Fig. 2: Electric field control of magnons in Bi_0.85La_0.15FeO₃.

a Nonlocal magnon-transport measurement scheme in Bi_0.85La_0.15FeO₃ with Pt as a source/detector for spin-charge interconversion via magnon-transport. A resistive circuit schematic of in-plane devices where R_Pt is the resistance of Pt electrodes, and C is the capacitance of Bi_0.85La_0.15FeO₃, where the electric field is mainly distributed. The spin cycloid propagation vector k is set by the Bi_0.85La_0.15FeO₃ polarization, which is controlled by an external in-plane electric field (E). The coordinate system uses pseudocubic notations. b Polarization and quasi-static magnon hysteresis as a function of external electric field. The blue line represents the polarization as measured by a Radiant Technologies ferroelectric test system (right axis) and the red circles correspond to the non-local ISHE voltage raw data (left axis). Error bars in ISHE voltage represent the standard statistical variation of lock-in voltages from the least-squares analysis measured over 150 s. c, d The corresponding PFM images after electrical poling in two opposite directions (labeled by labeled by `1' and `2' in (b)). PFM images were recorded in the same area, as marked by the rectangles. The scale bar is 2 μm. Bright and dark contrast arises from single ferroelectric domains between the Pt electrodes. Arrows represent the direction of the electric field `E' and corresponding polarization `P' in a single domain. e Differential voltage (ΔV_ISHE) recorded in [010] devices as a function of the power injected into the source. Each data point is presented after averaging out to 150 s. The Bi_0.85La_0.15FeO₃ data presented were recorded in several devices (represented as D) with the same orientation and compared with the non-local voltage data belonging to the BiFeO₃ (100 nm)/Pt(6 nm) with the spacing of 2 μm. The data is reproduced from ref. ¹⁷ and corresponds to a metal electrode spacing of 1 μm. In the case of BiFeO₃, the ferroelectric domains were stripes whereas Bi_0.85La_0.15FeO₃ data was recorded in a ferroelectric single domain state. Lines are linear fit to the data.