We propose a Fokker-Planck equation (FPE) theory to describe stochastic fluctuation and relaxation processes of lattice vibration at a wide range of conditions, including those beyond the phonon gas limit. Using the time-dependent, multiple state-variable probability function of a vibration FPE, we first derive time-correlation functions of lattice heat currents in terms of correlation functions among multiple vibrational modes, and subsequently predict the lattice thermal conductivity based on the Green-Kubo formalism. When the quasiparticle kinetic transport theories are valid, this vibration FPE not only predicts a lattice thermal conductivity that is identical to the one predicted by the phonon Boltzmann transport equation, but also provides additional microscopic details on the multiple-mode correlation functions. More importantly, when the kinetic theories become insufficient due to the breakdown of the phonon gas approximation, this FPE theory remains valid to study the correlation functions among vibrational modes in highly anharmonic lattices with significant mode-mode interactions and/or in disordered lattices with strongly localized modes. At the limit of weak mode-mode interactions, we can adopt quantum perturbation theories to derive the drift/diffusion coefficients based on the lattice anharmonicity data derived from first-principles methods. As temperature elevates to the classical regime, we can perform molecular dynamics simulations to directly compute the drift/diffusion coefficients. Because these coefficients are defined as ensemble averages at the limit of $\delta t\to 0$, we can implement massive parallel simulation algorithms to take full advantage of the paralleled high-performance computing platforms. A better understanding of the temperature-dependent drift/diffusion coefficients up to melting temperatures will provide new insights on microscopic mechanisms that govern the heat conduction through anharmonic and/or disordered lattices beyond the phonon gas model.

Polarization is a fundamental property of waves that refers to the orientation of the oscillations. It has been widely used to encode information in photonics and phononics. However, the polarization of spin waves is rarely used yet in magnonics. The reason for this is that only the right-handed polarized spin waves can be accommodated in ferromagnets. Here, we report that stable left-handed polarized spin waves can be introduced into ferromagnets if a spin-polarized electrical current is presented. The right-handed and left-handed polarized spin waves coexist when the current density is larger than a critical value while the system stays stable. The results are confirmed by micromagnetic simulations. This work provides playgrounds to study spin waves and points to findings for future experimental studies.

We present the synthesis and a detailed investigation of structural and magnetic properties of polycrystalline ${\mathrm{NaVOAsO}}_4$ by means of x-ray diffraction, magnetization, electron spin resonance (ESR), and ${}^{75}\mathrm{As}$ nuclear magnetic resonance (NMR) measurements as well as density-functional band structure calculations. Temperature-dependent magnetic susceptibility, ESR intensity, and NMR line shift could be described well using an alternating spin-$1/2$ chain model with the exchange coupling $J/k_{\mathrm{B}}\simeq 52$ K and an alternation parameter $\alpha \simeq 0.65$. From the high-field magnetization measured at $T=1.5$ K, the critical field of the gap closing is found to be $H_{\mathrm{c}}\simeq 16$ T, which corresponds to the zero-field spin gap of ${\mathrm{\Delta }}_0/k_{\mathrm{B}}\simeq 21.4$ K. Both NMR shift and spin-lattice relaxation rate show an activated behavior at low temperatures, further confirming the singlet ground state. The spin chains do not coincide with the structural chains, whereas the couplings between the spin chains are frustrated. Because of a relatively small spin gap, ${\mathrm{NaVOAsO}}_4$ is a promising compound for further experimental studies under high magnetic fields.

We elaborate here why the antiferromagnetically ordered ${\mathrm{GdCrO}}_3$ responds in a diamagnetic way under certain conditions by monitoring the evolution of the microscopic global and local magnetic phases. Using high-energy ($\sim 0.3\mathrm{eV}$) neutrons, the magnetic ordering is shown to adopt three distinct magnetic phases at different temperatures: $G_x^{Cr}$, $A_y^{Cr}$, $F_z^{Cr}$ below Néel temperature (171 K); ($F_x^{Cr}$, $C_y^{Cr}$, $G_z^{Cr})·(F_x^{Gd}$, $C_y^{Gd}$) below 7 K; and an intermediate phase for 7 K $\le T\le$ 20 K in the vicinity of the spin-reorientation phase transition. Although bulk magnetometry reveals a huge negative magnetization (NM) in terms of both magnitude and temperature range [$M_{-max}\left(18\mathrm{K}\right)\sim 35M_{+max}\left(161\mathrm{K}\right)$, $\mathrm{\Delta }T\sim 110\mathrm{K}$ in the presence of ${\mu }_{0}H=0.01\mathrm{T}$], the long-range magnetic structure and derived ordered moments are unable to explain the NM. Real-space analysis of the total (Bragg's + diffuse) scattering reveals significant magnetic correlations extending up to $\sim 9\AA$. Accounting for these short-range correlations with a spin model reveals spin frustration in the $S=3$ ground state, comprising competing first-, second-, and third next nearest neighboring interactions with values $J_1=2.3\mathrm{K}$, $J_2=-1.66\mathrm{K}$ and $J_3=2.19\mathrm{K}$ in the presence of internal field, governs the observance of NM in ${\mathrm{GdCrO}}_3$.

Gauge-invariant Wigner theories are formulated in terms of the kinetic momentum, which—being a physical quantity—is conserved after a change of the gauge. These theories rely on a transform of the density matrix, originally introduced by Stratonovich, which generalizes the Weyl transform by involving the vector potential. We thus present an alternative derivation of the Weyl-Stratonovich transform, which bridges the concepts and notions used by the different, available gauge-invariant approaches and thus links physically intuitive with formal mathematical viewpoints. Furthermore, an explicit form of the Wigner equation, suitable for numerical analysis and corresponding to general, inhomogeneous, and time-dependent electromagnetic conditions, is obtained. For a constant magnetic field, the equation reduces to two models: in the case of a constant electric field, this is the ballistic Boltzmann equation, where classical particles are driven by local forces. The second model, derived for general electrostatic conditions, involves novel physics, where the magnetic field acts locally via the Liouville operator, while the electrostatics is determined by the manifestly nonlocal Wigner potential. A significant consequence of our work is the fact that now the constant magnetic field case can be treated with existing numerical approaches developed for the standard, scalar potential Wigner theory. Therefore, in order to demonstrate the feasibility of the approach, a stochastic method is applied to simulate a physically intuitive evolution problem.

The identification of physical parameters that lead to magnetism in apparent nonmagnetic semiconductor systems has continuously challenged our community. In particular, for quantum-dot systems, they are key factors that contribute to their magneto-optical properties. We report, experimentally, optical evidences of induced nanomagnetism in nonmagnetic CdSe quantum dots and assess theoretically the role played by charged and uncharged vacancies. The analysis of these effects rests upon both the chemical and strain environments where the quantum dots are embedded. The interplay of spin-orbit interaction with built-in axial strains has been demonstrated to be a key factor for the magnetic moment alignment. This has been achieved in this paper by emulating the electronic structure at atomistic levels, considering various defect configurations and taking into account both the quantum dot composition and the influence of the host lattice.

The ground-state magnetic structure of ${\mathrm{EuNi}}_2{\mathrm{As}}_2$ was investigated by single-crystal neutron diffraction. At base temperature, the ${\mathrm{Eu}}^{2+}$ moments are found to form an incommensurate antiferromagnetic spiral-like structure with a magnetic propagation vector of $k=(0,0,0.92)$. They align ferromagnetically in the $ab$ plane with the moment size of 6.75(6) ${\mu }_B$, but rotate spirally by $165.6{\left(1\right)}^{\circ }$ around the $c$ axis from layer to layer. The magnetic order parameter in the critical region close to the ordering temperature $T_N=15$ K shows critical behavior with a critical exponent of ${\beta }_{\text{Eu}}=0.35\left(2\right)$, consistent with the three-dimensional Heisenberg model. Moreover, within the experimental uncertainty, our neutron data are consistent with a model in which the Ni sublattice is not magnetically ordered.

The strongly constrained and appropriately normed (SCAN) semilocal functional for exchange correlation is deployed to study the ground-state properties of ternary Heusler alloys transforming martensitically. The calculations are performed for ferromagnetic, ferrimagnetic, and antiferromagnetic phases. Comparisons between SCAN and generalized gradient approximation (GGA) are discussed. We find that SCAN yields smaller lattice parameters and higher magnetic moments compared to the GGA corresponding values for both austenite and martensite phases. Furthermore, in the case of ferromagnetic and nonmagnetic Heusler compounds, GGA and SCAN display similar trends in the total energy as a function of lattice constant and tetragonal ratio. However, for some ferrimagnetic Mn-rich Heusler compounds, different magnetic ground states are found within GGA and SCAN.

We establish theoretically a thermal Hall effect of collective magnetic excitations in noncollinear but coplanar antiferromagnets. In agreement with superordinate symmetry arguments for linear transport tensors, our findings demonstrate that neither a ferromagnetic moment, nor a magnetic field, nor a scalar spin chirality are indispensable for a magnon thermal Hall effect. Similar to the electronic anomalous Hall effect, the two necessary requirements are broken effective time-reversal symmetry and a magnetic point group compatible with ferromagnetism. As an example, we construct a minimal model for an antiferromagnet on the kagome lattice with the coplanar negative vector chiral order. In the presence of in-plane Dzyaloshinskii-Moriya interactions, the coplanar order stays intact but both magnon band gaps and a nonzero Berry curvature develop. This coplanar magnet realizes an antiferromagnetic magnon Chern insulator with a nonzero thermal Hall effect. We propose cadmium kapellasite ${\mathrm{CdCu}}_3{\left(\mathrm{OH}\right)}_6{\left({\mathrm{NO}}_3\right)}_2·{\mathrm{H}}_2\mathrm{O}$ as an approximate material realization.

Motivated by the recent experiments reporting the doping dependence of the short-range charge order (CO) in electron-doped cuprates, we study the resonant x-ray scattering spectrum from $d$-wave bond-charge fluctuations obtained in the two-dimensional $t\text{−}J$ model. We find that (i) the CO is short-range, (ii) the CO peak is pronounced at low temperature, (iii) the peak intensity increases with decreasing carrier doping $\delta$ down to $\delta \approx 0.10$ and is substantially suppressed below $\delta \approx 0.10$ due to strong damping, and (iv) the momentum of the CO decreases monotonically down to $\delta \approx 0.10$ and goes up below $\delta \approx 0.10$. These results reasonably capture the major features of the experimental data, and the observed short-range CO can be consistently explained in terms of bond-charge fluctuations with an internal $d$-wave symmetry.

Tungsten is known to have a Lorenz number $L$ larger than the Sommerfeld value ($L_0={\pi }^2{k}_B^2/3e^2=2.445\times {10}^{-8}{\mathtt{V}}^2/{\mathtt{deg}}^2$) by 30%. By performing fully first-principles calculations, we are able to calculate the electrical conductivity ($\sigma$) and quantify the electronic (${\kappa }_e$) and the lattice (${\kappa }_{\mathtt{ph}}$) contributions to the thermal conductivity with a high accuracy. We show that the deviation of $L$ is entirely due to ${\kappa }_{\mathtt{ph}}$, and ${\kappa }_e/\sigma T$ agrees with $L_0$ within 5%. At room temperature, ${\kappa }_{\mathtt{ph}}$ is 46 W/m-K, one order of magnitude larger than that in other metals even with smaller atomic mass and higher Debye temperature, and likely the largest of all metals. The large ${\kappa }_{\mathtt{ph}}$ is ascribed to the surprisingly weak anharmonic phonon scattering. Apart from the not-strong anharmonic interatomic interaction, the weak anharmonic phonon scattering is also facilitated with the large atomic mass, leading to small thermal displacement. The interplay between the phonon-phonon and electron-phonon scatterings leads to weak temperature dependence of ${\kappa }_{\mathtt{ph}}$, and signifies the importance of an accurate solution to the Boltzmann transport equation beyond the conventional relaxation time approximation. Our findings give insights into the phonon transport in metals.

$\mathrm{ZnNi}{\left(\mathrm{CN}\right)}_4$ is a three-dimensional (3D) framework material consisting of two interpenetrating PtS-type networks in which tetrahedral $\left[\mathrm{Zn}{\mathrm{N}}_4\right]$ units are linked by square-planar $\left[\mathrm{Ni}{\mathrm{C}}_4\right]$ units. Both the parent compounds, cubic $\mathrm{Zn}{\left(\mathrm{CN}\right)}_2$ and layered $\mathrm{Ni}{\left(\mathrm{CN}\right)}_2$, are known to exhibit 3D and 2D negative thermal expansion (NTE), respectively. Temperature-dependent inelastic neutron scattering measurements were performed on a powdered sample of $\mathrm{ZnNi}{\left(\mathrm{CN}\right)}_4$ to probe phonon dynamics. The measurements were underpinned by ab initio lattice dynamical calculations. Good agreement was found between the measured and calculated generalized phonon density-of-states, validating our theoretical model and indicating that it is a good representation of the dynamics of the structural units. The calculated linear thermal expansion coefficients are ${\alpha }_a=-21.2\times {10}^{-6}{\mathrm{K}}^{-1}$ and ${\alpha }_c=+14.6\times {10}^{-6}{\mathrm{K}}^{-1}$, leading to an overall volume expansion coefficient, ${\alpha }_V$ of $-26.95\times {10}^{-6}{\mathrm{K}}^{-1}$, pointing towards pronounced NTE behavior. Analysis of the derived mode-Grüneisen parameters shows that the optic modes around 12 and 40 meV make a significant contribution to the NTE. These modes involve localized rotational motions of the $\left[\mathrm{Ni}{\mathrm{C}}_4\right]$ and/or $\left[\mathrm{Zn}{\mathrm{N}}_4\right]$ rigid units, echoing what has previously been observed in $\mathrm{Zn}{\left(\mathrm{CN}\right)}_2$ and $\mathrm{Ni}{\left(\mathrm{CN}\right)}_2$. However, in $\mathrm{ZnNi}{\left(\mathrm{CN}\right)}_4$, modes below 10 meV have the most negative Grüneisen parameters. Analysis of their eigenvectors reveals that a large transverse motion of the Ni atom in the direction perpendicular to its square-planar environment induces a distortion of the units. This mode is a consequence of the Ni atom being constrained only in two dimensions within a 3D framework. Hence, although rigid-unit modes account for some of the NTE-driving phonons, the added degree of freedom compared with $\mathrm{Zn}{\left(\mathrm{CN}\right)}_2$ results in modes with twisting motions, capable of inducing greater NTE.

We start closing a gap in the comparison of experimental and theoretical data associated with the spin Hall effect. Based on a first-principles characterization of electronic structure and a semiclassical description of electron transport, we compute the skew-scattering contribution to the transverse spin and charge currents generated by spin and anomalous Hall effect in a Co/Cu multilayer system doped with Bi impurities. The fact that the created currents cross the interface between the two materials strongly influences the efficiency of charge-to-spin current conversion, as demonstrated by our results.

The electronic structure, magnetic properties, and phase formation of hexagonal ferromagnetic ${\mathrm{Fe}}_3\mathrm{Sn}$-based alloys have been studied from first principles and by experiment. The pristine ${\mathrm{Fe}}_3\mathrm{Sn}$ compound is known to fulfill all the requirements for a good permanent magnet, except for the magnetocrystalline anisotropy energy (MAE). The latter is large, but planar, i.e., the easy magnetization axis is not along the hexagonal $c$ direction, whereas a good permanent magnet requires the MAE to be uniaxial. Here we consider ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{\mathrm{M}}_{0.25}$, where $M=$ Si, P, Ga, Ge, As, Se, In, Sb, Te, Pb, and Bi, and show how different dopants affect the MAE and can alter it from planar to uniaxial. The stability of the doped ${\mathrm{Fe}}_3\mathrm{Sn}$ phases is elucidated theoretically via the calculations of their formation enthalpies. A micromagnetic model is developed to estimate the energy density product ${\left(BH\right)}_{\max }$ and coercive field ${\mu }_0{H}_{\mathrm{c}}$ of a potential magnet made of ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$, the most promising candidate from theoretical studies. The phase stability and magnetic properties of the ${\mathrm{Fe}}_3\mathrm{Sn}$ compound doped with Sb and Mn have been checked experimentally on the samples synthesised using the reactive crucible melting technique as well as by solid state reaction. The ${\mathrm{Fe}}_3\mathrm{Sn}$-Sb compound is found to be stable when alloyed with Mn. It is shown that even small structural changes, such as a change of the c/a ratio or volume, that can be induced by, e.g., alloying with Mn, can influence anisotropy and reverse it from planar to uniaxial and back.

In this paper, we consider the Kitaev toric code with specific open boundary conditions. Such a physical system has a highly degenerate ground state determined by the degrees of freedom localized at the boundaries. We can write down an explicit expression for the ground state of this model. Based on this, the entanglement properties of the model are studied for two types of bipartition: one, where subsystem $A$ is completely contained in $B$; and the second, where the boundary of the system is shared between $A$ and $B$. In the former configuration, the entanglement entropy is the same as for the periodic boundary condition case, which means that the bulk is completely decoupled from the boundary on distances larger than the correlation length. In the latter, deviations from the torus configuration appear due to the edge states and lead to an increase of the entropy. We then determine an effective theory for the boundary of the system. In the case where we apply a small magnetic field as a perturbation, the degrees of freedom on the boundary acquire a dispersion relation. The system can there be described by a Hamiltonian of the Ising type with a generic spin-exchange term.

Magnetism is a canonical example of a spontaneous symmetry breaking. The symmetry of a magnetic state below the Curie temperature is spontaneously broken even though the Hamiltonian is invariant under symmetry. Recently, machine learning algorithms have been successfully utilized to study topics in physics. We applied unsupervised machine learning algorithms to find the magnetic ground states of the Heisenberg model. A fully connected neural network was used to generate the spin configuration from randomly coded features, and the magnetic energy was selected as the cost to be minimized during the machine learning process. We found that ground states solved by the unsupervised learning process are consistent with the theoretical solution. Also, we compared the results with those from traditional computational methods and found that the machine learning algorithm provides an efficient method to solve the magnetic state numerically.

We compute specific heat $C\left(T\right)$ in a strongly hole-doped Fe-based superconductor, like ${\mathrm{KFe}}_2{\mathrm{As}}_2$, which has only hole pockets. We model the electronic structure by a three-orbital/three-pocket model with two smaller hole pockets made out of $d_{xz}$ and $d_{yz}$ orbitals and a larger pocket made out of $d_{xy}$ orbital. We use as an input the experimental fact that the mass of $d_{xy}$ fermion is several times heavier than that of $d_{xz}/d_{yz}$ fermions. We argue that the heavy $d_{xy}$ band gives the largest contribution to the specific heat in the normal state, but the superconducting gap on the $d_{xy}$ pocket is much smaller than that on $d_{xz}/d_{yz}$ pockets. We argue that in this situation the jump of $C\left(T\right)$ at $T_c$ is determined by $d_{xz}/d_{yz}$ fermions, and the ratio $(C_s-C_n)/C_n$ is a fraction of that in a one-band BCS superconductor. At $T<T_c,C\left(T\right)$ remains relatively flat down to some $T^{*}$, below which it rapidly drops. This behavior is consistent with the data for ${\mathrm{KFe}}_2{\mathrm{As}}_2$ and related materials. We use one-parameter model for the interactions and fix this only parameter by matching the experimental ratio of the gaps on the two $d_{xz}/d_{yz}$ pockets. We argue that the resulting parameter-free model reproduces quantitatively the data on $C\left(T\right)$ for ${\mathrm{KFe}}_2{\mathrm{As}}_2$. We further argue that the very existence of a finite $T^{*}<T_c$ favors $s^{+-}$ gap structure over $d$-wave, because in the latter case $T^{*}$ would almost vanish.

In a recent high-quality experimental work on normal metal–superconducting nanowire junctions (J. D. S. Bommer et al., arXiv:1807.01940), strong anisotropic suppression of induced superconductivity has been observed in tunnel conductance measurements in the presence of applied magnetic field with variable orientation. Following this finding, we investigate theoretically the dependence of tunnel conductance on the direction of the Zeeman field in order to understand the operational mechanisms and to extract effective system parameters. Second, motivated by a generic discrepancy between experiment and theory, i.e., many in-gap and above-gap conductance features predicted by theory are barely observed in experiments, we study several mechanisms possibly responsible for the suppression of the theoretically predicted conductance features (e.g., length of the nanowire, self-energy effect due to the proximity effect, finite temperature, finite dissipation, and multiband effect). One essential finding in the current work is that only by a combined understanding of both suppression mechanisms can we extract effective system parameters from the experimental data (e.g., the effective nanowire-superconductor coupling, the effective Landé $g$ factor, and the chemical potential of the semiconducting nanowire). In addition, we consider topologically trivial Andreev bound states in hybrid nanowires in the presence of potential inhomogeneities, such as external quantum dots or potential inhomogeneities inside the nanowire. We compare the anisotropic, field-dependent features induced by these nontopological Andreev bound states with the corresponding features produced by topological Majorana zero modes in pristine nanostructures, so that we can provide guidance to differentiate between the topologically trivial and nontrivial cases.

Near-field (NF) radiative heat transfer (RHT) over vacuum space between closely spaced bodies can exceed the Planck's far-field (FF) values by orders of magnitude. A strong effect of superconductivity on NF RHT between plane-parallel thin-film surfaces of niobium (Nb) was recently discovered and discussed in a short paper [T. Králík et al., Phys. Rev. B 95, 060503 (2017)]. We present here an extensive set of experimental results on NF as well as FF RHT for geometrically identical samples made of niobium nitride (NbN), including a detailed discussion of the experimental setup and errors. The results with NbN show more precise agreement with theory than the original experiments with Nb. We observed a steep decrease of the heat flux at the transition to superconductivity when the colder sample (absorber) passed from the normal to the superconducting (SC) state $(T_{\mathrm{c}}\approx 15.2\mathrm{K})$, corresponding to an up to eightfold contrast between the normal and SC states. This differs dramatically from the situation in the FF regime, where only a weak effect of superconductivity was observed. Surprisingly, the contrast remains sizable even at high temperatures of the hot sample (radiator) with the characteristic energy of radiation far above the SC energy gap. We explain the maximum of contrast in heat flux between the normal and SC states, found at a distance about ten times shorter than the crossover distance between NF and FF heat flux, being $d\approx 1000/T\left[\mu \mathrm{m}\right]$. We analyze in detail the roles of transversal electric (TE) and magnetic (TM) modes in the steep decrease of heat flux below the SC critical temperature and the subsequent flux saturation at low temperatures. Interestingly, we expose experimentally the effect of destructive interference of FF thermal radiation in the vacuum gap, which was observable at temperatures below the absorber superconducting transition.