Suppression of Stochastic Domain Wall Pinning Through Control of Gilbert Damping

www.nature.com/scientificreports OPEN Received: 22 September 2017 Accepted: 21 November 2017 Published: xx xx xxxx Suppression of Stochastic Domain Wall Pinning Through Control of Gilbert Damping T. J. Broomhall & T. J. Hayward Finite temperature micromagnetic simulations were used to investigate the magnetisation structure, propagation dynamics and stochastic pinning of domain walls in rare earth-doped Ni80Fe20 nanowires. We first show how the increase of the Gilbert damping, caused by the inclusion rare-earth dopants such as holmium, acts to suppress Walker breakdown phenomena. This allows domain walls to maintain consistent magnetisation structures during propagation. We then employ finite temperature simulations to probe how this affects the stochastic pinning of domain walls at notch-shaped artificial defect sites. Our results indicate that the addition of even a few percent of holmium allows domain walls to pin with consistent and well-defined magnetisation configurations, thus suppressing dynamically-induced stochastic pinning/depinning phenomena. Together, these results demonstrate a powerful, materials science-based solution to the problems of stochastic domain wall pinning in soft ferromagnetic nanowires. The past decade has seen substantial research into the development of memory and logic devices where data is encoded using the positions of domain walls in soft ferromagnetic nanowires1–4. These devices employ the motion of DWs though the nanowires to transport data, which can be achieved either through the application of external magnetic fields or electric currents5,6. However, the application of even modest magnetic fields or current densities typically lead to Walker breakdown (WB) phenomena7, which introduce new levels of complexity to DW motion through periodic oscillations in their internal magnetisation structure7–9. When combined with thermal perturbations, these changes in structure impart an inherent stochasticity to DW motion10 and thus, as well reducing DW velocities, result in stochastic pinning and depinning at both artificial and intrinsic defect sites, due to the pinning of different meta-stable DW configurations10–12. The role of stochastic behaviour in limiting the reliability of DW data storage and logic devices means that understanding and controlling these complex dynamical processes is of major importance for future applications and proposed devices. One clear route to enhancing the reliability, and thus feasibility, of DW devices is to directly supress the WB phenomena that lie at the heart of stochastic behaviour. A number of methods of suppressing WB have been previously proposed including the patterning of controlled nanowire edge profiles13,14, applying transverse magnetic fields15, inducing perpendicular magnetic anisotropies16, or increasing the Gilbert damping parameters, α, of the materials from which the nanowires are formed17. For the latter, increased values of α in soft materials such as Ni80Fe20 can be obtained by doping with a few percent of rare earth (RE) metals such as terbium or holmium18,19 which increase the strength of spin-orbit interactions and thus the rate at which energy is dissipated by precessing spins17,18. Typically, the magnetic moments of the RE dopants couple antiferromagnetically to those of the Ni and Fe atoms, resulting in ferrimagnetic order within the lattice20. Thus, in addition to modifying α, rare earth doping also causes a net reduction of MS relative to that of undoped films. This is expected to further modify DW structure and dynamics through a relative reduction of the nanowires’ dominant shape anisotropy. In this paper, we use micromagnetic simulations to explore the magnetisation structure, propagation dynamics and stochastic pinning behaviours of DWs in Ni80Fe20 nanowires doped with 0–10% of Ho. We first investigate how the reduction of MS resulting from the doping modifies the relative stability of transverse DWs (TDW) and vortex DWs (VDW) in nanowires of a variety of geometries. We then go on to study how corresponding increases in the Gilbert damping constant, α, increase the Walker breakdown field, such that the dynamics of DW propagation are stable over an increased range of driving fields. Finally, we use finite temperature micromagnetic simulations of DWs pinning at artificial defect sites to demonstrate how changes in DW propagation dynamics Department of Materials Science and Engineering, University of Sheffield, Sheffield, UK. Correspondence and requests for materials should be addressed to T.J.H. (email: ) SCiEnTifiC REPOrTS | 7: 17100 | DOI:10.1038/s41598-017-17097-4 1 www.nature.com/scientificreports/ Figure 1. (a) Presents example magnetisation configurations for transverse (TDW) and Vortex (VDW) DWs. (b) The values for α and MS for each doping value as found in ref.20, The solid lines are guides to the eye. (c) Phase diagram indicating the stability of TDWs and VDWs for a range of width and thicknesses with different values of holmium doping. The dashed lines are fits using equation 2. can be used to suppress the stochastic pinning effects. Together, our results demonstrate the feasibility of a materials science-based solution to the problems of stochastic DW behaviour. If experimentally realised, this could be applied to create devices where DW behaviour is intrinsically well-defined. Effect of Rare Earth Doping on Ground State Domain Wall Structures The magnetisation structures of DWs in planar nanowires depend on the balance between exchange and magnetostatic energies. Exchange interactions favour transverse domain wall configurations (TDW), whereas the magnetostatic energy favours vortex domain wall (VDW) configurations (Fig. 1(a)). Several studies have investigated how the relative energies of these DW structures depends on nanowire wire geometry and have shown that VDWs are favoured in thicker and wider nanowires, where magnetostatic energy dominates21. TDWs are favoured in thinner and narrower wires where exchange energy plays a more significant role22. In Ho doped nanowires, this geometric dependence is further complicated by the reduction of saturation magnetisation resulting from the antiferromagnetic coupling of rare earth atoms with the dominant ferromagnetic phase. This modifies the strength of magnetostatic interactions, and thus the relative stability of VDWs and TDWs compared to un-doped nanowires with the same geometries21,23. This would be expected to affect stochastic pinning/depinning by changing both the basic magnetisation dynamics of Walker breakdown8, and the relative stabilities of the different DW structures that may be pinned at a given defect site. To investigate the effects of Ho doping on ground state DW structure, the energies of TDWs and VDWs were simulated in Ho-doped nanowires with widths, w, in the range 100–400 nm and thicknesses, t, in the range 4–40 nm. Values of α and MS for Ho-doped Ni80Fe20, have previously been reported (...truncated)