Electric-Field Control of Magnetization, Jahn-Teller Distortion, and Orbital Ordering in Ferroelectric Ferromagnets

Controlling the direction of the magnetization by an electric field in multiferroics that are both ferroelectric and strongly ferromagnetic will open the door to the design of the next generation of spintronics and memory devices. Using first-principles simulations, we report that the discovery that the ${\mathrm{PbTiO}}_3/\mathrm{LaTi}{\mathrm{O}}_3$ ($\mathrm{PTO}/\mathrm{LTO}$) superlattice possesses such highly desired control, as evidenced by the electric-field-induced rotation of 90° and even a possible full reversal of its magnetization in some cases. Moreover, such systems also exhibit Jahn-Teller distortions, as well as orbital orderings, that are switchable by the electric field, therefore making $\mathrm{PTO}/\mathrm{LTO}$ of importance for the tuning of electronic properties too. The origin for such striking electric-field controls of magnetization, Jahn-Teller deformations, and orbital orderings resides in the existence of three different types of energetic coupling: one coupling polarization with antiphase and in-phase oxygen octahedral tiltings, a second one coupling polarization with antiphase oxygen octahedra tilting and Jahn-Teller distortions, and finally a biquadratic coupling between antiphase oxygen octahedral tilting and magnetization.

Figure 1

Geometry and major structural distortions of the ground state of the studied $\mathrm{PTO}/\mathrm{LTO}$ superlattice. (a) Polarization distortion $P$ about the in-plane $\mathbf{a}$ axis ([$-110$] direction). (b) Antiphase oxygen octahedral rotations ${\mathrm{\Phi }}_{xy}$ about the in-plane $\mathbf{a}$ axis ([110] direction). (c) In-phase oxygen octahedral rotations ${\mathrm{\Theta }}_z$ about the out-of-plane $\mathbf{c}$ axis ([001] direction). (d) $Q$ Jahn-Teller lattice distortion.

Figure 2

Dependence on the total energy on amplitude of distortion in the investigated $\mathrm{PTO}/\mathrm{LTO}$ superlattice. (a) Energy with respect to the amplitude of the main four lattice distortions, $P$, ${\mathrm{\Phi }}_{xy}$, ${\mathrm{\Theta }}_z$, and $Q_z$. (b) Energies as a function of amplitude of $P$ when fixing ${\mathrm{\Phi }}_{xy}$ and ${\mathrm{\Theta }}_z$ (black squares), as well as those when fixing ${\mathrm{\Phi }}_{xy}$, ${\mathrm{\Theta }}_z$, and $Q_z$ (red circles), to their values in the ground state.

Figure 3

(a),(b) Physical quantities as a function of the electric field applied along $-\mathbf{b}$, i.e., perpendicular to the initial direction of the polarization, and (c),(d) applied along $\mathbf{a}$, i.e., antiparallel to the initial direction of the polarization, in the studied $\mathrm{PTO}/\mathrm{LTO}$ superlattice. (a) Energy difference between ferromagnetic configurations along $\mathbf{a}$ and $\mathbf{b}$; oxygen octahedral tilting angles, ${\mathrm{\Phi }}_x$, ${\mathrm{\Phi }}_y$, and ${\mathrm{\Theta }}_z$; and polarization $\mathbf{P}$. (b) Schematization of the spin configurations on ${\mathrm{Ti}}^{3+}$ ions, which can be switched by 90° via the application of electric fields oriented along the $-\mathbf{b}$ axis or the $-\mathbf{a}$ axis. (c) JT distortion $Q$, and oxygen octahedral tilting angles and polarization. (d) Charge density of states near the Fermi level in energy range from $-0.5$ to 0 eV. The black open symbols in (a) and (c) represent the same quantities when the electric field is released.