On the Importance of the Interplaquette Spin Exchanges in Na3RuO4: Density Functional Theory Analysis of the Spin Exchange and Magnetic Properties

Na3RuO4 contains layers of high-spin Ru5+ d(3) ions grouped into isolated four-membered plaquettes, To determine the spin-lattice appropriate for Na3RuO4, we evaluated the intraplaquette exchanges J(1), J(2), and J(3) as well as the interplaquette exchanges J(4) and J(5) by performing mapping analysis based on first-principles density functional theory calculations. In addition, we examined how the trends in the calculated J(1)-J(5) are related to the distortions of the RuO6 octahedra in the four-membered plaquettes. The spin-lattice of Na3RuO4 is described by the intraplaquette exchanges J(1) and J(2) plus the interplaquette exchanges J(4) and J(5), with spin frustration arising from the (J(1), J(2), J(1)) and (J(5), J(4), J(5)) triangles. The trends in the calculated J(1)-J(5) reflect the distortions of the RuO6 octahedra in the four-membered plaquettes.