Unusual behavior of quantum materials commonly arises from their effective low-dimensional physics, which reflects the underlying anisotropy in the spin and charge degrees of freedom. Torque magnetometry is a highly sensitive technique to directly qu
antify the anisotropy in quantum materials, such as the layered high-T$_c$ superconductors, anisotropic quantum spin-liquids, and the surface states of topological insulators. Here we introduce the magnetotropic coefficient $k=partial^2 F/partial theta^2$, the second derivative of the free energy F with respect to the angle $theta$ between the sample and the applied magnetic field, and report a simple and effective method to experimentally detect it. A sub-$mu$g crystallite is placed at the tip of a commercially available atomic force microscopy cantilever, and we show that $k$ can be quantitatively inferred from a shift in the resonant frequency under magnetic field. While related to the magnetic torque $tau=partial F/partial theta$, $k$ takes the role of torque susceptibility, and thus provides distinct insights into anisotropic materials akin to the difference between magnetization and magnetic susceptibility. The thermodynamic coefficient $k$ is discontinuous at second-order phase transitions and subject to Ehrenfest relations with the specific heat and magnetic susceptibility. We apply this simple yet quantitative method on the exemplary cases of the Weyl-semimetal NbP and the spin-liquid candidate RuCl$_3$, yet it is broadly applicable in quantum materials research.
We report observations of magnetoresistance, quantum oscillations and angle-resolved photoemission in RhSb$_3$, a unfilled skutterudite semimetal with low carrier density. The calculated electronic band structure of RhSb$_3$ entails a $Z_2$ quantum n
umber $ u_0=0, u_1= u_2= u_3=1$ in analogy to strong topological insulators, and inverted linear valence/conduction bands that touch at discrete points close to the Fermi level, in agreement with angle-resolved photoemission results. Transport experiments reveal an unsaturated linear magnetoresistance that approaches a factor of 200 at 60 T magnetic fields, and quantum oscillations observable up to 150~K that are consistent with a large Fermi velocity ($sim 1.3times 10^6$ ms$^{-1}$), high carrier mobility ($sim 14$ $m^2$/Vs), and small three dimensional hole pockets with nontrivial Berry phase. A very small, sample-dependent effective mass that falls as low as $0.015(7)$ bare masses scales with Fermi velocity, suggesting RhSb$_3$ is a new class of zero-gap three-dimensional Dirac semimetal.
We present local optical measurements of thermal diffusivity in the $ab$ plane of underdoped YBCO crystals. We find that the diffusivity anisotropy is comparable to reported values of the electrical resistivity anisotropy, suggesting that the anisotr
opies have the same origin. The anisotropy drops sharply below the charge order transition. We interpret our results through a strong electron-phonon scattering picture and find that both electronic and phononic contributions to the diffusivity saturate a proposed bound. Our results suggest that neither well-defined electron nor phonon quasiparticles are present in this material.
We study magnetotransport properties of the electron-doped superconductor Pr$_{2-x}$Ce$_x$CuO$_{4pmdelta}$ with $x$ = 0.14 in magnetic fields up to 92~T, and observe Shubnikov de-Haas magnetic quantum oscillations. The oscillations display a single f
requency $F$=255$pm$10~T, indicating a small Fermi pocket that is $sim$~1% of the two-dimensional Brillouin zone and consistent with a Fermi surface reconstructed from the large hole-like cylinder predicted for these layered materials. Despite the low nominal doping, all electronic properties including the effective mass and Hall effect are consistent with overdoped compounds. Our study demonstrates that the exceptional chemical control afforded by high quality thin films will enable Fermi surface studies deep into the overdoped cuprate phase diagram.
Broken fourfold rotational (C$_4$) symmetry is observed in the experimental properties of several classes of unconventional superconductors. It has been proposed that this symmetry breaking is important for superconducting pairing in these materials,
but in the high superconducting transition temperature (high-T$_{mathrm{c}}$) cuprates this broken symmetry has never been observed on the Fermi surface. We have measured a pronounced anisotropy in the angle dependence of the interlayer magnetoresistance of the underdoped high-T$_{mathrm{c}}$) superconductor YBa$_2$Cu$_3$O$_{6.58}$, directly revealing broken C$_4$ symmetry on the Fermi surface. Moreover, we demonstrate that this Fermi surface has C$_2$ symmetry of the type produced by a uniaxial or anisotropic density-wave phase. This establishes the central role of C$_4$ symmetry breaking in the Fermi surface reconstruction of YBa$_2$Cu$_3$O$_{6+delta}$, and suggests a striking degree of universality among unconventional superconductors.
Torque magnetization measurements on YBa$_2$Cu$_3$O$_{y}$ (YBCO) at doping $y=6.67$($p=0.12$), in DC fields ($B$) up to 33 T and temperatures down to 4.5 K, show that weak diamagnetism persists above the extrapolated irreversibility field $H_{rm irr}
(T=0) approx 24$ T. The differential susceptibility $dM/dB$, however, is more rapidly suppressed for $Bgtrsim 16$ T than expected from the properties of the low field superconducting state, and saturates at a low value for fields $B gtrsim 24$ T. In addition, torque measurements on a $p=0.11$ YBCO crystal in pulsed field up to 65 T and temperatures down to 8 K show similar behaviour, with no additional features at higher fields. We discuss several candidate scenarios to explain these observations: (a) superconductivity survives but is heavily suppressed at high field by competition with CDW order; (b) static superconductivity disappears near 24 T and is followed by a region of fluctuating superconductivity, which causes $dM/dB$ to saturate at high field; (c) the stronger 3D ordered CDW that sets in above 15 T may suppress the normal state spin susceptibility sufficiently to give an apparent diamagnetism of the magnitude observed.
Some of the most remarkable phenomena---and greatest theoretical challenges---in condensed matter physics arise when $d$ or $f$ electrons are neither fully localized around their host nuclei, nor fully itinerant. This localized/itinerant duality unde
rlies the correlated electronic states of the high-$T_c$ cuprate superconductors and the heavy-fermion intermetallics, and is nowhere more apparent than in the $5f$ valence electrons of plutonium. Here we report the full set of symmetry-resolved elastic moduli of $PuCoGa_5$---the highest $T_c$ superconductor of the heavy fermions ($T_c$=18.5 K)---and find that the bulk modulus softens anomalously over a wide range in temperature above $T_c$. Because the bulk modulus is known to couple strongly to the valence state, we propose that plutonium valence fluctuations drive this elastic softening. This elastic softening is observed to disappear when the superconducting gap opens at $T_c$, suggesting that plutonium valence fluctuations have a strong footprint on the Fermi surface, and that $PuCoGa_5$ avoids a valence-transition by entering the superconducting state. These measurements provide direct evidence of a valence instability in a plutonium compound, and suggest that the unusually high-$T_c$ in this system is driven by valence fluctuations.
Vortices in a type-II superconductor form a lattice structure that melts when the thermal displacement of the vortices is an appreciable fraction of the distance between vortices. In an anisotropic high-Tc superconductor, such as YBa2Cu3Oy, the magne
tic field value where this melting occurs can be much lower than the mean-field critical field Hc2. We examine this melting transition in YBa2Cu3Oy with oxygen content y from 6.45 to 6.92, and fit the data to a theory of vortex-lattice melting. The quality of the fits indicates that the transition to a resistive state is indeed the vortex lattice melting transition, with the shape of the melting curves being consistent with the known change in penetration depth anisotropy from underdoped to optimally doped YBa2Cu3Oy. From the fits we extract Hc2(T = 0) as a function of hole doping. The unusual doping dependence of Hc2(T =0) points to some form of electronic order competing with superconductivity around 0.12 hole doping.
Close to optimal doping, the copper oxide superconductors show strange metal behavior, suggestive of strong fluctuations associated with a quantum critical point. Such a critical point requires a line of classical phase transitions terminating at zer
o temperature near optimal doping inside the superconducting dome. The underdoped region of the temperature-doping phase diagram from which superconductivity emerges is referred to as the pseudogap because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBCO cuprate superconductors is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behavior and therefore superconductivity in the cuprates.
The electrical resistivity rho_c of the underdoped cuprate superconductor YBCO was measured perpendicular to the CuO_2 planes on ultra-high quality single crystals in magnetic fields large enough to suppress superconductivity. The incoherent insulati
ng-like behavior of rho_c at high temperature, characteristic of all underdoped cuprates, is found to cross over to a coherent regime of metallic behavior at low temperature. This crossover coincides with the emergence of the small electron pocket detected in the Fermi surface of YBCO via quantum oscillations, the Hall and Seebeck coefficients and with the detection of a unidirectional modulation of the charge density as seen by high-field NMR measurements. The low coherence temperature is quantitatively consistent with the small hopping integral t_perp inferred from the splitting of the quantum oscillation frequencies. We conclude that the Fermi-surface reconstruction in YBCO at dopings from p = 0.08 to at least p = 0.15, attributed to stripe order, produces a metallic state with 3D coherence deep in the underdoped regime.
