Extraordinary Magnetic Hardening in Nanowire Assemblies: the Geometry and Proximity Effects

Abstract

Brown's theorem on coercivity of ferromagnetic materials has predicted that the coercivity level is substantially higher than in practice for all the materials studied in experiments in the past seven decades, which is known as the Brown's paradox. In this paper, a system with a coercivity close to the one predicted by Brown's theorem is investigated. Cobalt nanowires are obtained by chemical synthesis that give rise to coercive forces significantly higher than the magnetocrystalline anisotropy field, verifying the Brown's theorem. It is found that the coercivity is strongly dependent on the nanowire diameter, the alignment of the wires in an assembly, and the packing density of the assembly. An analysis based on the current experimental results and related literature reveals a coercivity ceiling in consideration of geometrical dimensions and the effective magnetic anisotropy. Quantitative information is obtained about the proximity effect on the coercivity and the magnetization which shows the correlation between the energy product and the packing density. Furthermore, it is found that by coating the nanowires with Fe, the energy density can be enhanced. These findings provide a guideline for materials design of future high‐performance permanent magnets that take advantage of shape anisotropy at the nanoscale.

Magnetic Nanoparticles: Synthesis, Anisotropy, and Applications

“…A strong dipolar interaction can make it difficult for NPs to rotate their magnetization directions, leading to dipole ferromagnetism with enhanced coercivity, as observed for 15 nm Co NP arrays by Fresnel Lorentz microscopy and electron holography (Figure C,D) . However, when single-domain magnetic nanowires are considered, their coercivity H c can decrease with increased nanowire packing fraction ( p ): in which H c0 is the coercivity of noninteracting nanowires (i.e., for p ≈ 0), where both the magnetocrystalline anisotropy and shape anisotropy prevail, and A is the proximity coefficient. The quantity Ap represents the induced magnetostatic interaction field, and its value is proportional to both the assembly packing fraction and the spontaneous magnetization of neighboring nanowires.…”

“…As these nanowires have an average diameter of 8 nm and length of 150 nm, their radius is smaller than the coherent radius ( R coh = 3.65 l ex , where l ex is the exchange length), and they exhibit coherent Stoner–Wohlfarth-type magnetization reversal behavior. As a result, a large coercivity of over 12.6 kOe can be obtained from their aligned assembly (Figure B) . The prealigned nanowires were compacted at various pressures to consolidate the assemblies with the packing densities ranging from 5.3 to 7.3 g/cm 3 and energy products as high as 20 MGOe (Figures C,D) .…”

“…(B) Magnetization loop of the aligned Co nanowire assembly (along the parallel direction) at 300 K. (C) SEM image of the compacted and aligned nanowire assembly. (D) Second-quadrant B – H , M – H , and ( BH ) max – H curves of the compacted nanowire assembly at 300 K. Reproduced with permission from ref . Copyright 2021 Wiley-VCH.…”

Hybrid Ni–Co–Ni Structures Prepared by Magnetophoresis as Efficient Permanent Magnets for Integration into Microelectromechanical Systems

“…Nanochemistry has recently made some decisive contributions in the field of hard magnetic materials and PMs by controlling the anisotropic growth of single‐domain and single‐crystal magnetic nanorods (NR), which exhibit high coercivity at room temperature. [ 23 ] Single‐domain cobalt NRs, prepared by organometallic chemistry [ 24 ] or polyol process, [ 25,26 ] combine shape and magnetocrystalline anisotropies. Thanks to their small diameter, which favors uniform magnetization reversal, and their very good crystallinity, which limits the nucleation of magnetization reversal on structural defects, [ 27 ] these objects exhibit coercivity close to the theoretical anisotropy field , with K 1 the magnetocrystalline constant of cobalt and M S its saturation magnetization, the 2 πM S term being related to the shape anisotropy.…”

Iron-Nickel Alloy with Starfish-like Shape and Its Unique Magnetic Properties: Effect of Reaction Volume and Metal Concentration on the Synthesized Alloy

“…One of the important magnetic properties is coercivity (Hc), which is a measure of the ability of a ferromagnetic material to keep its magnetization (i.e., without being demagnetized) when Nanomaterials 2021, 11, 3034 2 of 18 exposed to an external magnetic field [16]. Ferromagnetic materials with high coercivity are called magnetically hard and are used to make permanent magnets [17]. Materials with low coercivity are known as soft magnetic materials, which are used in many applications such as transformers [18], recording heads [19], microwave devices [20], and magnetic shielding [21].…”