Fig. 2

Magnetic spectrum along the MnO bond directions. (a) at \(T<T_{co}\) E(q) branches of the magnetic spectrum adapted from Ref.¹³ showing a dip at \(q=7/16\) rlu in the \(E=LA\) and \(E=LO\) branches corresponding to the “in-plane” magnetic fluctuations. The upper energy branch occurring at \(E=LO'\) at \(T<T_{co}\) has been omitted for clarity. (b) Quadratic law \(Dq^2\) measured at T=150K (blue circles) adapted from Ref.¹¹ showing an energy gap at \(q=1/8\) rlu outlined by an arrow and compared to the \(Dq^2\) measured at T=169K (red circles). (c) Maximum of energy observed at \(q=0.45\) rlu in the upper energy branches of the magnetic fluctuations. The \(q'\) scale is defined by \(q'=(0.83)^{-1}q\) (see the text). The E(0) branch, also observed in lattice excitations, but not displayed, can be attributed to a binding energy of the bipolaron to the lattice²⁹. \(\Gamma\) is the energy line-width.