Magnetic and transport properties of epitaxial films of ${\text{SrRuO}}_3$ in the ultrathin limit

We measured ultrathin epitaxial films of the itinerant ferromagnet ${\text{SrRuO}}_3$ to study effects of decreasing film thickness on transport and magnetic properties. We find that the resistivity ratio decreases, the ferromagnetic phase transition occurs at a lower Curie temperature, and the easy axis of magnetization rotates toward a more perpendicular orientation. We discuss possible interpretations of the observed behavior.

Figure 1

Resistivity as a function of temperature for six films with different thicknesses. Inset: A sketch of the patterned film. The growth orientation of ${\text{SrRuO}}_3$ and the definition of the angle $\theta$.

Figure 2

(a) The normalized conductivity as a function of $1/d$ at 300, 200, 100, and 10 K. (b) Linear fit to the 300 K data.

Figure 3

(a) Variation in the normalize resistivity as a function of $1/d$ at 300, 200, 100, and 10 K. (b) Linear fit to the 300 K data.

Figure 4

(a) The same data as in Figs. 2, 3 presented as a function of $1/\left(d-d^{\ast }\right)$. (b) Linear fit to the 300 K data.

Figure 5

(a) The easy axis direction relative to the film normal as a function of temperature of four films with different thicknesses. (b) Hall effect of a single-orientation film (3.9 nm) as a function of the magnetic field direction [$\theta$ is measured relative to the normal to the film, in the (001) plane] at $T=125\text{K}$, $H=1\text{T}$. (The two curves correspond to sweeps clockwise and anticlockwise in the angle.)

Figure 6

$\frac{d\rho }{dT}$ as a function of temperature for six films with different thicknesses.

Figure 7

The Curie temperature as a function of the number of MLs. Inset: The log-log plot of the finite-size scaling expression. The line is a fit to a linear function.

Figure 8

Temperature dependence of the resistivity near $T_C$. The solid line is the extrapolation of the resistivity from $T>T_C$. The definition of $\Delta {\rho }_{\text{sp}}$ is shown.

Figure 9

Critical behavior of $\Delta {\rho }_{\text{sp}}$ with respect to the reduced temperature $t=\left(T-T_C\right)/T_C$ (the graphs were shifted vertically for clarity). The slope of the graph is twice the value of the critical exponent $\beta$. The solid lines have the expected slopes for 2D Ising and 3D Ising. Inset: The critical exponent $\beta$ for samples with different thicknesses. The solid lines are the expected values from the theoretical methods 3D Ising and 2D Ising.