Indication for macroscopic quantum tunneling below 10 K in nanostructures of SrRuO${}_3$

We study magnetization reversal of nanostructures of the itinerant ferromagnet ${\mathrm{SrRuO}}_3$ ($T_c\sim 150\mathrm{K}$). We find that down to $10\mathrm{K}$ the magnetization reversal is dominated by thermal activation. From $2–10\mathrm{K}$, the magnetization reversal becomes independent of temperature, raising the possibility for reversal dominated by macroscopic quantum tunneling (MQT). A $10\mathrm{K}$ crossover to MQT is consistent with the extremely large anisotropy field ($\sim 7\mathrm{T}$) of ${\mathrm{SrRuO}}_3$.

Figure 1

A scanning electron microscope image of a typical pattern of ${\mathrm{SrRuO}}_3$.

Figure 2

(a) Normalized magnetization $M^{*}$ as a function of a magnetic field $H$ applied at ${60}^{\circ }$ relative to the sample normal in the (001) plane and $\sim {30}^{\circ }$ relative to the easy axis. The magnetic field is swept at a rate of 100 Oe/s and the magnetization is measured every $\sim 3$ s. The internal rectangle of pattern S1 is $115\pm 10\mathrm{nm}\times 85\pm 10\mathrm{nm}$. The internal square of pattern L1 is $\sim 20\mu \mathrm{m}\times 20\mu \mathrm{m}$. (b) The switching field, determined in sweeping field experiments, as a function of temperature for different samples. Pattern S2 is similar in its dimension to pattern S1.

Figure 3

(a) The transverse resistance $R_{xy}$ as a function of time at different temperatures. At 19 and 20.25 K, ${\mu }_{0}H=3.4$ T; at 3 and 14 K, ${\mu }_{0}H=3.725$ T. $H$ is applied at ${60}^{\circ }$ relative to the sample normal in the (001) plane and $\sim {30}^{\circ }$ relative to the easy axis. (b) The temperature dependence of the average waiting time of ten switching events for different values of $H$. Inset: the average waiting time $\overline{\tau }$ vs 1/T with a reversing field of 2.8 T. The error bars indicate a confidence interval of $90\%$. (c) The temperature dependence of the magnetic field for which the average waiting time $\overline{\tau }$ is closest to 300 s. The error bars indicate the higher and lower fields or the higher and lower temperatures for which $\overline{\tau }$ was measured.

Figure 4

The reversal probability for different time intervals at 4 K (red, solid line) and 14 K (green, dashed line) based on hundreds of reversals. The lines are fits to ${\int }_{t-\Delta /2}^{t+\Delta /2}(1/\overline{\tau })\exp (-t/\overline{\tau })dt$ where $\Delta$ is the chosen time interval for the histograms.