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Register a new userRKKY interactions of CeB6 based on effective Wannier model
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We examine the RKKY interactions of CeB$_6$ between multipole moments based on the effective Wannier model obtained from the bandstructure calculation including 14 Ce-$f$ orbitals and 60 conduction orbitals of Ce-$d,s$ and B-$p,s$. By using the $f$-$c$ mixing matrix elements of the Wannier model together with the conduction band dispersion, the multipole couplings with the RKKY oscillation are obtained for the active moments in $Gamma_{8}$ subspace. Both of the $Gamma_{5g}$ quadrupole $O_{xy}$ and the $Gamma_{2u}$ octupole $T_{xyz}$ couplings are largely enhanced with $bm{q}=(pi,pi,pi)$ which naturally explains the antiferro-quadrupolar phase of the phase II, and are also enhanced with $bm{q}=(0,0,0)$ corresponding to the elastic softening of $C_{44}$. Also the couplings of the $Gamma_{5u}$ octupole $T_{z}^{beta}$ is quite large for $bm{q}=(0,0,pi)$ which is related to the antiferro-octupolar ordering of a possible candidate for the phase IV of Ce$_{x}$La$_{1-x}$B$_6$.
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We have investigated the electronic states of CeB$_6$ and have directly calculated the RKKY interaction on the basis of the 74-orbital effective Wannier model which includes 14 Ce-$f$ orbitals and 60 conduction ($c$) orbitals of Ce-$d,s$ and B-$p,s$ derived from the density-functional theory bandstructure calculation. By using not only the $c$-band dispersion but also the $f$-$c$ mixing matrix elements of the Wannier model, the realistic couplings for all 15 active multipole moments in $Gamma_8$ quartet subspace are obtained in the wavevector $q$-space and real-space. Both of the $Gamma_{5g}$ quadrupoles $(O_{yz},O_{zx},O_{xy})$ and the $Gamma_{2u}$ octupole $T_{xyz}$ couplings are maximally enhanced with $q=(pi,pi,pi)$ which naturally explains the phase II of the antiferro-quadrupolar ordering at $T_{Q}=3.2$ K, and are also enhanced with $q=(0,0,0)$ corresponding to the elastic softening of $C_{44}$. Also the couplings of the $Gamma_{5u}$ octupoles $T_{x}^{beta}$, $T_{y}^{beta}$ and $T_{z}^{beta}$ are quite large for $q=(pi,0,0)$, $(0,pi,0)$ and $(0,0,pi)$, which yields the antiferro-octupolar ordering of a possible candidate for phase IV of Ce$_{x}$La$_{1-x}$B$_6$. The intersite vector dependence of the RKKY couplings exhibit different long-range, oscillating, isotropic and anisotropic behaviors depending on the types of the multipole moments. The present approach enables us to provide the information about the possible multipole ordering in an unbiased way and is easily available for other localized $f$ electron materials once the $c$ states and $f$-$c$ mixing elements are given from the bandstructure calculation.
We study the stabilization of an isolated magnetic skyrmion in a magnetic monolayer on a nonmagnetic conducting substrate via the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction. Two different types of the substrate are considered, usual normal metal and single-layer graphene. While the full stability analysis for skyrmions in the presence of the RKKY coupling requires a separate effort that is outside the scope of this work, we are able to study the radial stability (stability of a skyrmion against collapse) using variational energy estimates obtained within first-order perturbation theory, with the unperturbed Hamiltonian describing the isotropic Heisenberg magnet, and the two perturbations being the RKKY exchange and the easy-axis anisotropy. We show that a proper treatment of the long-range nature of the RKKY interaction leads to a qualitatively different stabilization scenario compared to previous studies, where solitons were stabilized by the frustrated exchange coupling (leading to terms with the fourth power of the magnetization gradients) or by the Dzyaloshinskii-Moriya interaction (described by terms linear in the magnetization gradients). In the case of a metallic substrate, the skyrmion stabilization is possible under restrictive conditions on the Fermi surface parameters, while in the case of a graphene substrate the stabilization is naturally achieved in several geometries with a lattice-matching of graphene and magnetic layer.
Precision measurements of charge transport parameters (resistivity, Hall and Seebeck coefficients) have been carried out on high-quality single-crystals of cerium hexaboride in a wide temperature range 1.8-300 K. It is shown that in the temperature interval of 5 K < T < T* = 80 K the magnetic contribution in resistivity obeys the power law rm = T -1/n, which corresponds to the regime of weak localization of charge carriers with the critical index 1/n = 0.39 +- 0.02. In the same temperature interval an asymptotic behavior of thermopower S = -lnT is found together with an essential decrease of the charge carriers mobility in CeB6. A negative Hall coefficient anomaly has been detected at liquid helium temperatures. The data obtained are compared with the results predicted by the Kondo-lattice model and discussed also in terms of the theory of excitonic ferromagnetism.
We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.
Electronic states and quadrupole orders in the 1-2-20 systems Pr$T_{2}$Al$_{20}$ ($T$=Ti, V) are investigated on the basis of the first-principles band calculation. As the de Haas-van Alphen experiments reveal that the Pr-4$f$ electrons in the systems are sufficiently localized and irrelevant for the Fermi surface, we derive the low-energy effective tight-binding models consists of 196 orbitals of conduction electrons so as to reproduce the first-principles electronic structures of La$T_{2}$Al$_{20}$ ($T$=Ti, V) without contribution from the 4$f$ electrons. Based on the effective models, we calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the quadrupole moments of the Pr ions mediated by the conduction electrons. The obtained results indicate that the wave vector of the expected quadrupole order is ${bm{Q}}=left(0,0,0right)$ for PrTi$_{2}$Al$_{20}$ while it is ${bm{Q}}=left(pi/a,pi/a,0right)$ for PrV$_{2}$Al$_{20}$ as consistent with experimental observations in PrTi$_{2}$Al$_{20}$ and PrV$_{2}$Al$_{20}$ which exhibit ferro- and antiferro-quadrupole orders, respectively.
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