Domain wall configurations in amorphous ferromagnetic nanowires with cylindrical symmetry

Long amorphous glass-coated magnetic nanowires with metallic nucleus diameters down to 90 nm have been recently prepared by an enhanced glass-coated melt spinning method [1]. These nanowires with cylindrical symmetry are composite materials, obtained in a single-step fabrication process, in which a ferromagnetic material (the actual nanowire) is embedded in a glass coating. Their main characteristic is a magnetically bistable behavior, i.e. a single step reversal of the axial magnetization when the applied field reaches a threshold value called switching field, and which appears irrespective of the sign and magnitude of the alloy’s magnetostriction constant, λ, i.e. in both nearly zero magnetostrictive samples, e.g., (Co
0.94
Fe
0.06
)
72
.
5
Si
12.5
B
15
with λ ≈ −1 × 10
⁻⁷
, considered as λ ≈ 0, and highly magnetostrictive ones, e.g., Fe
77.5
Si
7.5
B
15
with λ = +25 × 10
⁻⁶
, considered as λ >> 0. Here we report on the magnetization process and domain wall configurations in such bistable amorphous nanowires with cylindrical symmetry by taking into account the nonlinear distribution of their intrinsic magnetoelastic anisotropy, $K_{me}$. We investigated the axial magnetization process through a novel, finite element-based micromagnetic model, in order to describe the magnetization process and associated hysteresis loops in such rapidly solidified ultrathin samples. In this study, we have employed the parallel computing implementation of the MAGPAR finite element micromagnetics package [2]. Figure 1 shows the calculated loops in case of a zero-magnetostrictive sample $(\lambda \approx \text{0}\Rightarrow {{K}_{me}}\approx \text{0})$, as well as for a highly magnetostrictive one $(\lambda \gg \text{0}\Rightarrow {{K}_{me}}\ne \text{0})$ in two cases: (i) for a standard anisotropy distribution given by ${{K}_{me}}(r)={{K}_{max}}\times \cos [\pi (r/R)]$, in which $K_{max}$ is the maximum anisotropy, r the radial coordinate and R the nanowire radius, and (ii) for a radially shifted anisotropy distribution,$K_{me}(r) = K_{max} \times \cos \{ \pi [ ( r- r_{0})/ R]\}$, respectively. The radial shift $r_{0} = 0.3 R$ was included in order to get the shape of the distribution as close as possible to the one expected to emerge from the distribution of internal stresses found in this type of nanowires [3]. These results have been compared to experimentally measured inductive hysteresis loops, showing that the radially shifted anisotropy distribution offers a far more precise description of the magnetic behavior than the standard anisotropy distribution. The proposed model allows one to visualize the configurations of the magnetic moments, which are difficult to see experimentally. Figure 2 shows the distributions of magnetic moments at remanence for the case $K_{me} \approx 0$. One observes that the magnetization at the nanowire end displays an open vortex-like structure. Such a structure minimizes the magnetostatic energy at the nanowire ends and decreases the shape anisotropy. If the external field is increased or further rotated, these structures suffer depinning from the end of the nanowire and subsequently propagate as vortex domain walls. These vortex walls appear spontaneously at room temperature due to demagnetization. Their actual propagation at magnetization switching allows one to consider these ultrathin cylindrical amorphous nanowires as potential nanoconduits for the displacement of domain walls with vortex configurations. This is a key result, given the large domain wall propagation velocities that have been experimentally found in this novel type of nanowires, i.e. well over 1200 m/s [4]. Therefore, it is expected to have a significant impact on the applications of these cylindrical ferromagnetic nanowires, opening up extremely promising opportunities for their use in magnetic logic applications. Acknowledgements - Work supported by the Romanian Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCCDI) under project PN-III-P4-ID-PCE-2016-0358 – Contract no. 149/2017.