We conducted small-angle neutron scattering (SANS) experiments on the ferromagnetic semimetal EuB6, where we observed first-hand evidence for the presence of magnetic polarons. We carried out SANS experiments over a large range of scattering vectors |q|, ranging from 0.006 to 0.140 angstrom-1, and temperatures of 2 to 60 K. Just above TC our experiments show magnetic scattering intensity, which has a Lorentzian dependence on the wave vector, characteristic of the presence of magnetic polarons. Below TC the polarons merge, and most of the observed intensity is due to scattering from domains. We were able to extract a correlation length xi that ranges from 100 to 300 angstrom for the size of the magnetic polarons. This size is much larger than one would expect for magnetic fluctuations of a three-dimensional Heisenberg ferromagnet, demonstrating the influence of magnetic polarons on the phase transition.

Uniaxial pressure is a powerful tuning parameter for quantum materials, but conventional thermodynamic probes such as specific heat are difficult to realize in the constrained geometries of strain apparatus. We develop a quantitative analysis framework for a.c. elastocaloric effect measurements that enable the reconstruction of the absolute entropy and hence specific heat across complex phase diagrams. The absolute accuracy is achieved by combining measurements in the strong coupling regime at low frequencies with high signal-to-noise measurements in the quasi-adiabatic regime at high frequencies. Applying the approach to the correlated superconductor Sr_2RuO_4, we obtain an absolute entropy map across the phase diagram including across phase transitions deep into the superconducting state. We demonstrate that from such data one can derive the absolute specific heat which is currently not possible through other approaches. This data reinforces the finding that the quenching of entropy within the superconductor Sr_2RuO_4 is strongest at the critical strain consistent with the superconducting gap being maximized at the Van Hove singularity (VHs). Furthermore, we demonstrate that, although Δc /(γT) does increase at the VH strain, this increase is much weaker than previously inferred from more indirect caloric experiments.

The Weyl semimetal CeAlSi crystallises in the noncentrosymmetric tetragonal space group I4_1md and exhibits ferromagnetic order below 8 K, thereby breaking both spatial inversion and time-reversal symmetries. This unique combination of properties establishes CeAlSi as a model system for studying the interplay between non-trivial topological states and strong electron correlations. In this work, we report observations of Shubnikov-de Haas oscillations in the electrical resistivity under magnetic fields up to 68 T applied parallel to the [001] crystallographic axis. Our measurements reveal an abrupt change in the oscillation frequencies near 14 T, which is indicative of a field-induced Lifshitz transition. Additionally, our results are consistent with the ferromagnetic order bringing the Weyl nodes closer to the Fermi level in CeAlSi. Furthermore, they suggest that the RKKY interaction plays an important role.

Chiral crystals, whose key feature is the structural handedness, host exotic quantum phenomena driven by the interplay of band topology, spin-orbit coupling (SOC), and electronic correlations. Due to the limited availability of suitable chiral-crystal materials, their unconventional superconductivity (SC) remains largely unexplored. Here, the discovery of unconventional SC in the La(Rh,Ir)Si family of materials is reported by combining muon-spin spectroscopy, band-structure calculations, and perturbation theory. This family, characterized by a double-helix chiral structure, hosts exotic multifold fermions that are absent in other topological chiral crystals. While LaRhSi behaves as a fully-gapped superconductor, the substitution of 4d-Rh by 5d-Ir significantly enhances the SOC and leads to the emergence of topological nodal-line SC in LaIrSi. The developed model shows that the nodal-line SC arises from an isotropic SOC with a specific strength. Such an exotic mechanism expands the conventional understanding of material candidates for unconventional SC, which typically rely on a significantly anisotropic SOC to promote the triplet pairing. The current work establishes a new type of phase diagram, which provides a comprehensive roadmap for identifying and engineering unconventional SC in chiral crystals. Furthermore, it calls for renewed investigations of unconventional SC in other widely studied superconductors with a chiral structure.

At ambient pressure, HfTe_5 is a material at the boundary between a weak and a strong topological phase, which can be tuned by changes in its crystalline structure or by the application of high magnetic fields. It exhibits a Lifshitz transition upon cooling, and three-dimensional (3D) quantum Hall effect (QHE) plateaus can be observed at low temperatures. Here, we have investigated the electrical transport properties of HfTe_5 under hydrostatic pressure up to 3 GPa. We find a pressure-induced crossover from a semimetallic phase at low pressures to an insulating phase at about 1.5 GPa. Our data suggest the presence of a pressure-induced Lifshitz transition at low temperatures within the insulating phase around 2 GPa. The quasi-3D QHE is confined to the low-pressure region in the semimetallic phase. This reveals the importance of the semimetallic groundstate for the emergence of the QHE in HfTe_5 and thus favors a scenario based on a low carrier density metal in the quantum limit for the observed signatures of the quasi-quantized 3D QHE.

AbstractStrongly correlated spin systems can be driven to quantum critical points via various routes. In particular, gapped quantum antiferromagnets can undergo phase transitions into a magnetically ordered state with applied pressure or magnetic field, acting as tuning parameters. These transitions are characterized by z = 1 or z = 2 dynamical critical exponents, determined by the linear and quadratic low-energy dispersion of spin excitations, respectively. Employing high-frequency susceptibility and ultrasound techniques, we demonstrate that the tetragonal easy-plane quantum antiferromagnet NiCl2 ⋅ 4SC(NH2)2 (aka DTN) undergoes a spin-gap closure transition at about 4.2 kbar, resulting in a pressure-induced magnetic ordering. The studies are complemented by high-pressure-electron spin-resonance measurements confirming the proposed scenario. Powder neutron diffraction measurements revealed that no lattice distortion occurs at this pressure and the high spin symmetry is preserved, establishing DTN as a perfect platform to investigate z = 1 quantum critical phenomena. The experimental observations are supported by DMRG calculations, allowing us to quantitatively describe the pressure-driven evolution of critical fields and spin-Hamiltonian parameters in DTN.

High temperature superconductors start out as two-dimensional antiferromagnetic Mott insulators. These are then lightly doped, where the motion of these free charges distorts the surrounding Néel order and forms a string of distorted spins in the form of a magnetic polaron. Thus, magnetic polarons are thought to be central to the high-$T_c$ problem. The shape and size of such dynamic magnetic domains can be determined from small angle neutron scattering (SANS). In order to show that magnetic polarons can be detected by SANS we studied the three-dimensional ferromagnetic model system \eu, where the results of other measurements suggest the presence of magnetic polarons. In \eu, just above $T_{\mathrm{C}}$, our experiments show magnetic scattering intensity, which has a Lorentzian dependence on the wave vector, characteristic for the presence of magnetic polarons. Below $T_{\mathrm{C}}$ the polarons merge and most of the observed intensity is due to scattering from domain walls. We were able to extract a correlation length $\xi$ which ranges from 100 to 300~\AA\ for the size of the magnetic polarons. This size is much larger than one would expect for magnetic fluctuations of a 3D Heisenberg ferromagnet, demonstrating the usefulness of SANS for detecting magnetic polarons.

There is considerable evidence that the superconductivity of Sr2RuO4 has two components. Among this evidence is a jump in the shear elastic modulus c66 at the critical temperature Tc, observed in ultrasound measurements. Such a jump is forbidden for homogeneous single-component order parameters, and it implies that Tc should develop as a cusp under the application of shear strain with (110) principal axes. This shear strain should split the onset temperatures of the two components, if they coexist, or select one component if they do not. Here, we report measurements of Tc and the elastocaloric effect of Sr2RuO4 under uniaxial stress applied along the [110] lattice direction. Within experimental resolution, we resolve neither a cusp in the stress dependence of Tc, nor any second transition in the elastocaloric effect data. We show that reconciling these null results with the observed jumps in c66 requires extraordinarily fine tuning to a triple point of the Ginzburg-Landau parameter space. In addition, our results are inconsistent with homogeneous time-reversal symmetry breaking at a temperature T2 Tc as identified in muon spin relaxation experiments.

The unconventional superconductor CeRh2As2 (critical temperature T-c approximate to 0.4 K) displays an exceptionally rare magnetic-field-induced transition between two distinct superconducting (SC) phases, proposed to be states of even and odd parity of the SC order parameter, which are enabled by a locally noncentrosymmetric structure. The superconductivity is preceded by a phase transition of unknown origin at T (0) = 0.5 K. Electronic low-temperature properties of CeRh2As2 show pronounced non-Fermi-liquid behavior, indicative of a proximity to a quantum critical point (QCP). The role of quantum fluctuations and normal state orders for the superconductivity in a system with staggered Rashba interaction is currently an open question, pertinent to explaining the occurrence of the two-phase superconductivity. In this work, using measurements of resistivity and specific heat under hydrostatic pressure, we show that the T (0 )order vanishes completely at a modest pressure of P (0) approximate to 0.5 GPa, revealing a QCP. In line with the quantum criticality picture, the linear temperature dependence of the resistivity at P (0) evolves into a Fermi-liquid quadratic dependence as quantum critical fluctuations are suppressed by increasing pressure. Furthermore, the domelike behavior of T (c )around P (0) implies that the fluctuations of the T (0 )order are involved in the SC pairing mechanism.

Odd-parity superconductivity is a fundamentally interesting but rare state of matter with a potential for applications in topological quantum computing. Crystals with staggered locally noncentrosymmetric structures have been proposed as platforms where a magnetic field can induce a transition between even- and odd-parity superconducting (SC) states. The strongly correlated superconductor CeRh2As2 with the critical temperature T-c approximate to 0.4K is likely the first example material showing such a phase transition, which occurs at the magnetic field mu H-0(& lowast; )= 4T applied along the crystallographic c axis. CeRh2As2 also undergoes a phase transition of an unknown origin at T-0=0.5K. By subjecting CeRh2As2 to hydrostatic pressure and mapping the resultant changes to the SC phase diagrams we investigated how the lattice compression and changes to the electronic correlations affect the stability and relative balance of the two SC states. The abnormally high in-plane upper critical field becomes even higher close to a quantum critical point of the T-0 order. Remarkably, the SC phase-switching field H-& lowast; is drastically reduced under pressure, dropping to 0.3T at 2.7GPa. This result signals an apparent strengthening of the local noncentrosymmetricity and forecasts a possible stabilization of the putative odd-parity state down to zero field, hitherto not considered by theoretical models.

In-plane uniaxial pressure has been shown to strongly tune the superconducting state of Sr2RuO4 by approaching a Lifshitz transition and associated Van Hove singularity (VHS) in the density of states. At the VHS, $T_c$ and the in- and out-of-plane upper critical fields are all strongly enhanced, and the latter has changed its curvature as a function of temperature from convex to concave. However, due to strain inhomogeneity it has not been possible so far to determine how the upper critical fields change with strain. Here, we show the strain dependence of both upper critical fields, which was achieved due to an improved sample preparation. We find that the in-plane upper critical field is mostly linear in $T_c$. On the other hand, the out-of-plane upper critical field varies with a higher power in $T_c$, and peaks strongly at the VHS. The strong increase in magnitude and the change in form of $H_\mathrm{c2||c}$ occur very close to the Van Hove strain, and points to a strong enhancement of both the density of states and the gap magnitude at the Lifshitz transition.

Progress in magnetoelectric materials is hindered by apparently contradictory requirements for time-reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes can be provided by recent discoveries of a time-reversal symmetry breaking anomalous Hall effect (AHE) in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, the authors report the observation of a spontaneous AHE in doped AgCrSe2 , a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3 μ Ω c m $\mu \Omega \, \textnormal {cm}$ is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to ≈80° from the crystalline c-axis. The ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the p-type carrier density. They also present theoretical results that suggest the AHE is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe2 . The results open the possibility to study the interplay of magnetic and ferroelectric-like responses in this fascinating class of materials.

The interplay of electronic and structural degrees of freedom in solids is a topic of intense research. More than 60 years ago, Lifshitz discussed a counterintuitive possibility: lattice softening driven by conduction electrons at topological Fermi surface transitions. The effect that he predicted, however, was small and has not been convincingly observed. Using a piezo-based uniaxial pressure cell to tune the ultraclean metal strontium ruthenate while measuring the stress-strain relationship, we reveal a huge softening of the Young's modulus at a Lifshitz transition of a two-dimensional Fermi surface and show that it is indeed driven entirely by the conduction electrons of the relevant energy band.

In the ferromagnetic (FM) Weyl semimetal CeAlSi both space-inversion and time-reversal symmetries are broken. Our quantum oscillation (QO) data indicate that the FM ordering modifies the Fermi-surface topology and also leads to an unusual drop in the QO amplitude. In the FM phase, we find a pressure-induced suppression of the anomalous and the loop Hall effects. This cannot be explained based on the electronic band structure or magnetic structure, both of which are nearly pressure independent. Instead, we show that a simplified model describing the scattering of Weyl fermions off FM domain walls can potentially explain the observed topological features. Our study highlights the importance of domain walls for understanding transport in FM Weyl semimetals.

The Weyl semimetal CeAlGe is a promising material to study nontrivial topologies in real and momentum space due to the presence of a topological magnetic phase. Our results at ambient pressure show that the electronic properties of CeAlGe are extremely sensitive to small stoichiometric variations. In particular, the topological Hall effect (THE) present in CeAlGe is absent in some samples of almost identical chemical composition. The application of external pressure favors the antiferromagnetic ground state. It also induces a THE where it was not visible at ambient pressure. Furthermore, a small pressure is sufficient to drive the single region of the THE in magnetic fields into two different ones. Our results reveal an extreme sensitivity of the electronic properties of CeAlGe to tiny changes in its chemical composition, leading to a high tunability by external stimuli. We can relate this sensitivity to a shift in the Fermi level and to domain walls.

The unconventional superconductor CeRh_2As_2 (critical temperature T_c≈0.4 K) displays an exceptionally rare magnetic-field-induced transition between two distinct superconducting (SC) phases, proposed to be states of even and odd parity of the SC order parameter, enabled by a locally non-centrosymmetric structure. The SC state exhibits signatures of antiferromagnetism and is preceded by a phase transition of unknown origin at T_0≈0.5 K. Electronic low-temperature properties of CeRh_2As_2 show pronounced non-Fermi-liquid behavior, indicative of a proximity to a quantum critical point (QCP). The role of quantum fluctuations and normal state orders for the superconductivity in a system with staggered Rashba interaction is currently an open question, pertinent to explaining the occurrence of two-phase superconductivity. In this work, using measurements of resistivity and specific heat under hydrostatic pressure, we show that the T_0 order vanishes completely at a modest pressure of P_0=0.5-0.7 GPa, revealing a QCP. The linear temperature dependence of the resistivity at P_0 evolves into a Fermi-liquid quadratic dependence as the quantum criticality is suppressed by increasing pressure. The dome-like behavior of T_c around P_0 suggests that the fluctuations of the T_0 order are involved in the SC pairing mechanism. These results set the scene for further investigations into the fate of the multi-phase superconductivity across this phase diagram.

LuFe$_4$Ge$_2$ crystallizes in the ZrFe$_4$Si$_2$-type structure, hosting chains of Fe-tetrahedra giving rise to geometric frustration and low-dimensionality. The compound orders antiferromagnetically at around 36 K accompanied by a simultaneous structural transition from a tetragonal to an orthorhombic phase. The hydrostatic pressure dependence of the magnetic and structural transitions is investigated using electrical-transport, ac magnetic-susceptibility, ac calorimetry, M$\ddot{\rm o}$ssbauer, muon-spin relaxation ($\mu$SR), and x-ray diffraction measurements. External pressure suppresses the first-order transition to the antiferromagnetic phase (AFM1) around 1.8 GPa. The structural transition is largely unaffected by pressure and remains between 30 to 35 K for pressures up to 2 GPa. A second antiferromagnetic phase (AFM2) is observed at higher pressures. The transition from the paramagnetic to the AFM2 phase is of second-order nature and appears to be connected to the structural transition. The magnetic volume fraction obtained from $\mu$SR and M$\ddot{\rm o}$ssbauer measurements reveal that the entire sample undergoes magnetic ordering in both magnetic phases. In addition, similar low-temperature muon-precession frequencies in AFM1 and AFM2 phases point at similar ordered moments and magnetic structures in both phases. Our results further indicate enhanced magnetic fluctuations in the pressure induced AFM2 phase. The experimental observations together with density functional theory calculations suggest that the magnetic and structural order parameters in LuFe$_4$Ge$_2$ are linked by magnetic frustration, causing the simultaneous magneto-structural transition.

The Mn3X family of compounds was the first in which a large anomalous Hall effect (AHE) was predicted to arise from a purely antiferromagnetic structure, due to the Berry curvature in momentum space. Nearly simultaneously with this prediction, a large AHE was observed experimentally in one of the hexagonal members of this family, Mn3Sn. Aligning antiferromagnetic domains, a necessary step for observation of the AHE, is more challenging for the cubic members of the Mn3X family, due to a combination of smaller spontaneous ferromagnetic moments and much stronger magnetic anisotropy. Here, we use a combination of uniaxial stress and applied magnetic field to align domains of bulk single-crystal Mn3Pt, and demonstrate for the first time a substantial AHE in a bulk sample of a cubic member of the Mn3X family. The AHE remains locked in with essentially no quantitative variation when the stress is ramped back to zero, which shows that it is not a consequence of any stress-induced ferromagnetic moment.

Strontium ruthenate Sr$_2$RuO$_4$ is an unconventional superconductor whose pairing symmetry has not been fully clarified, despite more than two decades of intensive research. Recent NMR Knight shift experiments have rekindled the Sr$_2$RuO$_4$ pairing debate by giving strong evidence against all odd-parity pairing states, including chiral $p$-wave pairing that was for a long time the leading pairing candidate. Here, we exclude additional pairing states by analyzing recent elastocaloric measurements [YS. Li et al., Nature 607, 276--280 (2022)]. To be able to explain the elastocaloric experiment, we find that unconventional even-parity pairings must include either large $d_{x^2 - y^2}$-wave or large $\{d_{xz} \mid d_{yz}\}$-wave admixtures, where the latter possibility arises because of the body-centered point group symmetry. These $\{d_{xz} \mid d_{yz}\}$-wave admixtures take the form of distinctively body-centered-periodic harmonics that have horizontal line nodes. Hence $g_{xy(x^2-y^2)}$-wave and $d_{xy}$-wave pairings are excluded as possible dominant even pairing states.

Topological superconductors have long been sought for their potential use in quantum computing. The type-II Weyl semimetal MoTe$_{2}$ is an obvious candidate, exhibiting a superconducting state below 500 mK at ambient pressure, but the question remains whether the pairing is conventional $s^{++}$ or topological $s^{+-}$. The application of external pressure favors the superconducting state in MoTe$_{2}$ and suppresses the structural transition from $1T'$ to $T_{d}$. The competition between the two structures leads to a mixed phase that strongly enhances the disorder present in the system, remarkably without affecting the superconducting transition temperature, in contrast to the expectation of $s^{+-}$ pairing superconductivity. Our thorough analysis of the electrical and Hall resistivities as a function of pressure yields the most accurate temperature-pressure phase diagram available to date for MoTe$_{2}$ and a detailed view of the relationship between disorder and superconductivity, supporting a conventional $s^{++}$ pairing symmetry.