Antipolar 2D Metallicity with Tunable Valence W^<i>x</i>+ (5 ≤ <i>x</i> ≤ 5.6) in the Layered Monophosphate Tungsten Bronzes [Ba(PO₄)₂]W_<i>m</i>O_{3<i>m–</i>3}

The newly discovered series of layered monophosphate tungsten bronzes (L-MPTB) [Ba(PO₄)₂]W<i>_m</i>O_3<i>m</i>-3 consist of <i>m</i>-layer-thick slabs of WO6 octahedra separated by barium-phosphate spacers. They display a 2D metallic behavior confined in the central part of the perovskite slabs. Here, we report the missing <i>m</i> = 2 member of this series, containing the rather uncommon W5+ oxidation state. We have analyzed its structure-property relationships in relation to the other members of the L-MPTB family. In particular, we have determined its crystal structure by means of single-crystal X-ray and electron diffraction and investigated its physical properties from resistivity, Seebeck-coefficient and heat-capacity measurements combined with first-principles calculations. All the L-MPTB compounds show metallic behavior down to 1.8 K without any clear charge-density-wave (CDW) order. The <i>m</i> = 2 member, however, displays an increased influence of the spacer that translates into anisotropic negative thermal expansion, reversed thermopower and reversed crystal-field splitting of the tungsten t_2g orbitals. Our analysis of the full [Ba(PO₄)₂]W<i>_m</i>O_3<i>m</i>-3 series reveals a systematic and significant W off-centering in their octahedral coordination. We identify the resulting anti-polar character of these W displacements as the crucial aspect behind the 2D metallicity of these systems: It leads to the presence of bound charges whose screening determines the distribution of mobile charges, tending to accumulate at the center of the [W_<i>m</i>O_3-<i>m</i>] block. We argue that this mechanism is analogous to enhanced conductivity observed for charged domain walls in ferroelectrics, thus providing a general design rule to promote 2D metallicity in layered systems.