We study the ultrafast dynamics of the multiband iron-based superconductor ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ via time-resolved optical reflectivity. We observe a long-lived 5- GHz oscillation of the reflection changes within the superconducting regime. We assign this low-frequency oscillation to a soft Leggett mode associated with the collective fluctuation of multiple phase differences between Cooper pair condensates. Our observation evidences the presence of the time-reversal-symmetry breaking state in superconducting ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$.

We study numerically the formation of a vortex lattice inside a rotating bucket containing superfluid helium, paying attention to an important feature which is practically unavoidable in all experiments: the microscopic roughness of the bucket's surface. We model this using the Gross-Pitaevskii equation for a weakly interacting Bose gas, a model which is idealized when applied to superfluid helium but captures the key physics of the vortex dynamics which we are interested in. We find that the vortex lattice arises from the interaction and reconnections of nucleated U-shaped vortex lines, which merge and align along the axis of rotation. We quantify the effects which the surface roughness and remanent vortex lines play in this process.

Static spin susceptibility of superconductors with spin-orbit relaxation was calculated in the seminal work of Abrikosov and Gor'kov [Sov. Phys. JETP 15, 752 (1962)]. Surprisingly, the generalization of this result to finite frequencies has not been done despite being quite important for the modern topic of superconducting spintronics. The present paper fills this gap by deriving the analytical expression for spin susceptibility. The time-dependent spin response is shown to be captured by the quasiclassical Eilenberger equation with collision integrals corresponding to the ordinary and spin-orbit scattering. Using the developed formalism, we study the linear spin pumping effect between the ferromagnet and the adjacent superconducting film. The consequences for understanding recent experiments demonstrating the modification of Gilbert damping by the superconducting correlations are discussed.

Magnetic torque measurements in the spin-orbit coupled metal ${\mathrm{Cd}}_2{\mathrm{Re}}_2{\mathrm{O}}_7$ have been performed to investigate unique multipole orders associated with inversion symmetry breaking. The torque curves as a function of field angle are decomposed into two terms, a fourfold symmetry term (${\tau }_4\propto H^4$), corresponding to an electric quadrupole order, and a twofold symmetry term (${\tau }_2\propto H^2$), likely corresponding to an electric toroidal quadrupole order at low temperatures. Below 20 K, a strong enhancement of the fourfold symmetry term following a large phase change is observed toward the superconducting transition whereas no such behavior is evident in the twofold symmetry term. The results show anomalous changes of the electric quadrupole order at the low temperatures.

The exciton problem is solved in the two-dimensional Dirac model with allowance for strong electron-hole attraction. The exciton binding energy is assumed smaller than but comparable to the band gap. The exciton wave function is found in the momentum space as a superposition of all four two-particle states including electron and hole states with both positive and negative energies. The matrix element of exciton generation is shown to depend on the additional components of the exciton wave function. Both the Coulomb and the Rytova–Keldysh potentials are considered. The dependence of the binding energy on the coupling constant is analyzed for the ground and first excited exciton states. The binding energy and the oscillator strength are studied as functions of the environmental-dependent dielectric constant for real transition metal dichalcogenide monolayers. We demonstrate that the multicomponent nature of the exciton wave function is crucial for description of resonant optical properties of two-dimensional Dirac systems.

${\mathrm{VO}}_2$ experiences a metal-insulator transition at 340 K. Discontinuities in electronic transport properties, such as the Seebeck coefficient and the electronic conductivity, suggest that there is a significant change in the electronic structure upon metallization. However, the thermodynamic nature of this transformation remains difficult to describe using conventional computational and experimental methods. This has led to disagreement over the relative importance of the change in electronic entropy with respect to the overall transition entropy. A method is presented that links measurable electronic transport properties to the change in electronic state entropy of conduction electrons. The change in electronic entropy is calculated to be $9.2\pm 0.7$ J/mol K which accounts for 62%–67% of the total transition entropy. This compares favorably with some estimates of the vibrational entropy.

The layered topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has attracted great interest recently due to its intrinsic antiferromagnetic order, potentially hosting various topological phases. By temperature-dependent infrared spectroscopy over a broad frequency range, we studied the changes in the optical conductivity of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ at the magnetic ordering temperature. The temperature dependence of several optical parameters reveals an anomaly at the magnetic phase transition, which suggests the correlation between the bulk electronic band structure and the magnetism. We relate our findings to recent reports on the temperature dependence of the electronic band structure of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$.

We present an analytical and experimental study of the scattering parameters in a one dimensional (1D) symmetric photonic crystal and their relation to the density of states (DOS). The 1D photonic crystal is constituted by $N$ alternating wires and loops that are either inserted horizontally or attached vertically between the source and load on a transmission line. The complete knowledge of the scattering matrix coefficients ($S_{ij}$) allows us to access the DOS and eigenvalues of the finite periodic structure as well as the DOS and dispersion curves of an infinite periodic system. We show the usefulness of the transmission and reflection delay times and highlight their similarities and differences with respect to the DOS, in particular as a function of the absorption strength in the system. For both horizontal and vertical geometries, we show analytically that in a lossless structure, the DOS is proportional to the Friedel phase, namely the derivative of the argument of the determinant of the scattering matrix S. For a low loss system, this proportionality remains still valid with a good approximation and can be used as a practical tool to derive the DOS and therefore the dispersion curves from experimental data. Also, the absorption can be accurately extracted from the measurement of the modulus of the determinant of $S$. However, for increasing strength of dissipation, we show how and why these relationships cease to be valid. Still, the transmission delay time can remain an efficient tool to derive DOS even at relatively high dissipation strength. Additionally, we show that in the vertical geometry the transmission and reflection delay times exhibit negative delta peaks which are related directly to the eigenmodes of the finite system with different boundary conditions on its extremities. Our theoretical results are obtained by means of the Green's function approach, whereas the experimental demonstrations are performed using standard coaxial cables in the radio-frequency domain.

We explore the image charge interaction for organic semiconductor bipolarons near a conducting interface and find that the cross term between one of the constituent charges and the image of its neighbor stabilizes the bipolaron by up to ∼0.3 eV, dramatically increasing the concentration of this species near the interface. Using density functional theory calculations for the common hole transport molecule $N,N$′-bis(3-methylphenyl)-$N,N$′-diphenylbenzidine, we validate a simple point charge description of this effect and incorporate it within an interface energy level alignment model to predict the density of polarons and bipolarons near the interface. We find that the image effect greatly enhances bipolaron formation in the first few monolayers, leading to the expectation that bipolarons account for more than 1% of the total interface charge in many cases of practical interest. This result reinforces the notion that bipolarons are robust near the contacts of many organic semiconductor devices and thus helps to rationalize their involvement in the phenomenon of unipolar organic magnetoresistance.

The short-range order in a CoPt alloy was determined at 1203 and 1423 K using neutron diffuse scattering measurements. The effective pair interactions provided by data analysis reproduce well the experimental order-disorder transition temperature in Monte Carlo simulations. They complete previous results reported for the Co-Pt system and are compared to those obtained within tight-binding and ab initio formalisms. Our results show that the important dependence of the nearest-neighbor pair interactions with composition is not related to the sample magnetic state at the measured temperatures. Interactions measured in the paramagnetic domain for the CoPt alloy behave like those in the ferromagnetic domain for the ${\mathrm{Co}}_3\mathrm{Pt}$ and ${\mathrm{Co}}_{0.65}{\mathrm{Pt}}_{0.35}$ alloys. The effective pair interactions related to the tight-binding Ising model provide a relatively good description of the CoPt alloy thermodynamics close to the ordering temperature (short-range order and temperature of phase transformation), even if they strongly differ from those measured in this study. The average magnetic moment of Co atoms at high temperatures was determined from the analysis of the intensity contribution that is not dependent on the scattering vector. The obtained value is very close to the moment measured at room temperature or determined from ab initio calculations. This confirms the Curie-Weiss behavior of the CoPt alloy. Finally, transmission electron microscope observations carried out on samples annealed for about 30 days confirmed that the order-disorder transition takes place in the 830–843 K temperature interval at the ${\mathrm{Co}}_3\mathrm{Pt}$ composition.

The study and understanding of spin-transport mechanisms including thermal fluctuation are required for the development and design of spintronic devices. In this paper, we present an approach to investigate the temperature dependence of spin-transport behavior within the magnetic structure by using the generalized spin accumulation model. The temperature affects not only the magnetization orientation, but also the spin-transport properties. Its effect on transport parameters can be taken into account by considering the spin-dependent resistivity at any finite temperature. This leads to the calculation of temperature-dependent spin-transport parameters and eventually allows the calculation of the thermal effects on spin accumulation, spin current, and spin torque. It is observed that increasing temperature is likely to decrease the value of key transport parameters relevant to the magnitude of spin torque. This study demonstrates the importance of thermal effects on spin-transport behavior which needs to be considered for spin-transfer torque based device design with high performance.

Condensed matter magneto-optical investigations can be a powerful probe of a material's microscopic magnetoelectric properties. This is because subtle interactions between electric and magnetic multipoles on a crystal lattice show up in predictable and testable ways in a material's optical response tensor, which dictates the polarization state and absorption spectrum of propagating electromagnetic waves. Magneto-optical techniques are therefore strong complements to probes such as neutron scattering, particularly when spin-lattice coupling effects are present. Here we perform a magneto-optical investigation of vibronic spin-lattice coupling in the magnetically frustrated pyrochlore ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Coupling of this nature involving quadrupolar mixing between the ${\mathrm{Tb}}^{3+}$ electronic levels and phonons in ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ has been a topic of debate for some time. This is particularly due to its implication for describing the exotic spin-liquid phase diagram of this highly debated system. A manifestation of this vibronic effect is observed as splitting of the ground and first excited crystal field doublets of the ${\mathrm{Tb}}^{3+}$ electronic levels, providing a fine structure to the absorption spectra in the terahertz (THz) frequency range. In this investigation, we apply a static magnetic field along the cubic [111] direction while probing with linearly polarized THz radiation. Through the Zeeman effect, the magnetic field enhances the splitting within the low-energy crystal field transitions revealing new details in our THz spectra. Complementary magneto-optical quantum calculations including quadrupolar terms show that indeed vibronic effects are required to describe our observations at 3 K. A further prediction of our theoretical model is the presence of a novel magneto-optical birefringence as a result of this vibronic process. Essentially, spin-lattice coupling within ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ may break the optical isotropy of the cubic system, supporting two different electromagnetic wave propagations within the crystal. Together our results reveal the significance of considering quadrupolar spin-lattice effects when describing the spin-liquid ground state of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. They also highlight the potential for future magneto-optical investigations to probe complex materials where spin-lattice coupling is present and reveal new magneto-optical activity in the THz range.

Several previous reports on undoped $AE\mathrm{}{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($AE=$ alkaline earth metal) point to drops in resistivity indicative of possible superconductivity and some degree of Meissner effect in the magnetic susceptibility. Also, based on both resistivity and magnetic susceptibility measurements, controlled exposure to water vapor has been shown to induce superconductivity in $AE{\mathrm{Fe}}_2{\mathrm{As}}_2$. In our study, $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystals grown using the self-flux method showed a full resistive drop around 22 K and magnetic shielding, when exposed to fluorine gas postgrowth. Our measurements indicate electron (donor) doping via atomic substitution of F for As is concurrent with the observed superconductivity, which sheds light on the likely effect of exposure to water vapor in previous work. Like doping experiments (such as substitution of Co for Fe, P for As, or K for Ba) in $AE{\mathrm{Fe}}_2{\mathrm{As}}_2$ to date, the present work is consistent with suppression of the spin density wave transition coincident with the appearance of $T_c$. In addition to answering the puzzle of superconductivity in undoped or water vapor exposed $AE{\mathrm{Fe}}_2{\mathrm{As}}_2$, our results also represent a fast (20 min exposure to 5% F in He) and reliable method suitable for inducing superconductivity in thin films of $AE{\mathrm{Fe}}_2{\mathrm{As}}_2$. Some supportive work on $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ exposed to ${\mathrm{Cl}}_2$ is also presented.

We predict and observe numerically highly anisotropic magnetic patterns in the classical frustrated model of planar XY spins on the regular kagome lattice. Frustration is introduced by a specific spatial arrangement of both ferromagnetic and antiferromagnetic bonds between adjacent magnetic moments on the lattice vertices. Defining a quantitative measure of frustration, we find that at a critical value of frustration, $f=f_c=3/4$, the system displays a phase transition from an ordered ferromagnetic state to a frustrated regime featuring a highly degenerate ground state. In this frustrated regime, which extends for a finite range of frustrations $f_c<f\le 1$, we obtain an unexpected scaling of a spatially averaged magnetization $\langle \vec{M}\rangle$ with the total number of nodes $N$: $\langle \vec{M}\rangle \simeq N^{-1/4}$. This scaling results from highly anisotropic magnetic patterns displaying perfect ferromagnetic ordering along the $y$-direction, and short-range correlations of magnetic moments along the $x$-direction. We show that all these features are explained by the presence of the doubly degenerate ground state in the basic cell, i.e., a single triangle, of the kagome lattice combined with an extensive number of intrinsic constraints on the spins. This model represents an interesting class of frustrated magnetic systems, which might be present in other lattice geometries.

We studied the magnetization coupling between an yttrium-iron-garnet (YIG) film and a gadolinium-gallium-garnet (GGG) substrate at low temperature using magnetic resonance measurements. We observed both acoustic and optical mode hybridization between the magnetization of the 3-$\mu \text{m-thick}$ YIG film, $M_{\mathrm{YIG}}$, and the magnetization of the GGG substrate, $M_{\mathrm{GGG}}$, corresponding to in-phase and out-of-phase coupling, respectively. This experimental observation can be described by an antiferromagnetic-type interaction between $M_{\mathrm{YIG}}$ and $M_{\mathrm{GGG}}$ in the Landau-Lifshitz-Gilbert equation. Taking this approach we find that the effective field induced by magnetization coupling can be enhanced by decreasing the temperature or increasing the external field, providing a means to control magnon dynamics in YIG for magnonic device applications.

The structural distortion and magnetoelastic coupling induced through commensurate magnetism has been investigated by neutron diffraction in structurally related ${\mathrm{MnWO}}_4$ and $\mathrm{NaFe}{\left({\text{WO}}_4\right)}_2$. Both systems exhibit a competition of incommensurate spiral and commensurate spin up-up-down-down ordering along the magnetic chains. In the latter commensurate phases, the alternatingly parallel and antiparallel arrangement of ${\mathrm{Fe}}^{3+}$ or ${\mathrm{Mn}}^{2+}$ moments leads to sizable bond-angle modulation and thus to magnetic dimerization. For $\mathrm{NaFe}{\left({\text{WO}}_4\right)}_2$ this structural distortion has been determined to be strongest for the low-field up-up-down-down arrangement, and the structural refinement yields a bond-angle modulation of $\pm 1.15\left(16\right)$ degrees. In the commensurate phase of ${\mathrm{MnWO}}_4$, superstructure reflections signal a comparable structural dimerization and thus strong magneto-elastic coupling different to that driving the multiferroic order. Pronounced anharmonic second- and third-order reflections in the incommensurate and multiferroic phase of ${\mathrm{MnWO}}_4$ result from tiny commensurate fractions that can depin multiferroic domains.

In this work, we fabricated interlayer exchange-coupled magnetic thin films with ferromagnetic layers separated by a spacer layer. We investigated the dependencies of the sign and strength of the interlayer exchange coupling (IEC) and magnetic configurations on both the ferromagnetic layer thicknesses and the spacer thickness. The change of sign of the IEC between the ferromagnetic layers can occur for a thickness change of ferromagnetic layers by as small as approximately 0.1 nm. By comparison, a minimum of approximately 0.2 nm spacer thickness change is required for the same transformation. We attribute the ferromagnetic layer thickness dependence of the IEC to changes in thermal magnon excitations and quantum interferences inside ferromagnetic layers that affect interactions between the ferromagnetic layers and the spacer layer. Our experimental results suggest that the IEC modifications via changing the magnetic-layer thickness can be more efficient for magnetic memory and sensing applications.

A topological superconducting state can be induced in the surface state of a topological insulator (TI) by way of proximity coupling to a conventional $s$-wave superconductor ($s-\mathrm{SC}$). Planar $s-\mathrm{SC}/\mathrm{TI}$ junction structures were proposed as a scalable platform for controlled generation and manipulation of Majorana zero mode (MZM), which holds intriguing promise for fault-tolerant quantum computing. Despite intensive research efforts, the presence of MZM has not been definitively demonstrated in $s-\mathrm{SC}/\mathrm{TI}/s-\mathrm{SC}$ lateral junctions. A key factor is a lack of direct measurement and quantitative understanding of the proximity coupling between the $s-\mathrm{SC}$ and TI. Here we report evidence for strong superconducting proximity effect between a three-dimensional strong TI and Al, a conventional $s-\mathrm{SC}$ with minimal intrinsic spin-orbit coupling, in the form of pronounced enhancement of the in-plane critical field ($H_{c\left|\right|}$) of the thin Al. Specifically, the $H_{c\left|\right|}$ of a 6-nm-thick Al film deposited on a TI is found to be 2.7 times its Pauli limit and about three times that of a simultaneously deposited reference film on $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_2$. The analysis of the $H_{c\left|\right|}$ enhancement within the Maki theory indicates significant induced spin-orbit interaction in the Al due to electronic coupling to the TI. Our results revealed a pathway for producing SC/TI devices of high interfacial electrical transparency conducive for MZM generation and manipulation.

The Seebeck coefficient is one of the key ingredients in thermoelectric properties, and it is often calculated based simply on the electronic band structure, within the frame of Boltzmann's transport theory and the constant relaxation time approximation. Despite the simplicity and popularity of this approximation, its validity is not fully justified even in lightly doped semiconductors, and it breaks down completely in metals. On the other hand, more sophisticated first-principles approaches are available but require the computation of the full electron-phonon coupling. Here, we demonstrate with several simple (alkali and noble) metals viz., Li, Na, K, Cu, Ag, Au, and Pt, that the variational approach based on ab initio couplings can reproduce experimental Seebeck coefficients quantitatively, whereas the constant relaxation time approximation yields significant quantitative discrepancies and often fails to predict the correct sign. Calculations of the electrical resistivity of these metals via the variational approach are also reported.