Magnetic properties and electronic structure of Cr$_2$(Te$_{\mathrm{1-x}}$W$_{x})$O$_6$

We report magnetic properties of Cr$_{2}$(Te$_{\mathrm{1-x}}$W$_{x})$O$_{6}$ system combining neutron powder diffraction measurements and first principles electronic structure calculations. Both the end members possess an ordered inverse-trirutile structure, in which there are bilayers of Cr-O separated by a W(Te)-O layer, yet Cr$_{2}$TeO$_{6}$ and Cr$_{2}$WO$_{6}$ display distinct magnetic structures and antiferromagnetic transition temperatures: $T_{\mathrm{N}}$ $\sim$ 92 K for Cr$_{2}$TeO$_{6}$ with antiferromagnetic spin alignment within bilayers, while $T_{\mathrm{N}}$ $\sim$ 45 K for Cr$_{2}$WO$_{6}$ with spins aligned ferromagnetically within the bilayer. Spins belonging to neighboring bilayers are antiferromagnetically coupled for both the compounds. For the mixed system Cr$_{2}$(Te$_{\mathrm{1-x}}$W$_{x})$O$_{6}$, both $T_{\mathrm{N}}$ and sublattice magnetization ($M_{\mathrm{s}}$) reach a minimum ($T_{\mathrm{N}}$ $\sim$ 0 K) for $x$ $\sim$ 0.6, suggesting the existence of a quantum critical point. Electronic structure calculations using \textit{ab initio} density functional theory correctly give the ground state spin configurations for the end compounds (x$=$0,1). We suggest that unoccupied W 5d states play a key role in intra-bilayer ferromagnetic ordering seen in the x$=$1 system.