We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional $\mathrm{SU}\left(2\right)\otimes \text{XXZ}$ model with SU(2) spin exchange and anisotropic $\text{XXZ}$ orbital exchange interactions and negative exchange coupling constant. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions, we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational-invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic $\mathrm{SU}\left(2\right)\otimes \text{SU}$(2) limit. Surprisingly, for finite transverse orbital coupling, the long-range spin-singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover, we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore, we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly, one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.

Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as ${}^{87}\mathrm{Rb},{}^{39}\mathrm{K}$, or ${}^{23}\mathrm{Na}$ in the $F=1$ hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground-state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with on-site and near-neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators and ferromagnetic and AF superfluids.

We have explored the high-pressure structural, vibrational, electronic, and magnetic behavior of the multiferroic $\mathrm{CoC}{\mathrm{r}}_2{\mathrm{O}}_4$ spinel up to 30 GPa by means of x-ray diffraction, Raman spectroscopy, and density functional theory calculations. Our investigations revealed a reversible tetragonal distortion of the starting cubic structure above 16 GPa. We suggest that the structural modification is mainly driven by magnetic effects induced under pressure. The results obtained are compared with the high-pressure behavior of related spinels.

In this paper, we theoretically study the influence of a nonmagnetic spacer between ferromagnetic dots and a ferromagnetic matrix on the frequency dispersion of the spin-wave excitations in two-dimensional bicomponent magnonic crystals. By means of the dynamical matrix method we investigate structures that are inhomogeneous across the thickness represented by square arrays of cobalt or permalloy dots in a permalloy matrix. We show that the introduction of a nonmagnetic spacer significantly modifies the total internal magnetic field, especially at the edges of the grooves and dots. This permits the manipulation of the magnonic band structure of spin waves localized either at the edges of the dots or in matrix material at the edges of the grooves. According to the micromagnetic simulations two types of end modes were found. The corresponding frequencies are significantly influenced by the end modes’ localization region. We also show that, with the use of a single ferromagnetic material, it is possible to design a magnonic crystal preserving the properties of bicomponent magnonic crystals and magnonic antidot lattices. Finally, the influence of the nonmagnetic spacers on the technologically relevant parameters such as group velocity and magnonic bandwidth are discussed.

We present path integral Monte Carlo (PIMC) calculations of the superfluid fraction, ${\rho }_S/\rho$, and the one-body density matrix (OBDM) [Bose-Einstein condensation (BEC)] of liquid ${}^4\mathrm{He}$ confined in nanopores. Liquid ${}^4\mathrm{He}$ in nanopores represents a dense Bose liquid at reduced dimension and in disorder. The goal is to determine the effective dimensions of the liquid in the pores. It is to test whether observed properties, such as a very low onset temperature for superflow, $T_c$, can be predicted by a standard, static PIMC ${\rho }_S/\rho$. We simulate a cylinder of liquid of diameter $d_L$ surrounded by 5 Å of inert solid ${}^4\mathrm{He}$ in a nanopore of diameter $d$; $d=d_L+10\AA$. We find a PIMC ${\rho }_S\left(T\right)/\rho$ and OBDM that scales as a 1D fluid Luttinger liquid at extremely small liquid pore diameters only, $d_L=6\AA$. At this $d_L$, the liquid fills the pore in a 1D line at the center of the pore and there is no PIMC superflow. In the range $8\le d_L\le 22\AA$ the PIMC ${\rho }_S\left(T\right)/\rho$ scales as a 2D liquid. In this $d_L$ range the liquid fills the pores in 2D-like cylindrical layers. The crossover from no superflow at $d=16\AA$ to superflow at $d\ge 18\AA$ agrees with experiment. There is a crossover to 3D scaling at larger $d_L\simeq 22\AA$. In the range $8\le d_L\le 22\AA$, the $T_c$ predicted using the Kosterlitz-Thouless 2D scaling criterion of the OBDM agrees well with that obtained from ${\rho }_S\left(T\right)/\rho$. These results suggest that the superflow observed in small pore media is standard static superflow with the low $T_c$ arising from its 2D character. An operational onset temperature, $T_{\mathrm{BEC}}$, for BEC can be defined as the temperature at which there is a crossover from exponential to algebraic decay in the OBDM. This definition leads to a $T_{\mathrm{BEC}}\ge T_c$ as observed in larger pore media.

Spin-orbit coupling (SOC) for $d$-electron gas can be substantially enriched compared with the $sp$-electron gas due to the delicate ordering of the multiple $d$ subbands. Here, we demonstrate the nontrivial Rashba SOC effect at ${\mathrm{SrTiO}}_3$-based interfaces (${\mathrm{LaAlO}}_3\text{/}{\mathrm{SrTiO}}_3$ and ${\mathrm{LaVO}}_3\text{/}{\mathrm{SrTiO}}_3$) directly related to the Ti $3d$ subband ordering via magnetotransport characterizations. Unusual $k$-cubic Rashba SOC contributed from the $d_{xz/yz}$ states is revealed. More strikingly, when a gate voltage is swept to tune the band filling, the SOC strength initially increases and then decreases to form a dome feature, accompanied by an apparent single- to two-carrier transition. These two concomitant effects strongly indicate that the SOC behavior is largely determined by the Ti $3d$ subbands regardless of the overlayer boundary conditions, with the SOC strength peaked at the $d_{xy}-d_{xz/yz}$ crossings due to the band hybridization effect as predicted. The present findings offer new insights into exploration of oxide-based quantum phases and spintronic devices.

By means of ab initio calculations we study the effect of O doping of Au chains containing a nanocontact represented by a Ni atom as a magnetic impurity. In contrast to pure Au chains, we find that with a minimum O doping the $5d_{xz,yz}$ states of Au are pushed up, crossing the Fermi level. We also find that for certain O configurations, the Ni atom has two holes in the degenerate $3d_{xz,yz}$ orbitals, forming a spin $S=1$ due to a large Hund interaction. The coupling between the $5d_{xz,yz}$ Au bands and the $3d_{xz,yz}$ of Ni states leads to a possible realization of a two-channel $S=1$ Kondo effect. While this kind of Kondo effect is commonly found in bulk systems, it is rarely observed in low dimensions. The estimated Kondo scale of the system lies within the present achievable experimental resolution in transport measurements. Another possible scenario for certain atomic configurations is that one of the holes resides in a $3d_{z^2}$ orbital, leading to a two-stage Kondo effect, the second one with SU(4) symmetry.

Motivated by the possibility of superconductivity in doped graphene sheets, we investigate superconducting order in the extended Hubbard model on the two-dimensional graphene lattice using the variational cluster approximation (VCA) and the cellular dynamical mean-field theory (CDMFT) with an exact diagonalization solver at zero temperature. The nearest-neighbor interaction is treated using a mean-field decoupling between clusters. We compare different pairing symmetries, singlet and triplet, based on short-range pairing. VCA simulations show that the real (nonchiral), triplet $p$-wave symmetry is favored for small $V$, small onsite interaction $U$, or large doping, whereas the chiral combination $p+ip$ is favored for larger values of $V$, stronger onsite interaction $U$, or smaller doping. CDMFT simulations confirm the stability of the $p+ip$ solution, even at half-filling. Singlet superconductivity (extended $s$ wave or $d$ wave) is either absent or subdominant.

From the energies of various noncollinearly ordered spin configurations of ${\mathrm{YMnO}}_3$ obtained using first-principles density functional theory and spin-orbit coupling, we demonstrate a remarkable magnetocrystalline anisotropy in the ordering of spins of ${\mathrm{Mn}}^{3+}$ ions. We find that these spins are confined in the $\mathit{ab}$ plane and ordered according to the ${\mathrm{\Gamma }}_3$ representation of the $P{6}_3\mathit{cm}{1}^{\prime }$ space group in the insulating ground state, consistent with the observed magnetic order. In contrast, the state with the same magnetic symmetry (${\mathrm{\Gamma }}_3$) and spins oriented along the $\mathit{c}$ axis is metallic, with a distinct structure and significantly higher energy. We show how the spin-orbit coupling is crucial in giving the splitting and ordering of energies of $d$ orbitals of Mn, which determine and explain the magnitude of observed local magnetic moment at the Mn site. We uncover a strong and anisotropic coupling of spins with the phonon modes of ${\mathrm{\Gamma }}_1$ symmetry and strain, which is shown within a Landau theory to constitute the microscopic mechanism of giant magnetoelastic effect observed at Néel temperature in hexagonal ${\mathrm{YMnO}}_3$. The anisotropy in higher order spin-phonon coupling is evident in significantly different frequencies of the zone-center ${\mathrm{\Gamma }}_1, {\mathrm{\Gamma }}_5$, and ${\mathrm{\Gamma }}_6$ phonons of the isosymmetric magnetic states with spins along the $\mathit{c}$ axis and those in the $\mathit{ab}$ plane, which are proposed as the spectroscopic signatures to be verified experimentally.

We report on the structural, electronic, and magnetic phases of a previously unexplored region in the phase diagram of $\mathrm{GdBaC}{\mathrm{o}}_2{{\mathrm{O}}_5}_{+\delta }$ ($\delta =0.57$ and 0.63). Despite a homogenous average structure displayed by both the samples, the orthorhombic highly oxygenated $\mathrm{GdBaC}{\mathrm{o}}_2{\mathrm{O}}_{5.63}$ shows clear signatures of structural nanoscale phase separation. By combining a pair distribution function with photoluminescence and electron spin resonance techniques, we found that the nanoscale phase separation is induced by an inhomogeneous distribution of ferromagnetic $\mathrm{C}{\mathrm{o}}^{3+}-\mathrm{C}{\mathrm{o}}^{4+}$ clusters embedded in an antiferromagnetic $\mathrm{C}{\mathrm{o}}^{3+}$-rich matrix. In addition, we uncovered a phase evolution involving the collapse of the orthorhombic strain below room temperature. The origin of this noncanonical transition seems to be associated with the interplay of the observed nanoscale phase separation and a new magnetic phase transition occurring below $T\sim 180\mathrm{K}$.

Although the rutile structure of ${\mathrm{TiO}}_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000 K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile ${\mathrm{TiO}}_2$ from 300 to 1373 K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of $3d$ electrons of Ti and $2p$ electrons of O atoms. With thermal expansion, the energy variation in this “phonon-tracked hybridization” flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.

Using the theory of symmetry and the microscopic model we predict the possibility of a linear antiferrodistortive-antiferromagnetic effect in the perovskites with structural antiferrodistortive and antiferromagnetic long-range ordering and find the necessary conditions of its occurrence. The main physical manifestations of this effect are the smearing of the antiferromagnetic transition and the jump of the specific heat near it. In the absence of external fields, linear antiferrodistortive-antiferromagnetic coupling can induce a weak antiferromagnetic ordering above the Neel temperature, but below the temperature of antiferrodistortive transition. Therefore, there is the possibility of observing weak improper antiferromagnetism in multiferroics such as bismuth ferrite ($\mathrm{BiFe}{\mathrm{O}}_3$) at temperatures $T>T_N$, for which the Neel temperature $T_N$ is about 645 K, and the antiferrodistortive transition temperature is about 1200 K. The improper mechanism may explain the antiferromagnetic order existence well above $T_N$ in ${\mathrm{BiFeO}}_3$ revealed by optical second harmonic generation. By quantitative comparison to the experiment we made estimations of the linear antiferrodistortive-antiferromagnetic effect in the solid solutions of multiferroic $\mathrm{B}{\mathrm{i}}_{1-\mathrm{x}}{\mathrm{R}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$ ($\mathrm{R}=\mathrm{La},\mathrm{Nd}$).

We theoretically study coherent subharmonic (multiphoton) transitions of a harmonically driven spin. We consider two cases: magnetic resonance (MR) with a misaligned, i.e., nontransversal, driving field, and electrically driven spin resonance (EDSR) of an electron confined in a one-dimensional, parabolic quantum dot, subject to Rashba spin-orbit interaction. In the EDSR case, we focus on the limit where the orbital level spacing of the quantum dot is the greatest energy scale. Then, we apply time-dependent Schrieffer-Wolff perturbation theory to derive a time-dependent effective two-level Hamiltonian, allowing us to describe both MR and EDSR using the Floquet theory of periodically driven two-level systems. In particular, we characterize the fundamental (single-photon) and the half-harmonic (two-photon) spin transitions. We demonstrate the appearance of two-photon Rabi oscillations, and analytically calculate the fundamental and half-harmonic resonance frequencies and the corresponding Rabi frequencies. For EDSR, we find that both the fundamental and the half-harmonic resonance frequencies change upon increasing the strength of the driving electric field, which is an effect analogous to the Bloch-Siegert shift known from MR. Remarkably, the drive-strength-dependent correction to the fundamental EDSR resonance frequency has an anomalous, negative sign, in contrast to the corresponding Bloch-Siegert shift in MR which is always positive. Our analytical results are supported by numerical simulations, as well as by qualitative interpretations for simple limiting cases.

We investigate the mixed state properties in a type II multiband superconductor with uniaxial anisotropy under the Pauli paramagnetic effects. Eilenberger theory extended to a multiband superconductor is utilized to describe the detailed vortex lattice properties, such as the flux line form factors, the vortex lattice anisotropy, and magnetic torques. We apply this theory to ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ to analyze those physical quantities obtained experimentally, focusing on the interplay between the strong two-dimensional anisotropy and the Pauli paramagnetic effects. This study allows us to understand the origin of the disparity between the vortex lattice anisotropy ($\sim 60$) and the $H_{\mathrm{c}2}$ anisotropy ($\sim 20$). Among the three bands—$\gamma$ with the effective mass anisotropy $\sim 180, \alpha$ with $\sim 120$, and $\beta$ with $\sim 60$—the last one is found to be the major band, responsible for various magnetic responses while the minor $\gamma$ band plays an important role in the vortex formation. Namely, in a field orientation slightly tilted away from the two-dimensional basal plane those two bands cooperatively form the optimal vortex anisotropy which exceeds that given by the effective mass formula with infinite anisotropy. This is observed by small-angle neutron scattering experiments on ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. The pairing symmetry of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ realized is either spin singlet or spin triplet with the $d\text{-vector}$ strongly locked in the basal plane. The gap structure is that the major $\beta$ band has a full gap and the minor $\gamma$ band has a $d_{x^2-y^2}\text{-like}$ gap.

Considerable evidence for proximity-induced triplet superconductivity on the ferromagnetic side of a superconductor-ferromagnet (S-F) interface now exists; however, the corresponding effect on the superconductor side has hardly been addressed. We have performed scanning tunneling spectroscopy measurements on NbN superconducting thin films proximity coupled to the half-metallic ferromagnet $\mathrm{L}{\mathrm{a}}_{2/3}\mathrm{C}{\mathrm{a}}_{1/3}\mathrm{Mn}{\mathrm{O}}_3$ (LCMO) as a function of magnetic field. We have found that at zero and low applied magnetic fields the tunneling spectra on NbN typically show an anomalous gap structure with suppressed coherence peaks and, in some cases, a zero-bias conductance peak. As the field increases to the magnetic saturation of LCMO where the magnetization is homogeneous, the spectra become more BCS-like and the critical temperature of the NbN increases, implying a reduced proximity effect. Our results therefore suggest that triplet-pairing correlations are also induced in the S side of an S-F bilayer.

Using ab initio calculations and symmetrized plane waves, we analyze the basal-plane generalized stacking fault energies in pure Mg and Mg-Y alloys and show that the knowledge of energies of only five specific points is sufficient to accurately predict the core structures and Peierls stresses of $\langle a\rangle$-type edge dislocations in these alloys. Our five-point approach substantially reduces the computational cost related to the Peierls-Nabarro (PN) model and allows for a high-throughput application of the PN model to study Peierls stress changes in Mg upon alloying. We employ our approach to study Mg binary alloys containing nine rare-earth (RE) and 11 other solutes. Based on the Peierls stresses of these 20 Mg alloys calculated from the Peierls-Nabarro model, the solutes are divided into three groups: (i) the first group, consisting of Be, Zn, Tl, Tc, Os, Ru, Re, and Co, when added as solutes into Mg, lead to more compact dislocation core structures and larger Peierls stresses than found for pure Mg. (ii) Elements in the second group, including Ti, Nd, Lu, Zr, Hf, La, and Pr change the core widths and Peierls stresses moderately. (iii) The solutes in the third group containing Y, Er, Tm, Ho, and Sc extend the stacking fault width, and the resulting Peierls stresses are generally very low. Based on an error analysis, we conclude that the first group has a clear solute strengthening effect and the third group has a clear solute softening effect, while the effects of the elements in the second group are too small to be resolved by the present approach.

Substitution of an oxygen anion with a hydrogen anion induced the low dimensionalization of magnetic ordering in a transition metal oxide $\mathrm{S}{\mathrm{r}}_2\mathrm{V}{\mathrm{O}}_4$. Upon increasing $x$ up to $\sim 1$ in $\mathrm{S}{\mathrm{r}}_2\mathrm{V}{\mathrm{O}}_{4-x}{\mathrm{H}}_x$, the hydride ions were ordered linearly, and the magnetic susceptibility was simultaneously suppressed. It was found that this suppression was attributed to the formation of a quasi-one-dimensional antiferromagnetic spin chain, maintaining that each of the vanadium cations is two-dimensionally bridged by hydride and oxide ions. Density functional theory calculations demonstrate that the quasi-one-dimensional property is caused by much enhanced anisotropic exchange couplings $(J_1/J_2\sim 6)$ originating from the absence of $\pi$ bonding between $\mathrm{H}1s$ and $\mathrm{V}3d$ orbitals. Utilizing a hydride ion that has an ionic radius similar to an oxygen anion and only one energetically available orbital of $1s$ is a different approach to realization of magnetic low dimensionalization in $3d$ early transition metal oxides.

A superconductor illuminated by an ac electric field with frequency $\mathrm{\Omega }$ is theoretically found to generate a collective precession of Anderson's pseudospins, and hence a coherent amplitude oscillation of the order parameter, with a doubled frequency $2\mathrm{\Omega }$ through a nonlinear light-matter coupling. We provide a fundamental theory, based on the mean-field formalism, to show that the induced pseudospin precession resonates with the Higgs amplitude mode of the superconductor at $2\mathrm{\Omega }=2\mathrm{\Delta }$ with $2\mathrm{\Delta }$ being the superconducting gap. The resonant precession is accompanied by a divergent enhancement of the third-harmonic generation (THG). By decomposing the THG susceptibility into the bare one and vertex correction, we find that the enhancement of the THG cannot be explained by individual quasiparticle excitations (pair breaking), so that the THG serves as a smoking gun for an identification of the collective Higgs mode. We further explore the effect of electron-electron scattering on the pseudospin resonance by applying the nonequilibrium dynamical mean-field theory to the attractive Hubbard model driven by ac electric fields. The result indicates that the pseudospin resonance is robust against electron correlations, although the resonance width is broadened due to electron scattering, which determines the lifetime of the Higgs mode.