Geometrical frustration and incommensurate magnetic order in Na$_3$RuO$_4$ with two triangular motifs

TL;DR

This study reveals incommensurate magnetic order in Na$_3$RuO$_4$ driven by geometrical frustration, with neutron diffraction and ab initio calculations showing complex interactions among layered tetramers on a triangular lattice.

Contribution

It uncovers the incommensurate magnetic structure in Na$_3$RuO$_4$ and highlights the role of long-range couplings and geometrical frustration in its magnetic ordering.

Findings

Incommensurate magnetic order with propagation vector (0.242, 0, 0.313).

Tetramers form a frustrated triangular lattice.

Long-range Ru-O-O-Ru couplings influence magnetic structure.

Abstract

Incommensurate magnetic order in the spin-3/2 antiferromagnet Na$_3$RuO$_4$ is uncovered by neutron diffraction combined with ab initio calculations. The crystal structure of Na$_3$RuO$_4$ contains two triangular motifs on different length scales. The magnetic Ru$^{5+}$ ions form a lozenge (diamond) configuration, with tetramers composed of two isosceles triangles. These tetramers are further arranged in layers, such that an effective triangular lattice is formed. The tetramers are nearly antiferromagnetic but frustration between them leads to an incommensurately modulated magnetic structure described by the propagation vector $\vec{k}=(0.242(1), 0, 0.313(1))$. We show that the long-range Ru-O-O-Ru couplings between the tetramers play a major role in Na$_3$RuO$_4$ and suggest an effective description in terms of the spatially anisotropic triangular lattice if the tetramers are treated as single sites.