We report measurements performed on a polycrystalline sample of the pyrochlore compound ${\mathrm{Nd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$. It undergoes a second order magnetic phase transition at $T_c\approx 0.91$ K to a noncoplanar all-in–all-out magnetic structure of the ${\mathrm{Nd}}^{3+}$ magnetic moments. The thermal behavior of the low temperature specific heat fingerprints excitations with linear dispersion in a three-dimensional lattice. The temperature independent spin-lattice relaxation rate measured below $T_c$ and the anomalously slow paramagnetic spin dynamics detected up to $\approx 30T_c$ are suggested to be due to magnetic short-range correlations in unidimensional spin clusters, i.e., spin loops. The observation of a spontaneous field in muon spin relaxation measurements is associated with the absence of a divergence-free field for the ground state of an all-in–all-out pyrochlore magnet as predicted recently.

We show that the spin-orbit torque induced magnetization switching in nanomagnets presenting Dzyaloshinskii-Moriya (DMI) interaction is governed by a chiral domain nucleation at the edges. The nucleation is induced by the DMI and the applied in-plane magnetic field followed by domain-wall propagation. Our micromagnetic simulations show that the dc switching current can be defined as the edge nucleation current, which decreases strongly with increasing amplitude of the DMI. This description allows us to build a simple analytical model to quantitatively predict the switching current. We find that domain nucleation occurs down to a lateral size of $25\mathrm{nm}$, defined by the length scale of the DMI, beyond which the reversal mechanism approaches a macrospin behavior. The switching is deterministic and bipolar.

In response to ultrafast laser pulses, single-phase metals have been classified as “fast” (with magnetization quenching on the time scale of the order of 100 fs and recovery in the time scale of several picoseconds and below) and “slow” (with longer characteristic time scales). Disordered ferrimagnetic alloys consisting of a combination of “fast” transition (TM) and “slow” rare-earth (RE) metals have been shown to exhibit an ultrafast all-optical switching mediated by the heat mechanism. The behavior of the characteristic time scales of coupled alloys is more complicated and is influenced by many parameters such as the intersublattice exchange, doping (RE) concentration, and the temperature. Here, the longitudinal relaxation times of each sublattice are analyzed within the Landau-Lifshitz-Bloch framework. We show that for moderate intersublattice coupling strength both materials slow down as a function of slow (RE) material concentration. For larger coupling, the fast (TM) material may become faster, while the slow (RE) one is still slower. These conclusions may have important implications in the switching time of disordered ferrimagnets such as GdFeCo with partial clustering. Using atomistic modeling, we show that in the moderately coupled case, the reversal would start in the Gd-rich region, while the situation may be reversed if the coupling strength is larger.

Magneto-optical Kerr effect, normally found in magnetic materials with nonzero magnetization such as ferromagnets and ferrimagnets, has been known for more than a century. Here, using first-principles density functional theory, we demonstrate large magneto-optical Kerr effect in high-temperature noncollinear antiferromagnets ${\mathrm{Mn}}_{3}X(X=\mathrm{Rh},\mathrm{Ir},\mathrm{Pt})$, in contrast to usual wisdom. The calculated Kerr rotation angles are large, being comparable to that of transition-metal magnets such as bcc Fe. The large Kerr rotation angles and ellipticities are found to originate from the lifting of band double degeneracy due to the absence of spatial symmetry in the ${\mathrm{Mn}}_{3}X$ noncollinear antiferromagnets which together with the time-reversal symmetry would preserve the Kramers theorem. Our results indicate that ${\mathrm{Mn}}_{3}X$ would provide a rare material platform for exploration of subtle magneto-optical phenomena in noncollinear magnetic materials without net magnetization.

Correlation between geometry, electronic structure, and magnetism of solids is both intriguing and elusive. This is particularly strongly manifested in small clusters, where a vast number of unusual structures appear. Here, we employ density functional theory in combination with a genetic search algorithm $\mathrm{GGA}+U$ and a hybrid functional to determine the structure of gas phase ${\text{Fe}}_x{\text{O}}_y^{+/0}$ clusters. For ${\mathrm{Fe}}_x{\mathrm{O}}_y^{+}$ cation clusters we also calculate the corresponding vibration spectra and compare them with experiments. We successfully identify ${\mathrm{Fe}}_3{\mathrm{O}}_4^{+}, {\mathrm{Fe}}_4{\mathrm{O}}_5^{+}, {\mathrm{Fe}}_4{\mathrm{O}}_6^{+}, {\mathrm{Fe}}_5{\mathrm{O}}_7^{+}$ and propose structures for ${\mathrm{Fe}}_6{\mathrm{O}}_8^{+}$. Within the triangular geometric structure of ${\mathrm{Fe}}_3{\mathrm{O}}_4^{+}$, a noncollinear, ferrimagnetic, and ferromagnetic state are comparable in energy. ${\mathrm{Fe}}_4{\mathrm{O}}_5^{+}$ and ${\mathrm{Fe}}_4{\mathrm{O}}_6^{+}$ are ferrimagnetic with a residual magnetic moment of $1{\mu }_{\mathrm{B}}$ due to ionization. ${\mathrm{Fe}}_5{\mathrm{O}}_7^{+}$ is ferrimagnetic due to the odd number of Fe atoms. We compare the electronic structure with bulk magnetite and find ${\mathrm{Fe}}_4{\mathrm{O}}_5^{+}, {\mathrm{Fe}}_4{\mathrm{O}}_6^{+}, {\mathrm{Fe}}_6{\mathrm{O}}_8^{+}$ to be mixed valence clusters. In contrast, in ${\mathrm{Fe}}_3{\mathrm{O}}_4^{+}$ and ${\mathrm{Fe}}_5{\mathrm{O}}_7^{+}$, all Fe are found to be trivalent.

Universal single-frequency oscillations in the local nonequilibrium dynamics of a quantum many-body system are an exceptional phenomenon. In fact, till now, this has never been observed or predicted for the physically relevant case where a system is prepared to be quenched from one quantum phase to another. Here we show how the quench dynamics of the entanglement spectrum may reveal the emergence of such oscillations in a correlated quantum system with Kondo impurities. The oscillations we find are characterized by a single frequency. This frequency is independent of the amount of energy released by the local quench, and scales with the inverse system size. Importantly, the quench-independent frequency manifests itself also in local observables, such as the spin-spin correlation function of the impurities.

Two-dimensional (2D) materials, especially their most prominent member, graphene, have greatly influenced many scientific areas. Moreover, they have become a base for investigating the relativistic properties of condensed matter within the emerging field of “Dirac physics.” This has ignited an intense search for new materials where charge carriers behave as massless or massive Dirac fermions. Here, by the use of density functional theory and symmetry analysis, we theoretically show the existence of Dirac electrons in a series of 2D transition-metal carbides, known as MXenes. They possess eight conical crossings in the first Brillouin zone with giant spin-orbit splitting. Our findings indicate that the 2D band structure of MXenes is protected against external perturbations and preserved even in multilayer phases. These results, together with the broad possibilities to engineer the properties of these phases, make them a potential candidate for studying novel Dirac-physics-based applications.

The three-band $p\text{−}d$ model of strongly correlated electrons interacting with optical phonons via diagonal and off-diagonal electron-phonon interactions is considered within the cluster perturbation theory. In the beginning, the exact diagonalization of the Hamiltonian of a ${\mathrm{CuO}}_4$ cluster results in the construction of local polaronic eigenstates $\left|p\right.〉$ with hole numbers $n_h=0,1,2$ per unit cell. The intercluster hoppings and interactions are exactly written in terms of Hubbard operators $X_f^{pq}=\left|p\right.〉\left.〈q\right|$ determined via the multielectron polaronic eigenstates $\left|p\right.〉$ at site $\mathbf{f}$. The Fermi-type single-electron quasiparticle dispersion and spectral weight are calculated for the undoped antiferromagnetic parent insulator like ${\mathrm{La}}_2{\mathrm{CuO}}_4$. The quasiparticle dispersion of Hubbard polarons is determined by a hybridization of the Hubbard fermion subbands with local Franck-Condon resonances so the main polaronic effect of the quasiparticle band structure is a splitting of the Hubbard bands on the number of Hubbard polaron subbands. Increasing of the EPI constant results in an increase of splitting, decrease of the subband width, transfer of the spectral weight to high-energy multiphonon excitations, and subsequent localization of the charge carriers. Herewith, the effect of such renormalization for the conduction band and the valence one differs depending on the ratio of the diagonal and off-diagonal EPI. In the framework of the GTB method, the Franck-Condon broadening of the spectral function of polaronic excitations is also reproduced for strongly correlated systems with strong electron-phonon interaction.

We report ${}^{139}\mathrm{La}$ nuclear magnetic resonance studies performed on a ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ single crystal. The data show that the structural phase transitions $(\text{high-temperature tetragonal}\to \text{low-temperature orthorhombic}\to \text{low-temperature tetragonal phase})$ are of the displacive type in this material. The ${}^{139}\mathrm{La}$ spin-lattice relaxation rate $T_1^{-1}$ sharply upturns at the charge-ordering temperature $T_{\text{CO}}=54$ K, indicating that charge order triggers the slowing down of spin fluctuations. Detailed temperature and field dependencies of the $T_1^{-1}$ below the spin-ordering temperature $T_{\text{SO}}=40$ K reveal the development of enhanced spin fluctuations in the spin-ordered state for $H\parallel \left[001\right]$, which are completely suppressed for large fields along the ${\mathrm{CuO}}_2$ planes. Our results shed light on the unusual spin fluctuations in the charge and spin stripe ordered lanthanum cuprates.

We investigate the dynamically polarized nuclear spin system in $\text{Fe}/n$-GaAs heterostructures using the response of the electron-spin system to nuclear magnetic resonance (NMR) in lateral spin-valve devices. The hyperfine interaction is known to act more strongly on donor-bound electron states than on those in the conduction band. We provide a quantitative model of the temperature dependence of the occupation of donor sites. With this model we calculate the ratios of the hyperfine and quadrupolar nuclear relaxation rates of each isotope. For all temperatures measured, quadrupolar relaxation limits the spatial extent of nuclear spin polarization to within a Bohr radius of the donor sites and is directly responsible for the isotope dependence of the measured NMR signal amplitude. The hyperfine interaction is also responsible for the $2\text{kHz}$ Knight shift of the nuclear resonance frequency that is measured as a function of the electron-spin accumulation. The Knight shift is shown to provide a measurement of the electron-spin polarization that agrees qualitatively with standard spin transport measurements.

We employ a simple analytic model to calculate the thermopower of low-transparency molecular nanosystems. It turns out that the sign of the thermovoltage for this model depends sensitively on the participating molecular orbital, and one finds a sign change when the transport channel switches from the highest occupied molecular orbital to the lowest unoccupied molecular orbital. Comparing our results to recent experimental data obtained for a benzenedithiol molecule contacted with a scanning tunneling microscope tip, we observe good agreement.

We present a theoretical study of indirect exchange interaction between magnetic adatoms in graphene. The coupling between the adatoms to a graphene sheet is described in the framework of a tunneling Hamiltonian. We account for the possibility of this coupling being of resonant character if a bound state of the adatom effectively interacts with the continuum of 2D delocalized states in graphene. In this case the indirect exchange between the adatoms mediated by the 2D carriers appears to be substantially enhanced compared to the results known from Ruderman-Kittel-Kasuya-Yosida (RKKY) theory. Moreover, unlike the results of RKKY calculations in the case of resonant exchange, the magnetic coupling between the adatoms sitting over different graphene sublattices does not cancel each other. Thus, for a random distribution of the magnetic adatoms over a graphene surface, a nonzero magnetic interaction is expected. We also suggest the idea of controlling the magnetism by driving the tunnel coupling in and out of resonance by a gate voltage.

The structure of the ultimately thin crystalline allotrope of silicon oxide, prepared on a ruthenium surface, is unveiled down to the atomic scale with chemical sensitivity, owing to high resolution scanning tunneling microscopy and first principles calculations. An ordered oxygen lattice is imaged which coexists with the two-dimensional monolayer oxide. This coexistence signals a displacive transformation from an oxygen-reconstructed Ru(0001) to silicon oxide, along which laterally shifted domains form, each with equivalent and degenerate epitaxial relationships with the substrate. The unavoidable character of defects at the boundaries between these domains appeals for the development of alternative methods capable of producing single-crystalline two-dimensional oxides.

A nonlocal Hall bar geometry is used to detect neutral-current Hall effects in graphene on silicon dioxide. Disorder is tuned by the addition of $\mathrm{Au}$ or $\mathrm{Ir}$ adatoms in ultrahigh vacuum. A reproducible neutral-current Hall effect is found in both as-fabricated and adatom-decorated graphene. The Hall angle exhibits a complex but reproducible dependence on gate voltage and disorder, and notably breaks electron-hole symmetry. An exponential dependence on length between Hall and inverse Hall probes indicates a neutral-current relaxation length of approximately $300\mathrm{nm}$. The short relaxation length and lack of precession in a parallel magnetic field suggest that the neutral currents are valley currents. No signature of the spin-orbit coupling induced spin Hall effect is observed in the $\mathrm{Au}$- or $\mathrm{Ir}$-decorated graphene. The near lack of temperature dependence from 7 to 300 K is unprecedented among reports of valley Hall effect in graphene, and promising for using controlled disorder for room temperature neutral-current electronics.

Based on the Green's function (GF) equation-of-motion formalism, we develop a method to expand the double-time Green's function into Taylor series of the parameter $\lambda$ in the Hamiltonian $H=H_0+\lambda H_1$. Here $H_0$ is the exactly solvable part and $H_1$ is regarded as the perturbation. To restore the analytical structure of GF, we use the continued fraction to do resummation for the obtained series. The problem of zero-temperature divergence is identified and remedied by the self-consistent series expansion. To demonstrate the implementation of this method, we carry out the weak- as well as the strong-coupling expansion for the Anderson impurity model to order ${\lambda }^2$. Improved result for the local density of states is obtained by self-consistent second-order strong-coupling expansion and continued fraction resummation.

The Hall viscosity describes a nondissipative response to strain in systems with broken time-reversal symmetry. We develop a method for computing the Hall viscosity of lattice systems in strong magnetic fields based on momentum transport, which we compare to the method of momentum polarization used by Tu et al. [Phys. Rev. B 88, 195412 (2013)] and Zaletel et al. [Phys. Rev. Lett. 110, 236801 (2013)] for noninteracting systems. We compare the Hall viscosity of square-lattice tight-binding models in magnetic field to the continuum integer quantum Hall effect (IQHE) showing agreement when the magnetic length is much larger than the lattice constant, but deviation as the magnetic field strength increases. We also relate the Hall viscosity of relativistic electrons in magnetic field (the Dirac IQHE) to the conventional IQHE. The Hall viscosity of the lattice Dirac model in magnetic field agrees with the continuum Dirac Hall viscosity when the magnetic length is much larger than the lattice constant. We also show that the Hall viscosity of the lattice model deviates further from the continuum model if the $C_4$ symmetry of the square lattice is broken to $C_2$, but the deviation is again minimized as the magnetic length increases.

Interband optical transitions in graphene are subject to pseudospin selection rules. Impulsive excitation with linearly polarized light generates an anisotropic photocarrier occupation in momentum space that evolves at time scales shorter than 100 fs. Here, we investigate the evolution of nonequilibrium charges towards an isotropic distribution by means of fluence-dependent ultrafast spectroscopy and develop an analytical model able to quantify the isotropization process. In contrast to conventional semiconductors, the isotropization is governed by optical phonon emission, rather than electron-electron scattering, which nevertheless contributes in shaping the anisotropic photocarrier occupation within the first few femtoseconds.

We show that nonreciprocal bands can be formed in a magnetized periodic chain of spherical plasmonic particles with two particles per unit cell. Simplified forms of symmetry operators in dipole approximations are used to demonstrate explicitly the relation between spectral nonreciprocity and broken spatial-temporal symmetries. Due to hybridization among plasmon modes and free-photon modes, strong spectral nonreciprocity appears in the region slightly below the light line, where highly directed guiding of energy can be supported. The results may provide clear guidance on the design of one-way waveguides.

The precise gap structure in LiFeAs $(T_{\mathrm{c}}=18\text{K})$ given by ARPES studies offers significant information that helps us understand the pairing mechanism in iron-based superconductors. The most remarkable characteristic in the LiFeAs gap structure would be that “the largest gap emerges on the tiny hole-pockets around the $Z$ point.” This result has been naturally explained in terms of the orbital-fluctuation scenario [T. Saito et al., Phys. Rev. B 90, 035104 (2014)], whereas the opposite result is obtained by the spin-fluctuation scenario. In this paper, we study the gap structure in LiFeAs by taking the spin-orbit interaction (SOI) into account, motivated by the recent ARPES studies that revealed a significant SOI-induced modification of the Fermi surface topology. For this purpose, we construct two possible tight-binding models with finite SOI by referring the band structures given by different ARPES groups. In addition, we extend the gap equation for multiorbital systems with finite SOI, and calculate the gap functions by applying the orbital-spin fluctuation theory. On the basis of both SOI-induced band structures, the main characteristics of the gap structure in LiFeAs are naturally reproduced only in the presence of strong interorbital interactions between $\left(d_{xz/yz}\text{−}{d}_{xy}\right)$ orbitals. Thus the experimental gap structure in LiFeAs is a strong evidence for the orbital-fluctuation pairing mechanism.

$\mathrm{CaCr}{\mathrm{O}}_3$ is at the crossover from localized to itinerant electronic behavior, and interpretation of its electronic state has remained controversial. It is a metal from an optical study. However, the collinear type-C antiferromagnetic spin ordering below $T_N\approx 90\mathrm{K}$ is characteristic of localized electron magnetism. We have performed many runs of high-pressure synthesis. $\mathrm{CaCr}{\mathrm{O}}_3$ crystals can be found in some batches. We have used specific-heat measurement as a diagnostic tool to probe the electronic states near the Fermi energy. An electronic bandwidth is broadened by applying high pressure. The magnetization measurement under pressure reveals a $d{T}_N/dP<0$. The crystal structural change corresponding to the pressure-induced electron structural change has been monitored by in situ neutron diffraction under high pressure. The $t_2^2$ d-electron configuration on octahedral site $\mathrm{C}{\mathrm{r}}^{4+}$ is orbitally threefold degenerate. Local site distortions are argued to show that in $\mathrm{CaCr}{\mathrm{O}}_3$ the crossover from localized to itinerant 3d electrons does not result in a charge-density wave in which segregation of the interatomic interactions results in the stabilization of molecular clusters, but in an intraatomic orbital ordering that stabilizes a half-filled localized-electron $xy$ orbital and a $1/4$-filled $c$-axis ${\pi }^{*}$ band. Local structural changes under pressure reveal a weakening of long-range magnetic order is associated with a smooth Mott-Hubbard transition of the $xy$ electrons.