White paper: First-order reversal curves enhance understanding of nanoscale magnetic materials
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First-order reversal curves enhance understanding of nanoscale magnetic materials LAKE SHORE CRYOTRONICS, INC. B.C. Dodrill and L. Spinu
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agnetic nanowires, nanodots, and nanoparticles make up an important class of nanostructured magnetic materials. Due to size confinement in the nanometer range, new phenomena arise in these materials. These structures are ideal candidates for technological applications in spintronics, high-density recording media, microwave electronics, and permanent magnets as well as for medical diagnostics and targeted drug delivery applications. In addition to being of technological value, these materials represent an experimental playground for fundamental studies of magnetic interactions and magnetization mechanisms at the nanoscale level.1,2 When investigating the magnetic interactions in these materials, one of the most interesting configurations is a periodic array of magnetic nanowires because both the size of the wires and their arrangement with respect to one another can be controlled. Inter-wire coupling is one of the most important effects in nanowire arrays because it significantly affects magnetization switching as well as microwave and magneto-transport properties. Experimentally, one of the most widely used methods to investigate the strength and measure the effects of these interactions is by using a magnetometry technique that measures and analyzes first-order reversal curves (FORCs).3 A FORC is measured by saturating a sample in a field Hsat, decreasing the field to a reversal field Ha, then sweeping the field back to Hsat in a series of regular
field steps Hb. This process is repeated for many values of Ha yielding a series of FORCs. The measured magnetization at each step as a function of Ha and Hb gives M(Ha,Hb) which is then plotted as a function of Ha and Hb in field space. The FORC distribution ρ(Ha, Hb) is the mixed second derivative, that is, ρ(Ha,Hb) = –∂2 M(Ha,Hb)/∂Ha∂Hb, and a FORC diagram is a contour plot of ρ(Ha,Hb) with the axis rotated by changing coordinates from (Ha,Hb) to Hc=(Hb–Ha)/2 and Hu=(Hb+Ha)/2 where Hu corresponds to the distribution of interaction fields, and Hc the distribution of switching fields. The magnetic response of a material is proportional to its intrinsic magnetism and the volume of material being measured. For nanoscale magnetic materials, the volume is inherently small and consequently the signal that is measured by a magnetometer is very low. Thus, the sensitivity of the magnetometry technique is an important parameter in connection with characterizing nanostructured magnetic materials. Magnetometry techniques can be broadly classified into two categories: inductive and force-based. Common inductive methods include vibrating sample magnetometry (VSM), extraction magnetometry, AC susceptometry, and superconducting quantum interference device (SQUID) magnetometry. The two most commonly used inductive techniques are VSM and SQUID magnetometry. Alternating gradient magnetometry (AGM) is the most often
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