Magnetic damping poses a significant impact on the performance of various magnetic and spintronic devices, making it a longstanding focus of research. The strength of magnetic damping is usually quantified by the Gilbert damping constants in the Landau-Lifshitz-Gilbert equation. Here we propose a first-principles-based approach to evaluate the damping constant contributed by spin-lattice coupling in magnetic insulators. The approach involves effective Hamiltonian models and spin-lattice dynamics simulations. As a case study, we applied our method to ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}, {\mathrm{MnFe}}_2{\mathrm{O}}_4$, and ${\mathrm{Cr}}_2{\mathrm{O}}_3$. Their damping constants were calculated to be $0.8\times {10}^{-4}, 0.2\times {10}^{-4}, 2.2\times {10}^{-4}$, respectively at a low temperature. The results for ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ and ${\mathrm{Cr}}_2{\mathrm{O}}_3$ are very close to the experimental results, while the large discrepancy in ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ can be attributed to the inhomogeneity and small band gap in real samples. The stronger damping observed in ${\mathrm{Cr}}_2{\mathrm{O}}_3$, compared to ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$, essentially results from its stronger spin-lattice coupling. In addition, we confirmed a proportional relationship between damping constants and the temperature difference of subsystems, which had been reported in previous studies. These successful applications suggest that our approach can be a viable candidate for estimating the Gilbert damping constant in magnetic insulators.

Polarization-resolved electronic Raman spectroscopy is an important experimental tool to investigate collective excitations in superconductors. In this paper, we present a general theory that allows us to study the evolution of all Raman active collective modes in multiple symmetry channels across a time reversal symmetry (TRS) breaking superconducting transition. This comprehensive approach reveals that multiple modes belonging to different symmetry channels show a tendency to soften, even when the interactions in the subleading channel are held constant. This indicates an increased competition induced by the proximity to the TRS breaking transition. The entry into the TRS broken phase is marked by the introduction of an additional mode into the gap in multiple symmetry channels. This additional modes have a phase character complementary to the ones that are already present. Even though all the modes in the TRS broken phase acquire an amplitude character, we explicitly demonstrate that the coupling to the Raman probe is exclusively through the phase sector. We demonstrate that the Raman spectrum collected in lower symmetry channels shows a selective sensitivity to the sign of the ground-state order parameters and the sign of the interband interactions. Finally, we demonstrate the applicability of an interaction induced selection rule that clearly explains the spectral weights of various modes in various irreducible representations, including the possible of dark Leggett and Bardasis-Schrieffer modes.

Thermodynamics studies of a prototypical quasi-two-dimensional frustrated magnet, ${\mathrm{Ba}}_2{\mathrm{Sn}}_2{\mathrm{ZnCr}}_{7p}{\mathrm{Ga}}_{10-7p}{\mathrm{O}}_{22}$, where the magnetic ${\mathrm{Cr}}^{3+}$ ions are arranged in a triangular network of bipyramids show that the magnetic zero-point entropy for $p=0.98$ is 55(1)% of the entropy expected when the ${\mathrm{Cr}}^{3+}$ moments are fully disordered. Furthermore, when combined with a previous neutron scattering study and the perimeter scaling entropy of a spin jam, the analysis reveals that with decreasing $p$, i.e., doping of the nonmagnetic ${\mathrm{Ga}}^{3+}$ ions, the variation in the magnetic zero-point entropy can be well explained by the combined effects of the zero-point entropy of the spin jam state and that of weakly coupled orphan spins, shedding light on the coexistence of the two types of spin states in quantum magnetism.

The mechanism of the peculiar transport properties around the magnetic ordering temperature of semiconducting antiferromagnetic ${\mathrm{EuCd}}_2{\mathrm{P}}_2$ is not yet understood. With a huge peak in the resistivity observed above the Néel temperature $T_{\mathrm{N}}=10.6\mathrm{K}$, it exhibits a colossal magnetoresistance effect. Recent reports on observations of ferromagnetic contributions above $T_{\mathrm{N}}$ as well as metallic behavior below this temperature have motivated us to perform a comprehensive characterization of this material, including its resistivity, heat capacity, magnetic properties, and electronic structure. Our transport measurements revealed quite different temperature dependence of resistivity with the maximum at 14 K instead of previously reported 18 K. Low-field susceptibility data support the presence of static ferromagnetism above $T_{\mathrm{N}}$ and show a complex behavior of the material at small applied magnetic fields. Namely, signatures of reorientation of magnetic domains are observed up to $T=16$ K. Our magnetization measurements indicate a magnetocrystalline anisotropy which also leads to a preferred alignment of the magnetic clusters above $T_{\mathrm{N}}$. The momentum-resolved photoemission experiments at temperatures from 24 down to 2.5 K indicate the permanent presence of a fundamental band gap without change of the electronic structure when going through $T_N$ that is in contradiction with previous results. We performed ab initio band structure calculations which are in good agreement with the measured photoemission data when assuming an antiferromagnetic ground state. Calculations for the ferromagnetic phase show a much smaller band gap, indicating the importance of possible ferromagnetic contributions for the explanation of the colossal magnetoresistance effect in the related ${\mathrm{EuZn}}_2{\mathrm{P}}_2$.

Along with the progression of the low-dimensional materials, the high-quality thin film and two-dimensional material come into the stage of spintronics, where the surfaces should be important or even dominate the transport phenomena. For anomalous Hall effect (AHE), however, the surfaces are mainly treated as an additional scattering source to the residual resistance, and the corresponding AHE is submerged by the bulk contributions. In this work, we have disentangled contributions from the surface and the bulk to the AHE in ${\mathrm{CoNi}}_3$ (001) epitaxial and ${\mathrm{CoNi}}_3$ polycrystalline films by varying thickness and temperature. The surface and the bulk anomalous Hall angles are found to have opposite signs for all temperatures and the corresponding surface anomalous Hall angles are surprisingly much larger than the bulk anomalous Hall angles. Furthermore, the first-principles calculations are carried out and the observed surface AHE is successfully replicated.

The generation of spin voltage by heat, known as the spin Seebeck effect (SSE), involves the injection of spin current from a ferromagnetic to a normal metal. In this study, the shunting effect in SSE is investigated within a hybrid structure consisting of iron (Fe) and cobalt (Co) films deposited on a Si-wafer substrate using thermal evaporation [Si/Fe(500 nm)/Co(10 nm)]. Spin voltage measurements performed in the in-plane configuration revealed a voltage reversal in the Co film and Fe film. However, in the hybrid structure (Si/Fe/Co), the voltage signal exhibited consistent directionality. This intriguing observation hints at a potential shunting effect, wherein the voltage influence from the Fe layer contributes to the Co film. Consequently, it is deduced that a significant shunting effect occurs when the resistivity of Fe is approximately three orders of magnitude lower than that of the Co film. This insight sheds light on the intricate dynamics of spin thermoelectric applications, emphasizing the role of material properties in optimizing performance.

Charge excitation spectra are getting clear in cuprate superconductors in momentum-energy space especially around a small momentum region, where plasmon excitations become dominant. Here, we study whether Landau quasiparticles survive in the presence of charge fluctuations observed in experiments. We employ the layered $t\text{−}J$ model with the long-range Coulomb interaction, which can reproduce the realistic charge fluctuations. We find that Landau quasiparticles are retained in a realistic temperature and doping region, although the quasiparticle spectral weight is strongly reduced to $0.08–0.24$. Counterintuitively, the presence of this small quasiparticle weight does not work favorably to generate a pseudogap.

The dynamics of magnetic flux quanta (Abrikosov vortices) determine the resistive response of superconductors. In pinning-free planar thin films, the penetration and motion of vortices are controlled by edge defects, leading to such arrangements as vortex chains, vortex jets, and phase-slip regimes. Here, relying upon the time-dependent Ginzburg-Landau equation, we predict that these vortex patterns should appear in superconductor open nanotubes even without edge defects, due to the inhomogeneity of the normal magnetic induction component $B_{\mathrm{n}}$, caused by the three-dimensional (3D) tube geometry. The crossing of the half tubes by dc-driven vortices induces GHz-frequency voltage $U$ oscillations with spectra $U_{\mathrm{f}}\left(B\right)$ evolving between $n{f}_1$ and $\frac{n}{m}{f}_1$ [$f_1$: vortex nucleation frequency; $n,m\ge 2$] and blurred in certain ranges of currents and fields. An $n{f}_1$ spectrum corresponds to a single vortex-chain regime typical for low $B$ and for tubes of small radii. At higher fields, an $\frac{n}{m}{f}_1$ spectrum points to the presence of $m$ vortex chains in the vortex jets which, in contrast to planar thin films, are not diverging because of constraint to the tube areas where $B_{\mathrm{n}}$ is close to maximum. A blurry spectrum implies complex arrangements of vortices because of multifurcations of their trajectories. Finally, due to a stronger confinement of single vortex chains in tubes of small radii, we reveal peaks in $dU/dB$ and jumps in the frequency of microwave generation, which occur when the number of fluxons moving in the half tubes increases by one. In all, our findings are essential for novel 3D superconductor devices which can operate in few- and multifluxon regimes.

The correlation between spin-orbit coupling and low crystal symmetry in the $1T^{\prime }$ phase of the tungsten ditellurides (${\mathrm{WTe}}_2$) monolayer (ML) plays a significant role in its electronic and topological properties. However, the centrosymmetric nature of the crystal maintains Kramer's spin degeneracy in its electronic states, which limits its functionality in spintronics. In this paper, through a systematic study using first-principles calculations, we show that significant spin splitting can be induced in the $1T^{\prime }\text{−}{\mathrm{WTe}}_2$ ML by introducing a one-dimensional (1D) vacancy line defect (VLD). We examine six configurations of the 1D VLD, which consist of three VLDs extended in the armchair direction including a ${\mathrm{Te}}_1$ armchair-VLD ($AC{V}_{{\mathtt{Te}}_1}$), ${\mathrm{Te}}_2$ armchair-VLD ($AC{V}_{{\mathtt{Te}}_2}$), and W armchair-VLD ($AC{V}_{\mathtt{W}}$), and three VLDs elongated along the zigzag direction comprising a ${\mathrm{Te}}_1$ zigzag-VLD ($ZZ{V}_{{\mathtt{Te}}_1}$), ${\mathrm{Te}}_2$ zigzag-VLD ($ZZ{V}_{{\mathtt{Te}}_2}$), and W zigzag-VLD ($ZZ{V}_{\mathtt{W}}$), where ${\mathrm{Te}}_1$ and ${\mathrm{Te}}_2$ are two nonequivalent Te atoms located at the lower and higher sites in the top layer, respectively. We find that both the $AC{V}_{{\mathtt{Te}}_1}$ and $AC{V}_{\mathtt{W}}$ systems have the lowest formation energy. Concerning these two most stable VLD systems, we identify large spin splitting in the defect states near the Fermi level driven by a strong coupling of the in-plane $p-d$ orbitals, displaying highly unidirectional Rashba states with perfectly collinear spin configurations in the momentum space. This unique spin configuration gives rise to a specific spin mode that protects the spin from decoherence and leads to an exceptionally long spin lifetime. Furthermore, the observed unidirectional Rashba states are enforced by the inversion symmetry breaking and the 1D nature of the VLD, as clarified by the $\vec{k}·\vec{p}$ model derived from the symmetry analysis. Our findings pave a possible way to induce significant spin splitting in the $1T^{\prime }\text{−}{\mathrm{WTe}}_2$ ML, which could be highly important for designing highly efficient spintronic devices.

We classify one-dimensional symmetry-protected topological (SPT) phases protected by dipole symmetries. A dipole symmetry comprises two sets of symmetry generators: charge and dipole operators, which together form a nontrivial algebra with translations. Using matrix product states (MPS), we show that for a $G$ dipole symmetry with $G$ a finite Abelian group, the one-dimensional dipolar SPTs are classified by the group $H^2[G\times G,U\left(1\right)]/H^2{[G,U\left(1\right)]}^2$. Because of the symmetry algebra, the MPS tensors exhibit an unusual property, prohibiting the fractionalization of charge operators at the edges. For each phase in the classification, we explicitly construct a stabilizer Hamiltonian to realize the SPT phase and derive the response field theories by coupling the dipole symmetry to background tensor gauge fields. These field theories generalize the Dijkgraaf-Witten theories to twisted finite tensor gauge theories.

Monolayer transition metal dichalcogenides (TMDCs) constitute the core group of materials in the emerging semiconductor technology of valleytronics. While the coupled spin-valley physics of pristine TMDC materials and their heterostructures has been extensively investigated, less attention has been given to TMDC alloys, which could be useful in optoelectronic applications due to the tunability of their band gaps. The experimental investigations presented herein focus on the exploration of the spin-valley physics of the monolayer and bilayer TMDC alloy ${\mathrm{MoS}}_{2x}{\mathrm{Se}}_{2(1-x)}$ in terms of valley polarization and the generation as well as electrical control of a photocurrent utilizing the circular photogalvanic effect. Piezoelectric force microscopy provides evidence for an internal electric field perpendicular to the alloy layer, thus breaking the out-of-plane mirror symmetry. The experimental observation is supported by first-principles calculations based on the density functional theory. A comparison of the photocurrent device, based on the alloy material, is made with similar devices involving other TMDC materials.

Full-shell nanowires have been proposed as an alternative nanowire design in the search of topological superconductivity and Majorana zero modes (MZMs). They are hybrid nanostructures consisting of a semiconductor core fully covered by a thin superconductor shell and subject to a magnetic flux. Compared to their partial-shell counterparts, full-shell nanowires present some advantages that could help to clearly identify the elusive Majorana quasiparticles, such as the operation at smaller magnetic fields and low or zero semiconductor $g$ factor, and the expected appearance of MZMs at well-controlled regions of parameter space. In this paper we critically examine this proposal, finding a very rich spectral phenomenology that combines the Little-Parks modulation of the parent-gap superconductor with flux, the presence of flux-dispersing Caroli–de Gennes–Matricon (CdGM) analog subgap states, and the emergence of MZMs across finite flux intervals that depend on the transverse wavefunction profile of the charge density in the core section. Through microscopic simulations and analytical derivations, we study different regimes for the semiconductor core, ranging from the hollow-core approximation, to the tubular-core nanowire appropriate for a semiconductor tube with an insulating core, to the solid-core nanowire with the characteristic dome-shaped radial profile for the electrostatic potential inside the semiconductor. We compute the phase diagrams for the different models in cylindrical nanowires and find that MZMs typically coexist with CdGM analogs at zero energy, rendering them gapless. However, we also find topologically protected parameter regions or islands with gapped MZMs. In this sense, the most promising candidate to obtain topologically protected MZMs in a full-shell geometry is the nanowire with a tubular-shaped core. Moving beyond pristine nanowires, we study the effect of mode mixing perturbations. On the one hand, mode mixing can gap CdGM analogs and open minigaps around existing MZMs. On the other hand and rather strikingly, mode mixing can act like a topological $p$-wave pairing between particle-hole Bogoliubov partners, and is therefore able to create new topologically protected MZMs in regions of the phase diagram that were originally trivial. As a result, the phase diagram is utterly transformed and exhibits protected MZMs in around half of the parameter space.

Modeling the underlying pairing mechanism of charge carriers in strongly correlated electrons, starting from a microscopic theory, is among the central challenges of condensed-matter physics. Hereby, the key task is to understand what causes the appearance of superconductivity at comparatively high temperatures upon hole doping an antiferromagnetic (AFM) Mott insulator. Recently, it has been proposed that at strong coupling and low doping, the fundamental one- and two-hole meson-type constituents—magnetic polarons and bipolaronic pairs—likely realize an emergent Feshbach resonance producing near-resonant $d_{x^2-y^2}$ interactions between charge carriers. Here, we provide detailed calculations of the proposed scenario by describing the open and closed meson scattering channels in the $t\text{−}{t}^{\prime }\text{−}J$ model using a truncated basis method. After integrating out the closed channel constituted by bipolaronic pairs, we find $d_{x^2-y^2}$ attractive interactions between open channel magnetic polarons. The closed form of the derived interactions allows us analyze the resonant pairing interactions and we find enhanced (suppressed) attraction for hole (electron) doping in our model. The formalism we introduce provides a framework to analyze the implications of a possible Feshbach scenario, e.g., in the context of BEC-BCS crossover, and establishes a foundation to test quantitative aspects of the proposed Feshbach pairing mechanisms in doped antiferromagnets.

Two-dimensional (2D) ferrovalley materials with intrinsic ferromagnetic ordering and spontaneous spin-valley splitting provide a great platform in nanoscale valleytronic devices. In this paper, the stability, mechanical, magnetic, transport, and valley properties of the Janus $2H$-CeBrCl monolayer are predicted based on density functional theory calculations. The Janus $2H$-CeBrCl monolayer exhibits an intrinsic ferromagnetic (FM) semiconductor character with a high Curie temperature ($T_c$) of 540 K, a large piezoelectric coefficient $d_{11}$ of 2.95 pm/V, a robust perpendicular magnetic anisotropy (PMA), and a spontaneous valley polarization ($\mathrm{\Delta }\mathrm{V}$) of 29.1 meV. Applying the in-plane biaxial strain from $-6$ to 6%, the $2H$-CeBrCl monolayer still remains FM ground states, and the $\mathrm{\Delta }V$ and $d_{11}$ monotonically increase from $-18.1$ to 59.4 meV and from 1.56 to 4.03 pm/V, respectively. It is noted that a transition from PMA to in-plane magnetic anisotropy occurs at the tensile strain of 2%, which is due to the sign reversal contributed by the Ce-$d_{xy}/d_{x^2-y^2}$ orbitals. The investigations of electrical transport show that the effective mass of the hole is isotropic, while the effective mass of the electron is anisotropic for the $2H$-CeBrCl monolayer, corresponding to mobilities of the hole and electron along the $x$ direction of 111.6 and 83.2 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, respectively. Moreover, the valley-contrast Berry curvature ${\mathrm{\Omega }}_z\left(k\right)$ and valley anomalous Hall effect can be clearly observed due to the breaking of time and space reversal symmetry in the $2H$-CeBrCl monolayer. Overall, the Janus $2H$-CeBrCl monolayer can be considered as an attractive 2D intrinsic ferrovalley material for nanoscale electronics and valleytronic devices.

Transition metal dichalcogenides (TMDs) are a class of layered materials that hold great promise for a wide range of applications. Their practical use can be limited by their thermal transport properties, which have proven challenging to determine accurately, both from a theoretical and experimental perspective. We have conducted a thorough theoretical investigation of the thermal conductivity of four common TMDs, ${\mathrm{MoSe}}_2, {\mathrm{WSe}}_2, {\mathrm{MoS}}_2$, and ${\mathrm{WS}}_2$, at room temperature, to determine the key factors that influence their thermal behavior. We analyze these materials using ab initio calculations performed with the siesta program, anharmonic lattice dynamics and the Boltzmann transport equation formalism, as implemented in the temperature-dependent effective potentials method. Within this framework, we analyze the microscopic parameters influencing the thermal conductivity, such as the phonon dispersion and the phonon lifetimes. The aim is to precisely identify the origin of differences in thermal conductivity among these canonical TMD materials. We compare their in-plane thermal properties in monolayer and bulk form, and we analyze how the thickness and the chemical composition affect the thermal transport behavior. We showcase how bonding and the crystal structure influence the thermal properties by comparing the TMDs with silicon, reporting the cases of bulk silicon and monolayer silicene. We find that the interlayer bond type (covalent vs. van der Waals) involved in the structure is crucial in the heat transport. In two-dimensional silicene, we observe a reduction by a factor $\sim 15$ compared to the Si bulk thermal conductivity due to the smaller group velocities and shorter phonon lifetimes. In the TMDs, where the group velocities and the phonon bands do not vary significantly passing from the bulk to the monolayer limit, we do not see as strong a decrease in the thermal conductivity: only a factor 2–3. Moreover, our analysis reveals that differences in the thermal conductivity arise from variations in atomic species, bond strengths, and phonon lifetimes. These factors are closely interconnected and collectively impact the overall thermal conductivity. We inspect each of them separately and explain how they influence the heat transport. We also study artificial TMDs with modified masses, in order to assess how the chemistry of the compounds modifies the microscopic quantities and thus the thermal conductivity.

Xenes, two-dimensional (2D) monolayers composed of a single element, with graphene as a typical representative, have attracted widespread attention. Most of the previous Xenes, $X$ from group-IIIA to group-VIA elements, have bonding characteristics of covalent bonds. In this paper, we unveil the pivotal role of a halogen bond, which is a distinctive type of bonding with interaction strength between that of a covalent bond and a van der Waals interaction, in 2D group-VIIA monolayers. Combing the ingenious non-edge-to-edge tiling theory and state-of-the-art ab initio method with refined local density functional M06-L, we provide a precise and effective bottom-up construction of 2D iodine monolayer sheets, iodinenes, primarily governed by halogen bonds, and successfully design a category of stable iodinenes encompassing herringbone, Pythagorean, gyrated truncated hexagonal, i.e., diatomic kagome, and gyrated hexagonal tiling patterns. These iodinene structures exhibit a wealth of properties, such as nontrivial topology, flat bands and fascinating optical characteristics, offering valuable insights and guidance for future experimental investigations. Our paper not only unveils the unexplored halogen bonding mechanism in 2D materials but also opens an avenue for designing other noncovalent bonding 2D materials.

First-principles calculations have been used to investigate the electronic and topological properties of the two-dimensional ${\mathrm{C}}_{6-2x}{\left(\mathrm{BN}\right)}_x$ biphenylene network, a graphenelike structure composed of not only hexagonal ring but also octagonal and square rings. Nontrivial topological properties have been found in two of them, with a stoichiometry of ${\mathrm{C}}_4\mathrm{BN}$ and ${\mathrm{C}}_2{\left(\mathrm{BN}\right)}_2$. The former ${\mathrm{C}}_4\mathrm{BN}$ is predicted to be a type-II Dirac semimetal with a superconducting critical temperature $T_{\mathrm{c}}=0.38$ K, which is similar to the pure carbon biphenylene network (C-BPN). The latter shows an isolated edge state exists between the conduction and valence bands. By regulation of strains and virtual-crystal approximation calculations, we found the annihilation of two pairs of Dirac points (DPs) in the nonhigh-symmetric region causes the two corresponding edge states to stick together to generate this isolated edge state. In addition, we found that one pair of DPs arises from the shift of DPs in the C-BPN, while another pair of DPs emerges around the time-reversal invariant momenta point $X$ due to the doping of boron and nitrogen. We constructed a tight-binding model to reveal the mechanism of forming the isolated edge state from the C-BPN to ${\mathrm{C}}_2{\left(\mathrm{BN}\right)}_2$. This study not only demonstrates the existence and mechanism of forming the isolated edge state in semimetals, but also provides an example in which the DPs can move away from the high-symmetry region.

Control of components in integrated photonic circuits is crucial in achieving programmable devices. Operation bandwidth of a plasmonic device cannot be generally tuned once it is manufactured, especially in the visible regime. Here, we demonstrate the electrical control of such a device for extraordinary optical transmission (EOT) in the visible regime. (i) Operation frequency of the EOT device can be tuned via a bias voltage applied through nanowires. (ii) Or, at a given frequency, the EOT signal (normalized to the incident field) can be tuned continuously, e.g., between ${10}^{-4}$ and 0.4. This corresponds to a three-orders-of-magnitude modulation depth. We utilize Fano resonances induced by a quantum emitter (QE) that is embedded into the nanoholes. The external bias-voltage tunes QE's resonance. We also discuss the lifetime extensions of surface plasmon polaritons as a response to an ultrashort optical pulse. Our proposed method provides the active electronic control of EOT signal, which makes it a feasible and compact element in integrated photonic circuits, for biosensing, high-resolution imaging, and molecular spectroscopy applications.

The stabilization of quantum spin liquids is vital to realize applications in spintronics and quantum computing. The unique magnetic structure of ${\mathrm{Ba}}_2{\mathrm{CuTeO}}_6$ comprising coupled spin ladders with finite interladder coupling brings the system close to the quantum critical point. This opens up possibilities to stabilize unconventional magnetic phases by tailoring the intra- and interladder exchange couplings. Here, we demonstrate a spin-liquid-like phase in ${\mathrm{Ba}}_2{\mathrm{CuTeO}}_6$ using the method of chemical substitution. We choose nonmagnetic ${\mathrm{La}}^{3+}$ cation to substitute the ${\mathrm{Ba}}^{2+}$ in ${\mathrm{Ba}}_2{\mathrm{CuTeO}}_6$ and present signature fingerprints such as a deprived magnetic transition, nondispersive ac susceptibility, magnetic-field-independent heat capacity, and a broad Raman continuum supporting the emergence of a spin-liquid-like phase. We believe that increased magnetic frustration and spin fractionalization upon chemical substitution play a crucial role in driving such a state. In addition, temperature and magnetic-field-dependent phonon responses indicate the presence of magnetostriction (spin-lattice coupling) in La-doped ${\mathrm{Ba}}_2{\mathrm{CuTeO}}_6$, a notable property of spin liquids.

The use of coherent x-ray reflectivity to image interfaces is illustrated using model calculations for three cases: a thin film, a semi-infinite substrate, and a coherently strained epitaxial thin film. The intensities and phases of the coherent scattering signals are calculated based on a fully atomistic model (where the phases are assumed to have been recovered by a phasing algorithm). We describe the characteristics of the effective density that are obtained by direct inverse Fourier transformation of the complex structure factors, using a window function to define the data range. These effective densities include significant artifacts like oscillations and negative values derived from the finite vertical momentum transfer of the window function. Two approaches are described to extract the surface topography from the effective densities for three-dimensional visualization: (i) multiplying the effective density by a phase factor and (ii) analyzing the data as a hybrid structure factor $F\left(x,Q_z\right)$. The explicit surface sensitivity and specificity of measurements is illustrated when the film or substrate Bragg peaks are excluded. These considerations show that images of interfacial topography can be obtained using currently available experimental capabilities with parameters corresponding to epitaxial thin films.