Predicting two-dimensional electron gas mediated magnetoelectric coupling at ferroelectric PbTiO$_{3}$/SrTiO$_{3}$ heterostructure

We predict the emergence of interfacial ferromagnetism in the two-dimensional electron gas (2DEG) at the ferroelectric PbTiO$_{3}$/SrTiO$_{3}$ heterostructure from first principles calculations. Free electrons provided by naturally existing oxygen vacancies in SrTiO$_{3}$ are driven to the heterostructure interface under the polarizing electric field of ferroelectric PbTiO$_{3}$. These spin-polarized electrons are captured by interfacial Ti atoms, forming a 2DEG, which surprisingly exhibits ferromagnetism even at room temperature, once the density of 2DEG reaches a relatively small critical value of $\sim$60 $\mu$C/cm$^2$. This critical value can be easily achieved in practice. The ferroelectricity-controlled ferromagnetism mediated by 2DEG via interface shows exceptional magnetoelectric coupling strength several times larger than that of other systems, which enables us to control the magnetism by electric field conveniently. Besides, the PbTiO$_{3}$/SrTiO$_{3}$ heterostructure is cheap, easy-growing and controllable, facilitating great promising applications in low cost spintronics and information storage at room temperature.