Anisotropic lattice changes and ferromagnetic order in ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$

Thin epitaxial films of ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ on (001)-oriented ${\mathrm{SrTiO}}_3$ and (${\mathrm{La}}_{0.3}{\mathrm{Sr}}_{0.7}$)(${\mathrm{Al}}_{0.65}{\mathrm{Ta}}_{0.35}$) ${\mathrm{O}}_3$ single-crystal substrates experience coherent compressive strain for $x$ < 0.5 and 0.9, respectively, resulting in a nearly tetragonal structure. The tetragonal distortion $c$/$a$ increases for ${\mathrm{SrRuO}}_3$ films ($x$ $=$ 0) up to 2.4% with respect to the pseudocubic structure of the corresponding bulk material. Increasing compressive strain leads, independently of the degree of Ca substitution, to a successive shrinkage of the unit-cell volume. For constant $x$, films under compressive (tensile) strain show a decrease (increase) of the ferromagnetic Curie temperature $T_C$ compared to the bulk value. The change of $T_C$ is found to be strongly correlated to the decrease of the unit-cell volume $V_{\mathrm{uc}}$, i.e., $\partial T_C/\partial V_{\mathrm{uc}}\approx 26.2$ K/ ${\AA }^3$, nearly independent of $x$. Remarkably, the biaxial epitaxial pressure leads to nearly the same value of $\partial T_C/\partial V_{\mathrm{uc}}$ as deduced for bulk ${\mathrm{SrRuO}}_3$ under isotropic hydrostatic pressure. In view of the strong magnetic anisotropy present in the tetragonally distorted thin films, where compressive strain enhances the out-of-plane magnetization significantly, this is a rather surprising result. For moderate epitaxial strain the tetragonal distortion seems to play only a minor role for the reduced $T_C$ in thin films.

Figure 1

Room-temperature lattice parameters and cube root of the unit-cell volume of polycrystalline ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ samples as a function of the Ca concentration $x$. The data are plotted with respect to the pseudocubic dimensions, i.e., $a=a^{\text{'}}/\surd 2$, $b=b^{\text{'}}/\surd 2$, $c=c^{\text{'}}/2$, and $V_{\mathrm{uc}}=(a\hspace{0.5em}b\hspace{0.5em}c)$, where $a^{\text{'}}$, $b^{\text{'}}$, and $c^{\text{'}}$ are the orthorhombic lattice parameters. Lines are guides to the eye.

Figure 2

Reciprocal-space mapping of the (103) SRO film and LSAT substrate reflections. The azimuth is along the [100] direction and the intensity (contour lines) is given on a logarithmic scale. The reflections are indexed with respect to the pseudocubic perovskite structure. The lattice point for complete strain-relaxed SRO (bulk value) is indicated by the white dot. The relaxation line for the (103) film reflection is shown by the dashed line. The in-plane component of the reciprocal lattice vector of the (103) LSAT and SRO reflection is observed at the same $q_x=2.58$ ${\mathrm{nm}}^{-1}$.

Figure 3

Cube root of the unit-cell volume $V_{\mathrm{uc}}$ of ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ films on LSAT and STO together with $V_{\mathrm{uc}}$ of polycrystalline bulk samples as a function of the Ca concentration $x$. The inset displays the tetragonal distortion $c$/$a$ vs $x$ of the films. Straight lines are linear fits to the data.

Figure 4

(a) Ru and Sr concentrations of a SRO film on LSAT with respect to the Ru and Sr content as a function of the distance $z$ from the LSAT/SRO interface. The SRO film is located to the right of the interface, i.e., $z$ > 0. (b) High-resolution TEM image imaged along the $[100]{}_{\mathrm{LSAT}}$ direction. The SRO/LSAT interface is marked by an arrow.

Figure 5

Selected-area electron diffraction of a SRO thin-film on LSAT imaged along the $[100]{}_{\mathrm{LSAT}}$ direction. The magnified inset (region marked by rectangle) renders the splitting of the SRO (red) and LSAT reflections (black) better visible.

Figure 6

(a) Magnetic moment of a polycrystalline SRO bulk sample and a SRO film on LSAT obtained by field-cooled measurements at ${\mu }_{0}H=20$ mT applied parallel to the film plane. (b) Normalized in-plane [$H$ parallel to (100)] and out-of-plane [$H$ parallel to (001)] magnetic moment versus magnetic field strength at $T$ $=$ 5 K. The saturated magnetic moment amounts to $m_s=1.5{\mu }_B$ /Ru.

Figure 7

(a) Magnetic moment of a ${\mathrm{Sr}}_{0.7}{\mathrm{Ca}}_{0.3}{\mathrm{RuO}}_3$ polycrystalline bulk sample and a ${\mathrm{Sr}}_{0.7}{\mathrm{Ca}}_{0.3}{\mathrm{RuO}}_3$ film on LSAT obtained by field-cooled measurements at ${\mu }_{0}H=20$ mT applied parallel to the film plane. (b) Normalized in-plane [$H$ parallel to (100)] and out-of-plane [$H$ parallel to (001)] magnetic moment vs magnetic field strength at $T$ $=$ 5 K. The saturated magnetic moment amounts to $m_s=1.0{\mu }_B$ /Ru.

Figure 8

Ferromagnetic Curie temperature $T_C$ as a function of the Ca concentration $x$ for ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ bulk samples and films grown on STO and LSAT. Straight lines are linear fits to the data.

Figure 9

(a) $T_C$ vs $V_{\mathit{uc}}$ for ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ ($x$ $=$ 0, 0.3, 0.4, and 0.6) films on LSAT and STO and polycrystalline bulk material. For comparison we also plot data of bulk SRO under hydrostatic pressure, taken from Hamlin et al. (Ref. 8) (see the text). The straight lines are linear fits to the data. (b) Same as (a) highlighting the volume dependence of $T_C$ ($x$). Lines are guides to the eye.