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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. The possible ground state preserves local $T_d$ symmetry presumably down to absolute zero. Of the ground states of atomic vacancies in diamond proposed thus far, the only relevant one is the positively charged single atomic vacancy V$^+$, which has not been observed in previous optical measurements in diamonds., Comment: 8 Pages, 3 figures with supplemental materials

We investigated the magnetic structure of the antiferromagnetic (AFM) ordered state ($T_{\rm N} \sim$ 34 K) in tetragonal UPt$_{2}$Si$_{2}$ using polarized and unpolarized neutron diffraction. Previous neutron scattering studies reported that this system possesses a simple AFM structure with a propagation vector, $Q = 0$, and the ordered magnetic moments aligned along the $c$-axis. By contrast, our latest resonant X-ray scattering (RXS) experiments have revealed that the magnetic structure is modulated by the charge-density-wave (CDW) order, which emerges in one of the two Pt atomic layers in the unit cell below $\sim$ 320 K. The modulation is characterized by a transverse wave in the $c$-plane, with the propagation vector of the CDW order, $q_{\rm CDW } =$ ($\sim$0.42, 0, 0). In the present study using neutron scattering, we observed that the superlattice reflections specified by $q_{\rm CDW }$ develop below $T_{\rm N}$, in addition to the magnetic reflections with $Q = 0$, thereby further confirming the presence of modulation in the AFM structure of this system. From detailed analyses, we revealed that the amplitude of the transverse-wave magnetic modulation to be 0.72(2) $\mu_{\rm B}$/U, which is a piece of quantitative information that could not be obtained through the RXS experiments. This implies that the CDW drives the ordered magnetic moments to be tilted up to 20$^\circ$ in the AFM state. The observations strongly suggest that the magnetism of UPt$_{2}$Si$_{2}$ is heavily influenced by the hybridization effects between 5f electrons of U and 5d electrons of Pt., Comment: 11 pages, 13 figures

We performed magnetization, resistivity, and neutron diffraction measurements under uniaxial stress applied along [1-10] direction on the tetragonal magnet CeRh$_2$Si$_2$ with commensurate magnetic orders. CeRh$_2$Si$_2$ has two successive antiferromagnetic (AF) orders in zero magnetic field. The high temperature phase (AF1 phase) has the magnetic modulation wave vector of $q = (\frac{1}{2}, \frac{1}{2}, 0)$, and the low temperature phase (AF2 phase) is characterized by the four $q$-vectors of $q = (\frac{1}{2}, \frac{1}{2}, 0), (\frac{1}{2}, -\frac{1}{2}, 0), (\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$, and $(\frac{1}{2}, -\frac{1}{2}, \frac{1}{2})$. By measuring the uniaxial stress dependence of the magnetization, resistivity and the intensities of magnetic Bragg reflections, we confirmed that the AF1 phase has the single-$q$ magnetic order with two-fold rotational symmetry and the AF2 phase has the multi-$q$ magnetic order with four-fold rotational symmetry. In order to understand the origin of multi-$q$ order of CeRh$_2$Si$_2$, we also performed inelastic neutron scattering measurement on the single crystal samples. We found a magnetic excitation at the transfer energy $\hbar \omega \sim$ 8 meV. By applying the linear spin-wave theory, we found that the nearest and the next-nearest neighbor exchange interactions on the $ab$-plane, $J_1$ and $J_2$, are dominant in the AF2 phase. However, the $J_1$-$J_2$ model cannot lift the degeneracy between the single-$q$ (AF1) and multi-$q$ (AF2) phases. We suggest that it can be lifted by taking into account the biquadratic interaction derived from the perturbative expansion for the Kondo lattice Hamiltonian. [S. Hayami et al., Phys. Rev. B 95, 224424 (2017)., Comment: 7 pages, 7 figures

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 elastic constants of an unconventional superconductor, UTe$_2$, were investigated using ultrasound. In this paper, we report the elastic response of the normal state at temperatures down to 2 K and up to 14 T for $H \parallel b$ at ambient pressure. The transverse ultrasonic mode $C_{55}$, which corresponds to the strain susceptibility of $\varepsilon_{zx}$, shows softening with decreasing temperature, whereas the $C_{44}$ and $C_{33}$ modes do not show such softening. This clear mode dependence strongly suggests that UTe$_2$ has a lattice instability for this specific symmetry., Comment: Proceedings of 29th International Conference on LOW TEMPERATURE PHYSICS

A Ce-based metallic compound CeCoSi with a tetragonal structure exhibits successive phase transitions: the one whose order parameter is unidentified at T_0 = 12 K and the antiferromagnetic one at T_N = 9.4 K. We performed specific heat, magnetoresistivity (MR), and magnetization measurements for a single crystal CeCoSi at low temperatures in magnetic fields B of up to 14 T and constructed detailed magnetic field--temperature phase diagrams for both B || [100] and [001]. The longitudinal MR measured for B || [100] shows a sign change from negative to positive across T_0 = 13 K updated in the present sample, indicating a clear change in an electronic state. In addition, the constructed magnetic phase diagrams for both the field directions have a B-induced region in each ordered state. The presence of the newly found regions would be attributed to a change in the symmetry of the order parameter or domain alignment by applying B.

9Be-NMR measurements were performed using single crystalline SmBe13 in order to investigate a magnetic structure of a low-temperature ordering state microscopically. We observed a spectral broadening in the ordered state, and the broadened spectral shape depends on the magnetic field directions. By comparing the experimentally obtained and simulated NMR spectra for magnetic fields along the cubic [001] and [011] directions, we argue a helical structure with a basal plane tilted from the (001) plane in low-field ordering region under the assumption of a helical with a propagation vector of (0, 0, 1/3) found in other RBe13 compounds (R = rare earths). Such a tilted helical structure is explained by a combination of an ellipse helical in the (001) plane and a longitudinal magnetic density wave along the [001] direction. Considering a magnetic easy axis parallel to [001] revealed by the magnetization measurements, the peculiar helical structure in SmBe13 may be built on delicate balance among exchange interactions, dipole-dipole interaction, and single-ion magnetic anisotropy due to the crystalline electric field.

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

Magnetic susceptibility, specific heat, and electrical resistivity measurements have been performed on single-crystal EuBe13 in the temperature range between 2 and 300 K to investigate its phonon property and the valence state of the Eu ion. The obtained temperature dependence of the magnetic susceptibility curves obey a typical Van Vleck susceptibility for Eu3+ with a nonmagnetic ground state in the entire measured temperature range. In the case of the specific heat, we observed the coexistence of Debye and Einstein phonon modes with characteristic Debye and Einstein temperatures of ~ 835 K and ~167 K, respectively, which are in good agreement with those previously reported for other isostructural MBe13 compounds (M = rare earths and actinides). The temperature dependence of the resistivity for EuBe13 shows an unusual T-cubed like dependence at low temperatures, as also observed for the nonmagnetic isostructural compound LaBe13, which can be reproduced well by calculations based on electron--phonon scattering using the estimated Debye temperature and Einstein temperature. We also summarized the relationship between the Eu-valence state and the free distance between the Eu ion and the first-nearest-neighbor atoms in several Eu-based cubic compounds, and argued that EuBe13 takes the Eu3+ state despite its larger free distance than other Eu3+ compounds.

The beryllides MBe13 (M = rare earths and actinides) crystallize in a NaZn13-type cubic structure, which can be categorized as a cage-structured compound. In this study, powder X-ray diffraction measurements have been performed on LaBe13, SmBe13, and UBe13 in the temperature range between 7 and 300 K in order to investigate their crystallographic characteristics systematically. They keep the NaZn13-type cubic structure down to the lowest temperature. We estimated their Debye temperature to be 600 - 750 K from analyses of the temperature dependence of a lattice parameter, being in good agreement with the values reported previously. Rietveld refinements on the obtained powder patterns revealed that the M atom in the 8a site is located in an almost ideal snub cube formed by 24 Be atoms in the 96i site, whose caged structure is unchanged even at the low temperatures. In addition, it is argued from the temperature variation of an isotropic mean-square displacement parameter that the MBe13 compounds commonly have a low-energy phonon mode, which can be described by a model assuming an Einstein oscillation of the M atom with a characteristic temperature of ~ 160 K., Comment: 8 pages with 6 figures and 2 tables

Magnetization measurements under direct electric currents were performed for toroidal magnetic ordered state of UNi$_4$B to test a recent theoretical prediction of current-induced magnetization in a metallic system lacking local inversion symmetry.We found that each of the electric currents parallel to [$2\bar{1}\bar{1}0$] and [$0001$] in the hexagonal 4-index notation induces uniform magnetization in the direction of [$01\bar{1}0$].The observed behavior of the induced magnetization is essentially consistent with the theoretical prediction; however it also shows an inconsistency suggesting that the antiferromagnetic state of UNi$_4$B could not simply be regarded as a uniform toroidal order in the ideal honeycomb layered structure., Comment: 5 pages, 5 figures, and 1 table

The physical properties of single-crystalline SmBe$_{13}$ with a NaZn$_{13}$-type cubic structure have been studied by electrical resistivity ($\rho$), specific heat ($C$), and magnetization ($M$) measurements in magnetic fields of up to 9 T. The temperature ($T$) dependence of $\rho$ shows normal metallic behavior without showing the Kondo -ln$T$ behavior, suggesting the weak hybridization effect in this system. Analyses of the temperature dependence of $C$ suggest that the Sm ions of this compound are trivalent and that the crystalline-electric-field (CEF) ground state is a $\Gamma_8$ quartet with a first-excited state of a $\Gamma_7$ doublet located at the energy scale of $\sim$ 90 K. Mean-field calculations based on the suggested CEF level scheme can reasonably well reproduce the $T$ dependence of magnetic susceptibility ($\chi$) below $\sim$ 70 K. These results in the paramagnetic state strongly indicate that the 4$f$ electrons are well localized with the Sm$^{3+}$ configuration. At low temperatures, the 4$f$ electrons undergo a magnetic order at $T_{\rm M}$ $\sim$ 8.3 K, where $\chi$($T$) shows an antiferromagnetic-like cusp anomaly. From the positive Curie--Weiss temperature obtained from the mean-field calculations and from a constructed magnetic phase diagram with multiple regions, we discussed the magnetic structure of SmBe$_{13}$ below $T_{\rm M}$, by comparing with other isostructural MBe$_{13}$ compounds showing helical-magnetic ordering.

The thermal and electrical transport properties of single-crystalline LaBe$_{13}$ have been investigated by specific-heat ($C$) and electrical-resistivity ($\rho$) measurements. The specific-heat measurements in a wide temperature range revealed the presence of a hump anomaly near 40 K in the $C$($T$)/$T$ curve, indicating that LaBe$_{13}$ has a low-energy Einstein-like-phonon mode with a characteristic temperature of $\sim$ 177 K. In addition, a superconducting transition was observed in the $\rho$ measurements at the transition temperature of 0.53 K, which is higher than the value of 0.27 K reported previously by Bonville et al. Furthermore, an unusual $T^3$ dependence was found in $\rho$($T$) below $\sim$ 50 K, in contrast to the behavior expected from the electron--electron scattering or the electron--Debye phonon scattering.

Single-crystalline UAu$_2$Si$_2$ has been grown by a floating-zone melting method, and its magnetic, thermal and transport properties have been investigated through measurements of magnetization, specific heat and electrical resistivity to reveal its peculiar magnetism. It is shown that UAu$_2$Si$_2$ undergoes a second-order phase transition at \tm = 19 K, which had been believed to be ferromagnetic ordering in the literature, from a paramagnetic phase to an uncompensated antiferromagnetic phase with spontaneous magnetization along the tetragonal $c$-axis (the easy magnetization direction). The magnetic entropy analysis points to the itinerant character of 5f electrons in the magnetic ordered state of UAu$_2$Si$_2$ with large enhancement of the electronic specific heat coefficient of $\gamma$ $\sim$ 150 mJ/K$^2$mol at 2 K. It also reveals the relatively isotropic crystalline electric field effect of this compound, with contrast to the other relative isostructural compounds. The observed magnetization curves strongly suggest that there is a parasitic ferromagnetic component developing below $\sim$ 50 K in high coercivity with the easy axis along the tetragonal $c$-axis. The results are discussed in the context of evolution of magnetism within the entire family of isostructural U$T_2$Si$_2$ compounds., Comment: 13 pages, 21 figures

Our ultrasound results obtained in pulsed magnetic fields show that the filled-skutterudite compound SmOs$_4$Sb$_{12}$ has the $\Gamma_{67}$ quartet crystalline-electric-field ground state. This fact suggests that the multipolar degrees of freedom of the $\Gamma_{67}$ quartet play an important role in the unusual physical properties of this material. On the other hand, the elastic response below $\approx$ 20 T cannot be explained using the localized 4$f$-electron model, which does not take into account the Kondo effect or ferromagnetic ordering. The analysis result suggests the presence of a Kondo-like screened state at low magnetic fields and its suppression at high magnetic fields above 20 T even at low temperatures., Comment: 4 pages, 4 figures

We have performed ultrasonic measurements on single-crystalline URu2Si2 with pulsed magnetic fields, in order to check for possible lattice instabilities due to the hybridized state and the hidden-order state of this compound. The elastic constant (C11-C12)/2, which is associated with a response to the {\Gamma}3-type symmetry-breaking (orthorhombic) strain field, shows a three-step increase at H > 35 T for H || c at low temperatures, where successive meta-magnetic transitions are observed in the magnetization. We discovered a new fact that the absolute change of the softening of (C11-C12)/2 in the temperature dependence is quantitatively recovered at the suppression of hybridized-electronic state and the hidden order in high-magnetic field for H \perp c associated with the successive transitions. The present results suggest that the {\Gamma}3-type lattice instability, is related to both the emergence of the hybridized electronic state and the hidden-order parameter of URu2Si2. On the other hand, magnetic fields H || [100] and [110] enhance the softening of (C11-C12)/2 in the hidden order phase, while no step-like anomaly is observed up to 68.7 T. We discuss the limitation of the localized-electron picture for describing these features of URu2Si2 by examination of a crystalline electric field model in terms of mean-field theory., Comment: 12 pages, 3 figures

We have performed low-temperature specific-heat measurements in magnetic fields for a single crystal UBe13. It has been observed that our sample exhibits a superconducting transition at an intermediate temperature between previously reported values for two variant samples called H type and L type. The specific heat C(T) of our sample shows a T^3 behavior in the temperature range below 0.7 Tc, which is similar to the behavior of the H-type sample, suggesting the existence of point nodes in the superconducting gap function. We have obtained the upper-critical-field curves Hc2 for the [001], [110], and [111] crystal axes, which show no anisotropy at least down to the lowest measured temperature of 0.5 K. We have also derived the Maki parameter kappa2, and it has been revealed that the kappa2 steeply decreases isotropically upon cooling just below Tc. Paramagnetic effects and the symmetry of Cooper pairing of UBe13 are discussed., Comment: 4 pages, 5 figures

Elastic properties of the filled skutterudite compound SmOs$_4$Sb$_{12}$ have been investigated by ultrasonic measurements. The elastic constant $C_{11}(\omega)$ shows two ultrasonic dispersions at $\sim$15 K and $\sim$53 K for frequencies $\omega$ between 33 and 316 MHz, which follow a Debye-type formula with Arrhenius-type temperature-dependent relaxation times, and remain unchanged even with applied magnetic fields up to 10 T. The corresponding activation energies were estimated to be $E_2$ = 105 K and $E_1$ = 409 K, respectively. The latter, $E_1$, is the highest value reported so far in the Sb-based filled skutterudites. The presence of magnetically robust ultrasonic dispersions in SmOs$_4$Sb$_{12}$ implies a possibility that an emergence of a magnetically insensitive heavy fermion state in this system is associated with a novel local charge degree of freedom which causes the ultrasonic dispersion., Comment: 5 pages, 4 figures