Tuning of magnetic frustration and emergence of a magnetostructural transition in Mn1−xCdxCr2O4

${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$ spinel series is engineered to host a controlled and wide-range tuning of magnetic frustration through a nonmagnetic ion (Cd) doping in ${\mathrm{MnCr}}_{2}{\mathrm{O}}_{4}$ spinel oxide. While ${\mathrm{MnCr}}_{2}{\mathrm{O}}_{4}$ exhibits weak geometric magnetic frustration (GMF), the doping brings in an interplay between various competing magnetic-exchange interactions involving the Jahn-Teller inactive ${\mathrm{Cr}}^{3+}$($3d{}^{3}$) spins that lie on a frustrated pyrochlore lattice in cubic spinel oxide. Magnetic frustration is observed to be the maximum for the intermediate values of $\mathit{x}$ which are associated with large spin-relaxation times and an evolution in the nature of glassy spin dynamics. The dominant antiferromagnetic coupling between the Mn sites and Cr sites (which induces the intra-Cr-lattice spins to be nearly ferromagnetically coupled in $x=0)$ becomes weaker due to magnetic dilution of the Mn site by diamagnetic ${\mathrm{Cd}}^{2+}$ ions. As a result, the net interactions between ${\mathrm{Cr}}^{3+}$ ions in the pyrochlore lattice become antiferromagnetic beyond $x\ensuremath{\gtrsim}0.6$. This causes the associated GMF to become very large for $x\ensuremath{\gtrsim}0.6$. As a result, while the structure remains cubic till the lowest temperature for $0\ensuremath{\le}x\ensuremath{\le}0.60$, the appearance of strong GMF induces spin-driven magnetostructural transitions from a high-temperature cubic (paramagnetic) to a low-temperature tetragonal (and antiferromagnetic) phase. The obtained results demonstrate a direct link between GMF and spin-lattice coupling and provide a road map to design compounds with engineered magnetostructural transitions associated with large spin-lattice coupling.