We discuss the signatures of a Kramers pair of Majorana modes formed in a Josephson junction on top of a quantum spin Hall system. We show that, while ignoring interactions on the quantum spin Hall edge allows arbitrary Andreev processes in the system, moderate repulsive interactions stabilize Andreev transmission—the hole goes into the opposite lead from where the electron has arrived. We analyze the renormalization group equations and deduce the phase diagram as a function of interaction strength.

The spin susceptibility of the localized $\mathrm{Mn}\left(t_{2g}\right)$ electrons, ${\chi }_s$, and the spatially distributed spin density of the doped electrons were investigated by ${}^{17}\mathrm{O}$ nuclear magnetic resonance (NMR) in the paramagnetic (PM) and antiferromagnetic (AF) phases of electron-doped ${\mathrm{SrMnO}}_{3-x}$ ceramics with the cubic structure. Three lightly doped samples $\left(2x<0.015\right)$ were studied with $T_N=220\text{K}–240$ K. In the PM state ${\chi }_s$ increases gradually from $T_N$ and reaches a broad maximum above $\sim 1.5T_N$. The gapped behavior of ${\chi }_s$ indicates a low-dimensional short-range spin order persisting above $T_N$. These short-range one-dimensional correlations are consistent with ${}^{17}\mathrm{O}$ NMR results obtained at room temperature, which show that Mn magnetic moments are aligned along the edges of the cubic unit cell. Above 350 K all doped electrons are fast-moving $e_g$ electrons. They provide the uniform polarization of the localized spins which increases ${\chi }_s$ and the increasing doping shifts the oxygen-deficient ${\mathrm{SrMnO}}_{3-x}$ oxide towards a ferromagnetic (FM) metallic state. At lower $T$ the doped electrons are heterogeneously distributed in the oxide: The fraction of the fast-moving electrons diminishes and vanishes below 100 K, while the remaining doped electrons slow down their hopping and each of them creates a FM domain. These FM domains which are detected below 10 K by ${}^{55}\mathrm{Mn}$ NMR can be considered as small-size magnetic polarons. Their $T$-activated hopping in the G-type AF lattice was probed by ${}^{17}\mathrm{O}$ spin-echo experiments. The energy barrier of hopping shows a trend to grow with increasing doping, indicating that the de Gennes metallic ground state cannot be achieved in oxygen-deficient ${\mathrm{SrMnO}}_{3-x}$ oxides, probably due to detrimental oxygen vacancy defects.

The linear magnetoelectric effect was measured in 500-nm $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ films grown by radio frequency sputtering on $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ substrates between top and bottom thin film Pt electrodes. Magnetoelectric susceptibility was measured directly by applying an alternating current (ac) electric field and measuring the induced ac magnetic moment using superconducting quantum interference device magnetometry. A linear dependence of the induced ac magnetic moment on the ac electric field amplitude was found. The temperature dependence of the magnetoelectric susceptibility agreed qualitatively and quantitatively with prior measurements of bulk single crystals, but the characteristic temperatures of the film were lower than those of single crystals. It was also possible to reverse the sign of the magnetoelectric susceptibility by reversing the sign of the magnetic field applied during cooling through the Néel temperature. A competition between total magnetoelectric and Zeeman energies is proposed to explain the difference between film and bulk $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ regarding the cooling field dependence of the magnetoelectric effect.

Discovering new magnetoelectric multiferroics is an exciting research area. Very recently, a collinear antiferromagnetic spin order was found to induce a ferroelectric polarization in a highly symmetric cubic perovskite ${\mathrm{LaMn}}_3{\mathrm{Cr}}_4{\mathrm{O}}_{12}$. This spin-driven ferroelectricity could not be explained by any of the existing multiferroic models. Here, we put forward a new model, i.e., anisotropic symmetric exchange, to understand this phenomenon, which was confirmed by density functional calculations and tight-binding simulations. Furthermore, our perturbation analysis shows that the anisotropic symmetric exchange term can be even stronger than the conventional contributions in some $5d$ systems. Our multiferroic model can not only explain the experimental results, but also may open a new avenue for exploring exotic magnetoelectric coupling effects.

A concept realizing giant spin Nernst effect in nonmagnetic metallic films is introduced. It is based on the idea of engineering an asymmetric energy dependence of the longitudinal and transverse electrical conductivities, as well as a pronounced energy dependence of the spin Hall angle in the vicinity of the Fermi level by the resonant impurity states at the Fermi level. We employ an analytical model and demonstrate the emergence of a giant spin Nernst effect in Ag(111) films using ab initio calculations combined with the Boltzmann approach for transport properties arising from skew scattering off impurities.

The mechanical properties and electronic structure of polymorphic tungsten carbides with different stacking sequences have been investigated by means of density functional theory. The stacking sequence strongly influences the stability and mechanical strength of these polymorphs. Using the plastic parameters based on resistance to slip, we found that the newly identified metastable $hP4\left[194\right]$ structure (expressed by the Pearson symbol and a space group number) possesses the highest plastic resistance despite its lower elastic moduli as compared to the thermodynamically stable $hP2\left[187\right]$. The $cF8\left[225\right]$ structure is thermodynamically and dynamically unstable at 0 K, but it shows anharmonic stabilization at finite temperature, in agreement with the experimental data. Our results provide a way to increase material strength and hardness by varying the crystal lattice stacking sequence.

We study the problem of magnetization and heat currents and their associated thermodynamic forces in a magnetic system by focusing on the magnetization transport in ferromagnetic insulators like YIG. The resulting theory is applied to the longitudinal spin Seebeck and spin Peltier effects. By focusing on the specific geometry with one ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (YIG) layer and one Pt layer, we obtain the optimal conditions for generating large magnetization currents into Pt or large temperature effects in YIG. The theoretical predictions are compared with experiments from the literature permitting to derive the values of the thermomagnetic coefficients of YIG: the magnetization diffusion length $l_M\sim 0.4\mu \mathrm{m}$ and the absolute thermomagnetic power coefficient ${\epsilon }_M\sim {10}^{-2}{\mathrm{TK}}^{-1}$.

Birnessite compounds are stable across a wide range of compositions that produces a remarkable diversity in their physical, electrochemical, and functional properties. These are hydrated analogs of the magnetically frustrated, mixed-valent manganese oxide structures, with general formula, $\mathrm{N}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_2$. Here we demonstrate that the direct hydration of layered rock-salt type α-$\mathrm{NaMn}{\mathrm{O}}_2$, with the geometrically frustrated triangular lattice topology, yields the birnessite type oxide, $\mathrm{N}{\mathrm{a}}_{0.36}\mathrm{Mn}{\mathrm{O}}_2·0.2{\mathrm{H}}_2\mathrm{O}$, transforming its magnetic properties. This compound has a much-expanded interlayer spacing compared to its parent α-$\mathrm{NaMn}{\mathrm{O}}_2$ compound. We show that while the parent α-$\mathrm{NaMn}{\mathrm{O}}_2$ possesses a Néel temperature of 45 K as a result of broken symmetry in the $\mathrm{M}{\mathrm{n}}^{3+}$ sublattice, the hydrated derivative undergoes collective spin freezing at 29 K within the $\mathrm{M}{\mathrm{n}}^{3+}/\mathrm{M}{\mathrm{n}}^{4+}$ sublattice. Scaling-law analysis of the frequency dispersion of the ac susceptibility, as well as the temperature-dependent, low-field dc magnetization confirm a cooperative spin-glass state of strongly interacting spins. This is supported by complementary spectroscopic analysis [high-angle annular dark-field scanning transmission electron miscroscopy (TEM), energy-dispersive x-ray spectroscopy, and electron energy-loss spectroscopy] as well as by a structural investigation (high-resolution TEM, x-ray, and neutron powder diffraction) that yield insights into the chemical and atomic structure modifications. We conclude that the spin-glass state in birnessite is driven by the spin frustration imposed by the underlying triangular lattice topology that is further enhanced by the in-plane bond-disorder generated by the mixed-valent character of manganese in the layers.

We report on a systematic study of exchange coupled heterostructures, consisting of ferromagnetic [Co/Pt] multilayers and ferrimagnetic (FI) $\mathrm{T}{\mathrm{b}}_x\mathrm{F}{\mathrm{e}}_{100-x-y}\mathrm{C}{\mathrm{o}}_y$ (20 nm) alloy thin films with varying composition exhibiting strong perpendicular magnetic anisotropy. In particular, the impact of the Tb content and ratio of Fe and Co of the amorphous FI alloy on the exchange interaction at the interface was investigated. In this paper, the magnetic properties of single ternary TbFeCo thin films were analyzed in a broad composition range and compared to coupled TbFeCo/[Co/Pt] heterostructures. While a rather linear dependence of the exchange coupling strength was observed for Fe/Co-dominated ferrimagnets with increasing amount of Co, a nonlinear behavior is observed for Tb-dominated alloys. The latter behavior is governed by the variation of the exchange stiffness of the ferrimagnet. Additionally, by using element-specific x-ray magnetic circular dichroism measurements, the thickness of the interface domain wall (IDW) in the ferrimagnet, which is formed during the reversal of the ferromagnet, can be extracted. An inverse correlation between the IDW thickness and the exchange coupling strength at the interface was deduced.

We investigate the Josephson critical current $I_c\left(\mathrm{\Phi }\right)$ of a wide superconductor-normal metal-superconductor (SNS) junction as a function of the magnetic flux $\mathrm{\Phi }$ threading it. Electronic trajectories reflected from the side edges alter the function $I_c\left(\mathrm{\Phi }\right)$ as compared to the conventional Fraunhofer-type dependence. At weak magnetic fields, $B\lesssim {\mathrm{\Phi }}_0/d^2$, the edge effect lifts zeros in $I_c\left(\mathrm{\Phi }\right)$ and gradually shifts the minima of that function toward half-integer multiples of the flux quantum. At $B>{\mathrm{\Phi }}_0/d^2$, the edge effect leads to an accelerated decay of the critical current $I_c\left(\mathrm{\Phi }\right)$ with increasing $\mathrm{\Phi }$. At larger fields, eventually, the system is expected to cross into a regime of “classical” mesoscopic fluctuations that is specific for wide ballistic SNS junctions with rough edges.

We compute the self-energy for the half-filled Hubbard model on a square lattice using lattice quantum Monte Carlo simulations and the dynamical vertex approximation. The self-energy is strongly momentum-dependent, but it can be parametrized via the noninteracting energy-momentum dispersion ${\varepsilon }_{\mathbf{k}}$, except for pseudogap features right at the Fermi edge. That is, it can be written as $\mathrm{\Sigma }({\varepsilon }_{\mathbf{k}},\omega )$, with two energylike parameters $(\varepsilon , \omega )$ instead of three ($k_x, k_y$, and $\omega$). The self-energy has two rather broad and weakly dispersing high-energy features and a sharp $\omega ={\varepsilon }_{\mathbf{k}}$ feature at high temperatures, which turns to $\omega =-{\varepsilon }_{\mathbf{k}}$ at low temperatures. Altogether this yields a $\mathcal{Z}$- and reversed-$\mathcal{Z}$-like structure, respectively, for the imaginary part of $\mathrm{\Sigma }({\varepsilon }_{\mathbf{k}},\omega )$. We attribute the change of the low-energy structure to antiferromagnetic spin fluctuations.

We have investigated temperature-dependent electronic structures of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ to unravel its insulating nature. Employing the combined scheme of the density functional theory (DFT) and the dynamical mean-field theory (DMFT), we have shown that the insulating state persists even above the Néel temperature $\left(T_N\right)$, which reveals that ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ is classified as a Mott-type insulator. The measured photoemission spectrum in the paramagnetic state is well described by the electronic structure obtained by the DFT+DMFT for the insulating state above $T_N$. The analysis of optical conductivity, however, suggests that the nonlocal correlation effect is also important in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$. Therefore, ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ is not a standard Mott insulator in that the extended nature and the nonlocal correlation effect of Ir $5d$ electrons are important as well in describing its electronic and magnetic properties.

Compared with conventional metal plasmonic materials, surface plasmons in graphene are advantageous in terms of higher confinement, relative low loss, flexible featuring, and good tunability. However, the working frequencies of the pristine graphene (undoped graphene) surface plasmons are located in the terahertz and infrared regions, which limit their applications. Here we show high-frequency plasmons in nitrogen (N)-doped graphene nanostructures investigated by time-dependent density functional theory. We found the optical absorption strength of systems containing two layers to be more than twofold stronger than that of systems with monolayers. The optical absorption strength increases as the interlayer distance increases, and the absorption spectra are red-shifted for impulse excitations polarized in the armchair edge direction $(x$ axis). For microstructures of more than two layers, the optical absorption strength increases as number of layers of the N-doped graphene nanostructures increases. In addition, when the number of layers becomes elevated at low-energy resonances, the absorption spectra are seen to blue-shift. The plasmon energy resonance points are located in the visible and ultraviolet regions. The N-doped graphene provides an effective strategy for nanoscale plasmon devices in the visible and ultraviolet regions, despite their weaker absorption intensities when compared with the pristine graphene.

The spin and valley transports and tunnel magnetoresistance are studied in a silicene-based asymmetrical magnetic tunnel junction consisting of a ferromagnetic tunnel barrier, sandwiched between a ferromagnetic electrode and a normal electrode. For such an asymmetrical silicene junction, a general formulism is established. The numerical results show that the spin-valley resolved conductances strongly depend on the magnetization orientation of the ferromagnetic tunnel barrier, and the fully spin-valley polarized current can be realized by tuning a perpendicularly applied electric field. We also find that the tunnel magnetoresistance in this case can be effectively modified by the external electric field when the conductance is fully spin-valley polarized. In particular, the exchange field in the ferromagnetic electrode can further substantially enhance the tunnel magnetoresistance of the system. Our work provides a practical method for electric and magnetic manipulation of valley/spin polarization and tunnel magnetoresistance.

We report a first-principles investigation of spin-dependent transport properties in two different graphene-based molecular junctions. By applying different temperatures between two leads without bias voltage, spin-dependent currents are driven which depend on reference temperature $T$, temperature gradient $\mathrm{\Delta }T$, and gate voltage $V_g$. Moreover, pure spin currents without charge currents can be obtained by adjusting $T,\mathrm{\Delta }T$, and $V_g$ for both molecular junctions. The directions of pure spin currents in these two molecular junctions are opposite, which can be understood by analyzing the transmission coefficients under equilibrium states. Spin thermopower, thermal conductance, and the figure of merit as functions of $T,V_g$, and chemical potential $\mu$ were also investigated in the linear response regime. Large spin thermopower and spin figure of merit can be obtained by adjusting $V_g$ and $\mu$ for each junction, which indicates proper application of spin caloritronic devices of our graphene-based molecular junctions.

The microscopic processes underlying magnetostriction in ferrites were studied for the case of $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ single crystals by high-resolution in situ x-ray diffraction and complementary magnetic microscopy techniques. The data support the reports of Yang and Ren [Phys. Rev. B 77, 014407 (2008)] that magnetostriction in these materials originates from the switching of crystallographic domains, similar to ferroelastic or ferroelectric domain switching, and reveals the presence of two coexisting tetragonal spinel structures, corresponding to domains of high and of low strain. The latter alternate in the crystal, separated by 90° domain boundaries, and can be explained by the effect of internal stress emerging during the transition into the ferrimagnetic phase. During magnetization of the sample two structural transitions are observed: a conversion of the transversal into axial domains at 1.95 kOe and a growth of the high-strain domains at the cost of the low-strain axial domains at 2.8 kOe. These microscopic changes are in good agreement with the macroscopic magnetization and magnetostriction behavior of $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$.

We report the detection of an isolated energy level in the band gap of crystalline ${\mathrm{Yb}}_2{\mathrm{Si}}_2{\mathrm{O}}_7$ in the low-energy-loss region of its electron energy-loss (EEL) spectrum, obtained using a monochromated scanning transmission electron microscope. The experimental results are corroborated by first-principles calculations of the theoretical EEL spectrum. The calculations reveal that unoccupied Yb $4f$ orbitals constitute an isolated energy level about 1 eV below the conduction band minimum (CBM), resulting in a terrace about 1 eV wide at the band edge of the EEL spectrum. In the case of ${\mathrm{Yb}}_2{\mathrm{O}}_3$, no band edge terrace is present because the unoccupied $f$ level lies just below the CBM. We also examined optical absorption properties of ${\mathrm{Yb}}_2{\mathrm{Si}}_2{\mathrm{O}}_7$ using UV-vis diffuse reflectance spectroscopy, which shows that the isolated energy level could not be detected in the band edge of the obtained absorbance spectrum. These findings demonstrate the utility of low-loss EEL spectroscopy with high energy resolution for probing semilocalized electronic features.