Discrepancy between the analytical for of the potential that describes a domain wall and numerical results,,,,,,
variable x,D=1.5mJ/m2,D=0,Analytical result,,,
-5,0.9996368335,0.9995424103,0.9926296868,,,
-4.95,0.9995986428,0.99949429,0.9922322671,,,
-4.9,0.9995564364,0.9994411099,0.9918124194,,,
-4.85,0.9995097921,0.9993823381,0.9913687784,,,
-4.8,0.9994582435,0.9993173868,0.9908998862,,,
-4.75,0.999401275,0.9992456065,0.9904041854,,,
-4.7,0.999338317,0.9991662794,0.9898800112,,,
-4.65,0.9992687399,0.9990786122,0.9893255829,,,
-4.6,0.9991918481,0.9989817286,0.9887389951,,,
-4.55,0.999106873,0.99887466,0.9881182075,,,
-4.5,0.9990129652,0.9987563362,0.9874610344,,,
-4.45,0.9989091862,0.9986255746,0.9867651328,,,
-4.4,0.9987944988,0.9984810685,0.9860279897,,,
-4.35,0.9986677574,0.9983213743,0.9852469081,,,
-4.3,0.9985276958,0.9981448967,0.9844189919,,,
-4.25,0.9983729152,0.9979498732,0.9835411298,,,
-4.2,0.9982018702,0.9977343564,0.9826099764,,,
-4.15,0.9980128532,0.997496195,0.9816219335,,,
-4.1,0.9978039779,0.9972330121,0.980573128,,,
-4.05,0.9975731604,0.9969421821,0.979459389,,,
-4,0.9973180986,0.9966208043,0.978276222,,,
-3.95,0.9970362497,0.9962656746,0.9770187812,,,
-3.9,0.9967248046,0.9958732538,0.9756818388,,,
-3.85,0.9963806611,0.995439633,0.9742597522,,,
-3.8,0.9960003928,0.9949604949,0.9727464275,,,
-3.75,0.9955802154,0.9944310714,0.9711352798,,,
-3.7,0.9951159505,0.9938460976,0.9694191902,,,
-3.65,0.994602984,0.9931997599,0.9675904581,,,
-3.6,0.9940362218,0.9924856395,0.9656407501,,,
-3.55,0.9934100399,0.9916966503,0.9635610432,,,
-3.5,0.9927182306,0.9908249705,0.9613415636,,,
-3.45,0.9919539421,0.9898619671,0.9589717193,,,
-3.4,0.9911096136,0.9887981132,0.956440027,,,
-3.35,0.9901769024,0.987622897,0.9537340321,,,
-3.3,0.989146605,0.9863247223,0.9508402217,,,
-3.25,0.9880085703,0.9848907986,0.9477439296,,,
-3.2,0.9867516043,0.9833070215,0.9444292332,,,
-3.15,0.9853633658,0.9815578409,0.940878841,,,
-3.1,0.9838302523,0.9796261179,0.9370739704,,,
-3.05,0.9821372756,0.9774929672,0.9329942156,,,
-3,0.9802679257,0.9751375863,0.9286174034,,,
-2.95,0.9782040228,0.9725370687,0.9239194382,,,
-2.9,0.9759255561,0.9696662007,0.9188741335,,,
-2.85,0.9734105091,0.9664972414,0.913453031,,,
-2.8,0.9706346698,0.9629996839,0.9076252051,,,
-2.75,0.9675714264,0.9591399973,0.9013570538,,,
-2.7,0.9641915465,0.9548813486,0.8946120746,,,
-2.65,0.9604629397,0.9501833041,0.8873506251,,,
-2.6,0.9563504046,0.9450015098,0.8795296698,,,
-2.55,0.9518153576,0.9392873506,0.8711025108,,,
-2.5,0.9468155466,0.9329875888,0.862018506,,,
-2.45,0.9413047483,0.9260439829,0.8522227747,,,
-2.4,0.9352324513,0.9183928887,0.8416558913,,,
-2.35,0.9285435272,0.9099648443,0.8302535729,,,
-2.3,0.9211778919,0.9006841439,0.8179463609,,,
-2.25,0.9130701622,0.8904684044,0.8046593045,,,
-2.2,0.9041493116,0.8792281326,0.7903116506,,,
-2.15,0.8943383339,0.8668663008,0.7748165482,,,
-2.1,0.8835539226,0.8532779424,0.7580807793,,,
-2.05,0.8717061769,0.8383497829,0.7400045259,,,
-2,0.8586983503,0.8219599214,0.7204811913,,,
-1.95,0.844426656,0.8039775865,0.6993972931,,,
-1.9,0.8287801527,0.7842629923,0.6766324502,,,
-1.85,0.811640734,0.7626673248,0.6520594921,,,
-1.8,0.7928832519,0.7390328974,0.6255447198,,,
-1.75,0.772375809,0.7131935193,0.5969483578,,,
-1.7,0.7499802587,0.684975126,0.566125237,,,
-1.65,0.7255529619,0.654196732,0.5329257583,,,
-1.6,0.6989458484,0.6206717689,0.4971971896,,,
-1.55,0.6700078439,0.5842098833,0.4587853557,,,
-1.5,0.6385867222,0.5446192699,0.417536784,,,
-1.45,0.6045314485,0.5017096251,0.3733013723,,,
-1.4,0.5676950819,0.4552958033,0.3259356459,,,
-1.35,0.5279383001,0.4052022582,0.2753066675,,,
-1.3,0.4851336066,0.3512683443,0.2212966562,,,
-1.25,0.4391702676,0.2933545372,0.1638083607,,,
-1.2,0.3899600076,0.2313496096,0.1027712074,,,
-1.15,0.3374434641,0.1651787647,0.0381482191,,,
-1.1,0.2815973677,0.0948126833,-0.0300563438,,,
-1.05,0.2224423616,0.0202773756,-0.1017887176,,,
-1,0.1600513168,-0.0583353409,-0.1769369055,,,
-0.95,0.0945579259,-0.1408570134,-0.2553217226,,,
-0.9,0.0261652777,-0.2270317501,-0.3366879357,,,
-0.85,-0.0448459757,-0.3165059294,-0.4206959138,,,
-0.8,-0.1181103355,-0.4088190227,-0.5069142929,,,
-0.75,-0.1931716166,-0.5033962369,-0.594814247,,,
-0.7,-0.26947918,-0.5995437668,-0.6837660192,,,
-0.65,-0.3463868998,-0.6964474937,-0.7730384072,,,
-0.6,-0.4231555252,-0.7931759617,-0.8618018827,,,
-0.55,-0.4989590364,-0.8886883858,-0.9491359591,,,
-0.5,-0.5728954659,-0.9818482871,-1.0340412856,,,
-0.45,-0.6440024587,-1.071443098,-1.1154567327,,,
-0.4,-0.7112775722,-1.1562097409,-1.1922814472,,,
-0.35,-0.7737029863,-1.2348657628,-1.2634015097,,,
-0.3,-0.8302739237,-1.3061451438,-1.3277204378,,,
-0.25,-0.8800296976,-1.368837419,-1.3841923848,,,
-0.2,-0.9220859659,-1.4218283171,-1.4318565247,,,
-0.15,-0.9556664935,-1.4641397818,-1.46987084,,,
-0.1,-0.9801325817,-1.4949670529,-1.4975433712,,,
-0.05,-0.9950083215,-1.5137104851,-1.5143589979,,,
0,-1,-1.52,-1.52,,,
0.05,-0.9950083215,-1.5137104851,-1.5143589979,,,
0.1,-0.9801325817,-1.4949670529,-1.4975433712,,,
0.15,-0.9556664935,-1.4641397818,-1.46987084,,,
0.2,-0.9220859659,-1.4218283171,-1.4318565247,,,
0.25,-0.8800296976,-1.368837419,-1.3841923848,,,
0.3,-0.8302739237,-1.3061451438,-1.3277204378,,,
0.35,-0.7737029863,-1.2348657628,-1.2634015097,,,
0.4,-0.7112775722,-1.1562097409,-1.1922814472,,,
0.45,-0.6440024587,-1.071443098,-1.1154567327,,,
0.5,-0.5728954659,-0.9818482871,-1.0340412856,,,
0.55,-0.4989590364,-0.8886883858,-0.9491359591,,,
0.6,-0.4231555252,-0.7931759617,-0.8618018827,,,
0.65,-0.3463868998,-0.6964474937,-0.7730384072,,,
0.7,-0.26947918,-0.5995437668,-0.6837660192,,,
0.75,-0.1931716166,-0.5033962369,-0.594814247,,,
0.8,-0.1181103355,-0.4088190227,-0.5069142929,,,
0.85,-0.0448459757,-0.3165059294,-0.4206959138,,,
0.9,0.0261652777,-0.2270317501,-0.3366879357,,,
0.95,0.0945579259,-0.1408570134,-0.2553217226,,,
1,0.1600513168,-0.0583353409,-0.1769369055,,,
1.05,0.2224423616,0.0202773756,-0.1017887176,,,
1.1,0.2815973677,0.0948126833,-0.0300563438,,,
1.15,0.3374434641,0.1651787647,0.0381482191,,,
1.2,0.3899600076,0.2313496096,0.1027712074,,,
1.25,0.4391702676,0.2933545372,0.1638083607,,,
1.3,0.4851336066,0.3512683443,0.2212966562,,,
1.35,0.5279383001,0.4052022582,0.2753066675,,,
1.4,0.5676950819,0.4552958033,0.3259356459,,,
1.45,0.6045314485,0.5017096251,0.3733013723,,,
1.5,0.6385867222,0.5446192699,0.417536784,,,
1.55,0.6700078439,0.5842098833,0.4587853557,,,
1.6,0.6989458484,0.6206717689,0.4971971896,,,
1.65,0.7255529619,0.654196732,0.5329257583,,,
1.7,0.7499802587,0.684975126,0.566125237,,,
1.75,0.772375809,0.7131935193,0.5969483578,,,
1.8,0.7928832519,0.7390328974,0.6255447198,,,
1.85,0.811640734,0.7626673248,0.6520594921,,,
1.9,0.8287801527,0.7842629923,0.6766324502,,,
1.95,0.844426656,0.8039775865,0.6993972931,,,
2,0.8586983503,0.8219599214,0.7204811913,,,
2.05,0.8717061769,0.8383497829,0.7400045259,,,
2.1,0.8835539226,0.8532779424,0.7580807793,,,
2.15,0.8943383339,0.8668663008,0.7748165482,,,
2.2,0.9041493116,0.8792281326,0.7903116506,,,
2.25,0.9130701622,0.8904684044,0.8046593045,,,
2.3,0.9211778919,0.9006841439,0.8179463609,,,
2.35,0.9285435272,0.9099648443,0.8302535729,,,
2.4,0.9352324513,0.9183928887,0.8416558913,,,
2.45,0.9413047483,0.9260439829,0.8522227747,,,
2.5,0.9468155466,0.9329875888,0.862018506,,,
2.55,0.9518153576,0.9392873506,0.8711025108,,,
2.6,0.9563504046,0.9450015098,0.8795296698,,,
2.65,0.9604629397,0.9501833041,0.8873506251,,,
2.7,0.9641915465,0.9548813486,0.8946120746,,,
2.75,0.9675714264,0.9591399973,0.9013570538,,,
2.8,0.9706346698,0.9629996839,0.9076252051,,,
2.85,0.9734105091,0.9664972414,0.913453031,,,
2.9,0.9759255561,0.9696662007,0.9188741335,,,
2.95,0.9782040228,0.9725370687,0.9239194382,,,
3,0.9802679257,0.9751375863,0.9286174034,,,
3.05,0.9821372756,0.9774929672,0.9329942156,,,
3.1,0.9838302523,0.9796261179,0.9370739704,,,
3.15,0.9853633658,0.9815578409,0.940878841,,,
3.2,0.9867516043,0.9833070215,0.9444292332,,,
3.25,0.9880085703,0.9848907986,0.9477439296,,,
3.3,0.989146605,0.9863247223,0.9508402217,,,
3.35,0.9901769024,0.987622897,0.9537340321,,,
3.4,0.9911096136,0.9887981132,0.956440027,,,
3.45,0.9919539421,0.9898619671,0.9589717193,,,
3.5,0.9927182306,0.9908249705,0.9613415636,,,
3.55,0.9934100399,0.9916966503,0.9635610432,,,
3.6,0.9940362218,0.9924856395,0.9656407501,,,
3.65,0.994602984,0.9931997599,0.9675904581,,,
3.7,0.9951159505,0.9938460976,0.9694191902,,,
3.75,0.9955802154,0.9944310714,0.9711352798,,,
3.8,0.9960003928,0.9949604949,0.9727464275,,,
3.85,0.9963806611,0.995439633,0.9742597522,,,
3.9,0.9967248046,0.9958732538,0.9756818388,,,
3.95,0.9970362497,0.9962656746,0.9770187812,,,
4,0.9973180986,0.9966208043,0.978276222,,,
4.05,0.9975731604,0.9969421821,0.979459389,,,
4.1,0.9978039779,0.9972330121,0.980573128,,,
4.15,0.9980128532,0.997496195,0.9816219335,,,
4.2,0.9982018702,0.9977343564,0.9826099764,,,
4.25,0.9983729152,0.9979498732,0.9835411298,,,
4.3,0.9985276958,0.9981448967,0.9844189919,,,
4.35,0.9986677574,0.9983213743,0.9852469081,,,
4.4,0.9987944988,0.9984810685,0.9860279897,,,
4.45,0.9989091862,0.9986255746,0.9867651328,,,
4.5,0.9990129652,0.9987563362,0.9874610344,,,
4.55,0.999106873,0.99887466,0.9881182075,,,
4.6,0.9991918481,0.9989817286,0.9887389951,,,
4.65,0.9992687399,0.9990786122,0.9893255829,,,
4.7,0.999338317,0.9991662794,0.9898800112,,,
4.75,0.999401275,0.9992456065,0.9904041854,,,
4.8,0.9994582435,0.9993173868,0.9908998862,,,
4.85,0.9995097921,0.9993823381,0.9913687784,,,
4.9,0.9995564364,0.9994411099,0.9918124194,,,
4.95,0.9995986428,0.99949429,0.9922322671,,,
5,0.9996368335,0.9995424103,0.9926296868,,,
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Numerical calculations of the Band structure of a periodic array of Dzyaloshinskii Domain walls,,,,,,
,,,,,,
,,,,,,
k vector,First band ,Second band,Third band,Fourth band,Fifth band,Sixth band
0,1,1,1,0,0,0
0.0001,0.9942114555,0.9999433579,0.999985754,0.0057885445,5.66421128980262E-05,0.000014246
0.0002,0.9772409759,0.9997734693,0.9999430184,0.0227590241,0.0002265307,5.69816471588185E-05
0.0003,0.9502084501,0.9994904476,0.9998717998,0.0497915499,0.0005095524,0.0001282002
0.0004,0.9147813385,0.9990944813,0.9997721095,0.0852186615,0.0009055187,0.0002278905
0.0005,0.87293564,0.9985858341,0.9996439634,0.12706436,0.0014141659,0.0003560366
0.0006,0.8267137246,0.997964844,0.9994873817,0.1732862754,0.002035156,0.0005126183
0.0007,0.7780257974,0.9972319233,0.9993023892,0.2219742026,0.0027680767,0.0006976108
0.0008,0.728518699,0.9963875575,0.9990890151,0.271481301,0.0036124425,0.0009109849
0.0009,0.6795133302,0.9954323044,0.9988472932,0.3204866698,0.0045676956,0.0011527068
0.001,0.6319973945,0.9943667938,0.9985772616,0.3680026055,0.0056332062,0.0014227384
0.0011,0.5866546606,0.9931917257,0.998278963,0.4133453394,0.0068082743,0.001721037
0.0012,0.5439130914,0.9919078698,0.9979524443,0.4560869086,0.0080921302,0.0020475557
0.0013,0.5039985443,0.9905160638,0.9975977571,0.4960014557,0.0094839362,0.0024022429
0.0014,0.4669856842,0.9890172123,0.9972149572,0.5330143158,0.0109827877,0.0027850428
0.0015,0.43284185,0.9874122853,0.9968041048,0.56715815,0.0125877147,0.0031958952
0.0016,0.4014624515,0.9857023165,0.9963652644,0.5985375485,0.0142976835,0.0036347356
0.0017,0.3726981438,0.983888402,0.9958985048,0.6273018562,0.016111598,0.0041014952
0.0018,0.3463748435,0.9819716982,0.9954038993,0.6536251565,0.0180283018,0.0045961007
0.0019,0.322307925,0.9799534201,0.9948815252,0.677692075,0.0200465799,0.0051184748
0.002,0.3003119049,0.9778348397,0.9943314641,0.6996880951,0.0221651603,0.0056685359
0.0021,0.2802067549,0.9756172837,0.993753802,0.7197932451,0.0243827163,0.006246198
0.0022,0.2618217696,0.9733021316,0.9931486287,0.7381782304,0.0266978684,0.0068513713
0.0023,0.2449977118,0.9708908137,0.9925160384,0.7550022882,0.0291091863,0.0074839616
0.0024,0.2295877738,0.9683848089,0.9918561293,0.7704122262,0.0316151911,0.0081438707
0.0025,0.2154577524,0.9657856425,0.9911690037,0.7845422476,0.0342143575,0.0088309963
0.0026,0.2024857211,0.9630948841,0.9904547679,0.7975142789,0.0369051159,0.0095452321
0.0027,0.1905613982,0.9603141451,0.9897135322,0.8094386018,0.0396858549,0.0102864678
0.0028,0.1795853477,0.9574450767,0.9889454108,0.8204146523,0.0425549233,0.0110545892
0.0029,0.1694681048,0.9544893675,0.9881505218,0.8305318952,0.0455106325,0.0118494782
0.003,0.1601292874,0.9514487411,0.9873289871,0.8398707126,0.0485512589,0.0126710129
0.0031,0.1514967296,0.9483249537,0.9864809325,0.8485032704,0.0516750463,0.0135190675
0.0032,0.1435056624,0.9451197919,0.9856064874,0.8564943376,0.0548802081,0.0143935126
0.0033,0.1360979512,0.9418350703,0.9847057852,0.8639020488,0.0581649297,0.0152942148
0.0034,0.1292213977,0.938472629,0.9837789626,0.8707786023,0.061527371,0.0162210374
0.0035,0.1228291062,0.9350343316,0.9828261602,0.8771708938,0.0649656684,0.0171738398
0.0036,0.1168789124,0.9315220623,0.9818475219,0.8831210876,0.0684779377,0.0181524781
0.0037,0.1113328708,0.9279377243,0.9808431953,0.8886671292,0.0720622757,0.0191568047
0.0038,0.1061567982,0.9242832368,0.9798133314,0.8938432018,0.0757167632,0.0201866686
0.0039,0.1013198658,0.9205605332,0.9787580845,0.8986801342,0.0794394668,0.0212419155
0.004,0.0967942375,0.9167715586,0.9776776123,0.9032057625,0.0832284414,0.0223223877
0.0041,0.0925547483,0.9129182678,0.9765720758,0.9074452517,0.0870817322,0.0234279242
0.0042,0.0885786195,0.9090026229,0.9754416392,0.9114213805,0.0909973771,0.0245583608
0.0043,0.0848452058,0.9050265915,0.9742864699,0.9151547942,0.0949734085,0.0257135301
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