Site-selective renormalization and competing magnetic instabilities in paramagnet Y$_{3}$Cu$_{2}$Sb$_{3}$O$_{14}$

Abstract

Quantum spin liquids (QSLs) are exotic phases of matter characterized by long-range entanglement and the absence of magnetic order even at zero temperature. Here, we present a comprehensive theoretical study of the frustrated magnet Y$_3$Cu$_2$Sb$_3$O$_{14}$ to elucidate its electronic and magnetic properties. We uncover completely opposite crystal-field splittings of the two inequivalent Cu sites owing to their fundamentally distinct oxygen coordination - trigonal distorted octahedral CuO$_6$ and axially compressed CuO$_8$. This inversion places the unpaired hole in the $d_{z^2}$ orbital at the Cu-2 site, while Cu-1 maintains conventional $d_{x^2-y^2}/d_{xy}$ character, which results in a selective band-renormalization of orbitals from the two Cu ions. We further find multiple magnetic instabilities competing with nearly equal strength in this system: the spin susceptibility lacks dominant peaks, and the leading eigenvalues approach unity simultaneously across all wavevectors with increasing interactions. This competitive interplay, originating from the distinct local environments and geometric frustration on the triangular lattice, agrees well with the absence of long-range magnetic order in experiment. Our results support Y$_3$Cu$_2$Sb$_3$O$_{14}$ as a promising QSL candidate where the unique combination of disparate crystal-field environments, strong correlations, and competing exchange interactions conspire to stabilize an exotic quantum ground state.

Figures (3)

• Figure 1: Crystal and electronic structure of Y$_3$Cu$_2$Sb$_3$O$_{14}$. (a) The crystal structure of Y$_3$Cu$_2$Sb$_3$O$_{14}$, in which the two inequivalent copper sites (yellow atoms), Cu-1 and Cu-2, individually form triangular planes. (b) shows the two different local environment of Cu-1 and Cu-2. In Cu-2, an additional shorter Cu-O bond along z axis inverts the crystal field created by the regular trigonal distortion in Cu-1. (c) The DFT electronic band structure of the primitive cell is shown along a high-symmetry path in the first BZ. The orange line around the Fermi level denotes the three bands with their Wannier functions shown in (d). Additionally including the purple bands leads to a ten bands effective model. Both the three-band and the ten-band models show excellent agreement with the DFT results. (d) The projected Wannier functions of the three yellow bands indicate that, among the three orbitals, two orbitals are from the Cu-1 ion and one from Cu-2 ion.
• Figure 2: DMFT spectral function and self-energy. (a, b) and (c, d) correspond to two different types of DMFT impurity construction. In (a, b), all three orbitals depicted in Fig. \ref{['fig:dft-result']}(d) are treated within one impurity, while in (c, d) Cu-1 and Cu-2 are considered to be independent and each forms a DMFT impurity problem. In all four calculations, $\beta$ = 30, $J$ = 0.1 eV. $U$ are set as 1 eV in (a, c), and 2 eV in (b, d).
• Figure 3: Fermi surface and spin susceptibility $\chi(\bm{q}, i\omega_m=0)$. (a). The Fermi surface in 3D BZ and in a 2D cut through $\Gamma$ point display multiple pockets and nesting structures. (b). The spin susceptibility calculated from Eq. \ref{['Eq:chis']} displays multiple peaks with only small variation, which is further suppressed by electronic correlations. The blue and yellow curves correspond to different interaction parameters as shown by the legend. (c). The leading eigenvalues of $\chi_0 U_s$ follow a similar structure as $\chi_s$ in (b), whose variation is also reduced by electronic correlations. (d). Both the leading eigenvalues of $\chi_0$ (the left-yaxis in red) and $\chi_0 U_s$ (the right-yaxis in blue) for different momentum wave vectors fall into a single curve under the evolution of electronic correlations, with the former decreases and the latter increases with $U$.