Uniaxial Strain Control of Bulk Ferromagnetism in Rare-Earth Titanates

The perovskite rare-earth titanates are model Mott insulators with magnetic ground states that are very sensitive to structural distortions. These distortions couple strongly to the orbital degrees of freedom and, in principle, it should be possible to tune the superexchange and the magnetic transition with strain. We investigate the representative system $(\mathrm{Y},\mathrm{La},\mathrm{Ca}){\mathrm{TiO}}_3$, which exhibits low crystallographic symmetry and no structural instabilities. From magnetic susceptibility measurements of the Curie temperature, we demonstrate direct, reversible, and continuous control of ferromagnetism by influencing the ${\mathrm{TiO}}_6$ octahedral tilts and rotations with uniaxial strain. The relative change in $T_C$ as a function of strain is well described by ab initio calculations, which provides detailed understanding of the complex interactions among structural, orbital, and magnetic properties in rare-earth titanates. The demonstrated manipulation of octahedral distortions opens up far-reaching possibilities for investigations of electron-lattice coupling, competing ground states, and magnetic quantum phase transitions in a wide range of quantum materials.

Figure 1

(a) Phase diagram of ${\mathrm{RTiO}}_3$ with FM (ferromagnetic), AFM (antiferromagnetic), insulating, and metallic phases. The compositions studied in this Letter are marked by diamonds. (b) Schematic of the uniaxial strain cell (for more details, see Ref. [25]). (c) ${\mathrm{YTiO}}_3$ structure constructed from theory, showing the two relevant octahedral rotations, $a^0{a}^0{c}^{+}$ and $a^{-}{a}^{-}{c}^0$, as deviations from a simple cubic structure. Small spheres depict oxygen ions, large spheres titanium ions. Upper section: oxygen base plane with the $a^0{a}^0{c}^{+}$ rotation mode. Bottom section: perpendicular view showing the $a^{-}{a}^{-}{c}^0$ rotation mode. The effects of uniaxial stress along $a\equiv [100]$, $b\equiv [010]$, or $c\equiv [001]$ on the rotation modes are qualitatively different for each direction.

Figure 2

Raw ac susceptibility data for (a) ${\mathrm{Y}}_{0.9}{\mathrm{Ca}}_{0.1}{\mathrm{TiO}}_3$ and (b) ${\mathrm{Y}}_{0.85}{\mathrm{Ca}}_{0.15}{\mathrm{TiO}}_3$, with applied stress along $b$ and susceptibility measured along $c$. The Curie temperatures are taken as the peak positions (arrows). Data for different sample stresses are shifted vertically for clarity. In (a), the negligible increase of the susceptibility peak width with increasing stress indicates that the strain is homogeneously distributed in the sample; see Ref. [25] for the extracted full-width-at-half-maximum values. After stress release, $T_C$ returns to its original value; the peak narrows slightly, indicative of residual inhomogeneous stress in the samples that decreases after the application of external pressure. In (b), the FM order disappears at a nonzero temperature, consistent with a first-order transition into a paramagnetic state. The small peak around 6 K likely originates from superconducting solder in the detection coils [25].

Figure 3

(a) Phase diagram of $T_C$ versus applied sample stress, spanning a wide range of $T_C$ values. Empty, filled, and crossed symbols show applied stress along $a$, $b$, and $c$, respectively (marked as ${\sigma }_{||a,b,c}$). Green symbols are ${\mathrm{YTiO}}_3$ (YTO). Light blue, blue, and dark blue show ${\mathrm{Y}}_{0.95}{\mathrm{Ca}}_{0.05}{\mathrm{TiO}}_3$, ${\mathrm{Y}}_{0.9}{\mathrm{Ca}}_{0.1}{\mathrm{TiO}}_3$, ${\mathrm{Y}}_{0.85}{\mathrm{Ca}}_{0.15}{\mathrm{TiO}}_3$, respectively. Yellow and orange are ${\mathrm{Y}}_{0.9}{\mathrm{La}}_{0.1}{\mathrm{TiO}}_3$ and ${\mathrm{Y}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{TiO}}_3$, respectively. Lines are guides to the eye. Small differences between the $\sigma =0$ transition temperatures for the same nominal compositions are due to a slight variation in oxygen offstoichiometry of crystals from the same growths [35]. (b) Single-parameter scaling of $T_C(\sigma /{\sigma }_0)/T_C(0)$ with stress along $b$. The doping-dependent scaling parameter ${\sigma }_0$ plays the role of an effective elastic modulus. The line shows the DFT calculation for ${\mathrm{YTiO}}_3$ [same as in Fig. 4]. See Ref. [25] for values of ${\sigma }_0$.

Figure 4

DFT results for ${\mathrm{YTiO}}_3$ as a function of compressive uniaxial stress along $a$, $b$, and $c$. (a) Mode amplitudes of the octahedral rotations corresponding to the $M_2^{+}$ and $R_5^{-}$ irreps in ${\mathrm{YTiO}}_3$. (b) Nearest-neighbor exchange parameters $J_{xy}$ and $J_z$ obtained from fits to the Heisenberg model. (c) Mean-field Curie temperatures using the DFT-obtained exchanges, including the subleading next-nearest-neighbor exchanges [25], along with experimental results for ${\mathrm{YTiO}}_3$. A similar analysis for tensile strain can be found in Ref. [25].