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We report the results of a spectroscopic survey of candidate T subdwarfs identified by the Backyard Worlds: Planet 9 program. Near-infrared spectra of 31 sources with red $J-W2$ colors and large $J$-band reduced proper motions show varying signatures of subsolar metallicity, including strong collision-induced H$_2$ absorption, obscured methane and water features, and weak K I absorption. These metallicity signatures are supported by spectral model fits and 3D velocities, indicating thick disk and halo population membership for several sources. We identify three new metal-poor T subdwarfs ([M/H] $\lesssim$ $-$0.5), CWISE J062316.19+071505.6, WISEA J152443.14$-$262001.8, and CWISE J211250.11-052925.2; and 19 new "mild" subdwarfs with modest metal deficiency ([M/H] $\lesssim$ $-$0.25). We also identify three metal-rich brown dwarfs with thick disk kinematics. We provide kinematic evidence that the extreme L subdwarf 2MASS J053253.46+824646.5 and the mild T subdwarf CWISE J113010.07+313944.7 may be part of the Thamnos population, while the T subdwarf CWISE J155349.96+693355.2 may be part of the Helmi stream. We define a metallicity classification system for T dwarfs that adds mild subdwarfs (d/sdT), subdwarfs (sdT), and extreme subdwarfs (esdT) to the existing dwarf sequence. We also define a metallicity spectral index that correlates with metallicities inferred from spectral model fits and iron abundances from stellar primaries of benchmark T dwarf companions. This expansion of the T dwarf classification system supports investigations of ancient, metal-poor brown dwarfs now being uncovered in deep imaging and spectroscopic surveys., Comment: 82 pages, 19 figures, accepted to ApJS

In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding representation, our result applies to a variety of point processes including discrete and continuous Hawkes processes. In particular, we establish an explicit convergence rate for stable continuous non-linear Hawkes processes and for discrete Hawkes processes. Finally, we obtain an upper bound in the context of nearly unstable Hawkes processes.

The suppression of ferroquadrupolar order in TmVO$_4$ in a magnetic field is well-described by the transverse field Ising model, enabling detailed studies of critical dynamics near the quantum phase transition. We describe nuclear magnetic resonance measurements in pure and Y-doped single crystals. The non-Kramers nature of the ground state doublet leads to a unique form of the hyperfine coupling that exclusively probes the transverse field susceptibility. Our results show that this quantity diverges at the critical field, in contrast to the mean-field prediction. Furthermore, we find evidence for quantum critical fluctuations present near Tm-rich regions in Y-doped crystals at levels beyond which long-range order is suppressed, suggesting the presence of quantum Griffiths phases., Comment: 13 pages, 6 figures

We report an investigation of the effect of substitution of Y for Tm in $Tm_{1-x}Y_xVO4$ via low-temperature heat capacity measurements, with the yttrium content $x$ varying from $0$ to $0.997$. Because the Tm ions support a local quadrupolar (nematic) moment, they act as reporters of the local strain state in the material, with the splitting of the ion's non-Kramers crystal field groundstate proportional to the quadrature sum of the in-plane tetragonal symmetry-breaking transverse and longitudinal strains experienced by each ion individually. Analysis of the heat capacity therefore provides detailed insights into the distribution of local strains that arise as a consequence of the chemical substitution. These local strains suppress long-range quadrupole order for $x>0.22$, and result in a broad Schottky-like feature for higher concentrations. Heat capacity data are compared to expectations for a distribution of uncorrelated (random) strains. For dilute Tm concentrations, the heat capacity cannot be accounted for by randomly distributed strains, demonstrating the presence of significant strain correlations between sites. For intermediate Tm concentrations, these correlations must still exist, but the data cannot be distinguished from that which would be obtained from a 2D Gaussian distribution. The cross-over between these limits is discussed in terms of the interplay of key length scales in the substituted material. The central result of this work, that local strains arising from chemical substitution are not uncorrelated, has implications for the range of validity of theoretical models based on random effective fields that are used to describe such chemically substituted materials, particularly when electronic nematic correlations are present.

Adiabatic decompression of para-quadrupolar materials has significant potential as a cryogenic cooling technology. We focus on TmVO$_4$, an archetypal material that undergoes a continuous phase transition to a ferroquadrupole-ordered state at 2.15 K. Above the phase transition, each Tm ion contributes an entropy of $k_B \ln{2}$ due to the degeneracy of the crystal electric field groundstate. Owing to the large magnetoelastic coupling, which is a prerequisite for a material to undergo a phase transition via the cooperative Jahn-Teller effect, this level splitting, and hence the entropy, can be readily tuned by externally-induced strain. Using a dynamic technique in which the strain is rapidly oscillated, we measure the adiabatic elastocaloric coefficient of single-crystal TmVO$_4$, and thus experimentally obtain the entropy landscape as a function of strain and temperature. The measurement confirms the suitability of this class of materials for cryogenic cooling applications, and provides insight to the dynamic quadrupole strain susceptibility.

Using spin-echo Nuclear Magnetic Resonance in the model Transverse-Field Ising system TmVO$_4$, we show that low frequency quantum fluctuations at the quantum critical point have a very different effect on $^{51}$V nuclear-spins than classical low-frequency noise or fluctuations that arise at a finite temperature critical point. Spin-echos filter out the low frequency classical noise but not the quantum fluctuations. This allows us to directly visualize the quantum critical fan and demonstrate the persistence of quantum fluctuations at the critical coupling strength in TmVO$_4$ to high temperatures in an experiment that remains transparent to finite temperature classical phase transitions. These results show that while dynamical decoupling schemes can be quite effective in eliminating classical noise in a qubit, a quantum critical environment may lead to rapid entanglement and decoherence., Comment: 10 pages, 5 figures

TmVO$_{4}$ exhibits ferroquadrupolar order of the Tm 4f electronic orbitals at low temperatures, and is a model system for Ising nematicity that can be tuned continuously to a quantum phase transition via magnetic fields along the $c$-axis. Here we present $^{51}$V nuclear magnetic resonance data in magnetic fields perpendicular to the $c$-axis in a single crystal that has been carefully cut by a plasma focused ion beam to an ellipsoidal shape to minimize the inhomogeneity of the internal demagnetization field. The resulting dramatic increase in spectral resolution enabled us to resolve the anisotropy of the electric field gradient and to measure the magnetic and quadrupolar relaxation channels separately. Perpendicular magnetic fields nominally do not couple to the low energy degrees of freedom, but we find a significant nonlinear contribution for sufficiently large fields that give rise to a rich phase diagram. The in-plane magnetic field can act either as an effective transverse or longitudinal field to the Ising nematic order, depending on the orientation relative to the principle axes of the quadrupole order, and leads to a marked in-plane anisotropy in both relaxation channels. We find that the small in-plane transverse fields initially enhance the ferroquadrupolar ordering temperature but eventually suppress the long-range order. We tentatively ascribe this behavior to the competing effects of field-induced mixing of higher energy crystal field states and the destabilizing effects of field-induced quantum fluctuations., Comment: 15 pages, 13 figures

We report results of low-temperature heat capacity, magnetocaloric effect and neutron diffraction measurements of TmVO$_{4}$, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially-filled $4f$ orbitals of the thulium (Tm$^{3+}$) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point using a magnetic field oriented along the $c$-axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well-described using a semi-classical mean field treatment of the transverse field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semi-classical behavior are observed due to quantum fluctuations. Although the phase transition is driven by the local $4f$ degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles, and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO$_{4}$ as a model material, and electronic nematicity as a paradigmatic example, for quantum criticality in insulators., Comment: 9 pages, 5 figures

TmVO$_4$ exhibits ferroquadrupolar order below 2.15 K with a well-isolated non-Kramers ground state doublet, and is a model system to understand Ising nematic order. We present $^{51}$V nuclear magnetic resonance data as a function of field orientation in a single crystal. Although the spectra are well understood in terms of direct dipolar hyperfine couplings, the spin lattice relaxation rate exhibits strong anisotropy that cannot be understood in terms of magnetic fluctuations. We find that the spin lattice relaxation rate scales with the shear elastic constant associated with the ferroquadrupole phase transition, suggesting that quadrupole (nematic) fluctuations dominate the spin lattice relaxation for in-plane fields., Comment: 7 pages, 5 figures

We investigate the iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ using intense terahertz (THz) light. In the superconducting state a THz Kerr signal is observed and assigned to non-linear THz coupling to superconducting degrees of freedom. The polarization dependence of the THz Kerr signal is remarkably sensitive to the coexistence of a nematic order. In the absence of nematic order the $C_4$ symmetric polarization dependence of the THz Kerr signal is consistent with a coupling to the Higgs amplitude mode of the superconducting condensate. In the coexisting nematic and superconducting state the signal becomes purely nematic with a vanishing $C_4$ symmetric component, signaling the emergence of a new superconducting collective mode activated by nematicity., Comment: 25 pages, 3 figures. Supplementary Material available upon request

We report the evolution of nematic fluctuations in FeSe$_{1-x}$S$_x$ single crystals as a function of Sulfur content $x$ across the nematic quantum critical point (QCP) $x_c\sim$ 0.17 via Raman scattering. The Raman spectra in the $B_{1g}$ nematic channel consist of two components, but only the low energy one displays clear fingerprints of critical behavior and is attributed to itinerant carriers. Curie-Weiss analysis of the associated nematic susceptibility indicates a substantial effect of nemato-elastic coupling which shifts the location of the nematic QCP. We argue that this lattice-induced shift likely explains the absence of any enhancement of the superconducting transition temperature at the QCP. The presence of two components in the nematic fluctuations spectrum is attributed to the dual aspect of electronic degrees of freedom in Hund's metals, with both itinerant carriers and local moments contributing to the nematic susceptibility., Comment: 10 pages, 5 figures

We studied the electronic structure of the heavy fermion compound Yb(Ru$_{1-x}$Rh$_{x}$)$_2$Ge$_2$ with $x=0$ and nominally $x=0.125$ using ARPES and LDA calculations. We find a valence band structure of Yb corresponding to a non-integer valence close to $3+$. The three observed crystal electric field levels with a splitting of 32 and 75 meV confirm the suggested configuration with a quasi-quartet ground state. The experimentally determined band structure of the conduction electrons with predominantly Ru $4d$ character is well reproduced by our calculations. YbRu$_2$Ge$_2$ undergoes a non-magnetic phase transition into a ferroquadrupolar ordered state below 10.2\,K and then to an antiferromagnetically ordered state below 6.5\,K. A small hole Fermi surface shows nesting features in our calculated band structure and its size determined by ARPES is close to the magnetic ordering wave vector found in neutron scattering. The transitions are suppressed when YbRu$_2$Ge$_2$ is doped with 12.5% Rh. The electron doping leads to a shift of the band structure and successive Lifshitz transitions., Comment: 7 pages, 6 figures

We report the evolution of the electronic nematic susceptibility in FeSe via Raman scattering as a function of hydrostatic pressure up to 5.8 GPa where the superconducting transition temperature $T_{c}$ reaches its maximum. The critical nematic fluctuations observed at low pressure vanish above 1.6 GPa, indicating they play a marginal role in the four-fold enhancement of $T_{c}$ at higher pressures. The collapse of nematic fluctuations appears to be linked to a suppression of low energy electronic excitations which manifests itself by optical phonon anomalies at around 2 GPa, in agreement with lattice dynamical and electronic structure calculations using local density approximation combined with dynamical mean field theory. Our results reveal two different regimes of nematicity in the phase diagram of FeSe under pressure: a d-wave Pomeranchuk instability of the Fermi surface at low pressure and a magnetic driven orthorhombic distortion at higher pressure., Comment: 7 pages, 4 figures. Supplementary Material available upon request

The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is one of the most intriguing property of the iron based superconductors (Fe SC), and has relevance for the cuprates as well. Establishing the critical electronic modes behind nematicity remains however a challenge, because their associated susceptibilities are not easily accessible by conventional probes. Here using FeSe as a model system, and symmetry resolved electronic Raman scattering as a probe, we unravel the presence of critical charge nematic fluctuations near the structural / nematic transition temperature, T$_S\sim$ 90 K. The diverging behavior of the associated nematic susceptibility foretells the presence of a Pomeranchuk instability of the Fermi surface with d-wave symmetry. The excellent scaling between the observed nematic susceptibility and elastic modulus data demonstrates that the structural distortion is driven by this d-wave Pomeranchuk transition. Our results make a strong case for charge induced nematicity in FeSe., Comment: 5 pages, 5 figures + SI