Stability of the Local Ni$^{2+}$ Electronic Structure to $A$-site Disorder in the Pyrochlore Antiferromagnet NaCaNi$_2$F$_7$

Abstract: NaCaNi$2$F$_7$ is a unique example of spin-1 Heisenberg antiferromagnet on the pyrochlore lattice, but the presence of Na$^{1+}$/Ca$^{2+}$ $A$-site disorder complicates the local electronic and magnetic environment of the Ni$^{2+}$ $B$-site. We utilize resonant inelastic X-ray scattering (RIXS) to study the influence of $A$-site disorder on the $B$-site electronic structure of NaCaNi$_2$F$_7$. Ni L-edge RIXS measurements reveal a Ni$^{2+}$ electronic structure in nearly ideal octahedral coordination, with only a small trigonal compression ($δ$ = -200$\;$meV) required to capture all spectral features. Within the $D{3d}$ symmetry of the Ni local environment, we extract an anisotropic $g$-factor of $g_{\parallel} = 2.26$ and $g_{\perp} = 2.27$, and a corresponding paramagnetic moment of $μ_{\rm{eff}}=3.2\;μ_B$. To simulate disorder, RIXS spectra were calculated with realistic distributions of crystal field parameters; however, these spectra are invariant relative to a disorder-free model, demonstrating the robustness of the Ni$^{2+}$ electronic environment to the $A$-site disorder, within the resolution of our measurement.