Nanostructured complex oxides as a route towards thermal behavior in artificial spin ice systems

We have used soft x-ray photoemission electron microscopy to image the magnetization of single-domain $\mathrm{L}{\mathrm{a}}_{0.7}\mathrm{S}{\mathrm{r}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ nanoislands arranged in geometrically frustrated configurations such as square ice and kagome ice geometries. Upon thermal randomization, ensembles of nanoislands with strong interisland magnetic coupling relax towards low-energy configurations. Statistical analysis shows that the likelihood of ensembles falling into low-energy configurations depends strongly on the annealing temperature. Annealing to just below the Curie temperature of the ferromagnetic film ($T_{\mathrm{C}}=338\mathrm{K}$) allows for a much greater probability of achieving low-energy configurations as compared to annealing above the Curie temperature. At this thermally active temperature of 325 K, the ensemble of ferromagnetic nanoislands explore their energy landscape over time and eventually transition to lower energy states as compared to the frozen-in configurations obtained upon cooling from above the Curie temperature. Thus, this materials system allows for a facile method to systematically study thermal evolution of artificial spin ice arrays of nanoislands at temperatures modestly above room temperature.

Figure 1

(a) X-PEEM XMCD image of an artificial square ice array brought to ground state through a magnetic field demagnetization protocol. Epitaxial $470\mathrm{nm}\times 175\mathrm{nm}\times 40\mathrm{nm}$ LSMO nanoisland locations are outlined in red. (b) Schematic of ground-state nanoisland magnetization configuration as seen with X-PEEM magnetic sensitivity axis along the horizontal direction parallel to the [100] crystallographic direction, with the red, gray, and blue arrows indicating orientation of the magnetization of the nanoislands. (c) X-PEEM XMCD image of the entire artificial square ice array brought to ground state via 325-K thermal demagnetization protocol.

Figure 2

Schematics of nanoisland magnetization orientation as in Fig. 1 for (a) one-ring, (b) two-ring, and (c) three-ring nanoisland ensembles, with 2a as the ring diameter. Comparison of the occupancy of low-energy magnetization configurations for (d) one-ring, (e) two-ring, and (f) three-ring nanoisland ensembles after a 350-K anneal as a function of dipolar coupling strength. The points at zero coupling strength are calculated from the occupancy of energy levels based on the degeneracy of possible random magnetic configurations.

Figure 3

Effect of demagnetizing protocol on occupancy of low-energy magnetization configurations for (a) one-ring and (b) two-ring ensembles, with the width of each ring of $2a=1\mu \mathrm{m}$ and a coupling strength of $1.8\times {10}^{-12}{\mathrm{A}}^2\mathrm{m}$. The configurations are binned by calculating the overall dipolar energy of each ensemble, with X-PEEM images of two low-dipolar-energy configurations shown as insets and green arrows showing magnetization direction of rings in flux-closure arrangements.

Figure 4

X-PEEM images of a three-ring frustrated nanomagnet ensemble (a) after an in situ ac magnetic field demagnetization at room temperature, (b) after an in situ 5-min anneal at 325 K, (c) after another in situ 5-min anneal at 325 K, and (d) after a 2-h ex situ anneal in air at 473 K. The green arrows indicate the sense of rotation for island groups that are in a low-energy vortex configuration, and the red and blue arrows indicate the direction of magnetization for the center frustrated three-island vertex.