  Two-dimensional (2D) multiferroics are key candidate materials towards
advancement of smart technology. Here, we employed a simple synthesis approach
to address the long-awaited dream of developing ferroelectric and multiferroic
2D materials, specially in the new class of materials called MXenes. The etched
Ti$_3$C$_2$T$_x$ MXene was first synthesized after HF-treatment followed by
delamination process for successful synthesis of free-standing Ti$_3$C$_2$T$_x$
film. The free-standing film was then exposed to air at room-temperature as
well as heated at different temperature to form TiO$_2$ layer derived from the
Ti$_3$C$_2$T$_x$ MXene itself. TiO$_2$ is reported to be an incipient
ferroelectric that assumes a ferroelectric phase in composite form. The
structural and morphological analysis confirmed successful synthesis of
free-standing film and the Raman spectroscopy revealed the formation of
different phases of TiO$_2$. The ferroelectric measurement showed a clear
polarization hysteresis loop at room-temperature. Also, the magnetic hysteresis
was observed in the film indicating a possibility of coupling between
ferroelectric and ferromagnetic phases at room-temperature. The magnetoelectric
coupling test was also performed that showed a clear, switchable spontaneous
polarization under applied magnetic field. This is the first report on
existence of ferroelectric phase and multiferroic coupling in 2D free-standing
MXene film at room-temperature which opens-up possibility of 2D materials-based
electric and magnetic data storage applications at room-temperature.
