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Recent experiments have pointed to the formation of a new state of matter, the electron quadrupling condensate in Ba$_{1-x}$K$_x$Fe$_2$As$_2$. The state spontaneously breaks time-reversal symmetry and is sandwiched between two critical points, separating it from the superconducting and normal-metal states. We report a theory of the acoustic effects of systems with an electron quadrupling phase based on ultrasound-velocity measurements of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals. The theoretical analysis suggests that the ultrasound data can be understood by considering a plain $s$+i$d_{xy}$ order parameter or an $s$+i$s$ order parameter with symmetry-breaking deformations in this material with enhanced nematic susceptibility for the [110] direction, or when the transition to the quartic state is a weakly first-order. Our work provides the theoretical basis and proposes the experimental strategy to study the order parameter symmetry of emerging quadrupling condensates in superconductors., Comment: v2: The crystal orientation is corrected and the ultrasound data re-analyzed. Data for a reference sample at a different doping without the BTRS state is added. 11 pages, 6 figures

This study reveals a novel phenomenon demonstrating the elastic softening of synthetic diamonds when cooled to very low temperatures below 1 K. We present the results of ultrasonic measurements of single-crystalline synthetic diamonds without irradiation, namely type-IIa (colorless) and Ib (yellow) diamonds grown by high-pressure-high-temperature synthesis as well as type-IIa diamond grown by chemical vapor deposition. We observed a divergent decrease of the elastic stiffness constant $C_{44}$ in all samples at low temperatures down to 20 mK. We argue for the existence of electric quadrupolar degrees of freedom with irreducible representation $T_2$ in diamond as the origin of this elastic softening. Although, understanding of the microscopic mechanism behind the observed softening is still an open question, present analysis strongly suggest sub-ppb level of neutral single-atomic vacancies or other unspecified non-magnetic vacancy concentrations in all investigated diamonds. Our findings also open new avenues for the quantitative determination of non-magnetic vacancies in diamonds, an important information needed for their potential application as a substrate for quantum computers and next-generation semiconductor devices., Comment: 7 Pages, 3 figures with supplemental materials (9 Pages, 3 figures)

Strongly 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 NiCl$_{2}\cdot$4SC(NH$_2$)$_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., Comment: Main text: 9 pages, 7 figures. Supplemental Material: 8 pages, 6 figures

High-field phase diagram of a chiral-lattice antiferromagnet Sr(TiO)Cu4(PO4)4 is studied by means of the ultrasound, dielectric, and magnetocaloric-effect measurements. These experimental techniques reveal two new phase transitions at high fields, which have not been resolved by the previous magnetization experiments. Specifically, the c66 acoustic mode shows drastic changes with hysteresis with applied fields along the c axis, indicating a strong magneto-elastic coupling. Combined with the cluster mean-field theory, we discuss the origins of these phase transitions. By considering the chiral-twist effect of Cu4O12 cupola units, which is inherent to the chiral crystal structure, the phase diagram is reasonably reproduced. The agreement between the experiment and theory suggests that this material is a unique quasi two-dimensional spin system with competing exchange interactions and chirality, leading to the rich phase diagram., Comment: 12 pages, 11 figures, 1 table

We measured the elastic constants $\left(C_{11}-C_{12}\right)/2$ and $C_{44}$ of the non-Kramers system $\rm{Y_{0.63}Pr_{0.37}Ir_{2}Zn_{20}}$ (Pr-37% system) by means of ultrasound to check how the single-site quadrupolar Kondo effect is modified by increasing the Pr concentration. The Curie-like softening of $\left(C_{11}-C_{12}\right)/2$ between 1 and 5 K of the present Pr-37% system can be reproduced by a multipolar susceptibility calculation based on the non-Kramers $\Gamma_3$ doublet crystalline-electric-field ground state. Further, on cooling below 0.15 K, a temperature dependence proportional to $\sqrt{T}$ was observed in $\left(C_{11}-C_{12}\right)/2$. This behavior rather corresponds to the theoretical prediction of the quadrupolar Kondo "lattice" model, unlike that of the Pr-3.4% system, which shows a logarithmic temperature dependence based on the "single-site" quadrupolar Kondo theory. In addition, we discuss the possibility to form a vibronic state by the coupling between the low-energy phonons and the electric quadrupoles of the non-Kramers doublet in the Pr-37% system, since we found a low-energy ultrasonic dispersion in the temperature region between 0.15 and 1 K.

The compound ZrTe$_5$ has recently been connected to a charge-density-wave (CDW) state with intriguing transport properties. Here, we investigate quantum oscillations in ultrasound measurements that microscopically originate from electron-phonon coupling and analyze how these would be affected by the presence or absence of a CDW. We calculate the phonon self-energy due to electron-phonon coupling, and from there deduce the sound-velocity renormalization and sound attenuation. We find that the theoretical predictions for a metallic Dirac model resemble the experimental data on a quantitative level for magnetic fields up to the quantum-limit regime., Comment: 14 pages, 7 figures

We report on the electronic and thermodynamic properties of the antiferromagnetic metal uranium mononitride with a N\'eel temperature $T_N\approx 53\,$K. The fabrication of microstructures from single crystals enables us to study the low-temperature metamagnetic transition at approximately $58\,$T by high-precision magnetotransport, Hall-effect, and magnetic-torque measurements. We confirm the evolution of the high-field transition from a broad and complex behavior to a sharp first-order-like step, associated with a spin flop at low temperature. In the high-field state, the magnetic contribution to the temperature dependence of the resistivity is suppressed completely. It evolves into an almost quadratic dependence at low temperatures indicative of a metallic character. Our detailed investigation of the Hall effect provides evidence for a prominent Fermi-surface reconstruction as the system is pushed into the high-field state., Comment: 9 pages, 9 figures

The quantum Hall effect (QHE) is traditionally considered a purely two-dimensional (2D) phenomenon. Recently, a three-dimensional (3D) version of the QHE has been reported in the Dirac semimetal ZrTe5. It was proposed to arise from a magnetic-field-driven Fermi surface instability, transforming the original 3D electron system into a stack of 2D sheets. Here, we report thermodynamic, thermoelectric and charge transport measurements on ZrTe5 in the quantum Hall regime. The measured thermodynamic properties: magnetization and ultrasound propagation, show no signatures of a Fermi surface instability, consistent with in-field single crystal X-ray diffraction. Instead, a direct comparison of the experimental data with linear response calculations based on an effective 3D Dirac Hamiltonian suggests that the quasi-quantization of the observed Hall response is an intrinsic property of the 3D electronic structure. Our findings render the Hall effect in ZrTe5 a truly 3D counterpart of the QHE in 2D systems.

In this study, ultrasonic measurements were performed on a single crystal of cubic PrNi$_2$Cd$_{20}$, down to a temperature of 0.02 K, to investigate the crystalline electric field ground state and search for possible phase transitions at low temperatures. The elastic constant $(C_{11}-C_{12})/2$, which is related to the $\Gamma_3$-symmetry quadrupolar response, exhibits the Curie-type softening at temperatures below $\sim$30 K, which indicates that the present system has a $\Gamma_3$ non-Kramers doublet ground state. A leveling-off of the elastic response appears below $\sim$0.1 K toward the lowest temperatures, which implies the presence of level splitting owing to a long-range order in a finite-volume fraction associated with $\Gamma_3$-symmetry multipoles. A magnetic field-temperature phase diagram of the present compound is constructed up to 28 T for $H \parallel$ [110]. A clear acoustic de Haas-van Alphen signal and a possible magnetic-field-induced phase transition at $H \sim$26 T are also detected by high-magnetic-field measurements., Comment: 13 pages, 7 figures

Ultrasonic investigations of the single-site quadrupolar Kondo effect in diluted Pr system Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ are reported. The elastic constant $(C_{11}-C_{12})/2$ is measured down to ~40 mK using ultrasound for the dilute system Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ and the pure compound YIr$_2$Zn$_{20}$. We found that the elastic constant $(C_{11}-C_{12})/2$ of the Pr-dilute system exhibits a logarithmic temperature dependence below $T_0$ ~0.3 K, where non-Fermi-liquid (NFL) behavior in the specific heat and electrical resistivity is observed. This logarithmic temperature variation manifested in the $\Gamma_3$-symmetry quadrupolar susceptibility is consistent with the theoretical prediction of the quadrupolar Kondo effect by D. L. Cox. On the other hand, the pure compound YIr$_2$Zn$_{20}$ without $4f$-electron contributions shows nearly no change in its elastic constants evidencing negligible phonon contributions. In addition, clear acoustic de Haas-van Alphen (dHvA) oscillations in the elastic constant were detected for both compounds on applying magnetic field. This is mainly interpreted as contribution from the Fermi surface of YIr$_2$Zn$_{20}$., Comment: 9 pages, 4 figures, Proceedings of J-Physics 2019 International Conference

Spin supersolids and spin superfluids reveal complex canted spin structures with independent order of longitudinal and transverse spin components. This work addresses the question whether these exotic phases can exhibit spin-driven ferroelectricity. Here we report the results of dielectric and pyrocurrent measurements of MnCr2S4 as function of temperature and magnetic field up to 60 T. This sulfide chromium spinel exhibits a Yafet-Kittel type canted spin structure at low temperatures. As function of external magnetic field, the manganese spins undergo a sequence of ordering patterns of the transverse and longitudinal spin components, which can be mapped onto phases as predicted by lattice-gas models including solid, liquid, super-fluid, and supersolid phases. By detailed dielectric and pyrocurrent measurements, we document a zoo of multiferroic phases with sizable ferroelectric polarization strongly varying from phase to phase. Using lattice-gas terminology, the title compound reveals multiferroic spin-superfluid and spin-supersolid phases, while the antiferromagnetic solid is paraelectric., Comment: 14 pages including 5 figures

In the heavy-fermion metal CePdAl long-range antiferromagnetic order coexists with geometric frustration of one third of the Ce moments. At low temperatures the Kondo effect tends to screen the frustrated moments. We use magnetic fields $B$ to suppress the Kondo screening and study the magnetic phase diagram and the evolution of the entropy with $B$ employing thermodynamic probes. We estimate the frustration by introducing a definition of the frustration parameter based on the enhanced entropy, a fundamental feature of frustrated systems. In the field range where the Kondo screening is suppressed the liberated moments tend to maximize the magnetic entropy and strongly enhance the frustration. Based on our experiments, this field range may be a promising candidate to search for a quantum spin liquid., Comment: 5+2 pages with 4 figures