Exchange-driven Magnetism and Spin Dynamics in Pyroxenes: Insights from NaFeSi₂O₆

The natural mineral aegirine NaFeSi₂O₆, which exhibits multiferroic properties, is of interest for both applied and fundamental physics. Magnetism in pyroxenes arises from competing intra- (J) and interchain (J₁, J₂) exchanges that stabilize a variety of commensurate and incommensurate states. Using NaFeSi₂O₆ as a model system, we investigate this interplay through inelastic neutron scattering and magnetization measurements in magnetic fields up to 8 T and 35 T. The incommensurate helical ground state remains robust, with no metamagnetic transitions observed and only gradual spectral changes under field. A phase diagram constructed in terms of the exchange ratios J₁/J and J₂/J captures the transition between commensurate and incommensurate regimes and unifies magnetic behavior across different pyroxenes. Despite structural variations (C2/c vs P2₁/c), the exchange topology and resulting magnetic frustration are closely related. These results establish NaFeSi₂O₆ as a benchmark for understanding exchange-driven magnetism and field-stable spin dynamics in pyroxenes with three-dimensional magnetic coupling.