For the one-dimensional spin-1/2 XX model with either periodic or open boundary conditions, it is shown by using a fermionic approach that the matrix element of the spin operator $S_j^{-}$ ($S_j^{-}{S}_{j^{\prime }}^{+}$) between two eigenstates with numbers of excitations $n$ and $n+1$ ($n$ and $n$) can be expressed as the determinant of an appropriate $(n+1)\times (n+1)$ matrix whose entries involve the coefficients of the canonical transformations diagonalizing the model. In the special case of a homogeneous periodic XX chain, the matrix element of $S_j^{-}$ reduces to a variant of the Cauchy determinant that can be evaluated analytically to yield a factorized expression. The obtained compact representations of these matrix elements are then applied to two physical scenarios: (i) Nonlinear optical response of molecular aggregates, for which the determinant representation of the transition dipole matrix elements between eigenstates provides a convenient way to calculate the third-order nonlinear responses for aggregates from small to large sizes compared with the optical wavelength; and (ii) real-time dynamics of an interacting Dicke model consisting of a single bosonic mode coupled to a one-dimensional XX spin bath. In this setup, full quantum calculation up to $N\le 16$ spins for vanishing intrabath coupling shows that the decay of the reduced bosonic occupation number approaches a finite plateau value (in the long-time limit) that depends on the ratio between the number of excitations and the total number of spins. Our results can find useful applications in various “system-bath” systems, with the system part inhomogeneously coupled to an interacting XX chain.

This paper builds on the recent demonstration of three-wave mixing based phononic frequency comb. Here, in this process, an intrinsic coupling between the drive and resonant frequency leads to a frequency comb of spacing corresponding to the separation between drive and resonant frequency. In this paper, through the coupling with other identical devices, we demonstrate the emergence of two different frequency comb regimes using a single tone external drive signal. Several interesting features for coupled frequency combs are identified, including the following: (1) the spacing of the component frequency combs are controlled by two different resonant frequencies, each associated with two different modes; (2) the nonlinear drive level dependence is different for the component frequency combs; (3) mutually exclusive well-bounded regimes for each component frequency comb exist, and such regimes are not merely described by well-known parametric resonance thresholds.

Artificial magnetic honeycomb lattices are expected to exhibit a broad and tunable range of novel magnetic phenomena that would be difficult to achieve in natural materials, such as long-range spin ice, entropy-driven magnetic charge-ordered states, and spin order due to the spin chirality. Eventually, the spin correlation is expected to develop into a unique spin-solid-state-density ground state, manifested by the distribution of the pairs of vortex states of opposite chirality. Here we report the creation of an artificial permalloy honeycomb lattice of ultrasmall connecting bonds, with a typical size of $\simeq 12$ nm. Detailed magnetic and neutron-scattering measurements on the newly fabricated honeycomb lattice demonstrate the evolution of magnetic correlation as a function of temperature. At low enough temperature, neutron-scattering measurements and micromagnetic simulation suggest the development of a loop state of vortex configuration in this system.

Crystals of ${\mathrm{SrMn}}_2{\mathrm{Sb}}_2$ and ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$ were grown using Sn flux and characterized by powder and single-crystal x-ray diffraction, respectively, and by single-crystal electrical resistivity $\rho$, heat capacity $C_{\mathrm{p}}$, and magnetic susceptibility $\chi$ measurements versus temperature $T$, and magnetization versus field $M\left(H\right)$ isotherm measurements. ${\mathrm{SrMn}}_2{\mathrm{Sb}}_2$ adopts the trigonal ${\mathrm{CaAl}}_2{\mathrm{Si}}_2$-type structure, whereas ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$ crystallizes in the tetragonal ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type structure. The $\rho \left(T\right)$ data indicate semiconducting behaviors for both compounds with activation energies of $\gtrsim 0.35$ eV for ${\mathrm{SrMn}}_2{\mathrm{Sb}}_2$ and 0.16 eV for ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$. The $\chi \left(T\right)$ and $C_{\mathrm{p}}\left(T\right)$ data reveal antiferromagnetic (AFM) ordering at $T_{\mathrm{N}}$ = 110 K for ${\mathrm{SrMn}}_2{\mathrm{Sb}}_2$ and 450 K for ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$. The anisotropic $\chi (T\le T_{\mathrm{N}})$ data also show that the ordered moments in ${\mathrm{SrMn}}_2{\mathrm{Sb}}_2$ are aligned in the hexagonal $ab$ plane, whereas the ordered moments in ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$ are aligned collinearly along the tetragonal $c$ axis. The $ab$-plane $M\left(H\right)$ data for ${\mathrm{SrMn}}_2{\mathrm{Sb}}_2$ exhibit a continuous metamagnetic transition at low fields $0<H\lesssim 1$ T, whereas ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$ exhibits no metamagnetic transitions up to 5.5 T. The $\chi \left(T\right)$ and $C_{{}_{\mathrm{p}}}\left(T\right)$ data for both ${\mathrm{SrMn}}_2{\mathrm{Sb}}_2$ and ${\mathrm{BaMn}}_2{\mathrm{Sb}}_2$ indicate strong dynamic short-range AFM correlations above their respective $T_{\mathrm{N}}$ up to at least 900 K within a local-moment picture, corresponding to quasi-two-dimensional magnetic behavior. The present results and a survey of the literature for Mn pnictides with the ${\mathrm{CaAl}}_2{\mathrm{Si}}_2$ and ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$ crystal structures show that the $T_{\mathrm{N}}$ values for the ${\mathrm{CaAl}}_2{\mathrm{Si}}_2$-type compounds are much smaller than those for the ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type materials.

The ferrimagnetic ${\mathrm{Mn}}_3\mathrm{Ge}$ compound has appealing properties for spintronic applications, e.g., a low saturation magnetization, and often a large coercive field is found. Here, we report on a combined experimental and theoretical approach to both reduce the magnetization and increase the coercivity of ${\mathrm{Mn}}_3\mathrm{Ge}$ by doping. By calculating defect formation energies, we predict several dopants that are expected to specifically occupy only one lattice site of the crystal structure. For Ni as a dopant, we predict a reduction in the magnetization, which we verify by preparing thin film samples by magnetron co-sputtering. We confirm the predicted reduction in magnetization as well as a greatly enhanced coercivity of more than 5 T. To improve the understanding of the sublattice magnetization in the doped ferrimagnetic material, we performed magnetic spectroscopy experiments on selected samples and compared the results with calculated data. An important finding from a detailed analysis of the spectroscopic data is that a frequently observed soft contribution in the magnetization loop arises from impurities in the film.

We present first-principles analysis of interfacial disorder effects on spin-dependent tunneling statistics in thin Fe/MgO/Fe magnetic tunnel junctions. We find that interfacial disorder scattering can significantly modulate the tunneling statistics in the minority spin of the parallel configuration (PC) while all other spin channels remain dominated by the Poissonian process. For the minority-spin channel of PC, interfacial disorder scattering favors the formation of resonant tunneling channels by lifting the limitation of symmetry conservation at low concentration, presenting an important sub-Poissonian process in PC, but is destructive to the open channels at high concentration. We find that the important modulation of tunneling statistics is independent of the type of interfacial disorder. A bimodal distribution function of transmission with disorder dependence is introduced and fits very well our first-principles results. The increase of MgO thickness can quickly change the tunneling from a sub-Poissonian to Poissonian dominated process in the minority spin of PC with disorder. Our results provide a sensitive detection method of an ultralow concentration of interfacial defects.

Earlier models for the room-temperature multiferroic ${\mathrm{BiFeO}}_3$ implicitly assumed that a very strong anisotropy restricts the domain wave vectors $\mathbf{q}$ to the threefold-symmetric axis normal to the static polarization $\mathbf{P}$. However, recent measurements demonstrate that the domain wave vectors $\mathbf{q}$ rotate within the hexagonal plane normal to $\mathbf{P}$ away from the magnetic field orientation $\mathbf{m}$. We show that the previously neglected threefold anisotropy $K_3$ restricts the wave vectors to lie along the threefold axis in zero field. Taking $\mathbf{m}$ to lie along a threefold axis, the domain with $\mathbf{q}$ parallel to $\mathbf{m}$ remains metastable below $B_{c1}\approx 7$ T. Due to the pinning of domains by nonmagnetic impurities, the wave vectors of the other two domains start to rotate away from $\mathbf{m}$ above 5.6 T, when the component of the torque $\mathbf{\tau }=\mathbf{M}\times \mathbf{B}$ along $\mathbf{P}$ exceeds a threshold value ${\tau }_{\mathrm{pin}}$. Since $\mathbf{\tau }=0$ when $\mathbf{m}\perp \mathbf{q}$, the wave vectors of those domains never become completely perpendicular to the magnetic field. Our results explain recent measurements of the critical field as a function of field orientation, small-angle neutron scattering measurements of the wave vectors, as well as spectroscopic measurements with $\mathbf{m}$ along a threefold axis. The model developed in this paper also explains how the three multiferroic domains of ${\mathrm{BiFeO}}_3$ for a fixed $\mathbf{P}$ can be manipulated by a magnetic field.

We report the temperature-dependent evolution of spin ordering and excitations of the frustrated tetragonal ($c>a$) spinel ${\mathrm{ZnMn}}_2{\mathrm{O}}_4$ across the two-dimensional antiferromagnetic transition. Muon spin relaxation indicates full development of ordered magnetic moments immediately below $T_{\mathrm{N}}=62.7\left(2\right)\mathrm{K}$ in spite of the apparent low-dimensional ordering. Using inelastic neutron scattering, we obtained the spin Hamiltonian accounting for the temperature-dependent spin excitations. The damped spin waves at high temperature exhibit a continuous increase in their lifetime on cooling across $T_{\mathrm{N}}$. In contrast, the finite anisotropy gap appears suddenly below $T_{\mathrm{N}}$ indicating that single-ion anisotropy stabilizes the antiferromagnetic chains. We also observed the frustrated out-of-plane exchange contributing to the high-energy modes.

The recent realization of two-dimensional (2D) synthetic spin-orbit (SO) coupling opens a broad avenue to explore novel topological states for ultracold atoms. Here, we propose a scheme to realize chiral Fulde-Ferrell superfluid for ultracold fermions, and show a generic theory that the topology of chiral superfluid phases can be uniquely determined from the normal states. The main findings are twofold. First, a semimetal is driven by a type of 2D SO coupling, and can be tuned into massive Dirac fermion phase with or without inversion symmetry. Without inversion symmetry, the superfluid phase of nonzero pairing momentum is favored under an attractive interaction. Furthermore, we show a fundamental theorem that the Chern number of a 2D chiral superfluid can be obtained from the 1D invariants of Fermi surfaces, with which the chiral Fulde-Ferrell superfluid with a broad topological region is predicted. This generic theorem is also useful for condensed-matter physics and material science in the search for new topological superconductors.

We demonstrate that the concept of Goldstone bosons can be exploited for phonon control and thermal conductivity reduction of materials. By studying lattice dynamics of the Sn filled skutterudite ${\mathrm{SnFe}}_4{\mathrm{Sb}}_{12}$, we find Sn off-centers in its coordination cage in contrast to the common rare earth fillers. This leads to low-frequency Goldstone-like modes below 1 THz associated mainly with Sn motions. Importantly, these involve collective motion of other atoms, especially Sb, in the host skutterudite lattice. The optical modes transversing to the Sn off-centering direction are identified as Goldstone type modes in association with a three-dimensional Mexican-hat-like potential energy surface. The interaction of these collective Goldstone modes with the host heat-carrying phonons is shown to lead to ultralow lattice thermal conductivity.

We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the system to a new steady state which can be approximately but efficiently described by a (generalized) Gibbs ensemble characterized by one Lagrange parameter for each conservation law. The value of those has to be determined from rate equations for conserved quantities. Remarkably, even weak perturbations can lead to large responses of conserved quantities. We present a perturbative expansion of the steady state density matrix; first we give the condition that fixes the zeroth-order expression (Lagrange parameters) and then determine the higher-order corrections via projections of the Liouvillian. The formalism can be applied to a wide range of problems including two-temperature models for electron-phonon systems, Bose condensates of excitons or photons, or weakly perturbed integrable models. We test our formalism by studying interacting fermions coupled to nonthermal reservoirs, approximately described by a Boltzmann equation.

The effects of applying external electric fields to the anomalous and spin Hall conductivities in Fe thin-film models with different layer thicknesses on MgO(001) are investigated by using first-principles calculations. We observe that, for the considered systems, the application of positive electric field associated with the accumulation of negative charges on the Fe side generally decreases (increases) the anomalous (spin) Hall conductivities. The mapping of the Hall conductivities within the two-dimensional Brillouin zone shows that the electric-field-induced modifications are related to the modification of the band structures of the atoms at the interface with the MgO substrate. In particular, the external electric field affects the Hall conductivities via the modifications of the $d_{xz},d_{yz}$ orbitals, in which the application of positive electric field pushes the minority-spin states of the $d_{xz},d_{yz}$ bands closer to the Fermi level. Better agreement with the anomalous Hall conductivity for bulk Fe and a more realistic scenario for the electric field modification of Hall conductivities are obtained by using the thicker layers of Fe on MgO (${\mathrm{Fe}}_3$/MgO and ${\mathrm{Fe}}_5$/MgO).

Gold (Au) and tantalum (Ta) metals are two important spin Hall materials with diametrically different crystalline structure, resistivity, and spin Hall angle. By vapor quenching, $\mathrm{A}{\mathrm{u}}_x\mathrm{T}{\mathrm{a}}_{1-x}$ alloys of different crystalline and amorphous structures, stable and metastable, have been formed over the entire composition range. We have studied the inverse spin Hall voltage induced by the longitudinal spin Seebeck effect in $\mathrm{A}{\mathrm{u}}_x\mathrm{T}{\mathrm{a}}_{1-x}$ alloy films. We have found that the inverse spin Hall voltage $\mathrm{\Delta }{V}_{\mathrm{ISHE}}$, resistivity $\rho$, and the spin Hall angle ${\theta }_{SH}$ vary smoothly with composition. Both the spin Hall angle and the spin Hall conductivity exhibit a quasilinear dependence on composition in the concentrated alloy regime, despite drastic differences in other properties. As corroborated by first-principles calculation, we show that the contribution to spin Hall effect in $\mathrm{A}{\mathrm{u}}_x\mathrm{T}{\mathrm{a}}_{1-x}$ alloy is dominated by the number of valence electrons. We also show that the magnetoresistance correlates with the spin Hall angle.

The composition-dependent behavior of the Dzyaloshinskii–Moriya interaction (DMI), the spin-orbit torque (SOT), as well as anomalous and spin Hall conductivities of ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Ge}$ alloys have been investigated by first-principles calculations using the relativistic multiple scattering Korringa–Kohn–Rostoker (KKR) formalism. The $D_{\mathrm{xx}}$ component of the DMI exhibits a strong dependence on the Fe concentration, changing sign at $x\approx 0.85$ in line with previous theoretical calculations as well as with experimental results demonstrating the change of spin helicity at $x\approx 0.8$. A corresponding behavior with a sign change at $x\approx 0.5$ is predicted also for the Fermi-sea contribution to the SOT, because this is closely related to the DMI. In the case of anomalous and spin Hall effects it is shown that the calculated Fermi-sea contributions are rather small and the composition-dependent behavior of these effects are determined mainly by the electronic states at the Fermi level. The spin-orbit-induced scattering mechanisms responsible for both these effects suggest a common origin of the minimum of the anomalous Hall effect and the sign change of the spin Hall effect conductivities.

Dzyaloshinskii-Moriya interaction (DMI) is a well-known phenomenon in ferromagnetic/heavy metal or ferromagnetic/nonmagnetic oxide thin layered films. Here, we show that DMI is also found in exchange biased ferromagnetic/antiferromagnetic oxide layer systems and that it is independent of the macroscopic direction of the interlayer exchange bias coupling. Using the relation between thickness of the ferromagnetic layer and asymmetric domain wall propagation at external magnetic fields applied in plane and perpendicular to a sample plane of a Au/Co/NiO layered system, the strength of interfacial Dzyaloshinskii-Moriya interaction was determined. Based on this relation, we found that observed clockwise chirality is related to strong negative Dzyaloshinskii-Moriya interaction, which is independent of the direction of the interlayer exchange bias coupling. We also demonstrate that in the Au/Co/NiO system, domain motion can be controlled precisely by alternating magnetic fields. This concept can be attractive for many applications based on field-induced domain and domain wall motion, particularly in systems where exchange bias is required.

${\mathrm{SrAuSi}}_3$ is a noncentrosymmetric superconductor (NCS) with $T_c=1.54$ K, which to date has been studied only via macroscopic techniques. By combining nuclear-magnetic-resonance and muon-spin-rotation measurements, we investigate both the normal and the superconducting phase of ${\mathrm{SrAuSi}}_3$ at a local level. In the normal phase, our data indicate a standard metallic behavior with weak electron correlations and a Korringa constant $S_{\exp }=1.31\times {10}^{-5}$ sK. The latter, twice the theoretical value, can be justified by the Moriya theory of exchange enhancement. In the superconducting phase, the material exhibits conventional BCS-type superconductivity with a weak-coupling $s$-wave pairing, a gap value $\mathrm{\Delta }\left(0\right)=0.213\left(2\right)$ meV, and a magnetic penetration depth $\lambda \left(0\right)=398\left(2\right)$ nm. The experimental proof of weak correlations in ${\mathrm{SrAuSi}}_3$ implies that correlation effects can be decoupled from those of antisymmetric spin-orbit coupling, thus enabling accurate band-structure calculations in the weakly correlated NCSs.

Determination of the pairing symmetry in monolayer FeSe films on ${\mathrm{SrTiO}}_3$ is a requisite for understanding the high superconducting transition temperature in this system, which has attracted intense theoretical and experimental studies but remains controversial. Here, by introducing several types of point defects in FeSe monolayer films, we conduct a systematic investigation on the impurity-induced electronic states by spatially resolved scanning tunneling spectroscopy. Ranging from surface adsorption, chemical substitution, to intrinsic structural modification, these defects generate a variety of scattering strengths, which renders insights on the pairing symmetry.