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    A<sub>2</sub>MnXO<sub>4</sub> Family (A = Li, Na, Ag; X = Si, Ge): Structural and Magnetic Properties

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    Four new manganese germanates and silicates, A<sub>2</sub>MnGeO<sub>4</sub> (A = Li, Na) and A<sub>2</sub>MnSiO<sub>4</sub> (A = Na, Ag), were prepared, and their crystal structures were determined using the X-ray Rietveld method. All of them contain all components in tetrahedral coordination. Li<sub>2</sub>MnGeO<sub>4</sub> is orthorhombic (<i>Pmn</i>2<sub>1</sub>) layered, isostructural with Li<sub>2</sub>CdGeO<sub>4</sub>, and the three other compounds are monoclinic (<i>Pn</i>) cristobalite-related frameworks. As in other stuffed cristobalites of various symmetry (<i>Pn</i> A<sub>2</sub>MXO<sub>4</sub>, <i>Pna</i>2<sub>1</sub> and <i>Pbca</i> AMO<sub>2</sub>), average bond angles on bridging oxygens (here, Mn–O–X) increase with increasing A/X and/or A/M radius ratios, indicating the trend to the ideal cubic (<i>Fd</i>3̅<i>m</i>) structure typified by CsAlO<sub>2</sub>. The sublattices of the magnetic Mn<sup>2+</sup> ions in both structure types under study (<i>Pmn</i>2<sub>1</sub> and <i>Pn</i>) are essentially the same; namely, they are pseudocubic eutaxy with 12 nearest neighbors. The magnetic properties of the four new phases plus Li<sub>2</sub>MnSiO<sub>4</sub> were characterized by carrying out magnetic susceptibility, specific heat, magnetization, and electron spin resonance measurements and also by performing energy-mapping analysis to evaluate their spin exchange constants. Ag<sub>2</sub>MnSiO<sub>4</sub> remains paramagnetic down to 2 K, but A<sub>2</sub>MnXO<sub>4</sub> (A = Li, Na; X = Si, Ge) undergo a three-dimensional antiferromagnetic ordering. All five phases exhibit short-range AFM ordering correlations, hence showing them to be low-dimensional magnets and a magnetic field induced spin-reorientation transition at <i>T</i> < <i>T</i><sub>N</sub> for all AFM phases. We constructed the magnetic phase diagrams for A<sub>2</sub>MnXO<sub>4</sub> (A = Li, Na; X = Si, Ge) on the basis of the thermodynamic data in magnetic fields up to 9 T. The magnetic properties of all five phases experimentally determined are well explained by their spin exchange constants evaluated by performing energy-mapping analysis
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