Carrier-Controlled Ferromagnetism in ${\mathrm{SrTiO}}_3$

Magnetotransport and superconducting properties are investigated for uniformly La-doped ${\mathrm{SrTiO}}_3$ films and ${\mathrm{GdTiO}}_3/{\mathrm{SrTiO}}_3$ heterostructures, respectively. ${\mathrm{GdTiO}}_3/{\mathrm{SrTiO}}_3$ interfaces exhibit a high-density 2D electron gas on the ${\mathrm{SrTiO}}_3$ side of the interface, while, for the ${\mathrm{SrTiO}}_3$ films, carriers are provided by the dopant atoms. Both types of samples exhibit ferromagnetism at low temperatures, as evidenced by a hysteresis in the magnetoresistance. For the uniformly doped ${\mathrm{SrTiO}}_3$ films, the Curie temperature is found to increase with doping and to coexist with superconductivity for carrier concentrations on the high-density side of the superconducting dome. The Curie temperature of the ${\mathrm{GdTiO}}_3/{\mathrm{SrTiO}}_3$ heterostructures scales with the thickness of the ${\mathrm{SrTiO}}_3$ quantum well. The results are used to construct a stability diagram for the ferromagnetic and superconducting phases of ${\mathrm{SrTiO}}_3$.

Popular Summary

Letting two insulating oxides, such as $\mathrm{LaAl}{\mathrm{O}}_3$ and $\mathrm{SrTi}{\mathrm{O}}_3$, meet at an interface, what do you see? The emergence of a two-dimensional electron liquid at the interface with many fundamentally exciting new collective electronic properties, as discovered by Ohtomo and Hwang in 2004, and investigated by many others since then. One of the most interesting and consuming puzzles is the coexistence of ferromagnetism and superconductivity in this electron gas, as the two properties are generally considered to be incompatible: The former arises from net spin alignment in a particular direction, whereas the latter involves the pairing of a spin-up and a spin-down electron, implying no net spin. By what mechanisms does the coexistence come about then, and what is the origin of the ferromagnetism in the electron gas since neither of the two bulk oxides involved is ferromagnetic? In this experimental paper, we present new crucial evidence, by studying the magnetotransport properties of a set of carefully designed samples, that the ferromagnetism arises from intrinsic properties of the $\mathrm{SrTi}{\mathrm{O}}_3$, taking a significant step forward toward ultimate answers to these questions.

The samples we have investigated are, by design, of two types: high-density electron liquids at $\mathrm{GdTi}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ interfaces and uniformly La-doped $\mathrm{SrTi}{\mathrm{O}}_3$ films with thickness in the range from nanometers to tens of nanometers. The charge-carrier electrons are introduced in two fundamentally different ways: through the interface in the first type, and through the dopant atoms in the second. By identifying a hysteretic dependence of each sample’s magnetoresistance on the applied magnetic field and analyzing the temperature dependence of the magnetoresistance, we are able to draw a number of conclusions: (1) The charge-carrier density and temperature are the parameters crucial to determining whether or not the ferromagnetism-superconductivity coexistence appears. (2) Superconductivity occurs in a low-carrier-density, low-temperature domelike region of the two-parameter space whereas ferromagnetism appears on the high-density side of the superconductivity dome; for a range of intermediate carrier densities, which correspond to those achieved in the doped $\mathrm{SrTi}{\mathrm{O}}_3$ films, both properties coexist. (3) The ferromagnetism emerges as a general result of collective electronic interaction intrinsic to doped $\mathrm{SrTi}{\mathrm{O}}_3$.

This study should stimulate further discussions and research. The $\mathrm{GdTi}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ interface is intrinsically interesting both in its own right, with $\mathrm{GdTi}{\mathrm{O}}_3$ being a ferrimagnetic Mott insulator, and as a system of comparison for $\mathrm{LaAl}{\mathrm{O}}_3$ and $\mathrm{SrTi}{\mathrm{O}}_3$. The origin of the ferromagnetism also suggests that magnetic properties of these systems may be manipulated, a possibility that would make these structures of interest for spintronic applications.

Figure 1

(a) Magnetoresistance of a 4-nm ${\mathrm{GdTiO}}_3/1\mathrm{\text{−}}\mathrm{nm}$ ${\mathrm{SrTiO}}_3/4\mathrm{\text{−}}\mathrm{nm}$ ${\mathrm{GdTiO}}_3/\mathrm{LSAT}$ heterostructure at 15 K, 10 K, 5 K, and 2 K. Hysteresis appears below approximately $10\mathrm{K}$ in sweeps with increasing and decreasing $B$, respectively; see arrows. (b) Magnetoresistance of an 8-nm ${\mathrm{GdTiO}}_3/1\mathrm{\text{−}}\mathrm{nm}$ ${\mathrm{SrTiO}}_3/\mathrm{LSAT}$ heterostructure at 5 K and 2 K.

Figure 2

Magnetization as a function of temperature at 10 mT for a 4-nm ${\mathrm{GdTiO}}_3/1\mathrm{\text{−}}\mathrm{nm}$ ${\mathrm{SrTiO}}_3/4\mathrm{\text{−}}\mathrm{nm}$ ${\mathrm{GdTiO}}_3/\mathrm{LSAT}$ heterostructure. The dotted line is a guide to the eye. The inset shows the magnetization M as a function of magnetic field at 2 K.

Figure 3

(a) Magnetoresistance of a La-doped ${\mathrm{SrTiO}}_3$ film with a carrier density of $9\times {10}^{20}{\mathrm{cm}}^{-3}$ at 12 mK, showing hysteresis during sweeps with increasing and decreasing $B$, respectively.

Figure 4

(a) Magnetoresistance of a La-doped ${\mathrm{SrTiO}}_3$ film with a carrier density of $1\times {10}^{20}{\mathrm{cm}}^{-3}$ as a function of temperature, measured with increasing $B$ field. (b) Magnified magnetoresistance at 12 mK. The hysteresis in sweeps with increasing and decreasing $B$ (see arrows) indicates the coexistence of superconductivity and ferromagnetism.

Figure 5

Superconducting and ferromagnetic transition temperatures of ${\mathrm{SrTiO}}_3$ as a function of carrier concentration. Literature data for the superconducting transition temperatures are from Appel et al. [33]. The sheet carrier densities of the quantum wells ($n_{2\mathrm{D}}$) were converted to 3D carrier concentrations ($n_{3\mathrm{D}}$) according to $n_{3\mathrm{D}}=n_{2\mathrm{D}}/t{\mathrm{cm}}^{-3}$, where $t$ is the thickness of the quantum well and $n_{2\mathrm{D}}$ is the carrier concentration determined from the Hall measurements at 5 K.