Size effect on the magnetic phase in Sr4Ru3O10

High quality Sr _4 Ru _3 O _10 nanoflakes are obtained by the scotch tape-based micro-mechanical exfoliation method. The metamagnetic transition temperature ${{T}_{m}}^{flake}$ is found to decrease in line with the decrease of thickness, while the ferromagnetic (FM) phase, the ordinary, and anomalous Hall effects (OHE and AHE) are independent on the thickness of the flake. Analysis of the data demonstrates that the AHE reflects the FM nature of Sr _4 Ru _3 O _10 , and the decrease of thickness favors the Ru moments aligned in the ab -plane, which induces a decrease of the metamagnetic transition temperature compared with the bulk.