in the case of nearest-neighbor couplings only, ${\mathbb{Z}}_2$ spin liquids on the square lattice always exhibit trivial spinon bands. Adding second-neighbor terms, the simplest projective symmetry-group solution closely resembles the Bernevig-Hughes-Zhang model for topological insulators. Assuming that the emergent gauge fields are static, we investigate vison excitations, which we confirm to be deconfined in all investigated spin phases. Particularly, if the spinon bands are topological, the spinons and visons form bound states consisting of several spinon-Majorana zero modes coupling to one vison. The existence of such zero modes follows from an exact mapping between these spin phases and topological $p+ip$ superconductors with vortices. We propose experimental probes to detect such states in real materials.

The interfacial phase-change memory (iPCM) ${\mathrm{GeTe}/\mathrm{Sb}}_2{\mathrm{Te}}_3$, a promising candidate for the next generation nonvolatile random-access memories, exhibits fascinating topological properties. Depending on the atomic-layer-stacking sequence of the GeTe block, the iPCM can be either in the SET (Ge-Te-Ge-Te) or RESET (Te-Ge-Ge-Te) states, where the former exhibits ferroelectric polarization and electrical conductivity two orders of magnitude larger than that of the RESET state. Yet, its microscopic origin remains elusive. Here, we predict the emergence of a Weyl semimetal phase in the SET state induced by the ferroelectric polarization which breaks the crystal inversion symmetry. We show that the giant conductivity enhancement of the SET phase is due to the appearance of gapless Weyl nodes. The Ge-Te- or Sb-Te-terminated surfaces of Weyl semimetal iPCM exhibit surface states with completely distinctive topology, where the former consists solely of Fermi arcs while the latter consists of both closed Fermi surface and open Fermi arcs. The iPCM with van der Waals interfaces offers an ideal platform for exploiting the exotic Weyl properties as well as for future memory device applications.

We consider a one-dimensional system combining local magnetic moments and a delocalized metallic band on top of a superconducting substrate. This system can describe a chain of magnetic impurities with both localized polarized orbitals and delocalized $s$-like orbitals or a conducting wire with embedded magnetic impurities. We study the interplay between the one-dimensional Shiba band physics arising from the interplay between magnetic moments and the substrate and the delocalized wire-like conduction band on top of the superconductor. We derive an effective low-energy Hamiltonian in terms of two coupled asymmetric Kitaev-like Hamiltonians and analyze its topological properties. We have found that this system can host multiple Majorana bound states at its extremities provided a magnetic mirror symmetry is present. We compute the phase diagram of the system depending on the magnetic exchange interactions, the impurity distance, and especially the coupling between both bands. In the presence of inhomogeneities which typically break this magnetic mirror symmetry, we show that the coexistence of a Shiba and wire delocalized topological band can drive the system into a nontopological regime with a splitting of Majorana bound states.

We study the temperature dependence (77–475 K) of the longitudinal resistivity and Hall coefficient of thin films (thickness 20 nm) of three-dimensional topological Dirac semimetal ${\mathrm{Na}}_3\mathrm{Bi}$ grown via molecular beam epitaxy. The temperature-dependent Hall coefficient is electronlike at low temperature, but transitions to holelike transport around 200 K. We develop a model of a Dirac band with electron-hole asymmetry in Fermi velocity and mobility (assumed proportional to the square of Fermi velocity) which explains well the magnitude and temperature dependence of the Hall resistivity. We find that the hole mobility is about seven times larger than the electron mobility. In addition, we find that the electron mobility decreases significantly with increasing temperature, suggesting electron-phonon scattering strongly limits the room-temperature mobility.

Islands of Bi showing (110)- and (111)-orientated facets were grown on a Nb(110) single crystal and were studied with a scanning tunneling microscope at low temperatures. On the (111) facets, several states localized at step edges are identified from maps of the local differential conductance. We find edge states on both types of zig-zag step edges that decay exponentially over a length scale of several nanometers into the terrace. These states agree with the necessary condition for topologically nontrivial edge states. Further, we find states localized at the atomic scale at the step edge, which we interpret as dangling bond states. To investigate the nature of these states, we studied the Bi(110) surface, where the sharply localized states form stripe patterns, while the more extended edge state does not show a strong lattice-periodic pattern. Thus, our findings indicate a causal link between the strongly localized edge states on Bi(111) and the stripe pattern on Bi(110) as they are both related to the zig-zag termination of the honeycomb structure of Bi. Finally, we observed a decay of the superconducting proximity gap of the Bi islands with island thickness.

Inelastic scattering of the medium-energy ($\sim 10–100$ eV) electrons underlies the method of the high-resolution electron energy-loss spectroscopy (HREELS), which has been successfully used for decades to characterize pure and adsorbate-covered surfaces of solids. With the emergence of graphene and other quasi-two-dimensional (Q2D) crystals, HREELS could be expected to become the major experimental tool to study this class of materials. We, however, identify a critical flaw in the theoretical picture of the HREELS of Q2D crystals in the context of the inelastic scattering only (“energy-loss functions” formalism), in contrast to its justifiable use for bulk solids and surfaces. The shortcoming is the neglect of the elastic scattering, which we show is inseparable from the inelastic one, and which, affecting the spectra dramatically, must be taken into account for the meaningful interpretation of the experiment. With this motivation, using the time-dependent density functional theory for excitations, we build a theory of the simultaneous inelastic and elastic electron scattering at Q2D crystals. We apply this theory to HREELS of graphene, revealing an effect of the strongly coupled excitation of the $\pi +\sigma$ plasmon and elastic diffraction resonances. Our results open a path to the theoretically interpretable study of the excitation processes in crystalline mesoscopic materials by means of HREELS, with its supreme resolution on the meV energy scale, which is far beyond the capacity of the now overwhelmingly used EELS in transmission electron microscopy.

Recently, two-dimensional (2D) multiferroics have attracted a lot of attention due to their fascinating properties and promising applications. Although the ferroelectric (FE)-ferroelastic and ferromagnetic (FM)-ferroelastic multiferroics have been observed/predicted in 2D systems, 2D ferromagnetic-ferroelectric (FM-FE) multiferroics remain to be discovered since FM insulators are very rare. Here we proposed the concept of 2D hyperferroelectric metals, with which the insulating prerequisite for the FM-FE multiferroic is no longer required in 2D systems. We validate the concept of 2D hyperferroelectric metals and 2D metallic FM-FE multiferroics by performing first-principle calculations on 2D CrN and $\mathrm{Cr}{\mathrm{B}}_2$ systems. The 2D buckled monolayer CrN is found to be a hyperferroelectic metal with the FM ground state, i.e., a 2D FM-FE multiferroic. With the global optimization approach, we find the 2D $\mathrm{Cr}{\mathrm{B}}_2$ system has an antiferromagnetic (AFM)/planar ground state and a FM/FE metastable state, suggesting that it can be used to realize electric field control of magnetism. Our analysis demonstrates that the spin-phonon coupling and metal-metal interaction are two mechanisms for stabilizing the out-of-plane electric polarization in 2D systems. Our work not only extends the concept of FE to metallic systems, but also paves a way to search the long-sought high temperature FM-FE multiferroics.

We study the electronic structure of Tsai-type cluster-based quasicrystalline approximants, ${\mathrm{Au}}_{64}{\mathrm{Ge}}_{22}{\mathrm{Yb}}_{14}$ (AGY-I), ${\mathrm{Au}}_{63.5}{\mathrm{Ge}}_{20.5}{\mathrm{Yb}}_{16}$ (AGY-II), and ${\mathrm{Zn}}_{85.4}{\mathrm{Yb}}_{14.6}$ (Zn-Yb), by means of photoemission spectroscopy. In the valence band hard x-ray photoemission spectra of AGY-II and Zn-Yb, we separately observe a fully occupied $\mathrm{Yb} 4f$ state and a valence fluctuation derived Kondo resonance peak, reflecting two inequivalent Yb sites, a single Yb atom in the cluster center and its surrounding Yb icosahedron, respectively. The fully occupied $4f$ signal is absent in AGY-I containing no Yb atom in the cluster center. The results provide direct evidence for a heterogeneous valence state in AGY-II and Zn-Yb.