Direct Evidence of a Near-Ideal Jeff = 1/2 Ground State in Triangular-Lattice Na2BaCo(PO4)2

TL;DR

This work uses temperature-dependent polarization-dependent X-ray absorption spectroscopy (XAS) together with full multiplet cluster calculations to directly probe the local Co$^{2+}$ electronic structure in Na2BaCo(PO4)2. The analysis reveals an exceptionally small trigonal distortion ($D_{ ext{trig}} \\approx 11$ meV) and a dominant $d^7$ configuration with covalency, placing the system in a near-$J_{ ext{eff}}= frac{1}{2}$ ground state, separated by ~40 meV from its $J_{ ext{eff}}= frac{3}{2}$ excited state. Magnetic-susceptibility measurements, modeled with the same cluster Hamiltonian, show only weak short-range antiferromagnetic correlations, yet they are consistent with the spectroscopic parameters. The combination of XAS and cluster theory demonstrates Na2BaCo(PO4)2 as a promising platform for investigating $J_{ ext{eff}}= frac{1}{2}$ physics on triangular lattices and highlights the efficacy of line-fit iPFY XAS for resolving meV-scale distortions in insulating materials.

Abstract

We investigated the local Co 3d electronic structure of Na2BaCo(PO4)2 using polarization-dependent X-ray absorption spectroscopy (XAS) in combination with full multiplet cluster calculations. We employed the line-fitting inverse partial fluorescence yield (IPFY) technique to obtain accurate XAS spectra from strong insulating materials. Our combined experimental and theoretical analysis reveals a very small effective trigonal distortion of only 11 meV in the CoO6 octahedra, indicating a close to ideal condition to render a ground state with the Jeff = 1/2 character. With our cluster model we were also able to simulate magnetic susceptibility measurements along different directions in the crystal. These findings highlight Na2BaCo(PO4)2 as a promising platform for exploring exotic magnetic phenomena associated with Jeff = 1/2 ground states on triangular lattices.

Figures (5)

• Figure 1: (a) Crystal structure of Na$_2$BaCo(PO$_4$)$_2$, showing layers of CoO$_6$ octahedra stacked along the c-axis. (b) The ab plane containing the Co$^{2+}$ triangular lattice. (c) Schematic of the experimental geometry, illustrating the orientation of the incident X-ray beam, linear polarization directions, and the silicon drift detector (SDD) relative to the sample.
• Figure 2: Experimental and calculated temperature dependence of isotropic spectra measured for Na$_2$BaCo(PO$_4$)$_2$
• Figure 3: Polarization-dependent Co $L_{2,3}$ XAS spectra taken at 40 K and 300 K: (a,b) experiment and (c,d) calculation. Incident beam polarization is along either a (LH) or along c direction (LV).
• Figure 4: Temperature dependence of the measured and calculated linear dichroic spectra defined as $I_{LD} = I_{LV}-I_{LH}$ (see text for definition of the polarizations directions)
• Figure 5: Inverse magnetic susceptibility, $\chi^{-1}$, measured under an applied field of 0.1 T set either along the [100] or [001] crystallographic directions, compared with calculations from our cluster model. Dashed lines indicate simulated susceptibilities obtained without including trigonal distortion in the calculations.