Non-Kramers doublet ground state in a quaternary cubic compound PrRu_(2)In_(2)Zn_(18) investigated by ultrasonic measurements

We performed ultrasonic measurements on a quaternary cubic compound PrRu_(2)In_(2)Zn_(18) to explore the ground state properties derived from non-Kramers Γ_(3) doublet of Pr^(3+).PrRu_(2)In_(2)Zn_(18) is a quaternary derivative of the ternary compound PrRu_(2)Zn_(20) that exhibits a structural phase transition at T_S=138 K.In PrRu_(2)In_(2)Zn_(18),the Zn atoms at the 16c site in PrRu_(2)Zn_(20) are selectively replaced by In atoms.A monotonic increase was observed in the temperature dependence of elastic constants C_L=(C_(11)+2C_(12)+4C_(44))/3 and C_(T)=(C_(11)-C_(12)+C_(44))/3 in the temperature range around T_(S) to which an elastic softening was observed in(C_(11)-C_(12))/2 for PrRu_(2)Zn_(20).The disappearance of the softening indicates that the structural transition in PrRu_(2)Zn_(20) is suppressed by the substitution of Zn ions by In ones with a larger ionic radius.Alternatively,the C_(T) of PrRu_(2)In_(2)Zn_(18) exhibits a precursor Curie-type elastic softening toward low temperatures being responsible for the non-Kramers Γ_(3) ground state.We discuss the ground state and the evolution of the elastic properties of the different single-crystal samples of PrRu_(2)In_(2)Zn_(18) grown under different conditions.

Magnetooptics of non-Kramers Eu^(3+) ions in garnets:analysis complemented by crystal-field splitting modeling calculations

Spectra of absorption, luminescence, magnetic circular dichroism （MCD）, and magnetic circular polarization of lumines- cence （MCPL） in Gd3Ga5O12：Eu3＋ and Eu3Ga3O12 garnets were studied within the visible spectral range at 300 K. Analysis of the spectral and temperature dependences of the magnetooptical and optical spectra made it possible to identify the magneto-dipole （MD） and electro-dipole （ED） 4f→4f transitions occurring between Stark sublevels of the 7FJ （J=1, 2） and 5D0 multiplets in Eua＋-containing garnet structures. Quantum mechanical ＂mixing＂ had significant influence on quasi-degenerate states of the non-Kramers rare-earth Eu3＋ ion for Eu3GasOl2 in MCD due to forbidden MD transition 7F1→SD0 and for GdaGasOiE：EU3＋ in MCPL due to MD 4f→4f transition 5Do→7F1 and forced ED-transition 5Do→7F2. A parameterized Hamiltonian defined to operate within the entire 4f（6） ground electronic configuration of Eu3＋ ion was used to model the experimental Stark levels, including their irreducible rep- resentations and wavefunctions. The crystal-field parameters were determined through a Monte-Carlo method in which nine in- dependent crystal-field parameters, Bkq, were given random starting values and optimized using standard least-squares fitting between calculated and experimental levels. The final fitting standard deviation between 57 calculated-to-experimental levels was 0.73 meV.

Composite electronic orders induced by orbital Kondo effect

In a large number of rare-earth and actinide systems,Kondo effect tends to suppress magnetic orders by making the spin singlet between localized and conduction electron spins.In the presence of orbital degrees of freedom,however,there emerge exotic electronic orders induced by Kondo effect.The orbital Kondo effect can collectively make diagonal and off-diagonal(superconducting) orders.With the particle-hole symmetry in conduction bands,these orders are all degenerate,forming a macroscopic SO(5) multiplet.This paper discusses recent theoretical development on these electronic orders which are relevant to Pr^(3+) and U^(4+) systems with even number of f electrons per site.In the superconducting order,each conduction–electron pair is coupled with local degrees of freedom,forming a composite entity with a staggered spatial pattern.The quasi-particle spectrum is best interpreted as virtual hybridization with resonant states at the Fermi level.Possible order parameter for URu_2Si_2 in the hidden order state is discussed in the context of composite orders.Briefly discussed are related issues such as homogeneous odd-frequency pairing and SO(5) theory for hightemperature superconductors.