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Phase separation and frustrated square lattice magnetism of Na<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:msub></mml:math>VOPO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>4</mml:mn></mml:msub></mml:math>F<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow…
Crystal structure, electronic structure, and magnetic behavior of the spin-$\frac{1}{2}$ quantum magnet Na${}_{1.5}$VOPO${}_{4}$F${}_{0.5}$ are reported. The disorder of Na atoms leads to a sequence of structural phase transitions revealed by synchrotron x-ray powder diffraction and electron diffraction. The high-temperature second-order $\ensuremath{\alpha}\ensuremath{\leftrightarrow}\ensuremath{\beta}$ transition at 500 K is of the order-disorder type, …