GdSi exhibits spin-density-wave (SDW) order arising from the cooperative interplay of sizeable local moments and a partially nested Fermi sea of itinerant electrons. Using magnetotransport, magnetization, and nonresonant magnetic x-ray diffraction techniques, we determine the H-T phase diagrams of GdSi for magnetic fields up to 21 T, where antiferromagnetic order is no longer stable, and field directions along each of the three major crystal axes. While the incommensurate magnetic ordering vector that characterizes the SDW is robust under magnetic field, the multiple spin structures of this compound are highly flexible and rotate relative to the applied field via either canting or spin-flop processes. The antiferromagnetic spin densities always arrange themselves transverse to the applied magnetic field direction. The phase diagrams are delineated by two types of phase boundaries: one separates a collinear from a planar spin structure associated with a lattice structural transition, and the other defines a spin flop transition that is only weakly temperature dependent. The major features of the phase diagrams along each of the crystal axes can be explained by the combination of local moment and global Fermi surface physics at play.

We compute current correlators of the $CP$${}^{N-1}$ field theory in 2+1 dimensions, both at the critical point and in the phase with spontaneously broken $\mathrm{SU}\left(N\right)$ symmetry. Universal constants are obtained to next-to-leading order in the $1/N$ expansion. Implications are noted for quantum critical points of antiferromagnets and their vicinity.

We reformulate the full quantum dynamics of spin systems using a phase-space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. This representation is superior in practice to an earlier phase-space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times severalfold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse-field Ising model in one and two dimensions.

In developing the phonon quasiparticle picture, Peierls discovered that, in a perfect crystal, without anharmonic umklapp ($U$) events, a current-carrying distribution can never relax to a zero-current distribution. Callaway introduced a simplified approximate model version of the Peierls-Boltzmann equation, retaining its ability to deal separately with normal ($N$) and $U$ events. This paper clarifies and improves the Callaway model, and shows that Callaway underestimated the suppression of $N$ processes in relaxing thermal current. The new result should improve computations of thermal conductivity from relaxation-time studies.

Transport coefficients, the elements of the so-called Onsager matrix, are essential quantities for modeling solid-state kinetics controlled by diffusion. Focusing on diffusion in binary alloys with a body-centered cubic crystal structure, we investigate the drag of solute atoms by vacancies, an effect induced by kinetic correlations. To accomplish this, an analytic method—the self-consistent mean field method—is extended to take into account interactions between the solute atom and a vacancy up to the third nearest neighbor sites. We identify kinetic effects involving one or more frequencies. Analytic results are compared with select atomic kinetic Monte Carlo simulations. We show that (1) solute drag is a more general phenomena than previously assumed, (2) it can induced by association and dissociation exchanges, and (3) we identify the mechanisms involved.

We investigate the electronic and thermodynamic properties of Zr and its oxides from first principles to elucidate phase stability in the Zr-O system. Hexagonally close-packed Zr is unusual in its ability to dissolve very high concentrations of oxygen over its interstitial octahedral sites, forming a variety of ordered suboxides that undergo both first-order and second-order phase transitions upon heating. We perform a first-principles, statistical-mechanical analysis of finite temperature phase stability of ZrO${}_x$ using a cluster expansion Hamiltonian and Monte Carlo calculations. This analysis predicts the existence of 0-K ground-state oxygen orderings at composition ZrO${}_{1/6}$, ZrO${}_{2/9}$, ZrO${}_{1/3}$, ZrO${}_{4/9}$, and ZrO${}_{1/2}$ along with evidence of an infinite sequence of ground-state suboxide orderings at intermediate oxygen concentrations consisting of different stackings of empty, $\frac{1}{3}$-filled and $\frac{2}{3}$-filled two-dimensional oxygen layers. We also predict the stability of a previously uncharacterized Zr-monoxide phase, which we label ${\delta }^{\prime }$-ZrO due to its crystallographic relation to $\delta$-TiO. The ${\delta }^{\prime }$-ZrO structure is equivalent to the high-pressure $\omega$-Zr phase but has interstitial oxygen ordering. Finally, as part of the technical implementation of our statistical mechanical study, we introduce a new algorithm to parametrize the coefficients of a cluster expansion Hamiltonian and apply a $k$-space analysis to rigorously track order-disorder phenomena at finite temperature.

We study response to a twist in the two-dimensional $p$-state clock model, which has the discrete $Z_p$ symmetry. The response is measured in terms of helicity modulus, which is usually defined with respect to an infinitesimal twist. However, we demonstrate that such a definition is inappropriate for the clock model. The helicity modulus must be defined with respect to a finite, quantized twist which matches the discrete $Z_p$ symmetry of the model. Numerical study of the appropriately defined helicity modulus resolves controversy over the clock model, showing the existence of two Berezinskii-Kosterlitz-Thouless transitions for $p>4$.

We show that rf irradiation drastically increases coherence of the charge-density wave (CDW) depinning and sliding in the electric field for NbS${}_3$ (phase II), TaS${}_3$, and (TaSe${}_4$)${}_2$I. The effect is observed in the range of the CDW currents at which the fundamental frequencies are well below the frequency of the irradiation. The result is evident from the shape of $I$-$V$ curves, Shapiro steps, and noise spectra. We treat the effect in terms of the rf-assisted relaxation of metastable states forming at CDW sliding. The rf irradiation can be helpful in experiments, where utmost coherence of the CDW transport is needed, e.g., in studies of the Shapiro steps, expanding the ranges of their observation.

The topological physics of quantum Hall states is efficiently encoded in purely topological quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy dynamical properties in a continuum description, however, typically requires proximity to a quantum critical point. We construct a field theory that describes the quantum transition from an isotropic to a nematic Laughlin liquid. The soft mode associated with this transition approached from the isotropic side is identified as the familiar intra-Landau level Girvin-MacDonald-Platzman mode. We obtain $z=2$ dynamic scaling at the critical point and a description of Goldstone and defect physics on the nematic side. Despite the very different physical motivation, our field theory is essentially identical to a recent “geometric” field theory for a Laughlin liquid proposed by Haldane.

We develop the formalism of the macroscopic monopolization—that is, the magnetoelectric monopole moment per unit volume—in periodic solids, and discuss its relationship to the magnetoelectric effect. For the series of lithium transition metal phosphate compounds, we use first-principles density functional theory to calculate the contributions to the macroscopic monopolization from the global distribution of magnetic moments within the unit cell, as well as from the distribution of magnetization around the atomic sites. We find one example within the series (LiMnPO${}_4$) that shows a macroscopic monopolization corresponding to a ferromonopolar ordering consistent with its diagonal magnetoelectric response. The other members of the series (Li$M$PO${}_4$, with $M=\text{Co}$, Fe, and Ni) have zero net monopolization but have antiferromonopolar orderings that should lead to $q$-dependent diagonal magnetoelectric effects.

Neutron time-of-flight spectroscopy has been employed to study the crystal-field splitting of Pr${}^{3+}$ in the pyrochlore stannate Pr${}_2$Sn${}_2$O${}_7$. The crystal field has been parameterized from a profile fit to the observed neutron spectrum. The single-ion ground state is a well-isolated non-Kramers doublet of ${\Gamma }_3^{+}$ symmetry with a large Ising-like anisotropy, ${\chi }_{zz}/{\chi }_{\perp }\approx 60$ at 10 K, but with a significant admixture of terms $|M_J\ne \pm J\rangle$, which can give rise to quantum zero-point fluctuations. This magnetic state satisfies the requirements for quantum spin-ice behavior.

It is well known that the three-dimensional (3D) electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry preserving, at the expense of having surface-topological order. In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian. We show that the surface-topological order provides a complete nonperturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topological Mott insulators.

We have performed a systematic representation-theory-based search for the simplest structures allowing isotropic magnetoelectric coupling. We find 30 such structures, all sharing a common pattern of atomic displacements in the direction of atomic magnetic moments. We focus on one of these 30 canonical structures and find that it is generically realized in a class of fractionally substituted pyrochlore compounds with an all-in-all-out magnetic order. Furthermore, we find that these substituted pyrochlore compounds have a substantial Chern-Simons orbital magnetoelectric component ($\theta =0.1$–$0.2$). While this component is also formally present in strong $Z_2$ topological insulators ($\theta =\pi$), its effects are observable there only if time-reversal symmetry is broken at the surface.

Spin transfer torques (STTs) occur when electric currents travel through inhomogeneously magnetized systems and are important for the motion of magnetic textures such as domain walls. Since superconductors are easy-plane ferromagnets in particle-hole (charge) space, it is natural to ask whether any charge duals of STT phenomena exist therein. We find that the superconducting analog of the adiabatic STT vanishes in a bulk superconductor with a momentum-independent order parameter, while the superconducting counterpart of the nonadiabatic STT does not vanish. This nonvanishing superconducting torque is induced by heat (rather than charge) currents and acts on the charge (rather than spin) degree of freedom. It can become significant in the vicinity of the superconducting transition temperature, where it generates a net quasiparticle charge and alters the dispersion and linewidth of low-frequency collective modes.

We show how disorder can be used to guide a broadband ultrasonic wave. The idea is to exploit the transverse localization regime that has been reported for light. Our waveguide consists of a set of parallel cylindrical scatterers randomly distributed in the transverse plane. An ultrasonic beam propagating along the direction of scatterers is found to remain confined in the two other directions on a size smaller than the waveguide diameter and driven by the localization length. Interestingly, the guided wave is also found to propagate with a very limited temporal dispersion.

We report on the measurement of first-order spatial correlations on a one-dimensional $97\%$ excitonic polariton condensate, excited in cooled ZnO microwires by nonresonant optical pulses. We find that, thanks to the tiny $3\%$ photonic fraction, a coherence length as large as 10 $\mu$m can build up, i.e., orders of magnitude larger than any reported so far for an ultracold exciton gas. Based on a driven-dissipative mean-field model we show that the decay of correlations is mainly due to a shallow disorder and driven-dissipative conditions.

We study the nonadiabatic dynamics of a two-dimensional $p+ip$ superfluid following an instantaneous quantum quench of the BCS coupling constant. The model describes a topological superconductor with a nontrivial BCS (trivial BEC) phase appearing at weak- (strong-) coupling strengths. We extract the exact long-time asymptotics of the order parameter $\Delta \left(t\right)$ by exploiting the integrability of the classical $p$-wave Hamiltonian, which we establish via a Lax construction. Three different types of asymptotic behavior can occur depending upon the strength and direction of the interaction quench. We refer to these as the nonequilibrium phases {I, II, III}, characterized as follows. In phase I, the order parameter asymptotes to zero due to dephasing. In phase II, $\Delta \to {\Delta }_{\infty }$, a nonzero constant. Phase III is characterized by persistent oscillations of $\Delta \left(t\right)$. For quenches within phases I and II, we determine the topological character of the asymptotic states. We show that two different formulations of the bulk topological winding number, although equivalent in the BCS or BEC ground states, must be regarded as independent out of equilibrium. The first winding number $Q$ characterizes the Anderson pseudospin texture of the initial state; we show that $Q$ is generically conserved. For $Q\ne 0$, this leads to the prediction of a “gapless topological” state when $\Delta$ asymptotes to zero. The presence or absence of Majorana edge modes in a sample with a boundary is encoded in the second winding number $W$, which is formulated in terms of the retarded Green's function. We establish that $W$ can change following a quench across the quantum critical point. When the order parameter asymptotes to a nonzero constant, the final value of $W$ is well defined and quantized. We discuss the implications for the (dis)appearance of Majorana edge modes. Finally, we show that the parity of zeros in the bulk out-of-equilibrium Cooper-pair distribution function constitutes a ${\mathbb{Z}}_2$-valued quantum number, which is nonzero whenever $W\ne Q$. The pair distribution can in principle be measured using rf spectroscopy in an ultracold-atom realization, allowing direct experimental detection of the ${\mathbb{Z}}_2$ number. This has the following interesting implication: topological information that is experimentally inaccessible in the bulk ground state can be transferred to an observable distribution function when the system is driven far from equilibrium.

Cation displacements, oxygen octahedral tilts, and magnetism of epitaxial, ferrimagnetic, insulating GdTiO${}_3$ films sandwiched between cubic SrTiO${}_3$ layers are studied using scanning transmission electron microscopy and magnetization measurements. With decreasing GdTiO${}_3$ film thickness, structural (GdFeO${}_3$-type) distortions are reduced, concomitant with a reduction in the Curie temperature. Ferromagnetism persists to smaller deviations from the cubic perovskite structure than is the case for the bulk rare-earth titanates. The results indicate that the ferromagnetic ground state is controlled by the narrow bandwidth, exchange and orbital ordering, and only to second order depends on the amount of the GdFeO${}_3$-type distortion.

A combined analysis of x-ray absorption and resonant reflectivity data was used to obtain the orbital polarization profiles of superlattices composed of four-unit-cell-thick layers of metallic LaNiO${}_3$ and layers of insulating $RX$O${}_3$ ($R=\text{La}$, Gd, Dy and $X=\text{Al}$, Ga, Sc), grown on substrates that impose either compressive or tensile strain. This superlattice geometry allowed us to partly separate the influence of epitaxial strain from interfacial effects controlled by the chemical composition of the insulating blocking layers. Our quantitative analysis reveals orbital polarizations up to 25$\%$. We further show that strain is the most effective control parameter, whereas the influence of the chemical composition of the blocking layers is comparatively small.

We have studied the influence of epitaxial strain on magnetic orderings and the couplings between the spin and polar phonons in the 1:1 SrMnO${}_3$/LaMnO${}_3$ superlattice from first principles. Magnetic phase transitions of the superlattice induced by epitaxial strain are observed, consistent with previous reports. We find that oxygen octahedral rotations lower the ground state energy but do not destroy the magnetic phase transitions induced by strain. We compute zone center phonon frequencies and eigenvectors as functions of epitaxial strain and magnetic ordering. A substantial increase of the coupling strength between the spin and the lowest-frequency polar mode is observed for tensile strains. This increase can be attributed to a change of character of the lowest mode resulting from different relative couplings of the various polar modes to epitaxial strain. Finally, spin-phonon coupling strengths are computed in a Heisenberg formalism. This analysis directly reveals the changes in exchange couplings due to specific atomic displacements or phonon modes, as well as the nonequivalence of the out-of-plane exchange couplings across LaO layers and across SrO layers, the latter being the result of the artificial structuring in the superlattice.