Carrier-Density-Induced Ferromagnetism in ${\mathrm{EuTiO}}_3$ Bulk and Heterostructures

${\mathrm{EuTiO}}_3$ is an antiferromagnetic (AFM) material showing strong spin-lattice interactions, large magnetoelectric response, and quantum paraelectric behavior at low temperatures. Using electronic-structure calculations, we show that adding electrons to the conduction band leads to ferromagnetism. The transition from antiferromagnetism to ferromagnetism is predicted to occur at $\sim 0.08\mathrm{electrons}/\mathrm{Eu}$ ($\sim 1.4\times {10}^{21}{\mathrm{cm}}^{-3}$). This effect is also predicted to occur in heterostructures such as ${\mathrm{LaAlO}}_3/{\mathrm{EuTiO}}_3$, where ferromagnetism is triggered by the formation of a high-density two-dimensional electron gas in the ${\mathrm{EuTiO}}_3$. Our analysis indicates that the coupling between Ti $3d$ and Eu $5d$ plays a crucial role in lowering the Ti $3d$ conduction band in the ferromagnetic (FM) phase, leading to an almost linear dependence of the energy difference between the FM and AFM ordering on the carrier concentration. These findings open up possibilities in designing field-effect transistors using ${\mathrm{EuTiO}}_3$-based heterointerfaces to probe fundamental interactions between highly localized spins and itinerant, polarized charge carriers.

Figure 1

Total-energy difference between the FM and $G$-AFM orderings, and first and second nearest-neighbor exchange constants, $J_1$ and $J_2$, as a function of carrier concentration in ${\mathrm{EuTiO}}_3$.

Figure 2

Ball and stick model of the 20-atom unit cell of ${\mathrm{EuTiO}}_3$ seen (a) from the [001] direction with antiphase rotations of oxygen octahedra around the $c$ axis; (b) perspective view of the $G$-AFM ordering.

Figure 3

Electronic band structures of ${\mathrm{EuTiO}}_3$ for (a) $G$-type AFM ordering, and (b) FM ordering. The zero in the energy axis was set to the top of the occupied Eu-$4f$ band.

Figure 4

Density of states projected on Eu-$4f$ orbitals (blue), Eu-$5d$ orbitals (green), Ti-$3d$ orbitals (red), and O-$2p$ orbitals (black), and the derived interband coupling diagrams for the (a) $G$-type AFM and (b) FM ordering of undoped ${\mathrm{EuTiO}}_3$. In the interband coupling diagrams, the solid curvy arrows indicate the most relevant couplings. The exchange splitting in the O-$2p$ bands and Ti-$3d$ bands are enlarged for ease of representation. The zero in the energy axis was set to the maximum of the occupied Eu-$4f$ band.

Figure 5

(a) Formation of a 2DEG at the ${\mathrm{LaAlO}}_3/{\mathrm{EuTiO}}_3(001)$ interface with a $\mathrm{LaO}\text{−}{\mathrm{TiO}}_2$ termination. (b) Band alignment at the ${\mathrm{LaAlO}}_3/{\mathrm{EuTiO}}_3$. (c) Distribution of the charge carriers in the ${\mathrm{LaAlO}}_3/{\mathrm{EuTiO}}_3(001)$ superlattice with two equivalent $\mathrm{LaO}\text{−}{\mathrm{TiO}}_2$ interfaces, with the isosurface set to 20% of the maximum value. (d) Planar-averaged excess charge as a function of the distance along the $c$ axis of the superlattice in (c), showing excess charge accumulation in the ${\mathrm{EuTiO}}_3$.