Scalar order in PrFe₄P₁₂ and PrRu₄P₁₂

We show by phenomenological Landau analysis that the properties of ordered phases in some skutterudites are consistently accounted for by a scalar-order parameter which preserves the cubic symmetry, even in the ordered phase. A universal value is found for the anisotropy ratio of the transition temperature in a magnetic field, homogeneous magnetization, and induced staggered magnetization. The difference in magnetic behavior between PrFe₄P₁₂ and PrRu₄P₁₂ near their phase transitions is explained within a single framework. For the low-field phase of PrFe₄P₁₂, the scalar order with Γ_1g symmetry can explain (i) the absence of field-induced dipoles perpendicular to the magnetic field, (ii) isotropic magnetic susceptibility in the ordered phase, (iii) the field-angle dependence of the transition temperature, and (iv) the splitting pattern of the ³¹P nuclear magnetic resonance (NMR) spectra.

A. Kiss and Y. Kuramoto: J. Phys. Soc. Jpn. 75, 103704 (2006).

Magnetic orders of NpTGa₅ with T=Co, Ni, Rh, or Fe

We explain the characteristics of magnetic transitions in NpTGa₅ with T=Co, Ni, Rh in a unified way with use of a crystalline electric field (CEF) model of localized 5f⁴ electrons of Np ion. The model takes a CEF doublet and a singlet as local states, and includes dipolar and quadrupolar intersite interactions in the mean-field theory. Diverse ordering phenomena are derived depending on the magnitude of interaction parameters, which qualitatively reproduce the experimentally observed magnetic behaviors in NpTGa₅. The quadrupole degrees of freedom are essential to the diverse magnetic orders. It is argued that NpRhGa₅ is close to a multicritical point where quadrupoles and dipoles with different directions are competing to order.
In addition, we extended the CEF model by including the Fe moments as the source of anisotropy in order to explain the mechanism of successive magnetic transitions in NpFeGa₅. All possible dipolar and quadrupolar interactions are taken into account, which are allowed by the doublet–singlet subspace. Phase diagrams are obtained which give either two or three successive transitions from the paramagnetic phase. In the latter case, Np moments first order along [110], then tilt around the c axis, and finally tilt out of the ab-plane. The ensuing splitting pattern of ⁶⁹Ga and ⁷¹Ga nuclear magnetic resonance (NMR) is analyzed theoretically, and compared with experimental results.

A. Kiss and Y. Kuramoto: J. Phys. Soc. Jpn. 75, 034709 (2006).

A. Kiss and Y. Kuramoto: J. Phys. Soc. Jpn. 77, 124708 (2008).

Ordering and crossover in SmRu₄P₁₂

We propose a crystalline electric field (CEF) model of localized 4f⁵ electrons of Sm ion for understanding intriguing ordering phenomena in SmRu₄P₁₂. We take the CEF quartet and doublet (pseudo-sextet) of the Hund’s rule ground state with J=5/2, and include intersite interactions between multipoles by the mean-field theory. The model leads to a multipole order with representation 5u, and shows the following features: (i) increasing transition temperature T_MI with increasing magnetic field; (ii) an anomaly in specific heat and other thermodynamic quantities at lower temperature T₁ < T_MI, (iii) sharpening of the anomaly at T₁ as the magnetic field increases. These behaviors reproduce salient features observed experimentally in SmRu₄P₁₂. Possible mechanisms for spontaneous magnetic moment are discussed as well.

A. Kiss and Y. Kuramoto: J. Phys. Soc. Jpn. 78, 124702 (2009).

Magnetic orders and fluctuations in strongly correlated electron systems

We review experimental and theoretical results on higher electronic multipoles in solids with strong correlations. Recent experiments and their theoretical interpretation have confirmed the ordering of octupoles and even higher multipoles in rare-earth and actinide compounds with f electrons. The concept of multipoles is critically examined in point groups where spherical tensors of different ranks mix. Using a phenomenological approach, we demonstrate how linear and nonlinear couplings of different multipoles lead to rich phase diagrams and anomalies in physical observables. As actual representative systems, we consider Ce_xLa_1-xB₆ with octupole order, NpO₂ where quadrupoles induced by the octupole order have been observed, PrFe₄P₁₂ with scalar order and URu₂Si₂. It is pointed out that multipole orders, particularly the scalar order, should provide a new route for studying the dichotomy between the itinerant and localized behaviors of electrons.

Y. Kuramoto, H. Kusunose, and A. Kiss: J. Phys. Soc. Jpn. 78, 072001 (2009).

Low-temperature ordered phase of Pr in PrBa₂Cu₃O_6+x

We present a theoretical model to describe the anomalous ordered phase of Pr ions in PrBa₂Cu₃O_6+x below T_Pr≈12–17K. The model considers the Pr multipole degrees of freedom and coupling between the Cu and Pr subsystems. We identify the symmetry allowed coupling of Cu and Pr ions and conclude that only an ab-plane Pr dipole ordering can explain the Cu spin rotation observed at T_Pr by neutron diffraction by Boothroyd et al. [Phys. Rev. Lett. 78, 130
(1997)]. A substantial enhancement of the Pr ordering temperature is shown to arise from the Cu-Pr coupling which is the key for the anomalous magnetic behavior in PrBa₂Cu₃O_6+x.

A. Kiss and F. Simon: Phys. Rev. B 82, 174413 (2010).

Reverse Kondo effect and antiresonance

We derive accurate numerical results for transport properties of Kondo impurity systems with potential scattering and orbital degeneracy. Using the continuous-time quantum Monte Carlo (CT-QMC) method, static and dynamic physical quantities are derived in a wide temperature range across the Kondo temperature T_K. With strong potential scattering, the resistivity tends to decrease with decreasing temperature, in contrast to the ordinary Kondo effect. Correspondingly, the quasiparticle density of states obtains the antiresonance around the Fermi level. Thermopower also shows characteristic deviation from the standard Kondo behavior, while magnetic susceptibility follows the universal temperature dependence even with strong potential scattering. It is found that the t -matrix in the presence of potential scattering is not a relevant quantity for the Friedel sum rule, for which a proper limit of the f -electron Green’s function is introduced. The optical theorem is also discussed in context of Kondo impurity models with potential scattering.

A. Kiss, Y. Kuramoto and S. Hoshino: Phys. Rev. B 84, 174402 (2011).

NMR relaxation and carbon hyperfine coupling in single-wall carbon nanotubes

Recent transport measurements [Churchill et al. Nature Phys. 5 321 (2009)] found a surprisingly large, 2–3 orders of magnitude larger than usual ¹³C hyperfine coupling (HFC) in ¹³C enriched single-wall carbon nanotubes. We formulate the theory of the nuclear relaxation time in the framework of the Tomonaga-Luttinger liquid theory to enable the determination of the HFC from recent data by Ihara et al. [ Europhys. Lett. 90 17004 (2010)]. Though we find that 1/T₁ is orders of magnitude enhanced with respect to a Fermi-liquid behavior, the HFC has its usual, small value. Thus, we reexamine the theoretical description used to extract the HFC from transport experiments. We find that similar features can be obtained with HFC-independent system parameters producing HFC with usual small value.

A. Kiss, A. Pályi, Y. Ihara, P. Wzietek, P. Simon, H. Alloul, V. Zólyomi, J. Koltai, J. Kürti, B. Dóra, and F. Simon: Phys. Rev. Lett. 107, 187204 (2011).