Fig. 1: SrCu2(BO3)2 and the magnetic excitation spectrum under field-induced condensation. | Nature Communications

Fig. 1: SrCu2(BO3)2 and the magnetic excitation spectrum under field-induced condensation.

From: Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 revealed by neutron scattering up to 25.9 T

Fig. 1

a Crystal structure of SrCu2(BO3)2 showing one layer of Cu2+ ions (half a unit cell along \(\hat{c}\)). b Representation of the superexchange couplings within ( J) and between (\({\;J}^{{\prime} }\)) the Cu-Cu dimers, which reproduce the Shastry-Sutherland model (SSM), and of the corresponding Dzyaloshinskii-Moriya (DM) interactions (\(\overrightarrow{D}\) and \({\overrightarrow{D}}^{{\prime} }\)). c, d Energy levels of a J1-J2 two-dimer cluster (inset in panel d) as a function of magnetic field. For J2 /J1 > 0 (c) the t+ one-triplon branch condenses first, whereas when J2 /J1 < 0 (d) the two-triplon bound state condenses first. The two scenarios result in distinctively different gradients after condensation. e Excitation spectra measured by inelastic neutron scattering (INS). Data at intermediate fields (4 − 12 T) were measured at Q = (1.5, 0.5, 0), as summarized in the Methods section. Data from our HFM/EXED measurements (0 T and ≥15 T) are presented with full momentum integration, as detailed in Sec. S1 of the Supplementary Information (SI). Colour contours represent the neutron intensity and symbols show the fitted positions of individual excitations (Fig. 2g–l) with the uncertainties in the mode positions estimated from the corresponding fitting errors. Solid grey lines show the locations of the one-triplon branches in SrCu2(BO3)2 for a scenario of one-triplon condensation and no DM interactions (analogous to panel c), dashed black lines for two-triplon condensation (analogous to panel d). The dashed green line shows the Sz = 0 branch of the S = 1 multiplet within the two-triplon bound state. The solid red line up to 15 T shows the lowest Sz = 2 branch of the S = 2 multiplet observed by electron spin resonance (ESR)33, and its extension to higher fields is our linear extrapolation. The dashed red line marks the estimated position of the absolute lowest Sz = 2 branch, based on our observation that the change in the one-triplon gradient occurs at 21 T. f Corresponding total momentum-integrated spectral functions obtained from MPS calculations on the SSM for SrCu2(BO3)2, meaning including DM interactions; overlaid are the solid grey and dashed black lines from panel e (i.e. without DM interactions).

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