Despite the complexity and diversity of nature, there exists universality in the form of critical scaling laws among various dissimilar systems and processes such as stock markets, earthquakes, crackling noise, lung inflation and vortices in superconductors. This universality is mainly independent of the microscopic details, depending only on the symmetry and dimension of the system. Exploring how universality is affected by the system dimensions is an important unresolved problem. Here we demonstrate experimentally that universality persists even at a dimensionality crossover in ferromagnetic nanowires. As the wire width decreases, the magnetic domain wall dynamics changes from elastic creep in two dimensions to a particle-like stochastic behaviour in one dimension. Applying finite-size scaling, we find that all our experimental data in one and two dimensions (including the crossover regime) collapse onto a single curve, signalling universality at the criticality transition. The crossover to the one-dimensional regime occurs at a few hundred nanometres, corresponding to the integration scale for modern nanodevices.

We examine magnetic domain wall motion in metallic nanowires Pt-Co-Pt. Regardless of whether the motion is driven by either magnetic fields or current, all experimental data fall onto a single universal curve in the creep regime, implying that both the motions belong to the same universality class. This result is in contrast to the report on magnetic semiconductor (Ga,Mn)As exhibiting two different universality classes. Our finding signals the possible existence of yet other universality classes which go beyond the present understanding of the statistical mechanics of driven interfaces.

Electric control of multiple domain walls (DWs) motion is demonstrated by Pt/Co/Pt nanotracks with perpendicular magnetic anisotropy. Due to the weak microstructural disorders with small DW propagation field, the purely current-driven DW motion is achieved in the creep regime at current densities less than 10 7 A/cm 2 at room temperature.It is confirmed that by use of a scanning magneto-optical Kerr effect microscope, several DWs are simultaneously and identically displaced by the same distance in the same 2 direction. Utilizing such DWs motion, we succeed to realize random bits writing and transferring as a device prototype of four-bit shift registers.

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