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Register a new userLandau theory of multipolar orders in Pr(TM)$_2$X$_{20}$ Kondo materials
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A series of Pr(TM)$_2$X$_{20}$ (with TM=Ti,V,Rh,Ir and X=Al,Zn) Kondo materials, containing non-Kramers Pr$^{3+}$ $4f^2$ moments on a diamond lattice, have been shown to exhibit intertwined orders such as quadrupolar order and superconductivity. Motivated by these experiments, we propose and study a Landau theory of multipolar order to capture the phase diagram and its field dependence. In zero magnetic field, we show that different quadrupolar states, or the coexistence of quadrupolar and octupolar orderings, may lead to ground states with multiple broken symmetries. Upon heating, such states may undergo two-step thermal transitions into the symmetric paramagnetic phase, with partial restoration of broken symmetries in the intervening phase. For nonzero magnetic field, we show the evolution of these thermal phase transitions strongly depends on the field direction, due to clock anisotropy terms in the free energy. Our findings shed substantial light on experimental results in the Pr(TM)$_2$Al$_{20}$ materials. We propose further experimental tests to distinguish purely quadrupolar orders from coexisting quadrupolar-octupolar orders.
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Among heavy fermion materials, there is a set of rare-earth intermetallics with non-Kramers Pr$^{3+}$ $4f^2$ moments which exhibit a rich phase diagram with intertwined quadrupolar orders, superconductivity, and non-Fermi liquid behavior. However, more subtle broken symmetries such as multipolar orders in these Kondo materials remain poorly studied. Here, we argue that multi-spin interactions between local moments beyond the conventional two-spin exchange must play an important role in Kondo materials near the ordered to heavy Fermi liquid transition. We show that this drives a plethora of phases with coexisting multipolar orders and multiple thermal phase transitions, providing a natural framework for interpreting experiments on the Pr(TM)$_2$Al$_{20}$ class of compounds.
Acoustic signatures of the single-site quadrupolar Kondo effect in Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ are presented. The elastic constant ($C_{11}-C_{12}$)/2, corresponding to the $Gamma_3$(E)-symmetry electric-quadrupolar response, reveals a logarithmic temperature dependence of the quadrupolar susceptibility in the low-magnetic-field region below $sim$0.3 K. Furthermore, the Curie-type divergence of the elastic constant down to $sim$1 K indicates that the Pr ions in this diluted system have a non-Kramers ground-state doublet. These observations evidence the single-site quadrupolar Kondo effect, as previously suggested based on specific-heat and electrical resistivity data.
Ultrasonic investigations of the single-site quadrupolar Kondo effect in diluted Pr system Y$_{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$_{20}$.
We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak but non-zero interaction strength $U_0$, and spin spiral order at larger $U_0$, separated by a narrow window of trivial insulator. We introduce a simplified model capturing essential features of the WTe$_2$ band structure, in which the two phases may be viewed as distinct valley ferromagnetic orders. We link the competition between the two phases to the orbital structure of the electronic wavefunctions at the Fermi surface and hence its proximity to the underlying gapped Dirac point in WTe$_2$. We briefly discuss collective modes of the two excitonic states, and comment on implications for experiments.
We present the electrical resistivity data under application of pressures up to $sim$ 26 GPa and down to 50 mK temperatures on YbFe$_2$Zn$_{20}$. We find a pressure induced magnetic phase transition with an onset at $p_c$=18.2$pm$0.8 GPa. At ambient pressure, YbFe$_2$Zn$_{20}$ manifests a heavy fermion, nonmagnetic ground state and the Fermi liquid behavior at low temperatures. As pressure is increased, the power law exponent in resistivity, $n$, deviates significantly from Fermi liquid behavior and tends to saturate with $n$ = 1 near $p_c$. A pronounced resistivity maximum, $T_text{max}$, which scales with Kondo temperature is observed. $T_text{max}$ decreases with increasing pressure and flattened out near $p_c$ indicating the suppression of Kondo exchange interaction. For $p>p_c$, $T_text{max}$ shows a sudden upward shift, most likely becoming associated with crystal electric field scattering. Application of magnetic field for $p>p_c$ broadens the transition and shifts it toward the higher temperature, which is a typical behavior of the ferromagnetic transition. The magnetic transition appears to abruptly develop above $p_c$, suggesting probable first-order (with changing pressure) nature of the transition; once stabilized, the ordering temperature does not depend on pressure up to $sim$ 26 GPa. Taken as a whole, these data suggest that YbFe$_2$Zn$_{20}$ has a quantum phase transition at $p_c$ = 18.2 GPa associated with the avoided quantum criticality in metallic ferromagnets.
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