Incommensurate atomic and magnetic modulations in the spin-frustrated {\beta}-NaMnO2 triangular lattice
Fabio Orlandi, Eleni Aza, Ioanna Bakaimi, Klaus Kiefer, Bastian, Klemke, Andrej Zorko, Denis Ar\v{c}on, Christopher Stock, George D. Tsibidis,, Mark A. Green, Pascal Manuel, and Alexandros Lappas

TL;DR
This study reveals complex incommensurate atomic and magnetic modulations in {eta}-NaMnO2, demonstrating the coexistence of multiple magnetic phases and the importance of superspace symmetry in understanding its structure and magnetic properties.
Contribution
It introduces a superspace symmetry model to accurately describe the incommensurate structure and uncovers the coexistence of collinear and modulated magnetic orders in {eta}-NaMnO2.
Findings
Incommensurate structural modulation with q= (0.077, 0, 0)
Two magnetic transitions at 200 K and 95 K with different magnetic orders
Magnetic excitation spectrum exhibits a spin gap of about 5 meV
Abstract
The layered {\beta}-NaMnO2, a promising Na-ion energy-storage material has been investigated for its triangular lattice capability to promote complex magnetic configurations that may release symmetry restrictions for the coexistence of ferroelectric and magnetic orders. The complexity of the neutron powder diffraction patterns underlines that the routinely adopted commensurate structural models are inadequate. Instead, a single-phase superspace symmetry description is necessary, demonstrating that the material crystallizes in a compositionally modulated q= (0.077(1), 0, 0) structure. Here, Mn3+ Jahn-Teller distorted MnO6 octahedra form corrugated layer stacking sequences of the {\beta}-NaMnO2 type, which are interrupted by flat sheets of the {\alpha}-like oxygen topology. Spontaneous long-range collinear antiferromagnetic order, defined by the propagation vector k= (1/2, 1/2, 1/2),…
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