Using the determinant quantum Monte Carlo method, we study the magnetic susceptibility in the parameter space of the on-site interaction $U$, temperature $T$, electron filling $\langle n\rangle$, and the frustration control parameter $t^{\prime }$ within the Hubbard model on a two-dimensional checkerboard lattice. It is shown that the system exhibits stable and strong ferromagnetic fluctuations about the electron filling $\langle n\rangle \ge 1.2$ for different $t^{\prime }$, and the ferromagnetic susceptibility is strongly enhanced by the increasing interaction and decreasing temperature. We also discuss the sign problem to clarify which parameter region is accessible and reliable. Our findings not only demonstrate important implications for modulating magnetism in the checkerboard lattice, but will also provide a theoretical platform for a flat-band model that demonstrates a variety of physical properties.

We present a general-purpose machine learning Gaussian approximation potential (GAP) for iron that is applicable to all bulk crystal structures found experimentally under diverse thermodynamic conditions, as well as surfaces and nanoparticles (NPs). By studying its phase diagram, we show that our GAP remains stable at extreme conditions, including those found in the Earth's core. The new GAP is particularly accurate for the description of NPs. We use it to identify new low-energy NPs, whose stability is verified by performing density functional theory calculations on the GAP structures. Many of these NPs are lower in energy than those previously available in the literature up to $N_{\mathrm{atoms}}=100$. We further extend the convex hull of available stable structures to $N_{\mathrm{atoms}}=200$. For these NPs, we study characteristic surface atomic motifs using data clustering and low-dimensional embedding techniques. With a few exceptions, e.g., at magic numbers $N_{\mathrm{atoms}}=59$, 65, 76, and 78, we find that iron tends to form irregularly shaped NPs without a dominant surface character or characteristic atomic motif, and no reminiscence of crystalline features. We hypothesize that the observed disorder stems from an intricate balance and competition between the stable bulk motif formation, with bcc structure, and the stable surface motif formation, with fcc structure. We expect these results to improve our understanding of the fundamental properties and structure of low-dimensional forms of iron and to facilitate future work in the field of iron-based catalysis.

Understanding of spin-heat coupling mechanisms and magnetothermoelectric phenomena, including the anomalous Nernst effect (ANE), in emergent quaternary Heusler alloys is of practical importance for applications in thermal management and energy harvesting. Here, we demonstrate an intrinsic Berry curvature mediated anomalous Nernst thermopower in CoFeVSb, which orders magnetically at high temperature ($T_C\approx 850\mathrm{K}$) with a large saturation magnetization of $\approx 2.2{\mu }_B/\mathrm{f}.\mathrm{u}.$ at room temperature. We show that the electron-electron elastic and electron-magnon inelastic scattering dominate longitudinal electrical transport at low temperatures ($T\le 50\mathrm{K}$), whereas the electron-phonon and electron-magnon scatterings govern it at higher $T$. The longitudinal thermopower is resulted mainly from the diffusive contribution with a very large longitudinal Seebeck coefficient ($42\mu \mathrm{V}{\mathrm{K}}^{-1}$ at 395 K). The value of the anomalous Nernst coefficient ($S_{\mathrm{ANE}}$) for CoFeVSb at room temperature is $0.039\mu \mathrm{V}{\mathrm{K}}^{-1}$ which is higher than the compressively strained $\mathrm{SrRu}{\mathrm{O}}_3$ film ($0.03\mu \mathrm{V}{\mathrm{K}}^{-1}$) as well as the spin gapless semiconductor CoFeCrGa ($0.018\mu \mathrm{V}{\mathrm{K}}^{-1}$). On lowering $T$, both the ordinary Nernst coefficient and carrier mobility increase but an opposite trend is found for $S_{\mathrm{ANE}}$. Our ab initio simulations reveal the topological semimetallic nature of CoFeVSb with a pair of Weyl points. These Weyl crossings result in a significant contribution to the Berry curvature, leading to an intrinsic anomalous Hall conductivity (${\sigma }_{xy}^{\mathrm{AHE}}$) of $\approx 85$ S/cm, which matches well with experiment (77 S/cm at 2 K). Our experimental findings and ab initio calculations support the dominance of the intrinsic Berry curvature in the observed ANE. The ratio of ${\sigma }_{xy}^{\mathrm{AHE}}$ to the transverse anomalous thermoelectric conductivity (${\alpha }_{xy}^{\mathrm{ANE}}$) shows an increasing trend with $T$ attaining a sizable fraction of $\frac{k_B}{e}\left(\approx 0.35\frac{k_B}{e}\right)$ at room temperature.

The synergistic interplay of different interactions in materials leads to the emergence of novel quantum phenomena. Spin-orbit and vibronic couplings usually counteract each other; however, in cubic $d^1$ double perovskites they coexist and give rise to spin-orbit-lattice entanglement with unquenched dynamic Jahn-Teller effect on the metal sites. The correlation of these entangled states induced by intersite interactions has not been assessed so far. Here, we investigate the joint cooperative effect of spin-orbit and vibronic interactions on the formation of the ordered phases in $d^1$ double perovskites. We found that the magnetically ordered states in these systems coexist with a dynamic vibronic order characterized by the ordering of vibronic quadrupole moments on sites. This treatment allows for the rationalization of a number of unexplained features of experimentally investigated phases.

We introduce a method for global optimization of the structure of atomic systems that uses additional atoms with fractional existence. The method allows for movement of atoms over long distances bypassing energy barriers encountered in the conventional position space. The method is based on Gaussian processes, where the extrapolation to fractional existence is performed with a vectorial fingerprint. The method is applied to clusters and two-dimensional systems, where the fractional existence variables are optimized while keeping the atomic positions fixed on a lattice. Simultaneous optimization of atomic coordinates and existence variables is demonstrated on copper clusters of varying size. The existence variables are shown to speed up the global optimization of large and particularly difficult-to-optimize clusters.

Sapphire (${\mathrm{Al}}_2{\mathrm{O}}_3$) is a major constituent of the Earth's mantle and has significant contributions to the field of high-pressure physics. Constraining its Hugoniot over a wide pressure range and identifying the location of shock-driven phase transitions allows for development of a multiphase equation of state and enables its use as an impedance-matching standard in shock physics experiments. Here, we present measurements of the principal Hugoniot and sound velocity from direct impact experiments using magnetically launched flyers on the Z machine at Sandia National Laboratories. The Hugoniot was constrained for pressures from 0.2–2.1 TPa and a four-segment piecewise linear shock-velocity–particle-velocity fit was determined. First-principles molecular dynamics simulations were conducted and agree well with the experimental Hugoniot. Sound-speed measurements identified the onset of melt between 450 and 530 GPa, and the Hugoniot fit refined the onset to $525\pm 13$ GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.

Buckling-driven shape-shifting is increasingly being used in metamaterials to achieve mechanical programmability and novel functionality. Here, we show that the post-buckling response and the ensuing behavior, of lattice metamaterials can be programed through so-called passive and active modal nudging. Numerical continuation is first used to explore exhaustively the bifurcation manifold of a compressed, elastomeric lattice metamaterial. We then tailor the natural postcritical behavior of the metamaterial by judiciously altering the baseline geometry using modal information extracted from the bifurcation landscape (passive modal nudging). Experimental tests verify the effectiveness of the approach. Subsequently, shape change is induced by actively nudging the metamaterial between two stable postcritical states using an embedded actuator, i.e., by changing the local topology of the metamaterial rather than by controlling a global field. Fundamentally, we use passive modal nudging to bias the metamaterial towards one of three possible postcritical states under applied compression and then employ active nudging to switch between different postcritical states. Based on this paradigm, we manufacture and test a crawling soft robot and demonstrate that locomotion through local actuation to switch between two postcritical states is significantly more energy efficient than the alternative strategy of switching between a precritical and a postcritical state through global actuation. Overall, this paper demonstrates the benefits and promise of programming the behavior of soft metamaterials by exploiting principles of bifurcation theory and using tailored imperfections and embedded actuators.

Nuclear spins and paramagnetic centers in a solid randomly group to form clusters featuring nearly degenerate, hybrid states whose dynamics are central to processes involving nuclear spin-lattice relaxation and diffusion. Their characterization, however, has proven notoriously difficult mostly due to their relative isolation and comparatively low concentration. Here, we combine magnetic field cycling experiments, optical spin pumping, and variable radiofrequency (RF) excitation to probe transitions between hybrid multispin states formed by strongly coupled electronic and nuclear spins in diamond. Leveraging bulk nuclei as a collective time-integrating sensor, we probe the response of these spin clusters as we simultaneously vary the applied magnetic field and RF excitation to reconstruct multidimensional spectra. We uncover complex nuclear polarization patterns of alternating sign that we qualitatively capture through analytical and numerical modeling. Our results unambiguously expose the impact that strongly hyperfine-coupled nuclei can have on the spin dynamics of the crystal, and inform future routes to spin cluster control and detection.

We investigate the intrinsic orbital Hall conductivity (OHC) and spin Hall conductivity (SHC) in a bismuth semimetal, by employing an $sp$-orbital tight-binding model. We report a notable difference between the anisotropy of OHC and SHC whose orbital and spin polarizations lie within the basal plane. We do not observe a substantial correlation between the orbital and spin Berry curvatures with spin-orbit coupling (SOC) at the Fermi energy, disproving the correlation between OHC and SHC in a strong SOC regime. We argue the huge SHC in a Bi semimetal is attributed to its gigantic SOC which strongly affects the hybridization of the $p$ orbitals, despite its relatively small magnitude of OHC. We hope the distinct anisotropy of OHC and SHC provides a feasible means to differentiate between the two effects in experiments.

Topological magnetic structures are promising candidates for resilient information storage. An elementary example is spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schrödinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. We find two classes of quantum spin helices that can reach and even exceed ground-state stability: spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered “phantom helices.” Beyond that, we show that the helicity itself (left or right rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon for stabilizing helical quantum structures, e.g., in ultracold atoms and solid-state systems. We also identify a third type of phantom helix in the system.

We present an experimental study of the strong to ultrastrong coupling regimes at room temperature in frequency-reconfigurable three-dimensional reentrant cavities coupled with a yttrium-iron-garnet slab. The observed coupling rate, defined as the ratio of the coupling strength to the cavity frequency of interest, ranges from 12% to 59%. We show that certain considerations must be taken into account when analyzing the polaritonic branches of a cavity spintronic device where the rf field is highly focused in the magnetic material. Our observations are in excellent agreement with electromagnetic finite-element simulations in the frequency domain.

The magnetic coupling mechanisms underlying ferromagnetism and magnetotransport in magnetically doped topological insulators (TIs) have been a central issue to gain controlled access to the magnetotopological phenomena such as the quantum anomalous Hall effect (AHE) and the topological axion insulating state. Here, we focus on the role of bulk carriers in magnetism of the family of magnetic TIs, in which the host material is either ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ or $\mathrm{BiSb}{\mathrm{Te}}_3$, containing Mn self-organized in $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ septuple layers. We tune the Fermi level using the electron irradiation technique and study how magnetic properties vary through the change in carrier density; the role of the irradiation defects is also discussed. Ferromagnetic resonance spectroscopy and magnetotransport measurements show no effect of the Fermi-level position on the magnetic anisotropy field and the Curie temperature, respectively, excluding bulk magnetism based on a carrier-mediated process. Furthermore, the magnetotransport measurements show that the AHE is dominated by the intrinsic and dissipationless Berry-phase-driven mechanism, with the Hall resistivity enhanced near the bottom/top of the conduction/valence band, due to the Berry curvature which is concentrated near the avoided band crossings. These results demonstrate that the AHE can be effectively managed, maximized, or turned off by adjusting the Fermi level.

We demonstrate that recent angle-resolved photoemission spectroscopy experiments provide strong evidence for the existence of two competing topological superconducting phases in ${\mathrm{FeSe}}_{0.45}{\mathrm{Te}}_{0.55}$. The coupling of their underlying microscopic mechanisms—one based on a three-dimensional topological insulator, one based on two-dimensional superconductivity—stabilizes topological superconductivity over a wide range of parameters, and gives rise to two disjoint topological regions in the phase diagram of ${\mathrm{FeSe}}_{0.45}{\mathrm{Te}}_{0.55}$. We show that the topological origin of these regions can be identified by considering the form of Majorana edge modes at domain walls.

At room temperature, bismuth undergoes several structural transitions with increasing pressure before taking on a body-centered cubic (bcc) phase at approximately 8 GPa. The bcc structure is stable to the highest measured pressure and its simplicity, along with its high compressibility and atomic number, makes it an enticing choice as a pressure calibrant. We present three data sets on the compression of bismuth in a diamond anvil cell in a neon pressure medium, up to a maximum pressure of about 260 GPa. The use of a soft pressure medium reduces deviatoric stress when compared to previous work. With an expanded pressure range, a higher point density, and a decreased uniaxial stress component, we are able to provide more reliable equation of state parameters. We also conduct density functional theory electronic-structure calculations that confirm that the bcc phase is energetically favored at high pressure.

Nanoscale compositional heterogeneity created by doping in ferroelectric systems leads to the formation of conventional relaxors in most cases, but reentrant relaxors in some unusual cases. It has remained a long-standing puzzle why reentrant relaxors rather than conventional relaxors form in these unusual cases. In this study, we use a binary ferroelectric system having a solid solution of a ferroelectric with cubic (C) to tetragonal (T) transition at one end and a ferroelectric with C to rhombohedral (R) transition at the other end, with nanoscale compositional heterogeneities, to reveal the origin of the reentrant relaxor transition. Our phase field simulations based on Landau theory demonstrate that the reentrant relaxor transitions in such a system are manifested by the formation of R nanodomains in the T microdomains upon cooling at compositions near the T/R phase boundary, which is accompanied by frequency-dependent permittivity peaks below $T_{\mathrm{C}}$. We found that the difference in phase transition sequence at different local compositions near the T/R phase boundary created by point defect doping is essential for the formation of reentrant relaxors. This work unravels the general conditions for the formation of reentrant relaxors and may shed light on the origin of other reentrant ferroic glasses.

The successful realization of the topological Weyl semimetals has revolutionized contemporary physics. In recent years, multi-Weyl semimetals, a class of topological Weyl semimetals, has attracted broad interest in condensed-matter physics. Multi-Weyl semimetals are emerging topological semimetals with nonlinear anisotropic energy dispersion, which is characterized by higher topological charges. In this study, we investigate how the topological charge affects the nonlinear optical response from multi-Weyl semimetals. It has been observed that the laser-driven electronic current is characteristic of the topological charge, and the laser polarization's direction influences the current's direction and amplitude. In addition, the anomalous current, perpendicular to the laser's polarization, carries a distinct signature of the topological charges and encodes the information about the parity and amplitude of the nontrivial Berry curvature. We show that the anomalous current associated with the anomalous Hall effect remains no longer proportional to the topological charge at higher laser intensity—a significant deviation from the linear response theory. High-harmonic spectroscopy is employed to capture the distinct and interesting features of the currents in multi-Weyl semimetals where the topological charge drastically impacts the harmonics' yield and energy cutoff.

Yu-Shiba-Rusinov (YSR) states arise as subgap excitations of a magnetic impurity in a superconducting host. Taking into account the quantum nature of the impurity spin in a single-site approximation, we study the spectral properties of the YSR excitations of a system of magnetic impurity in a spin-split superconductor, i.e., a superconductor in proximity to a ferromagnetic insulator at zero external magnetic fields. The YSR excitations of this system exhibit a robust spin polarization that is protected from fluctuations and environmental noise by the exchange field of the ferromagnetic insulator, which can be as large as a few Tesla. We compare the results of this quantum approach to the classical approach, which conventionally predicts fully polarized YSR excitations even in the absence of exchange and external magnetic field. Turning on a small magnetic field, we show the latter splits the YSR excitations in the regime where the impurity is strongly coupled to the superconductor, whilst the classical approach predicts no such splitting. The studied system can potentially be realized in a tunnel junction connected to a quantum dot in proximity to a spin-split superconductor.

Exploring the origin of the pseudogap is important for the understanding of superconductivity in cuprates. Here we report a systematical experimental study on the phonon vibrational properties of ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{Ca}}_{n-1}{\mathrm{Cu}}_n{\mathrm{O}}_{2n+4+\delta }$ ($n=1,2,3$) single crystals based on the Raman scattering measurements over the temperature range from 10–300 K. The temperature evolution of the frequency and linewidth of the observed phonon modes in each member of this family does not follow the expected self-energy effect when entering the superconducting state. The anomalies are observed for the phonon modes involving the vibrations of the atoms in the Tl-O layer and the apical oxygen at the temperature around 150 K, which is higher above the superconducting transition. The phonon mode of the apical oxygen exhibits a pronounced universal softening behavior. From the comparison with the existing experimental data for various orders, we find that the observed starting temperature for the phonon softening corresponds to the onset opening temperature of the pseudogap. This finding indicates a large lattice effect in the pseudogap state and the non-negligible spin-phonon coupling for such a phonon softening.