Unusually strong Stark effect in electronic ferroelectric Er$_{1-x}$Yb$_{x}$Fe$_{2}$O$_{4}$

Strong Stark splitting, which is nearly independent of the R-ions replacement, has been observed through the photoluminescence investigation of electronic ferroelectric Er$_{1-x}$Yb$_{x}$Fe$_{2}$O$_{4 }$(x=0, 0.8, 0.9, and 0.95). Initially multiple radiative decay channels have been investigated, especially the visible transition $^{4}F_{9/2}\to ^{4}I_{15/2}$, of which a quenching effect has been observed. A series of small non-Raman peaks have been observed superimposed on a broadband photoluminescence spectrum, of which we tentatively assign Stark splitting to be the cause. The splitting of the $^{4}F_{9/2}$ and $^{4}I_{15/2}$ levels is found to be 54 meV and 66 meV, respectively. This unusually large Stark splitting at visible range indicates the existence of strong local field originated from the W-layer in the charge-frustrated ErFe$_{2}$O$_{4}$.