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

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 – 100 nm and upper radius ( r ) varied between 10 nm to R − 10 nm 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 = 100 nm 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 K e f f = 13 . 508 kJ / m 3 , − 5 . 403 kJ / m 3 and − 4 . 322 kJ / m 3 respectively for σ = 0 . 9 , 0 . 5 and 0.1 with R = 100 nm . 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 .