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The study of magnetic frustration in classical spin systems was motivated by the prediction and discovery of classical spin liquid states. These uncommon magnetic phases are characterized by a massive degeneracy of their ground state implying a finite magnetic entropy at zero temperature. While the classical spin liquid state was originally predicted in the Ising triangular lattice antiferromagnet in 1950, this state has never been experimentally observed in any triangular magnets. We report here the discovery of an electric analogue of classical spin liquids on a triangular lattice of uniaxial electric dipoles in EuAl12O19 . This new type of frustrated antipolar phase is characterized by a highly degenerate state at low temperature implying an absence of long-range antiferroelectric order, despite short-range antipolar correlations. Its dynamics are governed by a thermally activated process, slowing down upon cooling towards a complete freezing at zero temperature.

The phase landscape of UTe$_2$ features a remarkable diversity of superconducting phases under applied pressure and magnetic field. Recent quantum oscillation studies at ambient pressure have revealed the quasi-2D Fermi surface of this material. However, the pressure-dependence of the Fermi surface remains an open question. Here we track the evolution of the UTe$_2$ Fermi surface as a function of pressure up to 19.5 kbar by measuring quantum interference oscillations. We find that in sufficient magnetic field to suppress both superconductivity at low pressures and incommensurate antiferromagnetism at higher pressures, the quasi-2D Fermi surface found at ambient pressure smoothly connects to that at 19.5 kbar, with no signs of a reconstruction over this pressure interval. The warping of the cylindrical Fermi sheets continuously increases with pressure, which is consistent with increased $f$-orbital contribution at the Fermi level, up to and beyond the critical pressure at which superconductivity is truncated. These findings highlight the value of high pressure quantum interference measurements as a new probe of the electronic structure in heavy fermion materials.

Quantum critical phenomena are widely studied across various materials families, from high temperature superconductors to magnetic insulators. They occur when a thermodynamic phase transition is suppressed to zero temperature as a function of some tuning parameter such as pressure or magnetic field. This generally yields a point of instability - a so-called quantum critical point - at which the phase transition is driven exclusively by quantum mechanical fluctuations. Here we show that the heavy fermion metamagnet UTe$_2$ possesses a quantum phase transition at extreme magnetic field strengths of over 70 T. Surprisingly, rather than terminating at one singular point, we find that the phase boundary is sensitive to magnetic field components in each of the three cartesian axes of magnetic field space. This results in the three-dimensional transition surface being bounded by a continuous ring of quantum critical points, the locus of which forms an extended line of quantum criticality - a novel form of quantum critical phase boundary. Within this quantum critical line sits an intensely field-resilient superconducting state in a striking toroidal shape, persisting to fields over 70 T. We model our data by a phenomenological free energy expansion, and show how a three-dimensional quantum critical phase boundary - rather than a more conventional singular point of instability - anchors the remarkable high magnetic field phase landscape of UTe$_2$.

UTe$_2$ is a spin-triplet superconductor candidate for which high quality samples with long mean free paths have recently become available, enabling quantum oscillation measurements to probe its Fermi surface and effective carrier masses. It has recently been reported that UTe$_2$ possesses a 3D Fermi surface component [Phys. Rev. Lett. 131, 036501 (2023)]. The distinction between 2D and 3D Fermi surface sections in triplet superconductors can have important implications regarding the topological properties of the superconductivity. Here we report the observation of oscillatory components in the magnetoconductance of UTe$_2$ at high magnetic fields. We find that these oscillations are well described by quantum interference between quasiparticles traversing semiclassical trajectories spanning magnetic breakdown networks. Our observations are consistent with a quasi-2D model of this material's Fermi surface based on prior dHvA-effect measurements. Our results strongly indicate that UTe$_2$ -- which exhibits a multitude of complex physical phenomena -- possesses a remarkably simple Fermi surface consisting exclusively of two quasi-2D cylindrical sections.

The unconventional superconductor UTe$_2$ exhibits numerous signatures of spin-triplet superconductivity -- a rare state of matter which could enable quantum computation protected against decoherence. UTe$_2$ possesses a complex phase landscape comprising two magnetic field-induced superconducting phases, a metamagnetic transition to a field-polarised state, along with pair- and charge-density wave orders. However, contradictory reports between studies performed on UTe$_2$ specimens of varying quality have severely impeded theoretical efforts to understand the microscopic origins of the exotic superconductivity. Here, we report a comprehensive suite of high magnetic field measurements on a new generation of pristine quality UTe$_2$ crystals. Our experiments reveal a significantly revised high magnetic field superconducting phase diagram in the ultraclean limit, showing a pronounced sensitivity of field-induced superconductivity to the presence of crystalline disorder. We employ a Ginzburg-Landau model that excellently captures this acute dependence on sample quality. Our results suggest that in close proximity to a field--induced metamagnetic transition the enhanced role of magnetic fluctuations -- that are strongly suppressed by disorder -- is likely responsible for tuning UTe$_2$ between two distinct spin-triplet superconducting phases.

The heavy fermion paramagnet UTe$_2$ exhibits numerous characteristics of spin-triplet superconductivity. Efforts to understand the microscopic details of this exotic superconductivity have been impeded by uncertainty regarding the underlying electronic structure. Here we directly probe the Fermi surface of UTe$_2$ by measuring magnetic quantum oscillations in pristine quality crystals. We find an angular profile of quantum oscillatory frequency and amplitude that is characteristic of a quasi-2D Fermi surface, which we find is well described by two cylindrical Fermi sheets of electron- and hole-type respectively. Additionally, we find that both cylindrical Fermi sheets possess considerable undulation but negligible small-scale corrugation, which may allow for their near-nesting and therefore promote magnetic fluctuations that enhance the triplet pairing mechanism. Importantly, we find no evidence for the presence of any 3D Fermi surface sections. Our results place strong constraints on the possible symmetry of the superconducting order parameter in UTe$_2$.

Multiple unconventional superconducting phases are suspected to be driven by magnetic fluctuations in the heavy-fermion paramagnet UTe$_2$, and a challenge is to identify the signatures of the electronic correlations, including the magnetic fluctuations, in the bulk physical quantities. Here, we investigate thoroughly the anisotropy of the electrical resistivity of UTe$_2$ under intense magnetic fields up to 70~T, for different electrical-current and magnetic-field configurations. Two characteristic temperatures and an anisotropic low-temperature Fermi-liquid-like coefficient $A$, controlled by the electronic correlations, are extracted. Their critical behavior near the metamagnetic transition induced at $\mu_0H_m\simeq35$~T for $\mathbf{H}\parallel\mathbf{b}$ is characterized. Anisotropic scattering processes are evidenced and magnetic fluctuations are proposed to contribute, via a Kondo hybridization, to the electrical resistivity. Our work appeals for a microscopic modeling of the anisotropic contributions to the electrical resistivity as a milestone for understanding magnetically-mediated superconductivity in UTe$_2$., Comment: - Main text: 10 pages, 5 Figures and 60 References - Supplemental Material: 5 pages, 5 Figures, 1 Table and 11 References - there was a problem with Refs. in version 1 of the preprint, this is corrected in version 2 of the preprint

The discovery of superconductivity in the heavy-fermion paramagnet UTe$_2$ has attracted a lot of attention, particularly due to the reinforcement of superconductivity near pressure- and magnetic-field-induced magnetic quantum phase transitions. A challenge is now to characterize the effects of combined pressure and magnetic fields applied along variable directions in this strongly anisotropic paramagnet. Here, we present an investigation of the electrical resistivity of UTe$_2$ under pressure up to 3~GPa and pulsed magnetic fields up to 58~T along the hard magnetic crystallographic directions $\mathbf{b}$ and $\mathbf{c}$. We construct three-dimensional phase diagrams and show that, near the critical pressure, a field-enhancement of superconductivity coincides with a boost of the effective mass related to the collapse of metamagnetic and critical fields at the boundaries of the correlated paramagnetic regime and magnetically-ordered phase, respectively. Beyond the critical pressure, field-induced transitions precede the destruction of the magnetically-ordered phase, suggesting an antiferromagnetic nature. By bringing new elements about the interplay between magnetism and superconductivity, our work appeals for microscopic theories describing the anisotropic properties of UTe$_2$ under pressure and magnetic field., Comment: 12 pages, 7 figures

We present an extensive powder and single-crystal neutron scattering investigation of the crystallographic structure and magnetic order of the frustrated metallic $f$-electron magnet UNi$_4$B. We carry out a full refinement of the crystallographic structure and conclude that the low-temperature lattice symmetry is orthorhombic (space group Pmm2; cell parameters: $a = 6.963(4)~\r{A}$ , $b = 14.793(9)~\r{A}$ , $c = 17.126(8)~\r{A}$). We determine the magnetically ordered structure, concluding that below $T_\mathrm{N} = 19.5~\mathrm{K}$ the material undergoes a transition into a partially ordered antiferromagnetic state. The magnetic structure is consistent with the existence of toroidal order in this material. We further test the proposal of a second magnetic transition occurring at $330~\mathrm{mK}$, concluding that the thermodynamic anomalies observed at these temperatures do not reflect modifications of the magnetic structure. Our study provides a consistent picture of the interrelationship of structural and magnetic properties in the frustrated magnet UNi$_4$B previously unresolved., Comment: Submitted to Phys. Rev. B

We present acoustic signatures of the electric quadrupolar degrees of freedom in the honeycomb-layer compound UNi$_4$B. The transverse ultrasonic mode $C_{66}$ shows softening below 30 K both in the paramagnetic phase and antiferromagnetic phases down to $\sim0.33$ K. Furthermore, we traced magnetic field-temperature phase diagrams up to 30 T and observed a highly anisotropic elastic response within the honeycomb layer. These observations strongly suggest that $\Gamma_6$(E$_{\rm 2g}$) electric quadrupolar degrees of freedom in localized $5f^2$ ($J = 4$) states are playing an important role in the magnetic toroidal dipole order and magnetic-field-induced phases of UNi$_4$B, and evidence some of the U ions remain in the paramagnetic state even if the system undergoes magnetic toroidal ordering., Comment: 6 pages, 4 figures + Supplemental Materials (11 pages, 9 figures)

We present a detailed study of the magnetic and electronic properties of U$_2$Rh$_3$Si$_5$, a material that has been demonstrated to exhibit a first order antiferromagnetic phase transition. From a high magnetic field study, together with extensive experiments in moderate fields, we establish the magnetic phase diagrams for all crystallographic directions. The possibility of an electronic phase in a narrow interval above the N\'eel temperature as a precursor of a magnetic phase is discussed., Comment: Submitted to Phys. Rev. B

Superconductivity induced by a magnetic field near metamagnetism is a striking manifestation of magnetically-mediated superconducting pairing. After being observed in itinerant ferromagnets, this phenomenon was recently reported in the orthorhombic paramagnet UTe$_2$. Under a magnetic field applied along the hard magnetization axis b, superconductivity is reinforced on approaching metamagnetism at $\mu_0H_m$ = 35 T, but it abruptly disappears beyond $H_m$. On the contrary, field-induced superconductivity was reported beyond $\mu_0H_m$ = 40-50 T in a magnetic field tilted by $\simeq25-30\deg$ from b in the (b,c) plane. Here we explore the phase diagram of UTe2 under these two magnetic-field directions. Zero-resistance measurements permit to confirm unambiguously that superconductivity is established beyond Hm in the tilted-field direction. While superconductivity is locked exactly at fields either smaller (for a H || b), or larger (for H tilted by $\simeq27\deg$ from b to c), than Hm, the variations of the Fermi-liquid coefficient in the electrical resistivity and of the residual resistivity are surprisingly similar for the two field directions. The resemblance of the normal states for the two field directions puts constraints for theoretical models of superconductivity and implies that some subtle ingredients must be in play., Comment: 18 pages, 5 Figures, includes Supplementary Information (9 pages, 8 Figures)

Multiple superconducting order parameters are extremely rare. Here we show that a very small pressure can induce this phenomenon in the recently discovered heavy fermion superconductor UTe2. This nearly ferromagnetic system shows several intriguing phenomena, including an extraordinary reinforcement of superconductivity in very strong magnetic fields. We find that pressure can tune the system to a more correlated state and probable magnetic order. The superconducting critical temperature is strongly enhanced, reaching almost 3K, a new record for Ce- and U-based heavy fermion superconductors. Most spectacularly under pressure we find a transition within the superconducting state, putting UTe2 among the very rare systems having multiple superconducting phases. UTe2 under pressure is a treasure trove of several of the most fascinating phenomena in unconventional superconductivity and may well be a keystone in their understanding.

Thermal expansion, magnetostriction and magnetization measurements under magnetic field and hydrostatic pressure were performed on a $\mathrm{UAu_{2}Si_{2}}$ single crystal. They revealed a large anisotropy of magnetoelastic properties manifested by prominent length changes leading to a collapse of the unit-cell volume accompanied by breaking the fourfold symmetry (similar to that in $\mathrm{URu_{2}Si_{2}}$ in the hidden-order state) in the antiferromagnetic state as consequences of strong magnetoelastic coupling. The magnetostriction curves measured at higher temperatures confirm a bulk character of the 50 K weak ferromagnetic phase. The large positive pressure change of the ordering temperature predicted from Ehrenfest relation contradicts the more than an order of magnitude smaller pressure dependence observed by the magnetization and specific heat measured under hydrostatic pressure. A comprehensive magnetic phase diagram of $\mathrm{UAu_{2}Si_{2}}$ in magnetic field applied along the $c$ axis is presented. The ground-state antiferromagnetic phase is suppressed by a field-induced metamagnetic transition that changes its character from the second to the first order at the tricritical point.

We compare the magnetic and electronic configuration of single Mn atoms in molecular beam epitaxy (MBE) grown Bi$_2$Se$_3$ thin films, focusing on electron paramagnetic (ferromagnetic) resonance (EPR and FMR, respectively) and superconducting quantum interference device (SQUID) techniques. X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) reveal the expected increase of disorder with increasing concentration of magnetic guest atoms, however, Kikuchi patterns show that disorder consists majorly of mum-scale 60deg twin domains in the hexagonal Bi$_2$Se$_3$ structure, which are promoted by the presence of single unclustered Mn impurities. Ferromagnetism below T$_C$ ~ (5.4 +/- 0.3) K can be well described by critical scaling laws M(T) ~ (1-T/T$_C$)$^\beta$ with a critical exponent $\beta$ = (0.34 +/- 0.2)), suggesting 3D Heisenberg class magnetism instead of e.g. 2D-type coupling between Mn-spins in van der Waals gap sites. From EPR hyperfine structure data we determine a Mn$^{2+}$ (d$^5$, S = 5/2) electronic configuration with a g-factor of 2.002 for -1/2 --> +1/2 transitions. In addition, from the strong dependence of the low temperature FMR fields and linewidth on the field strength and orientation with respect to the Bi$_2$Se$_3$ (0001) plane, we derive magnetic anisotropy energies of up to K1 = -3720 erg/cm3 in MBE-grown Mn-doped Bi$_2$Se$_3$, reflecting the first order magneto-crystalline anisotropy of an in-plane magnetic easy plane in a hexagonal (0001) crystal symmetry. Across the ferromagnetic-paramagnetic transition the FMR intensity is suppressed and resonance fields converge the paramagnetic limit of a Mn$^{2+}$ (d$^5$, S = 5/2).

Homojunctions between Bi$_2$Se$_3$ and its Mn-doped phase are investigated as a sample geometry to study the influence of spin degrees of freedom on topological insulator properties. $n$ quintuple layers (QLs) of Bi$_2$Se$_3$ are grown ontop of Mn-doped Bi$_2$Se$_3$ by molecular beam epitaxy for $0\le n \le 30\,$QLs, allowing to unhamperedly monitor the development of electronic and topological properties by surface sensitive techniques like angle resolved photoemission spectroscopy. With increasing $n$, a Mn-induced gap at the Dirac point is gradually filled in an "hourglass" fashion to reestablish a topological surface state at $n \sim 9\,$QLs. Our results suggest a competition of upwards and downwards band bending effects due to the presence of an n-p type interface, which can be used to tailor topological and quantum well states independently., Comment: 5 pages, 5 figures