Interplay of electron correlations, spin-orbit couplings, and structural effects for Cu centers in the quasi-two-dimensional magnet $\mathrm{In}{\mathrm{Cu}}_{2/3}{\mathrm{V}}_{1/3}{\mathrm{O}}_3$

Less common ligand coordination of transition-metal centers is often associated with peculiar valence-shell electron configurations and outstanding physical properties. One example is the ${\mathrm{Fe}}^{+}$ ion with linear coordination, actively investigated in the research area of single-molecule magnetism. Here we address the nature of $3d^9$ states for ${\mathrm{Cu}}^{2+}$ ions sitting in the center of trigonal bipyramidal ligand cages in the quasi-two-dimensional honeycomb compound $\mathrm{In}{\mathrm{Cu}}_{2/3}{\mathrm{V}}_{1/3}{\mathrm{O}}_3$, whose unusual magnetic properties were intensively studied in the recent past. In particular, we discuss the interplay of structural effects, electron correlations, and spin-orbit couplings in this material. A relevant computational finding is a different sequence of the Cu ($xz$, $yz$) and ($xy$, $x^2-y^2$) levels compared to existing electronic-structure models, which has implications for the interpretation of various excitation spectra. Spin-orbit interactions, both first- and second-order, turn out to be stronger than previously assumed, suggesting that rather rich single-ion magnetic properties can in principle be achieved also for the $3d^9$ configuration by properly adjusting the sequence of crystal-field states for such less usual ligand coordination.

Figure 1

Angular dependence of the $g$ factor (a) and of the peak-to-peak ESR linewidth $\mathrm{\Delta }{H}_{\mathrm{pp}}$ (b) of the oriented powder sample of $\mathrm{In}{\mathrm{Cu}}_{2/3}{\mathrm{V}}_{1/3}{\mathrm{O}}_3$ measured at room temperature at the $X$-band frequency $\nu =9.58$ GHz (symbols). Inset: A typical ESR signal (field derivative of the microwave absorption). Dashed and solid curves represent the results of numerical modeling (see the text).

Figure 2

Frequency $\nu$ versus magnetic field $H$ dependence of the ESR signal of the oriented powder sample of $\mathrm{In}{\mathrm{Cu}}_{2/3}{\mathrm{V}}_{1/3}{\mathrm{O}}_3$ measured at $T=60$ K with $\mathbf{H}\parallel o$ axis (open circles). A corresponding fit is shown as the dashed line. Exemplary ESR signals are shown for frequencies of 160 and 345 GHz. The asterisk labels a small additional peak presumably due to ${\mathrm{Cu}}^{2+}$ spins at defect sites.