Controlling the electrical and magnetic ground states by doping in the complete phase diagram of titanate ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ thin films

${\mathrm{EuTiO}}_3$, a band insulator, and ${\mathrm{LaTiO}}_3$, a Mott insulator, are both antiferromagnetic with transition temperatures ∼5.5 and ∼160 K, respectively. Here, we report the synthesis of ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ thin films with $x=0$ to 1 by oxide molecular beam epitaxy. The films in the full range have high crystalline quality and show no phase segregation, allowing us to carry out transport measurements to study their electrical and magnetic properties. From $x=0.03$ to 0.95, ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ films show conduction by electrons as charge carriers, with differences in carrier densities and mobilities, contrary to the insulating nature of pure ${\mathrm{EuTiO}}_3$ and ${\mathrm{LaTiO}}_3$. Following a rich phase diagram, the magnetic ground states of the films vary with increasing La-doping level, changing ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ from an antiferromagnetic insulator to an antiferromagnetic metal, a ferromagnetic metal, a paramagnetic metal, and back to an antiferromagnetic insulator. These emergent properties reflect the evolutions of the band structure, mainly at the Ti $t_{2\mathrm{g}}$ bands near the Fermi level, when ${\mathrm{Eu}}^{2+}$ are gradually replaced by ${\mathrm{La}}^{3+}$. This work sheds light on this method for designing the electrical and magnetic properties in strongly correlated oxides and completes the phase diagram of the titanate ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$.

Figure 1

(a) Schematic density of states of ${\mathrm{EuTiO}}_3$ ($x=0$) and ${\mathrm{LaTiO}}_3$ ($x=1$), where UHB and LHB are defined as upper and lower Hubbard band, respectively. (b) Reflection high-energy electron diffraction (RHEED) oscillations during the growth showing the layer-by-layer growth of atomically smooth films. (c)–(e) RHEED images of 10 unit cell (uc) ${\mathrm{EuTiO}}_3$, ${\mathrm{Eu}}_{0.5}{\mathrm{La}}_{0.5}{\mathrm{TiO}}_3$, and ${\mathrm{LaTiO}}_3$ films, respectively.

Figure 2

(a) AFM image of an uncapped 10 uc ETO film surface. (b) Line profile of the dashed region in (a) showing step and terrace structure, with ∼4 Å = 1 ETO unit cell. (c) Symmetric XRD scans of 10 uc ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ (ELTO) films around the (001) peak, ♦ at 2θ = 22.99° and ★ near 2θ ∼22° are peaks from the LSAT substrate and ELTO films, respectively. (d) The normalized ratio of film in- and out-of-plane lattice parameters $a$ and $c$ as a function of substitution level $x$ (Purple: $a_{\mathrm{ELTO}}$/$a_{\mathrm{LSAT}}$; Red: $c_{\mathrm{ELTO}}$/$a_{\mathrm{LSAT}}$.). The fitting and error bars of the $a$ axis are obtained from the line spacing and its standard deviation between diffracted spots in the RHEED image. The fitting and the error bars of $c$ axis are obtained from XRD spectra with the error bars smaller than the symbols.

Figure 3

(a) The resistivity vs $T^2$ and $T$ for different substitution level $x$, where ${\rho }_{\mathrm{RT}}$ is resistivity at 300 K. Inset: insulating behavior of $x=0$, 0.01, 0.97, and 1. (b) The resistivity vs $x$ at 3 and 300 K. (c) Kinks present in $\rho$ vs $T$ (d) Charge carrier density $n$ (left axis, red circle) and mobility μ (right axis, green triangle) versus $x$ at 3 K. $n$ are extracted from the Hall measurement under perpendicular B field in ± 7 T at 3 K, and are constant between 3 and 20 K. The purple dashed line indicates 100% activated carrier density from the assumption that each La substitution supplies one electron. (e) Coefficient of the $A{T}^2$ resistivity versus carrier density $n$. The dashed line is a guide to the eye for $A\propto n^{-1}$ from the three-band model [31].

Figure 4

(a) Magnetoresistance $R_{xx}$ vs $B$ at 3 K measured under perpendicular B-field swept from 7 to −7 T and back at 3 K. (b) Zoomed in data around zero magnetic field, ± 0.6 T for $x=0.1$ and 0.3. (c) Anomalous Hall effect (AHE) ${\rho }_{\mathrm{AHE}}$ extracted from conventional Hall measurement (${\rho }_{\mathrm{xy}}-{\rho }_{\mathrm{Hall}}$). ${\rho }_{\mathrm{AHE}}$ is saturated after 3 T in all samples. Inset: zoomed in data for $x=0.3$ near zero magnetic field. (d) Saturated anomalous Hall resistivity (${\rho }_{\mathrm{AHE}}^{\mathrm{s}}$) as a function of charge carrier density. The dashed line is a guide to eye. Inset: The relation between anomalous Hall conductivity (${\sigma }_{\mathrm{AHE}}^{\mathrm{s}}$) and longitudinal conductivity (${\sigma }_{\mathrm{xx}}$). The blue dashed line shows the relation ${\sigma }_{\mathrm{AHE}}^{\mathrm{s}}\propto {\sigma }_{\mathrm{xx}}^{1.6}$ indicating the Berry phase mechanism for AHE. The data with symbols ⊡ is taken from Ref. [17].

Figure 5

Phase diagram of ELTO for its metallic and magnetic phase. Each colored region indicates a different metallic/magnetic phase. AFI, AFM, FM, and PM represent antiferromagnetic insulator, antiferromagnetic metal, ferromagnetic metal, and paramagnetic metal, respectively. The symbol F indicates published FM phase data that fall outside the FM region reported here. Filled symbols and empty symbols represent the result from thin films and single crystal, respectively. The $T_{\mathrm{C}}$ with error bar in $x=0.5$ is extracted from the change of magnetoresistance in several temperatures.