Tailoring of effective biaxial anisotropy in a 2-D array of thin truncated conical nanodisk

Abstract

In the present study, the magnetization reversal of 2-D rectangular array of soft magnetic permalloy thin truncated conical disks is simulated by using micromagnetic modeling. The base radius (R) of the conical disk is varied between 20–100nm and upper radius (r) varied between 10nm to R−10nm such that the ratio σ=r/R lies between 0 to 1. The analysis of angular dependence (θ=0° to 90°) of hysteresis loops for the case of R=100nm is done in particular and its comparison with Stoner–Wohlfarth (SW) model reveals the presence of a bi-axial anisotropy which is attributed to the dipolar interaction between the nanodisks in the array. When the nanodisks are close to regular cylindrical shape (for σ∼0.9), the orthogonal axes of the facet of the array acts as magnetic easy axes. As the nanodisks are tapered to σ∼0.5 and 0.1, the same set of axes turns as hard axis of the bi-axial anisotropic system. Corresponding bi-axial anisotropy constant is estimated from the coercivity of the hysteresis loop along the easy axis as Keff=13.508kJ/m3, −5.403kJ/m3 and −4.322kJ/m3 respectively for σ=0.9,0.5 and 0.1 with R=100nm. In addition to this, an analytical expression is also formulated to calculate the total demagnetization energy of the 2-D array as a function of the magnetization orientation. This demagnetization energy is fitted with the effective bi-axial anisotropy energy expression considering an angular dispersion of the bi-axial anisotropy. The fitting suggests that the extent of angular dispersion of bi-axial anisotropy reduces as the conical disks are tapered (σ decreased). Irrespective of the magnetic field orientation, the remanent state exhibits a s-state of spatial magnetization profile when σ is large whereas a buckled magnetization state symmetric to body diagonal is exhibited for lower σ.