The first-order reversal curve (FORC) method is one of the most appealing magnetic characterization methods that has been used over decades for detailed analyses of nanoscaled magnetic systems. These detailed analyses are accompanied by numerous magnetic features in FORC heat-maps that usually cannot be fully explained1. In this direction, several theoretical studies have been done to provide a coherent framework to demonstrate those features1,2. However, due to computational limitations, the theoretical models consider mostly perfect arrangements of ideal nanomagnets, such as magnetic nanowires (MNWs), that do not match the real experiments3,4. Here, the FORC heat-maps of several MNW arrays were modeled and discussed. First, several MNW arrays with different arrangements (e.g. hexagonal, square, and random) are modeled and the effect of arrangement on the interaction fields (Hu) are explored. Next, the FORC heat-maps of these MNW arrays are calculated to visualize the importance of the arrangement on the magnetic characteristics of these systems. Then, geometrical imperfections (e.g. variations in shape and size) of MNWs were modeled and randomly assigned to investigate their effects on the FORC heat-maps. Figure 1 shows simulation results for different MNWs arrangements and geometrical imperfections that dictate the Hu among MNWs and the FORC heat-maps, respectively. It was found that the average interaction field (Huave) in hexagonal arrangements is higher than those in square arrangements regardless of the filling factor (defined as the area of MNWs to the total area of the simulation box). That is because the hexagonal arrangement has an odd number of MNWs in which the middle one is always in a frustrated state. The MNWs in random arrangements have significantly higher Hu variations (defined as the difference between the interaction field maximum (Humax) and minimum (Humin)) because the interwire distance in this arrangement is not constant, as opposed to hexagonal and square arrangements. Thus, the Hu is less uniform, and the mean-field effect theory ceased to be a reasonable approximation for simulating these randomly arranged MNWs. Moreover, modeling the geometrical imperfections as variations in coercivity (Hc) will result in presence of the well-known “Wish-bone” and “T-shape” features in the FORC heat-maps. Interestingly, we show that the presence of these features not only depends on the variation of the Hc but also depends on the relative strength of both Hc and Hu.

**References:**

1 C.-I. Dobrotă and A. Stancu, J. Appl. Phys., 2013, 113, 043928. 2 D. A. Gilbert, G. T. Zimanyi, R. K. Dumas, M. Winklhofer, A. Gomez, N. Eibagi, J. L. Vicent and K. Liu, Sci. Rep., 2014, 4, 1–5. 3 M. R. Zamani Kouhpanji, A. Ghoreyshi, P. B. Visscher and B. J. H. Stadler, Sci. Rep., 2020, 10, 15482. 4 M. R. Zamani Kouhpanji and B. J. H. Stadler, Nano Express, 2020, 1, 010017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/18107c60ea58df5b3d2fffb6001ab6fa.jpg)
Figure 1: Subfigures (a) and (b) show the average interaction field (Hu) and the difference between the maximum and minimum Hu for various MNW arrangements. Subfigures (c) and (d) show the FORC heat-maps for the hexagonal arrangement, where the filling factor and average coercivity (Hc) are 5% and 100 Oe, respectively, for both cases. The Hc standard deviation is 10 Oe and 50 Oe for (c) and (d), respectively. As the ratio of Hu standard deviation (which is constant here because both cases have the same filling factor) to Hc standard deviation decreases from 10 to 2, the FORC heat-map of MNWs changes from “T-shape”, (c), to “Wish-bone”, (d), respectively.

Exploring effects of magnetic nanowire arrangements and imperfections on first-order reversal curve heat-maps

Magnetic nanowires (MNWs) have been proposed for nanobarcoding and biolabeling for decades, but surprisingly, they have never been successfully realized for these applications due to the lack of reliable decoding strategies. Here, several types of MNWs were electrodeposited into track-etched polycarbonate templates for application as nanobarcodes. The coercivity (Hc) and interaction fields (Hu) of the MNWs were engineered using the composition, dimensions, and spatial distributions to tune the remanence spectra1 of each barcode. This remanence spectrum is the irreversible switching field distribution measured at zero applied field after applying a pre-defined field sequence. It is therefore a complex function of both coercivity and interaction field. An automated algorithm was also introduced to reliably decode unknown remanence spectra measured in unknown combinations of the magnetic nanobarcodes2,3. Up-to-date, Hc and Hu distributions themselves have been the most popular magnetic signatures using in decoding, usually measured using the first-order reversal curve (FORC) method1,4. Despite numerous works on tuning Hc and Hu, these parameters can only be independently decoded for a limited number of unique signatures. For instance, Hu for arrays of non-interacting MNWs is always zero, which limits signatures to simply Hc and its distribution. Typical decoding is even harder when both non-interacting and highly interacting magnetic nanobarcodes are at the readout simultaneously3. Although the Hc distribution may be inherently distinct for each MNW; fully decoupling the interaction field effects from the coercivity distribution is a very tedious procedure5. Our recently proposed approach of decoding via the remanence spectra6 has overcome these limitations while also using orders of magnitude fewer measurement points compared to FORC leading to a significantly faster decoding procedure. Figure 1 shows the remanence spectra of a combined measurement with two barcodes: 30nm-diameter Ni MNWs and 100nm-diameter Ni MNWs. The automated algorithm makes a best fit assuming the number of barcodes presence are 1, then 2, then 3. The root-mean-square (RMS) error between the fit and the measurement is calculated at each step. At “n” steps (here 3), the RMS error is not significantly improved, so the number of barcodes is determined to be “n-1” (here 2). This presentation will demonstrate how to expand the number of magnetic nanobarcodes remanence spectra using coercivity and interaction field as independent encoding parameters tuned through various strategies. We will also describe our automated algorithm to reliably and rapidly decode unknown remanence spectra, which is also capable to decode other nanobarcodes including magneto-optic nanobarcodes. In summary, remanence spectra are promising for decoding nanobarcodes for three reasons. First, the coercivity and interaction field can be tailored individually to expand the number of remanence spectra encoded magnetic nanobarcodes. Second, the decoding can reliably be done even when one of these parameters is zero or negligible and also when the number of nanobarcodes presence is unknown. Third, remanence spectra are much faster to measure and less tedious to decouple than standard signatures.

**References:**

1 Y. G. Velázquez, A. L. Guerrero, J. M. Martínez, E. Araujo, M. R. Tabasum, B. Nysten, L. Piraux and A. Encinas, Sci. Rep., 2020, 10, 21396. 2 M. R. Zamani Kouhpanji and B. Stadler, Part. Part. Syst. Charact., 2020, 2000227. 3 M. R. Zamani Kouhpanji and B. J. H. Stadler, Nanoscale Adv., 2021, DOI:10.1039/D0NA00924E. 4 D. A. Gilbert, G. T. Zimanyi, R. K. Dumas, M. Winklhofer, A. Gomez, N. Eibagi, J. L. Vicent and K. Liu, Sci. Rep., 2014, 4, 1–5. 5 C.-I. Dobrotă and A. Stancu, J. Appl. Phys., 2013, 113, 043928. 6 M. R. Zamani Kouhpanji, A. Ghoreyshi, P. B. Visscher and B. J. H. Stadler, Sci. Rep., 2020, 10, 15482.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fae2d498dd387a1e4ac20feae07613b1.jpg)
Figure 1: shows encoding and decoding remanence spectra of magnetic nanowires (MNWs) for nanobarcoding, (a) depicts the normalized backward remanence (BRM) spectra of the individual MNWs “encoded” using their dimensions, and (b-d) illustrate the decoding of an unknown BRM spectrum composed of Ni MNWs with diameters of 30nm and 100nm. The reduction percentage of the root-mean-square (RMS) error is the convergence criteria for identifying the number and type of magnetic nanobarcodes in the unknown BRM spectra.

 A roadmap toward expanding magnetic nanobarcodes signatures

*Session Chair: Salvatore Perna, University of Naples Federico II*

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Winner of the Best Student Presentation Award:  ***JI-05 - Non-planar geometrical effects on the magnetoelectrical signal in a 3D nanomagnetic circuit***

Mohammad Reza Zamani Kouhpanji

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Exploring effects of magnetic nanowire arrangements and imperfections on first-order reversal curve heat-maps

A roadmap toward expanding magnetic nanobarcodes signatures

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