The influence of spin-Hall-effect spin torque (SHE-ST) induced by in-plane charge current was studied in microscale Ta/Co${}_{20}$Fe${}_{60}$B${}_{20}$/TaO${}_x$ films with perpendicular magnetization. Simultaneous electrical transport and polar magneto-optical Kerr effect (MOKE) imaging experiments were used to investigate the switching dynamics. A rich set of switching behaviors was observed, which can be well understood by analyzing a switching-phase diagram and polar MOKE images, considering the competition between SHE-ST and the externally applied magnetic field. Furthermore, we found that domain walls with a particular chirality were dominant in our devices, which suggests the presence of the Dzyaloshinskii-Moriya interaction in the present material system.

${\text{NiFe}}_2$${\text{O}}_4$/${\text{BaTiO}}_3$ (NFO/BTO) multilayer heterostructures grown on (001)-${\text{SrTiO}}_3$ substrates with alternating ferroelectric BTO and ferrimagnetic NFO layers exhibit magnetoelectric (ME) coupling, which increases with the number of layers and, hence, with the number of NFO/BTO interfaces. We have studied the local electronic and magnetic states of Ni and Fe ions in the NFO/BTO multilayers with various NFO and BTO thicknesses by x-ray absorption spectroscopy and x-ray magnetic circular dichroism. With an increasing number of layers, both Ni and Fe magnetic moments decrease. With decreasing NFO layer thickness, the average magnetic moment of Ni decreases, while the average magnetic moment of Fe ions remains unaffected, meaning that Ni ions at the interface lose ferromagnetic moments. This suggests that the enhancement of ME coupling is associated with Ni ions at the interface whose ferromagnetic behavior is weakened through hybridization with the BTO electronic states.

We present a theoretical study of the influence of relativistic effects on the electronic band structure and thermopower of Mg${}_{2}X$ ($X=$ Si, Ge, Sn) semiconductors. The full potential Korringa-Kohn-Rostoker (KKR) method is used, and a detailed comparison between the fully relativistic and semirelativistic electronic structure features is done. We show that the spin-orbit (S-O) interaction splits the valence band at $\Gamma$ point in good agreement with the experimental data, and this effect strongly depends on $X$ atom. The S-O modifications of the topology of the $\Gamma$-centered holelike Fermi surface pockets lead to a change in electron transport properties, which are investigated using the Boltzmann approach. In addition, a simple and efficient method is presented for the calculation of density of states effective mass $m^{*}$, and then used to examine the impact of relativistic effects on $m^{*}$. It is found that the S-O coupling of the valence bands reduces the effective mass and therefore significantly lowers the thermopower, primarily in ${\mathrm{Mg}}_2\mathrm{Sn}$, but also in ${\mathrm{Mg}}_2\mathrm{Ge}$. A detrimental influence of the S-O interaction on the thermoelectric performance of $p$-type Mg${}_{2}X$ is analyzed as a function of temperature ($10\text{–}900$ K) and carrier concentration (${10}^{18}\text{–}{10}^{22}$ cm${}^{-3}$). Interestingly, similar calculations in $n$-type Mg${}_2$X, show a negligible effect of the S-O interaction on the lowest conduction bands and, consequently, also on the Seebeck coefficient.

We investigate polarization-resolved fine structure in the photoluminescence (PL) in the fractional quantum Hall effect regime at $B=4$–6 T, where small Zeeman energy allows spin-depolarized ground states. We observe up to five distinct peaks with characteristic polarization and temperature dependence in the vicinity of $\nu =1/3$ and quenching of the PL from triplet charged quasiexcitons at around $\nu =1/4$. Those findings appear to be consistent with results of exact diagonalization on a Haldane sphere including all spin configurations and are understood to be PL from fractionally charged quasiexcitons.

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities, mediated by Dirac surface states on the surface of a topological insulator, leads to impurities' ferromagnetic ordering. We present a self-consistent theory of the ordering, which takes into account a gap in the surface spectrum induced by the exchange field of magnetic impurities. We show that the gap does not change the general structure of RKKY interaction but considerably influences its strength. This feedback can be both positive and negative, depending on the ratio between the chemical potential and the gap, and it qualitatively modifies the temperature dependence of the spin polarization of magnetic impurities. The resulting unusual temperature dependence can be directly measured in angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) experiments.

We study the leading low-temperature dependence of magnetic susceptibility of one-dimensional electrons with a fixed total number of particles at the magnetic fields equal to zero-temperature critical values where the magnetic field induces commensurate-incommensurate quantum phase transitions. For free and repulsively interacting electrons there is only one such critical field corresponding to the transition to the fully polarized state. For attractively interacting electrons besides saturation field there is another critical field equal to the spin gap where zero-temperature magnetization sets in. For all cases, except for the lattice models at half filling, the magnetic susceptibility at critical values of magnetic field has a universal logarithmic temperature dependence, $\chi \left(T\right)=\chi \left(0\right)(1+2/lnT+\cdots )$ for $T\to 0$.

In a recent paper by Neupert, Santos, Chamon, and Mudry [Phys. Rev. B 86, 165133 (2012)], it is claimed that there is an elementary formula for the Hall conductivity ${\sigma }_{xy}$ of fractional Chern insulators. We show that the proposed formula cannot generally be correct, and we suggest one possible source of the error. Our reasoning can be generalized to show that no quantity (such as Hall conductivity) expected to be constant throughout an entire phase of matter can possibly be given as the expectation of any time-independent short-ranged operator.

When deriving a formula for the Hall conductivity of interacting electrons in our original paper [Neupert et al., Phys. Rev. B 86, 165133 (2012)], we have relied on an unjustified implicit assumption that a certain gauge choice could be made. Only under this condition would the formula follow. If this condition fails, the formula we derived does not lead to the exactly quantized value of the Hall conductance in fractional Chern insulators.

Electric-field-induced transformations are studied experimentally in cube-on-cube-type epitaxial film of relaxor ferroelectric (FE) ${\text{PbMg}}_{{}^1/{}_3}$${\text{Nb}}_{{}^2/{}_3}$${\text{O}}_3$ grown on (001) MgO substrate. The dielectric response, polarization, and current are measured along the out-of-plane $\langle 100\rangle$ direction of the film and analyzed as a function of temperature, frequency, and applied field. Compared to the $\langle 100\rangle$ crystal, transformation of the low-temperature relaxor state to a new state in the (001) film takes place at considerably lower temperatures and larger fields. Based on the found bisigmoidal shape and the two scaling regimes of the current-voltage curves, the two corresponding electric-field-induced processes are suggested to be dipolar flips and flow of a phase boundary in the film. The field-induced state in the film is dynamic and unstable, and it differs from the field-induced FE state in the crystal. The robustness of the relaxor state to electric field in the film is discussed in relation to spatial anisotropy of the dipolar system in the (001) film.

Using ab initio electronic structure calculations, we have investigated the effect of an electric field and of a heavy-metal cap of Pd on the magnetocrystalline anisotropy (MCA) of FePd ultrathin film. Analysis of the energy- and $k$-resolved distribution of the orbital character of the minority-spin band reveals that the perpendicular MCA of the uncapped film mainly arises from the spin-orbit coupling (SOC) between unoccupied Fe $d_{xy}$ and occupied Fe $d_{x^2-y^2}$ states. On the other hand, the SOC between the Pd- and Fe-derived $d$ states yields negative contributions to the MCA. We find that the sensitivity of the surface anisotropy energy to the applied electric field is 18 fJ/(Vm) and is due to changes in the occupation of the surface Fe atoms $d_{x^2-y^2}$ and ($d_{xz},d_{yz}$) orbitals. We demonstrate that the thickness of the Pd cap has a dramatic effect on the MCA and can even switch the magnetization from out-of- to in-plane orientation. The underlying origin is the change of the position and orbital character of the spin-polarized quantum well states induced in the Pd cap by varying its thickness. These results have important implications for exploiting heavy metals with large spin-orbit coupling (Ru, Pd, Ta, Pt, or Au) as contacts with ferromagnetic thin films to tailor the magnetic switching of spintronic devices by tuning the cap thickness.

A model is presented for the control of the magnetic relaxation in a ferromagnetic insulator (FMI) in contact with a normal metal (NM) under a thermal gradient applied across the thickness of the bilayer. We show that the thermal gradient modifies the spin pumping damping created by the contact of the NM with the FMI. This results from the bulk magnon spin current generated through the longitudinal spin Seebeck effect that superimposes to the spin pumping current at the FMI/NM interface, changing the FMI magnetic damping. The results of the model explain the experimental data on the control of the magnetic relaxation by thermal gradients measured by the linewidth of the ferromagnetic resonance absorption and by the attenuation of spin-wave packets propagating along a film of single-crystal yttrium iron garnet covered by a very thin platinum layer. Depending on the sign of the gradient, the relaxation rate can be increased or decreased, leading in the latter case to an apparent amplification.

Chemical substitution, combined with strain, allows the charge-transfer energy in hole-doped cuprates to be broadly tuned. We theoretically characterize the structural and electronic properties of the family of compounds $R_2$CuO${}_2$S${}_2$, constructed by sulfur replacement of the apical oxygens and rare-earth substitutions in the parent cuprate La${}_2$CuO${}_4$. Additionally, the enthalpies of formation for possible synthesis pathways are determined.

Chiral edge modes of topological insulators and Hall states exhibit nontrivial behavior of conductance in the presence of impurities or additional channels. We present a simple formula for the conductance through a chiral edge mode coupled to a disordered bulk. For a given coupling matrix between the chiral mode and bulk modes, and a Green's function matrix of bulk modes in real space, the renormalized Green's function of the chiral mode is expressed in closed form as a ratio of determinants. We demonstrate the usage of the formula in two systems: (i) a 1d wire with random on-site impurity potentials for which we found that the disorder averaging is made simpler with the formula, and (ii) a quantum Hall fluid with impurities in the bulk for which the phase picked up by the chiral mode due to the scattering with the impurities can be conveniently estimated.

In this paper, we report on the structural and magnetic properties, as deduced from susceptibility measurements and neutron powder diffraction experiments, of an orthorhombic nickel disulfate, Li${}_2$Ni(SO${}_4$)${}_2$. This phase presents NiO${}_6$ octahedra linked via SO${}_4$ groups only, leading to an antiferromagnetic behavior resulting from super-super-exchange interactions. Magnetic moments order below $T_N$ = 28 K and the observed magnetic structure can be explained using two antiferromagnetic and one ferromagnetic exchange interactions, which are discussed in relation with the Goodenough-Kanamori-Anderson rules. The magnetic structure, with k = (0, 0, 0), has the symmetry $P{b}^{\prime }{c}^{\prime }{a}^{\prime }$ that has the inversion center associated with time inversion, so the compound should be a linear magnetoelectric.

We have investigated the magnetic and electric ground states of a quasi-two-dimensional triangular lattice antiferromagnet (TLAF), ${\mathrm{Ba}}_3{\mathrm{CoNb}}_2{\mathrm{O}}_9$, in which the effective spin of Co${}^{2+}$ is 1/2. At zero field, the system undergoes a two-step transition upon cooling at $T_{N2}=1.36$ K and $T_{N1}=1.10$ K and enters a 120${}^{\circ }$ ordered state. By applying magnetic fields, a series of spin states with fractions of the saturation magnetization $M_s$ are observed. They are spin states with 1/3, 1/2, 2/3 (or $\sqrt{3}/3$) $M_s$. The ferroelectricity emerges in all spin states, either with collinear or noncollinear spin structure, which makes ${\mathrm{Ba}}_3{\mathrm{CoNb}}_2{\mathrm{O}}_9$ another unique TLAF exhibiting both a series of magnetic phase transitions and multiferroicity. We discuss the role of quantum fluctuations and magnetic anisotropy in contributing more complex phase diagram compared to its sister multiferroic TLAF compound ${\mathrm{Ba}}_3$NiNb${}_2{\mathrm{O}}_9$ [J. Hwang et al., Phys. Rev. Lett. 109, 257205 (2012)].

We determine the size of the elementary quasihole in $\nu =1/3$ and $\nu =7/3$ quantum Hall states via exact-diagonalization and density-matrix renormalization group calculations on the sphere and cylinder, using a variety of short- and long-range pinning potentials. The size of the quasihole at filling factor $\nu =1/3$ is estimated to be $\approx 4{\ell }_B$, and that of $\nu =7/3$ is $\approx 7{\ell }_B$, where ${\ell }_B$ is the magnetic length. In contrast, the size of the Laughlin quasihole, expected to capture the basic physics in these two states, is around $\approx 2.5{\ell }_B$. Our work supports the earlier findings that the quasihole in the first excited Landau level is significantly larger than in the lowest Landau level.

The quantum spin liquid is an enigmatic entity that is often hard to characterize within the conventional framework of condensed matter physics. We here present theoretical and numerical evidence for the characterization of a quantum spin liquid phase extending from the exact ground state to a finite critical temperature. We investigate a three-dimensional variant of the Kitaev model on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables on a diamond lattice. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from the quantum spin liquid to a paramagnet at a finite critical temperature $T_c$, accompanied by a divergent singularity of the specific heat. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above $T_c$, while it obeys the Curie law at high temperature and approaches a nonzero Van Vleck–type constant at low temperature. Although the susceptibility changes continuously at $T_c$, its temperature derivative shows a critical divergence at $T_c$. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables or of the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition can be interpreted as one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. The correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently discovered hyperhoneycomb compound $\beta$-${\text{Li}}_2$${\text{IrO}}_3$ is mentioned.