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Crystal structure, electronic structure, and magnetic behavior of thespin-1/2 quantum magnet Na1.5VOPO4F0.5 are reported. The disorder of Na atomsleads to a sequence of structural phase transitions revealed by synchrotronx-ray powder diffraction and electron diffraction. The high-temperaturesecond-order alpha <--> beta transition at 500 K is of the order-disorder type,whereas the low-temperature beta <--> gamma+gamma' transition around 250 K isof the first order and leads to a phase separation toward the polymorphs withlong-range (gamma) and short-range (gamma') order of Na. Despite the complexstructural changes, the magnetic behavior of Na1.5VOPO4F0.5 probed by magneticsusceptibility, heat capacity, and electron spin resonance measurements is welldescribed by the regular frustrated square lattice model of thehigh-temperature alpha-polymorph. The averaged nearest-neighbor andnext-nearest-neighbor couplings are J1 ~ -3.7 K and J2 ~ 6.6 K, respectively.Nuclear magnetic resonance further reveals the long-range ordering below TN =2.6 K in low magnetic fields. Although the experimental data are consistentwith the simplified square-lattice description, band structure calculationssuggest that the ordering of Na atoms introduces a large number of inequivalentexchange couplings that split the square lattice into plaquettes. Additionally,the direct connection between the vanadium polyhedra induces an unusuallystrong interlayer coupling having effect on the transition entropy and thetransition anomaly in the specific heat. Peculiar features of thelow-temperature crystal structure and the relation to isostructural materialssuggest Na1.5VOPO4F0.5 as a parent compound for the experimental study oftetramerized square lattices as well as frustrated square lattices withdifferent values of spin.

Phase separation and frustrated square lattice magnetism of Na1.5VOPO4F0.5