Nanomagnetic logic with non-uniform states of clocking

Nanomagnetic logic transmits information along a path of nanomagnets. The basic mechanism to drive such a transmission, known as clocking, can be achieved by exploiting the spin-Hall effect, as recently observed in experiments on Ta/CoFeB/MgO multilayers [D. Bhowmik, et al., Nat. Nano. 9, 59 (2013)]. This paper shows the fundamental mechanism of the spin-Hall driven clocking by using a full micromagnetic framework and considering two different devices, Ta/CoFeB/MgO and Pt/CoFeB/MgO. The former is used for a direct comparison of the numerical results with the experiments while the latter permits to predict the effect of the Dzyaloshinskii-Moriya interaction (DMI) in the clocking mechanism. Results show that the clocking state is non-uniform and it is characterized by the presence of domains separated by Bloch (N\'eel) domain walls depending on the absence (presence) of the DMI. Our findings point out that for the design of nanomagnetic logic a full micromagnetic approach is necessary.