Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRKKY Interaction and Quadrupole Order in Pr$T_{2}$Al$_{20}$ ($T$=Ti, V) Based on Effective 196 Orbital Model Extracted from First-Principles Calculation
47
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
The electronic nematic phase emerging with spontaneous rotation symmetry breaking is a central issue of modern condensed matter physics. In particular, various nematic phases in iron-based superconductors and high-$T_{rm c}$ cuprate superconductors are extensively studied recently. Electric quadrupole moments (EQMs) are one of the order parameters characterizing these nematic phases in a unified way, and elucidating EQMs is a key to understanding these nematic phases. However, the quantum-mechanical formulation of the EQMs in crystals is a nontrivial issue because the position operators are non-periodic and unbound. Recently, the EQMs have been formulated by local thermodynamics, and such {it thermodynamic EQMs} may be used to characterize the fourfold rotation symmetry breaking in materials. In this paper, we calculate the thermodynamic EQMs in iron-based superconductors LaFeAsO and FeSe as well as a cuprate superconductor La$_2$CuO$_4$ by a first-principles calculation. We show that owing to the orbital degeneracy the EQMs in iron-based superconductors are mainly determined by the geometric properties of wave functions. This result is in sharp contrast to the cuprate superconductor, in which the EQMs are dominated by distortion of the Fermi surface.
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 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$_6$.
The nature of multipolar order and hyperfine-enhanced (HE) $^{141}$Pr nuclear spin dynamics in PrV$_2$Al$_{20}$ was investigated using the muon spin relaxation technique. No explicit sign of time-reversal symmetry breaking was found below the multipolar order temperature $T_Qsim 0.6$ K in a zero applied field as anticipated on the basis of the antiferroquadrupolar (AFQ) order picture proposed by Sakai and Nakatsuji [J. Phys. Soc. Jpn. 80, 063701 (2011)]. Further evidence of the nonmagnetic ground state was obtained from the observation of HE $^{141}$Pr nuclear spin fluctuations in the MHz scale. A marked increase in the muon spin-lattice relaxation rate (1/$T_{rm 1,mu}$) was observed below 1 K with decreasing temperature, which was attributed to the perturbation on the HE $^{141}$Pr nuclear spin dynamics associated with the development of AFQ correlations. The longitudinal field dependence of 1/$T_{rm 1,mu}$ revealed that the enhanced $^{141}$Pr nuclear spin accidentally has an effective gyromagnetic ratio close to that of the muon.
Electrical resistivity, magnetic susceptibility, and specific heat measurements on single crystals of La$Tr_{2}$Al$_{20}$ ($Tr$ = Ti, V, Nb, and Ta) revealed that these four compounds exhibit weak-coupling superconductivity with transition temperatures $T_{rm c}$ = 0.46, 0.15, 1.05, and 1.03 K, respectively. LaTi$_{2}$Al$_{20}$ is most probably a type-I superconductor, which is quite rare among intermetallic compounds. Single-crystal X-ray diffraction suggests rattling anharmonic large-amplitude oscillations of Al ions (16$c$ site) on the Al$_{16}$ cage, while no such feature is suggested for the cage-center La ion. Using a parameter $d_{rm GFS}$ quantifying the guest free space of the cage-center ion, we demonstrate that nonmagnetic $RTr_{2}$Al$_{20}$ superconductors are classified into two groups, i.e., (A) $d_{rm GFS} e 0$ and $T_{rm c}$ correlates with $d_{rm GFS}$, and (B) $d_{rm GFS} simeq 0$ and $T_{rm c}$ seems to be governed by other factors.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
