Fig. 2
Distinct single-spin-cycloid configuration for each polarization state in the bulk of the BiFeO3 film. a, b Shows reciprocal space maps (RSMs) of magnetic (½,½,½) ±k ND peaks (k is the cycloid propagation vector) measured in the down state and the up state, respectively. The positions of three, ±k pairs of peaks, corresponding to the three magnetic domains observed in bulk single crystals, are superimposed as white circles. Below RSMs, a 1D slice through Q x = 0 (dotted black lines) from RSMs in which the peaks are fit (solid black lines) to determine the cycloid period λ. c, d Shows magnetic ND data measured from the down and up states, respectively. In the top and middle panels of both c, d the respective ±k satellites of the majority domain exactly overlap in d-spacing. In the panels of both c, d the ±k satellites are separated in d-spacing, as seen, and the symmetry equivalent (½,-½,½)pc ±k and (-½,½,½)pc ±k reflections are summed. Note that the crystallographic basis switches with the polarization such that, for example, the top panel of c and the middle panel of d are acquired with the same film orientation in the diffractometer. The fit model is shown as a black line, in which the lattice parameters, propagation vector, peak profile parameters, background, ferroelastic domain populations, and the tilt angle of the cycloidal plane were refined. ND identifies a single-cycloid plane lying 12° from in-plane in the down state that rotates to almost in-plane in the up state with the same sense of the polarization switching (inset of c, d). The dotted green lines are the magnetic ND intensity simulations of the bulk BiFeO3 single-crystal spin-cycloid plane. The additional weak peaks in the panels for (½,½,½) ±k and (½,½,-½) ±k in d (up state) originate from a minority ferroelastic domain. The bulk of BiFeO3 film refers to properties averaged over the entire film thickness, for which contributions from the near the interfaces are negligible. Error bars are given by \( \pm \sqrt N ,\) where N is the number of counts
