Nonmonotonic length dependence of switching field of nanolithographically defined single-domain nickel and cobalt bars (abstract)

Abstract

Previously, the switching field of nanolithographically defined single-domain permalloy and nickel bars was found to increase monotonically as the bar aspect ratio increases or as the bar width decreases. In this work, we will show, for the first time, that when the bar width is fixed, the switching field of nanolithographically defined single-domain nickel and cobalt bars changes nonmonotonically with the bar length (hence the aspect ratio). The isolated Ni and Co bars were fabricated using electron-beam lithography and a lift-off process, and have a thickness of 35 nm, a fixed width of 100 nm, and a length varying from 200 nm to 5 μm. The magnetic force microscopy (MFM) showed that all the as-fabricated bars, except for the Ni bars with a length less than 500 nm, are single domain. The switching field of the single-domain bars was found to increase with the bar length first, then decrease after reaching a peak. The peak switching field and corresponding bar length are 640 Oe and 1 μm for Ni, and 1250 Oe and 2 μm for Co. This behavior, which clearly deviates from Stoner-Wohlfarth model, suggests that two different mechanisms should be responsible for the magnetization reversal process in different bar lengths. When the bar length is small, the exchange energy can be much larger than the magnetostatic energy to keep the bar switching quasicoherently and the switching field increases with the bar length. However, when the bar length is large, the exchange energy cannot overweigh the magnetostatic energy for quasi-coherent switching and therefore the lowest switching energy state would be incoherent switching which involves multidomain (or vortex) reversal leading to an decrease of switching field. The detailed analysis will be presented in the paper.