Anisotropy of the quadratic Zeeman effect for the ${}^3\mathrm{H}_6\to {}^3\mathrm{H}_4$ transition at 793 nm wavelength in ${}^{169}\mathrm{Tm}^{3+}\text{-doped} {\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ is studied, revealing shifts ranging from near zero up to $+4.69{\mathrm{GHz}/\mathrm{T}}^2$ for ions in magnetically inequivalent sites. This large range of shifts is used to spectrally resolve different subsets of ions and study nuclear spin relaxation as a function of temperature, magnetic field strength, and orientation in a site-selective manner. A rapid decrease in spin lifetime is found at large magnetic fields, revealing the weak contribution of direct phonon absorption and emission to the nuclear spin-lattice relaxation rate. We furthermore confirm theoretical predictions for the phonon coupling strength, finding much smaller values than those estimated in the limited number of past studies of thulium in similar crystals. Finally, we observe a significant—and unexpected—magnetic field dependence of the two-phonon Orbach spin relaxation process at higher field strengths, which we explain through changes in the electronic energy-level splitting arising from the quadratic Zeeman effect.

Using first-principles calculations based on density functional theory (DFT) we compare the generalized gradient approximation (GGA-PBE) with a screened hybrid functional by studying the electronic and optical properties of bulk ${\mathrm{LaAlO}}_3$ in the cubic and rhombohedral phases. We find that both atomic and electronic structures are accurately described by the hybrid functional. The hybrid functional not only corrects the band gap, when compared to GGA-PBE, it also shifts the unoccupied La $4f$ bands to higher energies with respect to the hybridized conduction-band minimum, composed of 83% La $4d$, 5% La $4f$, 6% O $2s$, and 6% O $2p$ states. We show that this shift is essential to accurately describe the complex dielectric function, in good agreement with experimental results. We conclude that the screened hybrid functional offers a reliable description of the position of empty $f$ bands with respect to the valence- and conduction-band edges in ${\mathrm{LaAlO}}_3$.

Using the Landau-Ginzburg-Devonshire theory, we established the role of the flexoelectric coupling between the gradients of elastic strain and polarization in the stability of spatially modulated phases in ferroics, such as incipient and proper ferroelectrics with commensurate and incommensurate long-range-ordered phases. We included the square of elastic strain gradient in the Landau-Ginzburg-Devonshire functional because this term provides the functional stability for all values of the strain gradient. Analytical expressions for polarization, strain, dielectric susceptibility, and stability threshold were derived for a one-dimensional case. The expressions show that the maximal possible values of the static flexoelectric effect coefficients (upper limits) established by Yudin, Ahluwalia, and Tagantsev without the square of elastic strain gradient and other higher order gradients terms lose their direct meaning. Considering the gradients, the temperature dependent condition for the flexocoupling magnitude exists instead of the upper limits. Also, we established that spatially modulated phases appear and become stable in commensurate ferroelectrics if the flexocoupling constant exceeds a critical value. The critical value depends on the electrostriction and elastic constants, temperature, and gradient coefficients in the Landau-Ginzburg-Devonshire functional. We calculated soft phonon dispersion in commensurate and incommensurate long-range-ordered phases of ferroelectrics with the square of elastic strain gradient, static, and dynamic flexocoupling. It appeared that the dispersion of the optical mode is slightly sensitive to the flexocoupling, and the dispersion of acoustic mode strongly depends on the coupling magnitude. Obtained results demonstrate that nontrivial differences in the dispersion of optical and acoustic modes occur with the change of flexocoupling constant. Therefore, experimental determination of soft phonon dispersion might be very informative to study the influence of strain gradients and flexocoupling on the spatially modulated phase in ferroelectrics with commensurate and incommensurate long-range order.

Highly disordered superconductors, in the magnetic-field-driven insulating state, can show discontinuous current-voltage characteristics. Electron overheating has been shown to give a consistent description of this behavior, but there are other possible explanations, including an electric-field-induced breakdown of the insulating state and a novel “superinsulating” state. We present ac-dc crossed measurements, in which the application of a dc voltage is applied along our sample, while a small ac voltage is applied in the transverse direction. We varied the dc voltage and observed a simultaneous discontinuity in both ac and dc currents. We show that the inferred electron temperature in the transverse measurement matches that in the longitudinal one, strongly supporting electron overheating as the source of observed current-voltage characteristics. Our measurement technique may be applicable as a method of probing electron overheating in various other physical systems, which show discontinuous or nonlinear current-voltage characteristics.

We report on the experimental study of the angular dependent magnetoresistance (MR) of heavy metal/ferromagnetic insulator bilayer structures. Through altering the relative composition in heavy metal $\mathrm{P}{\mathrm{t}}_{\delta }\mathrm{T}{\mathrm{a}}_{1–\delta }$ alloy, we continuously tune its spin Hall angle from positive, crossing zero, and to negative and study its impact on the MR. Most notably, both spin Hall effect and MR disappear simultaneously in $\mathrm{P}{\mathrm{t}}_{0.32}\mathrm{T}{\mathrm{a}}_{0.68}$ (3 nm)/YIG when the effective spin Hall angle vanishes, evidencing the essential role of spin-orbit coupling in heavy metal for the MR. By introducing Fe impurities, we further identify that magnetic scattering is also essential to induce the MR in Pt/Fe-doped $\mathrm{Si}{\mathrm{O}}_2$ at large magnetic field, where the MR ratio increases monotonically with doping level.

In frustrated magnetic systems, geometric constraints or the competition among interactions introduce extre-mely high degeneracy and prevent the system from readily selecting a low-temperature ground state. The most frustrated known spin arrangement is on the pyrochlore lattice, but nearly all magnetic pyrochlores have unquenched orbital angular momenta, constraining the spin directions through spin-orbit coupling. Pyrochlore ${\mathrm{Mn}}_2{\mathrm{Sb}}_2{\mathrm{O}}_7$ is an extremely rare Heisenberg pyrochlore system with directionally unconstrained spins and low chemical disorder. We show that it undergoes a spin-glass transition at 5.5 K, which is suppressed by disorder arising from Mn vacancies, indicating this ground state to be a direct consequence of the spins' interactions. The striking similarities to $3d$ transition-metal pyrochlores with unquenched angular momenta suggests that the low spin-orbit coupling in the $3d$ block makes Heisenberg pyrochlores far more accessible than previously imagined.

We investigate the effects of magnetic inhomogeneities and thermal fluctuations on the magnetic properties of a rare-earth intermetallic compound, ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$. The constrained Monte Carlo method is applied to a ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ bulk system to realize the experimentally observed spin reorientation and magnetic anisotropy constants $K_m^{\mathrm{A}}(m=1,2,4)$ at finite temperatures. Subsequently, it is found that the temperature dependence of $K_1^{\mathrm{A}}$ deviates from the Callen-Callen law, $K_1^{\mathrm{A}}\left(T\right)\propto M{\left(T\right)}^3$, even above room temperature, $T_{\mathrm{R}}\sim 300\mathrm{K}$, when the Fe (Nd) anisotropy terms are removed to leave only the Nd (Fe) anisotropy terms. This is because the exchange couplings between Nd moments and Fe spins are much smaller than those between Fe spins. It is also found that the exponent $n$ in the external magnetic field $H_{\mathrm{ext}}$ response of barrier height ${\mathcal{F}}_{\mathrm{B}}={\mathcal{F}}_{\mathrm{B}}^0{(1-H_{\mathrm{ext}}/H_0)}^n$ is less than 2 in the low-temperature region below $T_{\mathrm{R}}$, whereas $n$ approaches 2 when $T>T_{\mathrm{R}}$, indicating the presence of Stoner-Wohlfarth-type magnetization rotation. This reflects the fact that the magnetic anisotropy is mainly governed by the $K_1^{\mathrm{A}}$ term in the $T>T_{\mathrm{R}}$ region.

We study the collective magnetic excitations of the recently discovered $C_4$-symmetric spin-density-wave states of iron-based superconductors with particular emphasis on their orbital character based on an itinerant multiorbital approach. This is important since the $C_4$-symmetric spin-density-wave states exist only at moderate interaction strengths where damping effects from a coupling to the continuum of particle-hole excitations strongly modify the shape of the excitation spectra compared to predictions based on a local moment picture. We uncover a distinct orbital polarization inherent to magnetic excitations in $C_4$-symmetric states, which provide a route to identify the different commensurate magnetic states appearing in the continuously updated phase diagram of the iron-pnictide family.

We demonstrate coherent dynamics of quantized magnetic fluxes in a superconducting loop with a weak link, a nanobridge patterned from the same thin NbN film as the loop. The bridge is a short, rounded shape constriction, close to 10 nm long and 20–30 nm wide, having minimal width at its center. It superposes neighboring fluxoid states of the loop. Quantum state control and coherent oscillations in the driven time evolution of the tunnel-junctionless system are achieved. Decoherence and energy relaxation in the system are studied using a combination of microwave spectroscopy and direct time-domain techniques. The effective flux noise behavior suggests inductance fluctuations as a possible cause of the decoherence.

Both ${180}^{\circ }$ and ${90}^{\circ }$ intrinsic polarization switching (IPS) in $\mathrm{BaTi}{\mathrm{O}}_3$ crystal were investigated by Landau-Ginzburg-Devonshire (LGD) theory under combined electric field and stress loading. Results show that for ${180}^{\circ }\mathrm{PS}$, the coercive electric field $\left(E_{IC}^{{180}^{\circ }}\right)$ increases under tension but decreases under compression with increasing stresses. The ${90}^{\circ }\mathrm{PS}$ was classified into two types. For type I ${90}^{\circ }\mathrm{PS}, E_{IC}^{\mathrm{I}\left({90}^{\circ }\right)}$ increases under tension but decreases under compression with increasing stresses, similar to ${180}^{\circ }\mathrm{PS}$; while for type II ${90}^{\circ }\mathrm{PS}$, an opposite variation trend is observed. (The definition of the type I and the type II ${90}^{\circ }\mathrm{PS}$ is given in the text.) Additionally, the calculation demonstrates that under tensile stresses or under compressive stresses between −140 and 0 MPa, the electric field needed to drive both types of ${90}^{\circ }\mathrm{PS}$ is smaller than that needed for driving ${180}^{\circ }\mathrm{PS}$, implying that ${180}^{\circ }\mathrm{PS}$ is favorable to accomplish by two-step ${90}^{\circ }\mathrm{PS}$. As $E_{IC}$ refers to ${180}^{\circ }\mathrm{PS}$ in the past investigations, these demonstrate that the $E_{IC}$ calculated by others may be overestimated. Moreover, the coercive stresses needed to drive ${90}^{\circ }$ ferroelastic IPS was also calculated as a function of preloading bias electric fields.

Structural properties of ${\mathrm{SmRu}}_4{\mathrm{P}}_{12}$ in the anomalous magnetic ordered phase between $T^{*}\sim 14$ K and $T_{\text{N}}=16.5$ K in magnetic fields has been studied by x-ray diffraction. Atomic displacements of Ru and P, reflecting the field-induced charge order of the $p$ electrons, have been deduced by analyzing the intensities of the forbidden Bragg peaks, assuming a cubic space group $Pm\overline{3}$. Also, by utilizing a high-resolution x-ray diffraction experiment, we observed a splitting of fundamental Bragg peaks, clarifying that the unit cell in the magnetic ordered phase is rhombohedral elongated along the $\left[111\right]$ axis. The response of the rhombohedral domains to the magnetic field, which reflects the direction of the magnetic moment, is studied in detail.

Using a high-pressure reaction, we successfully synthesized $\mathrm{BaF}{\mathrm{e}}_2\mathrm{S}{\mathrm{e}}_2\mathrm{O}$ with a uniform stack of $[\mathrm{F}{\mathrm{e}}_2\mathrm{S}{\mathrm{e}}_2\mathrm{O}]$ layers. Magnetic susceptibility, heat capacity, Mössbauer spectroscopy, and neutron-diffraction measurements revealed that $\mathrm{BaF}{\mathrm{e}}_2\mathrm{S}{\mathrm{e}}_2\mathrm{O}$ undergoes antiferromagnetic order at 106 K with a 2-$k$ spin structure where each Fe moment points to a neighboring oxide anion. The same spin structure has been observed in the related iron oxyselenides but with a staggered stack of $\left[\mathrm{F}{\mathrm{e}}_2\mathrm{C}{\mathrm{h}}_2\mathrm{O}\right]$ (where Ch represents chalcogen) layers $(\mathrm{Ch}=\mathrm{S},\mathrm{Se})$. We propose that the strong uniaxial anisotropy inferred from the 2-$k$ structure originates from spin-orbit coupling (SOC) induced by a $\mathit{trans}-\mathrm{Fe}{\mathrm{O}}_2\mathrm{S}{\mathrm{e}}_4$ octahedron, which provides a quasilinear coordination environment as often found in single molecule magnetic complexes. A first-principles calculation with inclusion of SOC supports the stabilization of the 2-$k$ spin structure, giving an unquenched orbital momentum of $0.1{\mu }_{\mathrm{B}}/\mathrm{Fe}$. The present paper provides an idea of how to design magnetic lattices of uniaxial anisotropy using oxychalcogenides and more generally mixed-anion compounds.

Superconductivity in one-atom-layer iron selenide (FeSe) on a strontium titanate (STO) substrate is enhanced by almost an order of magnitude with respect to bulk FeSe. There is recent experimental evidence suggesting that this enhancement persists in FeSe/STO nanoislands. More specifically, for sizes $L\sim 10$ nm, the superconducting gap is a highly nonmonotonic function of $L$ with peaks well above the bulk gap value. This is the expected behavior only for weakly-coupled metallic superconductors such as Al or Sn. Here we develop a theoretical formalism to describe these experiments based on three ingredients: Eliashberg theory of superconductivity in the weak coupling limit, pairing dominated by forward scattering, and periodic orbit theory to model spectral fluctuations. We obtain an explicit analytical expression for the size dependence of the gap that describes quantitatively the experimental results with no free parameters. This is a strong suggestion that superconductivity in FeSe/STO is mediated by STO phonons. We propose that, since FeSe/STO is still a weakly coupled superconductor, quantum size effects can be used to further enhance the bulk critical temperature in this interface.

Ever since BCS theory was first formulated it was recognized that a large electronic density of states at the Fermi level was beneficial to enhancing $T_c$. The A15 compounds and the high temperature cuprate materials both have had an enormous amount of effort devoted to studying the possibility that such peaks play an important role in the high critical temperatures existing in these compounds. Here we provide a systematic study of the effect of these peaks on the superconducting transition temperature for a variety of tight-binding models of simple structures, both in two and three dimensions. In three dimensions large enhancements in $T_c$ can occur, due to van Hove singularities that result in divergences in the density of states. Furthermore, even in more realistic structures, where the van Hove singularity disappears, large enhancements in $T_c$ continue due to the presence of “robust” peaks in the densities of states. Such a peak, recently identified in the bcc structure of ${\mathrm{H}}_3\mathrm{S}$, is likely the result of such a van Hove singularity. In certain regimes, anomalies in the isotope coefficient are also expected.

A very efficient method for the calculation of the effective optical response of nanostructured composite systems allows the design of metamaterials tailored for specific optical polarization properties. We use our method to design two-dimensional periodic arrays of subwavelength dielectric inclusions within nanometric supported metallic thin films which behave as either an almost perfect linearly dichroic system, as a quarter-wave plate, as a system with a large circular dichroism, or as a circular polarizer. All of these systems may be tuned over a wide energy range.

Understanding decoherence in cryogenically cooled rare-earth-ion doped glass fibers is of fundamental interest and a prerequisite for applications of these material in quantum information applications. Here we study the coherence properties in a weakly doped erbium silica glass fiber motivated by our recent observation of efficient and long-lived Zeeman sublevel storage in this material and by its potential for applications at telecommunication wavelengths. We analyze photon echo decays as well as the potential mechanisms of spectral diffusion that can be caused by coupling with dynamic disorder modes that are characteristic for glassy hosts, and by the magnetic dipole-dipole interactions between ${\mathrm{Er}}^{3+}$ ions. We also investigate the effective linewidth as a function of magnetic field, temperature, and time, and then present a model that describes these experimental observations. We highlight that the operating conditions (0.6 K and 0.05 T) at which we previously observed efficient spectral hole burning coincide with those for narrow linewidths (1 MHz)—an important property for applications that has not been reported before for a rare-earth-ion doped glass.

Hybrid functionals mixing the exact exchange with (semi)local functionals to reinstall the missing derivative discontinuity have been successfully employed to predict band gaps $\left(E_{\mathrm{g}}\right)$ in bulk semiconductors. Here we show that traditional hybrid functionals with fixed fractions of exact exchange do not perform significantly better than the most popular semilocal PBE-GGA functional for $E_{\mathrm{g}}$ of semiconductor nanostructures, since their band-gap corrections are essentially size independent. This is because they cannot respond properly to the variation in screening when size changes. They merely predict constant band-gap corrections to the PBE gaps in silicon nanowires (Si NWs) when wire diameter reduces, instead of the dramatic increase predicted by many-body $GW$ calculations. Moreover, these hybrid functionals generate almost identical wave functions compared with PBE for both bulk Si and Si NWs, whose overlaps with corresponding quasiparticle wave functions become much smaller than 1 for narrow NWs.

We explore thermodynamics of a quantum membrane, with a particular application to suspended graphene membrane and with a particular focus on the thermal expansion coefficient. We show that an interplay between quantum and classical anharmonicity-controlled fluctuations leads to unusual elastic properties of the membrane. The effect of quantum fluctuations is governed by the dimensionless coupling constant, $g_0\ll 1$, which vanishes in the classical limit $(\hslash \to 0)$ and is equal to $\simeq 0.05$ for graphene. We demonstrate that the thermal expansion coefficient ${\alpha }_T$ of the membrane is negative and remains nearly constant down to extremely low temperatures, $T_0\propto exp(-2/g_0)$. We also find that ${\alpha }_T$ diverges in the classical limit: ${\alpha }_T\propto -ln(1/g_0)$ for $g_0\to 0$. For graphene parameters, we estimate the value of the thermal expansion coefficient as ${\alpha }_T\simeq -0.23{\mathrm{eV}}^{-1}$, which applies below the temperature $T_{\mathrm{uv}}\sim g_0{\varkappa }_0\sim 500$ K (where ${\varkappa }_0\sim 1$ eV is the bending rigidity) down to $T_0\sim {10}^{-14}$ K. For $T<T_0$, the thermal expansion coefficient slowly (logarithmically) approaches zero with decreasing temperature. This behavior is surprising since typically the thermal expansion coefficient goes to zero as a power-law function. We discuss possible experimental consequences of this anomaly. We also evaluate classical and quantum contributions to the specific heat of the membrane and investigate the behavior of the Grüneisen parameter.

We develop a manifest non-Hermitian approach of spectral and transport properties of two-dimensional mesoscopic systems in a strong magnetic field. The finite system to which several terminals are attached constitutes an open system that can be described by an effective Hamiltonian. The lifetime of the quantum states expressed by the energy imaginary part depends specifically on the lead-system coupling and makes the difference among three regimes: resonant, integer quantum Hall effect, and superradiant. The discussion is carried on in terms of edge state lifetime in different gaps, channel formation, role of hybridization, and transmission coefficients quantization. A toy model helps in understanding non-Hermitian aspects in open systems.