Probing the $J_{\mathrm{eff}}=0$ ground state and the Van Vleck paramagnetism of the ${\mathrm{Ir}}^{5+}$ ions in layered ${\mathbf{Sr}}_2{\mathbf{Co}}_{0.5}{\mathbf{Ir}}_{0.5}{\mathbf{O}}_4$

We report a combined experimental and theoretical x-ray magnetic circular dichroism (XMCD) spectroscopy study at the Ir-$L_{2,3}$ edges on the ${\mathrm{Ir}}^{5+}$ ions of the layered hybrid solid state oxide ${\mathrm{Sr}}_2{\mathrm{Co}}_{0.5}{\mathrm{Ir}}_{0.5}{\mathrm{O}}_4$ with the ${\mathrm{K}}_2{\mathrm{NiF}}_4$ structure. From theoretical simulation of the experimental Ir-$L_{2,3}$ XMCD spectrum, we found a deviation from a pure $J_{\mathrm{eff}}=0$ ground state with an anisotropic orbital-to-spin moment ratio ($L_x/2S_x=0.43$ and $L_z/2S_z=0.78$). This deviation is mainly due to multiplet interactions being not small compared to the cubic crystal field and due to the presence of a large tetragonal crystal field associated with the crystal structure. Nevertheless, our calculations show that the energy gap between the singlet ground state and the triplet excited state is still large and that the magnetic properties of the ${\mathrm{Ir}}^{5+}$ ions can be well described in terms of singlet Van Vleck paramagnetism.

Figure 1

Experimental $\mathrm{Ir}-L_{2,3}$ XAS and XMCD spectra of ${\mathrm{Sr}}_2{\mathrm{Co}}_{0.5}{\mathrm{Ir}}_{0.5}{\mathrm{O}}_4$, red and blue circles, respectively, and of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, magenta and green circles, respectively, and XAS of ${\mathrm{Sr}}_2{\mathrm{ScIrO}}_6$ (orange). The spectra were measured at $T=2\mathrm{K}$ and $B_{\mathrm{app}}=17\mathrm{T}$. The vertical dotted lines illustrate the energy shift between the spectra of the ${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$ samples. The black dotted curves represent the edge jumps. Bottom: calculated $\mathrm{Ir}-L_{2,3}$ XAS (red line) and XMCD (blue line) of ${\mathrm{Sr}}_2{\mathrm{Co}}_{0.5}{\mathrm{Ir}}_{0.5}{\mathrm{O}}_4$.

Figure 2

Energy level diagram of the ${\mathrm{Ir}}^{5+}$ ($d^4$) ion as a function of the effective tetragonal crystal field in a $D_{4h}$ local symmetry and $10D{q}^{\mathrm{eff}}=3.0\mathrm{eV}$. The vertical magenta line indicates the ${\mathrm{\Delta }}_{t2g}^{\mathrm{eff}}$ of ${\mathrm{Sr}}_2{\mathrm{Co}}_{0.5}{\mathrm{Ir}}_{0.5}{\mathrm{O}}_4$ as obtained by the simulation of the XAS and XMCD spectra. The color lines represent the evolution of the expectation value of $J_{\mathrm{eff}}$ versus ${\mathrm{\Delta }}_{t2g}^{\mathrm{eff}}$. The value of $J_{\mathrm{eff}}$ ranges from 0 (red) to 2.5 (black) as indicated by the palette on the right.

Figure 3

Calculated spin and orbital moments as a function of the applied field (a) or exchange field (b).

Figure 4

$\mathrm{Ir}-L_{2,3}$ XMCD simulations (solid lines) calculated using different values of $H_{ex}$, together with the experimental XMCD spectrum of ${\mathrm{Sr}}_2{\mathrm{Co}}_{0.5}{\mathrm{Ir}}_{0.5}{\mathrm{O}}_4$ (red circles). For a better comparison of the line shapes, the simulated spectra are normalized to the XMCD peak height, with the normalization factor also indicated in the legend.

Figure 5

Magnetization of ${\mathrm{Sr}}_2{\mathrm{Co}}_{0.5}{\mathrm{Ir}}_{0.5}{\mathrm{O}}_4$ as a function of magnetic field, together with the derived magnetic susceptibility.