Facile decoding of quantitative signatures from magnetic nanowire arrays

Magnetic nanoparticles have been proposed as contact-free minimal-background nanobarcodes, and yet it has been difficult to rapidly and reliably decode them in an assembly. Here, high aspect ratio nanoparticles, or magnetic nanowires (MNWs), are characterized using first-order reversal curves (FORC) to investigate quantitative decoding. We have synthesized four types of nanowires (differing in diameter) that might be used for barcoding, and identified four possible “signature” functions that might be used to quickly distinguish them. To test this, we have measured the signatures of several combination samples containing two or four different MNW types, and fit them to linear combinations of the individual type signatures to determine the volume ratios of the types. We find that the signature which determines the ratios most accurately involves only the slope of each FORC at its reversal field, which requires only 2–4 data points per FORC curve, reducing the measurement time by a factor of 10 to 50 compared to measuring the full FORC.


FORC measurements
The magnetic measurements were done using MicroMag Vibrating Sample Magnetometer (µVSM), Princeton Measurements Corporation, at room temperature. To determine the field ranges for our FORC measurements, we first made a hysteresis loop measurement. The FORC range is specified by giving minimum and maximum interaction fields, which were chosen as the negative and positive half of the anisotropy field, respectively. The coercivity field range was selected from zero to the anisotropy field. The saturation field was set at 1.0 T. Depending on the magnetic strength of the samples and the overall shape of their hysteresis loop, the number of FORC curves and the averaging time were selected. For example, since the overall shape of the 30nm sample's hysteresis loop was showing almost no interactions between the nanowires (meaning the FORC distribution is confined to the horizontal axis), we chose larger FORC number (smaller field steps) to capture all details. The data was processed using the

Magnetic nanowire (MNW) electrodeposition
Cobalt (Co) MNWs were electrodeposited into track-etched polycarbonate templates with a broad range of fill factors (the cross-section ratio of the MNWs to the total surface of the template = 0.5% -12%). Figure  First, a 50nm layer of chromium (Cr) was evaporated on one side of the templates as the adhesion layer for the conductive layer, which was a 500nm copper (Cu) film. The templates were placed as the cathode in a three-electrode electrodeposition system, where a platinum (Pt) mesh was the counter electrode and a standard Ag/AgCl electrode was used as the reference electrode. The electrolyte consisted of 0.5M boric acid and 0.9M cobalt sulfate, where the pH was adjusted at 6.5 using sodium hydroxide. The electrodeposition was conducted by applying a constant voltage of 1V.

Proposed measurements
The ISFD measurement starts by applying a large field to ensure the saturation of the sample. The field then is reduced the field to a reversal field. Then the field returns back one step to the same field of the previous reversal field while measuring the magnetization. Then the field should jump back to the saturation filed at one step to repeat the same process for the next reversal fields. The solid black lines in Figure SI-4 shows the data collected in this method, here we collected 5 data points from the reversal field for better visualization. Similarly, the protocol for the backfield remanence magnetization (BRM) starts by applying a large field to ensure the saturation of the sample. The field then is reduced the field to a reversal field. Then the field goes to zero at one step to measure the magnetization. Afterward, the field jumps back to the saturation filed at one step to repeat the same process for the next reversal fields.
Figure  showing the data in the context of the proposed measurements. The black solid lines are the data for calculating the ISFD, and the red dots are for calculating the BRM.
In Figure SI-5, we examine the number of the data point's effects on the ISFD to evaluate the robustness of the proposed measurements. As can be seen, the deviation for the ISFD is not significant, and 2 data points are sufficient.
Figure SI-5: Illustrating the number of collected data points on each reversal curve. In all subfigures, "Norm." stands for "Normalized". For MNWs arrays with diameters of 32nm and 55nm, since the porosity is very small, the MNWS to not exert much interaction on each other. This causes more noise in the ISFD data.

Data analysis
We electrodeposited several types of the MNWs inside polycarbonate (PC) templates, and then we performed the FORC measurements on each individual sample.
We (1). The fitting quality was evaluated using the root mean square (RMS) error of the difference between the "Exp.
(2). The RMS error was minimized to find the optimum weights that give the volume ratio (x) of each type of the MNWs in the combination, Eq. (3).