Manipulating magnetic properties of ${\text{SrRuO}}_3$ and ${\text{CaRuO}}_3$ with epitaxial and uniaxial strains

Using density-functional theory within the local spin-density approximation, ${\text{SrRuO}}_3$ and ${\text{CaRuO}}_3$ are investigated under epitaxial and uniaxial strains. Strains of the order of 2%–3% are predicted to radically alter the magnetic properties of ${\text{SrRuO}}_3$ and ${\text{CaRuO}}_3$ ultrathin films, indicating a large magnetostructural coupling in these systems. In particular, ${\text{SrRuO}}_3$ is shown to become nonmagnetic for sufficient tensile epitaxial and compressive uniaxial strains; in contrast, ${\text{CaRuO}}_3$ is predicted to become ferromagnetic for tensile epitaxial strains. These results suggest routes for the manipulation of the magnetic order of perovskite oxides ultrathin films via coherent epitaxial growth.

Figure 1

Calculated total-energy differences between FM-NM and FM-AF in ${\text{SrRuO}}_3$ as a function of strain, evaluated at constant in-plane strain. Structural parameters are fully relaxed for each strain state.

Figure 2

(Color online) Octahedral tilting and rotation angles for ${\text{SrRuO}}_3$ as a function of strain. The arrow indicates the value of strain where a magnetic transition is possible by uniaxial compression, as illustrated below. The data for this figure are taken from Ref. 28.

Figure 3

(Color online) (a) Variation in magnetic moment, (b) Ru-Ox, Ru-Oy, and Ru-Oz bond lengths, and (c) octahedral rotation and tilt angles for epitaxially strained ${\text{SrRuO}}_3$ (2.5% tensile strain) with uniaxial compression along [001]. Note that at larger compressions, the angles in (c) differ slightly from those presented in Fig. 2 (NM curve at 2.5% strain), owing to the decrease in volume/formula units with increasing compression.

Figure 4

(Color online) Schematic picture of the octahedral distortion leading to the loss of magnetization in ${\text{SrRuO}}_3$ .

Figure 5

(Color online) (Left axis) Octahedral rotation and tilt angles with epitaxial strain for ${\text{CaRuO}}_3$. For ${\text{CaRuO}}_3$ $e\text{−}Pbnm\left[001\right]$, these angles are not significantly different in NM and FM states, in contrast to ${\text{SrRuO}}_3$ (see Fig. 2). (Right axis) The bonding distance between the oxygen and Ca from Fig. 7 as a function of the in-plane strain in ${\text{CaRuO}}_3$. This plot shows that tensile strain increases the distance and weakens the bond between the oxygen and Ca atoms. As the bonding vanishes, the spin moment in ${\text{CaRuO}}_3$ is restored.

Figure 6

(Color online) Magnetic moment vs epitaxial in-plane strain for ${\text{SrRuO}}_3$ and ${\text{CaRuO}}_3$. The ${\text{CaRuO}}_3$ magnetic moment becomes nonzero under epitaxial strain and grows rapidly with the increasing tensile strain. No such effect is observed for compressive strains. For ${\text{SrRuO}}_3$, the initial (zero strain) magnetic moment undergoes changes, which can be attributed to distortions favorable for the exchange coupling. The data for ${\text{SrRuO}}_3$ is taken from Ref. 28.

Figure 7

(Color online) (Left) $e\text{−}Pbnm$ structure of ${\text{CaRuO}}_3$ and charge density through a slice perpendicular to [001]. Here we qualitatively assess the degree of covalency by looking at the charge-density buildup at the center of the Ca-O(4c) bond. As a result of tilting, Ca and O(4c) are effectively pushed together, yielding a stronger covalent interaction between them. Increasing this covalency destroys the spin moment of the Ru ion. (Right) The charge-density isosurfaces taken in the same plane as shown at left. Three cases are illustrated: (a) the relaxed $e\text{−}Pbnm$ structure of ${\text{CaRuO}}_3$, which is nonmagnetic; (b) $e\text{−}Pbnm$ ${\text{CaRuO}}_3$ under 2% tensile strain with magnetic moment $\sim 0.6{\mu }_B/\text{f}.\text{u}$; and (c) ${\text{CaRuO}}_3$ in the structure of ${\text{SrRuO}}_3$ with completely fixed geometry, showing a magnetic moment of $1.45{\mu }_B/\text{f}.\text{u}$. The magnetic moment is anticorrelated with the degree of covalency of the Ca-O(4c) bond. If the atoms of Ca and O(4c) are close enough, the magnetic moment vanishes.

Figure 8

(Color online) The magnetic moment of CRO as it increases due to the shifting of Ca ions. The shifting of Ca is made along the line Ca-O(4c) (see Fig. 7) away from the oxygen. Positions of Ru and O ions have not been changed.