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Effect of internal electric field on ferroelectric polarization in multiferroic TbMnO$_3$

Pyro-current measurements have been widely used to study ferroelectric properties in multiferroic materials. However, determination of intrinsic polarization by this method is not straightforward because of leakage current and trapped charge carriers. Here, we demonstrate the formation of internal electric field due to thermally stimulated charge carriers and its influence on ferroelectric polarization in a polycrystalline sample of the well known multiferroic TbMnO$_3$. While an electric field ($E_{ext}$) poling across the ferroelectric transition ($T_C$ $\sim$ 26 K) is essential to obtain depolarization current at $T_C$, the sample poled only in the paraelectric state ($T_{pole}$ = 130 $-$ 50 K) also exhibits a pyro-current peak at $T_C$ but with the same polarity ($-$ $I_{pyro}$) as that of the external field ($-$ $E_{ext}$). We demonstrate that these unusual behavior of pyro-current are caused by a positive internal electric field ($+$ $E_{int}$) which in turn is created by thermally stimulated free charge carriers during the poling process in the paraelectric state. We also show that a combination of DC-biased current and pyro-current measurements is a promising method to study the intrinsic ferroelectric properties in multiferroic materials.