DOI: 10.5061/dryad.3ffbg79vh
title: Fractional magnetic charges and channeling of Faraday lines by disclinations in artificial spin ice

description: We have studied the magnetic moments of artificial spin ice arrays of
 nanomagnets in both undistorted square arrays and in arrays with
 a topological defect induced by a single disclination. We confirm
 that the disclination induces global, macroscopic changes in
 the low-energy collective states of the nanomagnet moment
 configuration. Specifically, the disclination leads to Faraday
 lines of effective magnetic flux that run from the center all the
 way to the edge of the arrays. Moreover, the geometric deformation,
 induced by the topological defect, curves the geometry such that
 these Faraday lines are channeled preferentially by the arrays’ curved
 geometry. Our results demonstrate how the intentional combination
 of topology and geometry can be designed to control magnetic charges
 and the flow of local magnetization and thus manipulate
 associated collective excitations.
description: The experimental data in this work was collected via magnetic
 force microscopy (MFM), which provides black and white images indicating
 the magnetization of individual nanoislands in the measured arrays. The
 direction of each island can be categorized as +1 or -1 via image
 recognition and then analyzed by the included codes to recreate the work
 of the main manuscript.  The simulation data in this
 work was produced via the software Mumax3. The scripts to run this were
 produced by included MatLab files. 
description: # Fractional magnetic charges and channeling of Faraday lines by
 disclinations in artificial spin ice \[Access this dataset on Dryad](DOI:
 10.5061/dryad.3ffbg79vh) This dataset contains raw magnetic force
 microscopy (MFM) images and results of micromagnetic simulations. Codes
 for analyzing data and creating the micromagnetic simulations are also
 included. ## Description of the data and file structure This data is
 separated into folders that contain data and code. There are two data
 folders, "Mumax3 Data" and "MFM Data", containing the
 results of the micromagnetic simulations and magnetic force microscopy
 images, respectively. Organization of "MFM Data" * 2 subfolders
 "AH-D-2_S8_A1" and "AH-D-2_S8_A2" which represent data
 taken from the same sample but after a new anneal for each data set. * The
 .csv file "AH-D-2_S8" is a master file that connects the image
 numbers in "AH-D-2_S8_AX" to the specific sample that is
 represented. * For example, consider image "Phase961.jpg" in the
 folder "AH-D-2_S8_A2". The .csv file indicates this image is of
 a disclination of size N=21 with lattice spacing a = 280. * Important
 conventions in the .csv file: * The sample used has 16 total copies of a
 given disclination with a certain N and lattice spacing (a). The letter
 identifier indicates which copy of the disclination array is measured.
 Specifically disclination arrays are arranged in a 4 x 4 grid, labelled in
 alphabetical order, starting from the top left and continuing to the
 right. * The next column indicates if the image could be successfully
 transcribed from a black and white image to an actual data file. if
 "proc" is written, this procedure was successful and this image
 was able to be used in the full data analysis. If anything else was
 written (or nothing was written), this image was not able to be used in
 the full data analysis. * Folders "AH-D-2_S8_AX" first have all
 the MFM images labelled "PhaseXXXX.jpg". These folders have a
 subfolder called "processed" which contain csv files that have
 used image recognition on the images to get spin values. Files of the
 naming convention "dataXXXX.csv" belong to disclination samples,
 while "XXXXoutput.csv" belong to square samples. This contains
 another subfolder "files for batch programs" which are the
 results of running the aforementioned data through the "Initial"
 programs listed in "Analysis Code - Undistorted" for
 convenience. "Mumax3 Data" contains csv files that are the
 processed results of the micromagnetic simulations (after running Mumax3
 then using "rotanlyze"). These can be processed by the code
 "Initial Mumax Processing v2" in the "Analysis Code -
 Undistorted" folder. * The naming conventions vary for the
 undistorted and distorted cases. For the undistorted case: nXaYYY.csv
 where X is the size of the disclination (e.g. 21) and YYY is the lattice
 spacing (e.g. 280) - For the distorted case: all included files are at a
 lattice spacing of a = 280. The values following a and b represent the
 distortion parameters alpha and beta used in the manuscript. In this case
 N21a1_01b0_05 represents data for N = 21, lattice spacing = 280, alpha =
 1.01, and beta = 0.05 ## Code/Software There are three folders containing
 code, "Mumax3 Code", "Analysis Code - Distorted", and
 "Analysis Code - Undistorted". * "Mumax3 Code"
 contains MATLAB code for generating scripts that can then be run using the
 Mumax3 software. It also contains code for doing some basic analysis of
 results and modification into data formats that can be read in by programs
 in the Analysis Code folders. This folder contains a README.md file which
 details how to use the code in folder * "Analysis Code -
 Undistorted" contains code responsible for analyzing undistorted
 disclination arrays as well as square arrays. This folder contains a
 README.md file which details how to use the code in folder *
 "Analysis Code - Distorted" contains code responsible for
 analyzing distorted disclination arrays as well as functions for the
 Boltzmann calculation done in the manuscript. This folder contains a
 README.md file which details how to use the code in folder