• M. Schöbitz
  • A. De Riz
  • S. Martin
  • S. Bochmann
  • C. Thirion
  • J. Vogel
  • M. Foerster
  • L. Aballe
  • T. O. Menteş
  • A. Locatelli
  • F. Genuzio
  • S. Le-Denmat
  • L. Cagnon
  • J. C. Toussaint
  • D. Gusakova
  • J. Bachmann
  • O. Fruchart

In the Letter and Supplemental Material we used values for the spontaneous magnetization M s = 0.67 MA / m and exchange stiffness A = 1.1 × 10 - 11 J / m for both numerical and analytical micromagnetic modeling. We stated that these are suitable for nanowires with composition Co 30 Ni 70 ; however, the given values correspond instead to a composition of Co 20 Ni 80 . Thus, the simulated critical current density, j c = 1.5 × 10 12 A / m 2 , required for the switching of circulation of the Bloch-point domain wall in a 90 nm diameter nanowire, cannot be directly compared to the experimental value j c = 1.4 × 10 12 A / m 2 for the same wire diameter but composition Co 30 Ni 70 . For this composition, one should use M s = 0.77 MA / m [1] and A = 1.5 × 10 - 11 J / m [2] instead (room temperature values). These values were calculated based on the fact that M s and A are expected to vary nearly linearly with respect to their composition at dominant Ni content. M s was also determined experimentally through room temperature magnetometry measurements performed on our nanowire samples still within the alumina template, with corrections made for demagnetization that comes with uncertainties on wire diameter, template porosity, and curve fitting [3]. This gives M s = 0.86 ± 0.14 MA / m , which considering the error range is in reasonable agreement with the theoretical calculation. We can employ the usual micromagnetic scaling procedure for soft magnetic materials to translate the results mentioned in the Letter for Co 20 Ni 80 to those for Co 30 Ni 70 . Magnetic fields are normalized to magnetization and lengths to the dipolar exchange length, d = v 2 A / ( µ 0 M 2 s ) (6.25 nm for Co 20 Ni 80 and 6.34 nm for Co 30 Ni 70 ), which translates the density of current normalized by M s / d as the source of the Œrsted field. The scaling leads to j c ˜ 1.7 × 10 12 A / m 2 , however, valid for a diameter scaled to 91.4, instead of 90 nm in the simulation. We now need to consider the expected scaling of critical current with 1 / R 3 , mentioned in the Letter, to finally translate to a nanowire with composition Co 30 Ni 70 and diameter 90 nm, giving j c ˜ 1.8 × 10 12 A / m 2 . In the end, the agreement of the switching current between experiments and simulations remains reasonable, especially considering the uncertainty on the exact value of A for these CoNi alloys and the temperature dependence of both A and M s . Note also that the amplitude of the effect of spin-polarized current u , defined on p. 3, is instead 52.6 m / s per 10 12 A / m 2 for composition Co 30 Ni 70 . This does not affect the conclusion that the domain wall speed v u , and thus of the absence of Walker breakdown in nanowires.

Original languageEnglish
Article number249901
JournalPhysical Review Letters
Volume125
Issue number24
DOIs
StatePublished - 9 Dec 2020

    Scopus subject areas

  • Physics and Astronomy(all)

ID: 77894302