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Abstrak :
This research aims i) to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D) with a harmonic oscillator potential using orbital-free density functional theory, and ii) to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.

Abstrak :
Simulasi Mikromagnetik Medan Depinning Domain Wall pada Sebuah Notch Bentuk Simetris Ganda Feromagnetik Wire. Dalam makalah ini, kami telah melakukan investigasi medan depinning domain wall pada sebuah notch bentuk simetris ganda feromagnetik wire menggunakan simulasi mikromagnetik untuk material Permalloy (Py), Kobalt (Co) dan Nikel (Ni). Medan depinning domain wall meningkat seiring dengan berkurangnya ukuran notch. Pada kondisi medan depinning domain wall kecil, struktur domain wall menunjukkan bentuk struktur transverse wall (TW) sedangkan terjadi perubahan struktur dari struktur transverse wall menjadi struktur antivortex wall (AVW) pada medan depinning besar. Kami telah mengamati juga bahwa profil energi magnetisasi mirip dengan profil medan depinning. Artinya dibutuhkan energi yang lebih banyak untuk melepaskan sebuah domain wall dari ukuran notch yang lebih kecil. Simulasi mikromagnetik menunjukkan medan depinning domain tergantung pada ukuran notch dan juga sifat anisotropi material feromagnetik.

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In this paper, we investigate the depinning field domain wall on symmetric double notch ferromagnetic wires by means of micromagnetic simulation for Permalloy (Py), Cobalt (Co), and Nickel (Ni) materials. The depinning field domain wall increases as the size of the notch decreases. At a lower depinning field, the domain wall inner structure exhibited a transverse wall (TW), while at a higher depinning field, there was a transformation of the domain wall inner structure from transverse wall to antivortex wall (AVW). We also observed that the magnetization energy increased as the size of the notch decreased. This means that more energy was needed to release the domain wall from a smaller notch. Micromagnetic simulation showed that the depinning field domain wall depends on the size of the notch and on the ferromagnetic anisotropy.