Origin of correlated diffuse scattering in the hexagonal manganites

We use a combination of first-principles density-functional calculations and spin-dynamics simulations to explain the unusual diffuse inelastic neutron scattering in the hexagonal multiferroic yttrium manganite, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>YMnO</a:mi><a:mn>3</a:mn></a:msub></a:math>. Using symmetry considerations, we construct a model spin Hamiltonian with parameters derived from our density-functional calculations and show that it captures the measured behavior. We then show that the observed directionality in the structured diffuse scattering in momentum space is a hallmark of the triangular geometry, and that its persistence across a wide range of temperatures, both above and below the Néel temperature <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>T</b:mi><b:mi>N</b:mi></b:msub></b:math>, is a result of the strong magnetic frustration. We predict that this diffuse scattering exists in a yet-to-be-observed modulated continuum of energies, that its associated spin excitations have distinct in-plane and out-of-plane character, and that vestiges of the magnetic frustration persist into the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>sub</c:mi><c:mtext>−</c:mtext><c:msub><c:mi>T</c:mi><c:mi>N</c:mi></c:msub></c:mrow></c:math> state. Finally, we show that visualizing the magnetic order in terms of composite trimer magnetoelectric monopoles and toroidal moments, rather than individual spins, provides insight into the real-space fluctuations, revealing clusters of emerging order in the paramagnetic state, as well as collective short-range excitations in the ordered antiferromagnetic phase. Our understanding of this directional diffuse scattering in such a wide temperature range, both below and above <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>T</d:mi><d:mi>N</d:mi></d:msub></d:math>, provides new insight into the magnetic phase transitions in classical frustrated systems. Published by the American Physical Society 2024