Γ3 Doublet Ground State Research Articles

Inelastic neutron scattering study of crystalline electric field excitations in a cubic compound PrMgNi4

We performed inelastic neutron scattering experiments on PrMgNi4 with the cubic MgSnCu4-type structure. The magnetic excitations were observed at 1.1, 2.5, 5.9, 10.7, and 11.7 meV. Since the energy of the excitations is constant for | Q | < 5 Å−1, they are ascribed to the crystalline electric field (CEF) excitations of the Pr3+ ions. We adopted CEF parameters of W = −3.3 K and x = 0.8 for the cubic T d point group to reproduce the strong excitations at 1.1, 10.7, and 11.7 meV. The calculated CEF level scheme reveals the Γ3 doublet ground state with the quadrupolar degrees of freedom and the excited states of Γ4 triplet (1.4 meV), Γ1 singlet (3.4 meV), and Γ5 triplet (13.5 meV). This scheme, however, does not explain the observed two excitations at 2.5 and 5.9 meV. These additional excitations may arise from splitting of the doublet by symmetry lowering due to excess Mg atoms occupying the Pr sites. This splitting is probably responsible for the absence of the long-range quadrupole order in PrMgNi4.

Antiferroquadrupolar Ordering in Quadrupolar Kondo Lattice of Non-Kramers System PrTa2Al20

Single crystals of PrTa2Al20 have been investigated by means of single-crystal structural analysis and measurements of magnetization, specific heat, and electrical resistivity. The crystalline-electric-field level scheme of the Pr ions has a nonmagnetic Γ3 doublet ground state and a Γ5 magnetic excited state with an energy separation of 53 K. The 4f-electron contribution to the electrical resistivity shows −log T magnetic Kondo scattering above 50 K and a downward curvature characteristic of a quadrupolar Kondo lattice formation below 20 K. A phase transition appears at 0.65 K in zero field and shifts to higher temperatures in applied fields, indicating that this transition is antiferroquadrupolar (AFQ) in nature. The largely enhanced Sommerfeld coefficient ∼1.5 J/(mol K2) in the AFQ state may indicate the formation of heavy quasiparticles. The hierarchically arranged sequence of the magnetic Kondo regime, quadrupolar Kondo lattice regime, and AFQ ordered state in the wide temperature range 0.2–300 K demo...

Broad Excitation Spectra between Crystalline-Electric-Field Levels Associated with Non-Kramers Doublet Ground State offElectrons in PrNb2Al20

Inelastic neutron scattering measurements of PrNb2Al20, which exhibits non-Fermi-liquid behaviors, were carried out in order to determine the f-electron crystalline-electric-field split. Magnetic inelastic scattering intensities were observed at excitation energies of up to 15 meV, which are attributed to the crystalline-electric-field level scheme with the non-Kramers Γ3 doublet ground state of 4f2 in Pr3+ ions. The intrinsic full width at half maximum of the excitations from Γ3 to Γ5 and Γ4 are estimated to be approximately 3.7 meV. These values are much larger than those of the isomorphic PrTr2Zn20 (Tr = Rh and Ir). The considerably broad spectrum of PrNb2Al20 supports the existence of hybridization between Pr 4f electrons and conduction electrons, which mediates the Kondo effect in this material.

Single crystal growth and electronic state of new compounds RPt2Cd20 (R = La-Nd, Sm)

We succeeded in growing five new single crystalline compounds RPt2Cd20 (R = La, Ce, Pr, Nd, and Sm) by the Cd self-flux method. These compounds are found to crystallize in the cubic CeCr2Al20-type crystal structure by the X-ray diffraction using single crystals. We measured the electrical resistivity, magnetic properties, and specific heat for all compounds. The resistivity for R = Ce, Nd, and Sm indicates an abrupt decrease, which might correspond to a magnetic transition. It is suggested that the ground state of CePt2Cd20 is Γ7 doublet from the magnetization measurement. The magnetization of PrPt2Cd20 shows a metamagnetic behavior at 1.6 T in the paramagnetic state, which could be due to the crystalline electric field effect with non-Kramers Γ3 doublet or Γ1 singlet ground state. The contribution of optical phonon modes to the lattice specific heat is discussed in LaPt2Cd20.

Effect of Ga Substitution on the Γ3 Doublet Ground State in PrIr2Zn20

Electrical resistivity ρ, specific heat C, and magnetic susceptibility χ measurements are reported on PrIr2Zn20–xGax for x=0.5 and 1.0. On cooling, ρ(T)’s monotonically decrease to the residual values which are two orders of magnitudes larger than that of PrIr2Zn20. A broad hump in Cm(T)’s at around 10 K can be reproduced by the two-level model with the Γ3 doublet ground state and the Γ4 triplet excited state. The magnetic entropy release shifts to higher temperatures with increasing x. The increase in χ(T) at T < 5 K contrasts with the saturation of χ(T) for x=0. These observations indicate the splitting of the ground state doublet due to the lowering of the local symmetry at the Pr site by the Ga substitution.

Very Low Temperature Magnetoresistance in the Quadrupole Ordered System PrV2Al20

We measured magnetoresistance of the quadrupole ordered system PrV2Al20 with a Γ3 doublet ground state under high-DC magnetic field up to 30 T. The field dependence of the magnetoresistance is strongly different between H ∥ [111] and H ∥ [110] in spite of the cubic crystal structure. For H ∥ [110], we observed a jump with distinct hysteresis between 13 and 16 T and a shoulder structure in the field of 8 T at 23 mK.

Non-Fermi Liquid Properties in a Cubic Pr-Based Compound PrPb3 under Magnetic Fields

We have studied the electrical resistivity ρ of the Pr-based cubic compound PrPb3 with the Γ3 doublet ground state. The temperature dependence of the resistivity is found to exhibit a non-Fermi liquid behavior with convex curve at high temperatures, as suggestive of the putative realization of the quadrupole Kondo effect. At low temperatures under magnetic fields, we observe anomalies associated with antiferroquadrupole (AFQ) ordering, incommensurate/commensurate transition inside the AFQ phase, and field-induced phase transition. The constructed phase diagram based on these observations well reproduces the one determined by the specific heat and magnetization measurements. Deep inside each phase, the resistivity turns to show the Fermi liquid behavior with the quadratic temperature dependence. The estimated slope of the T2 term is almost independent of field in contrast to our previous work of PrIr2Zn20 and PrRh2Zn20 in which the slope is largely enhanced at the edge of the AFQ phase.

Effect of La Substitution in PrIr2Zn20 on the Superconductivity and Antiferro-Quadrupole Order

The electrical resistivity ρ and the specific heat C of Pr1−xLaxIr2Zn20 (0 ≤ x ≤ 1) were measured to study the effect of La substitution in PrIr2Zn20 on the superconducting transition at Tc = 0.05 K and the antiferro-quadrupolar (AFQ) order at TQ = 0.11 K, which occur in a nonmagnetic Γ3 doublet ground state. For x = 0.04, a cusp in C(T) due to the AFQ order was observed at TQ = 0.07 K, while the cusp disappeared for x ≥ 0.09, indicating that the AFQ order rapidly collapses with the dilution of the Pr lattice. On the other hand, in the whole range of 0 ≤ x ≤ 1, the superconducting transition to zero resistance was observed. With increasing x, Tc hardly changes up to x = 0.47, above which Tc increases linearly with x. The results indicate a rather weak interplay between Tc and TQ. We have measured the magnetic field variation of Tc to determine the upper critical field of the superconducting state. The estimated effective mass m* for x = 0 is twice larger than that for x = 1, suggesting that moderately strong hybridization between 4f and conduction electrons stabilizes the superconducting state in PrIr2Zn20.

Low-temperature magnetic properties of RE2Ni21B6 (RE = Er, Tm, Yb and Lu)

The low-temperature magnetic properties of RE2Ni21B6 (RE=Er, Tm, Yb and Lu) crystallizing into a cubic C6Cr23-type structure were investigated by measuring magnetic susceptibility, electrical resistivity and specific heat. An off-stoichiometric Er compound with a single phase undergoes antiferromagnetic ordering at 0.61K. Tm and Yb compounds have no magnetic ordering down to 50mK. The 4f-electron ground state under a cubic crystalline electric field was deduced by the analysis of the specific heat for each magnetic compound. Tm2Ni21B6 is considered to have the non-Kramers Γ3-doublet ground state with a quadrupolar moment. The quadrupolar moment does not show a long-range order, but probably enters into a glass state owing to the presence of atomic disorder. Our study suggests that atomic disorder degrades the long-range nature of quadrupolar interactions.

Susceptibility measurements in PrxLa1-xInAg2 with Γ3 doublet ground state

We have measured the susceptibility and magnetization of PrxLa1-xInAg2 at Pr concentrations x=1 and 0.1 down to T ∼ 0.5 K by SQUID magnetometer with a home-made 3He insert. The susceptibility above T = 15 K is well reproduced by the crystal-electric-field level scheme with a non-Kramers Γ3 doublet in the ground state for each concentration, while that below T = 15 K shows a non-Fermi-liquid (NFL) behavior with — ln T-dependence at low magnetic field. With increasing magnetic field, — ln T-dependence is suppressed and —T1−2-dependence appears at H = 7 T The magnetization at T = 0.5 K increases with increasing magnetic fields up to H = 7 T, indicating that the increase of the susceptibility does not come from impurity ions. These results suggest that the quadrupolar Kondo effect is responsible for NFL behavior of the susceptibility.

Nonmagnetic Γ3 doublet ground state in a caged compound PrRh2Zn20

We have prepared single crystals of PrRh2Zn20, which is isostructural and isoelectronic to PrIr2Zn20 where coexistence of superconductivity and antiferroquadrupolar order has been recently found. The electrical resistivity ρ, magnetic susceptibility χ, isothermal magnetization M, and specific heat C have been measured. Hysteretic behavior appears in ρ(T) for 170 K < T < 470 K, suggesting a structural phase transition. On cooling below 10 K, χ approaches a constant value, indicating a non-magnetic ground state. Anisotropic behavior in M(B) at 1.8 K for B > 2 T and a broad peak in C(T) at around 10 K are reproduced by the two crystal-field levels split by 32 K; a nonmagnetic Γ3 doublet ground state and a magnetic Γ4 triplet excited state.

Low-Temperature Elastic Properties of Non-Kramers Doublet Compound PrMg3

We have investigated low-temperature elastic properties of PrMg3 with a non-Kramers Γ3 doublet ground state by using ultrasonic measurements under high field up to 18 T down to 20 mK. A softening of the elastic constant (C11–C12)/2 has been observed below 8 K due to the non-magnetic Γ3 doublet possessing electric quadrupole Ou and Ov with Γ3 symmetry and magnetic octupole Txyz with Γ2. This result appreciably is deviated from a theoretical fitting of the quadrupole susceptibility based on the crystal-electric-field levels below 800 mK. Furthermore, the (C11–C12)/2 shows strange magnetic dependence up to 18 T below 1.7 K, which are inconsistent with the theoretical results.

Quadrupole Ordering and Rattling in Clathrate Compound Pr3Pd20Ge6

We have studied quadrupole ordering and rattling in clathrate compound Pr3Pd20Ge6 using ultrasonic measurements. The softening were observed in temperature dependence of elastic constants C11, (C11 - C12)/2 and C44. The C11 and (C11 - C12)/2 show minimums at 250 mK indicating a transition point to an antiferroquadrupole ordered phase due to a Γ3 doublet ground state at 8c site. Furthermore, the C11, (C11 - C12)/2 and C44 exhibit discontinuitive anomalies at 60 mK revealing a ferroquadrupole ordering due to a Γ5 triplet ground state at 4a site. Two distinctive ultrasonic dispersions caused by thermally activated Γ5-type rattling were observed in C44 around 15 K and 25 K.

Crystalline electric field effects in the filled skutterudite compoundPrOs4P12

The filled skutterudite compoundPrOs4P12 was synthesized in single-crystal form using a molten metal flux growth technique.Low-temperature magnetization, specific heat, and electrical resistivity measurements showedno indication of a phase transition down to 0.1 K but had features indicative of crystallineelectric field (CEF) effects. Analyses of these features in terms of a cubic CEF suggest aΓ1 singletor a Γ3 doublet ground state separated by 30–50 K from aΓ5 triplet first excited state.

Modulated Quadrupolar Structures in Rare-earth Compound PrPb3

In the rare-earth compound PrPb3, it was proposed that antiferroquadrupolar (AFQ) ordering occurs at TQ=0.4K only by means of macroscopic measurements. Recently, we have performed neutron diffraction measurements in a magnetic field to confirm the existence of the AFQ ordered state. In magnetic fields applied along the [001] axis, antiferromagnetic components with q=(1/2±δ1/2 0), (1/2 1/2±±0)(±-1/8) are observed below TQ (0.4K at H=0) whose amplitudes vary linear with H and vanish at zero field, providing the first evidence for a modulated quadrupolar phase. For H<1, a nonsquare modulated state persists even below 100 mK, suggesting quadrupole moments associated with a Γ3 doublet ground state to be partially quenched by hybridization with conduction electrons.