Magnetic Excitations and Electronic Interactions in ${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$: A Spin-$1/2$ Square Lattice Heisenberg Antiferromagnet

${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$ presents an opportunity for exploring low-dimensional magnetism on a square lattice of $S=1/2{\mathrm{Cu}}^{2+}$ ions. We employ ab initio multireference configuration interaction calculations to unravel the ${\mathrm{Cu}}^{2+}$ electronic structure and to evaluate exchange interactions in ${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$. The latter results are validated by inelastic neutron scattering using linear spin-wave theory and series-expansion corrections for quantum effects to extract true coupling parameters. Using this methodology, which is quite general, we demonstrate that ${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$ is an almost ideal realization of a nearest-neighbor Heisenberg antiferromagnet but with relatively weak coupling of 7.18(5) meV.

Figure 1

(a) and (b) Crystallographic and magnetic structure of ${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$. The ${\mathrm{Cu}}^{2+}$ ions order magnetically into an arrangement indicated by the red arrows. The different exchange couplings are shown by arrows connecting two ${\mathrm{Cu}}^{2+}$ ions. (c) Energy level diagram of $d$ states in octahedral ($O_h$) symmetry, for a tetragonally elongated octahedron and for the ${\mathrm{Cu}}^{2+}$ ion in ${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$ whose Cu-O bond lengths are labeled.

Figure 2

(a) Dynamic susceptibility ${\chi }^{\prime \prime }(|\mathbf{Q}|,E)$ map obtained by subtraction of 120 K from 2 K data. (b) Calculated powder average inelastic spectrum using ${\tilde{J}}_1=7.60(3)$ and ${\tilde{J}}_2=0.60(3)\mathrm{meV}$. The solid white lines show the detector edges. The SWT intensity is scaled to match the measured pattern in units of $\mathrm{mb}{\mathrm{sr}}^{-1}{\mathrm{me}\mathrm{V}}^{-1}\mathrm{f}.\mathrm{u}{.}^{-1}$. (c) A constant wave vector cut for $|\mathbf{Q}|\approx 1.7{\AA }^{-1}$ through the dynamic susceptibility with a solid red line showing the calculated cut from SWT. (d) $|\mathbf{Q}|$ dependence of the magnetic band around 15.4 meV and a comparison to SWT calculations.

Figure 3

(a) Dispersion between $(\pi ,0)$ and $(\pi /2,\pi /2)$ calculated using SE and SWT methods for $J_1=1$ and $J_2/J_1$ values given in the legend. (b) Calculated change of zone boundary energies at $(\pi ,0)$ and $(\pi /2,\pi /2)$ obtained from SE and SWT. The dashed horizontal line denotes the dispersion expected for the calculated ratio of ${\tilde{J}}_2/{\tilde{J}}_1=0.078$ and the horizontal lines either side show the corresponding uncertainty of $\pm 0.005$ in ${\tilde{J}}_2/{\tilde{J}}_1$.