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تسجيل مستخدم جديدQuadrupolar Susceptibility and Magnetic Phase Diagram of PrNi$_2$Cd$_{20}$ with Non-Kramers Doublet Ground State
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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$26 T are also detected by high-magnetic-field measurements.
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Praseodymium-based 1-2-20 cage compounds Pr$T_2X_{20}$ ($T$ is generally Ti, V, Nb, Ru, Rh, Ir; and $X$ is either Al, Zn or Cd) provide yet another platform to study non-trivial electronic states of matter ranging from topological and magnetic orders
to unconventional multipolar orders and superconductivity. In this paper, we report measurements of the electronic heat capacity in two Pr-based 1-2-20 materials: PrNi$_2$Cd$_{20}$ and PrPd$_2$Cd$_{20}$. We find that the lowest energy multiplet of the Pr $4f^2$ valence configuration is a $Gamma_3$ non-Kramers doublet and can, therefore, be described as a two-level system. By analyzing the dependence of the energy splitting between the ground and first excited singlet states on external magnetic field, we found that the interactions between the two-level systems are weak in PrNi$_2$Cd$_{20}$. However, in PrPd$_2$Cd$_{20}$, the exchange interactions that ultimately promote magnetic or multipolar order are strong enough and must be taken into account to accurately describe the dependence of the energy level splitting on external magnetic field.
We have investigated the low temperature quadrupolar phenomena of the non-Kramers system PrRh2Zn20 under magnetic fields in the [100] and [110] directions. Our experiments reveal the B-T phase diagram of PrRh2Zn20 involving four electronic states reg
ardless of the field direction, namely, a non-Fermi liquid (NFL) state, an antiferro-quadrupolar (AFQ) ordered state, a novel heavy-fermion (HF) state, and a field-induced singlet (FIS) state. In the wide range of the NFL state, the resistivity can be well scaled by a characteristic temperature, suggesting the realization of the quadrupole Kondo effect. The HF state exhibits a Fermi liquid behavior with a large A coefficient of the T^2 term in the resistivity, suggesting the formation of nontrivial heavy quasi-particles. The FIS state results from the considerable splitting of a non-Kramers doublet by a magnetic field. The phase diagram shows a large anisotropy with respect to the field direction. It is found that the anisotropy of the phase diagram can be explained in terms of that of the energy splitting of the non-Kramers doublet by a magnetic field. This indicates that the low temperature properties of PrRh2Zn20 are governed by the non-Kramers doublet, namely, quadrupole degrees of freedom. Since a similar phase diagram has been obtained for the related compound PrIr2Zn20, it is expected that the B-T phase diagram constructed in this work is universal throughout non-Kramers systems.
We discuss possible competition between magnetic and quadrupole Kondo effects in non-Kramers doublet systems under cubic symmetry. The quadrupole Kondo effect leads to non-Fermi-liquid (NFL) ground state, while the magnetic one favors ordinary Fermi
liquid (FL). In terms of the $j$-$j$ coupling scheme, we emphasize that the orbital fluctuation must develop in the vicinity of the NFL-FL boundary. We demonstrate a change of behavior in the f-electron entropy by the Wilsons numerical renormalization-group (NRG) method on the basis of the extended two-channel Kondo exchange model. We present implications to extensively investigated PrT$_{2}$X$_{20}$ (T=Ti, V, Ir; X=Al, Zn) systems that exhibit both quadrupole ordering and peculiar superconductivity. We also discuss the magnetic-field effect which lifts weakly the non-Kramers degeneracy. Our model also represents the FL state accompanied by a free magnetic spin as a consequence of stronger competition between the magnetic and the quadrupole Kondo effects.
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