Ferroelectric-ferromagnetic coupling in hexagonal YMnO$_{3}$ film.

Simultaneously achieving ferroelectricity and ferromagnetism in a single phase material is an important research topic in recent decades. Here, we demonstrate that with the modulation of oxygen vacancies, the ferroelectric-ferromagnetic coupling can be realized in the typical hexagonal manganite: YMnO$_{3}$. The first-principal calculations are used to reveal the importance of oxygen vacancies on the alterations of magnetic behaviors for YMnO$_{3}$. In order to obtain net magnetic moments, the on-top oxygen vacancies of MnO$_{5}$ clusters should be created, thus the initial 2D spin frustration structure of Mn ions will be broken. By growing YMnO$_{3}$ film on Al$_{2}$O$_{3}$ substrate, large in-plane compressive strain is induced, thus we can experimentally realize the on-top oxygen vacancies. With the help of SQUID and spherical aberration corrected TEM, the magnetic moments are experimentally measured and the correlations between the crystal structures and magnetic properties can be clearly understood. Our findings may pave a way for future applications of single phase multiferroic materials.