519:(exceptions related to non-collinear magnetic order notwithstanding, see Sec. 4(b) in the review ) and its detailed mechanism depends on the material. It can be for example due to a larger probability of s-d scattering of electrons in the direction of magnetization (which is controlled by the applied magnetic field). The net effect (in most materials) is that the electrical resistance has maximum value when the direction of current is parallel to the applied magnetic field. AMR of new materials is being investigated and magnitudes up to 50% have been observed in some uranium (but otherwise quite conventional) ferromagnetic compounds. Very recently, materials with extreme AMR have been identified driven by unconventional mechanisms such as a metal-insulator transition triggered by rotating the magnetic moments (while for some directions of magnetic moments, the system is semimetallic, for other directions a gap opens).
455:
500:
464:-field (for motion perpendicular to this field) is apparent. Electric current (proportional to the radial component of velocity) will decrease with increasing magnetic field and hence the resistance of the device will increase. Critically, this magnetoresistive scenario depends sensitively on the device geometry and current lines and it does not rely on magnetic materials.
90:
234:
816:(a ferromagnetic material exhibiting the AMR effect) inclined at an angle of 45°. This structure forces the current not to flow along the “easy axes” of thin film, but at an angle of 45°. The dependence of resistance now has a permanent offset which is linear around the null point. Because of its appearance, this sensor type is called '
111:
147:
An example of magnetoresistance due to direct action of magnetic field on electric current can be studied on a
Corbino disc (see Figure). It consists of a conducting annulus with perfectly conducting rims. Without a magnetic field, the battery drives a radial current between the rims. When a magnetic
85:
first discovered ordinary magnetoresistance in 1856. He experimented with pieces of iron and discovered that the resistance increases when the current is in the same direction as the magnetic force and decreases when the current is at 90° to the magnetic force. He then did the same experiment with
846:
As theoretical aspects, I. A. Campbell, A. Fert, and O. Jaoul (CFJ) derived an expression of the AMR ratio for Ni-based alloys using the two-current model with s-s and s-d scattering processes, where s is a conduction electron and d is 3d states with the spin-orbit interaction. The AMR ratio is
69:
structures are known. In these, a magnetic field can adjust the resistance by orders of magnitude. Since different mechanisms can alter the resistance, it is useful to separately consider situations where it depends on a magnetic field directly (e.g. geometric magnetoresistance and multiband
1610:
De
Ranieri, E.; Rushforth, A. W.; Výborný, K.; Rana, U.; Ahmed, E.; Campion, R. P.; Foxon, C. T.; Gallagher, B. L.; Irvine, A. C.; Wunderlich, J.; Jungwirth, T. (10 June 2008), "Lithographically and electrically controlled strain effects on anisotropic magnetoresistance in (Ga,Mn)As",
450:{\displaystyle \mathbf {v} ={\frac {\mu }{1+(\mu B)^{2}}}\left(\mathbf {E} +\mu \mathbf {E\times B} +\mu ^{2}(\mathbf {B\cdot E} )\mathbf {B} \right)={\frac {\mu }{1+(\mu B)^{2}}}\left(\mathbf {E} _{\perp }+\mu \mathbf {E\times B} \right)+\mu \mathbf {E} _{\parallel },\ }
945:
38:, or the common positive magnetoresistance in metals. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems (e.g. magnetic tunnel junctions),
114:
Corbino disc. With the magnetic field turned off, a radial current flows in the conducting annulus due to the battery connected between the (infinite) conductivity rims. When a magnetic field along the axis is turned on (B points directly out of the screen), the
93:
1168:, respectively. In addition, recently, Satoshi Kokado et al. have obtained the general expression of the AMR ratio for 3d transition-metal ferromagnets by extending the CFJ theory to a more general one. The general expression can also be applied to half-metals.
97:
96:
92:
91:
98:
645:
95:
223:
811:
To compensate for the non-linear characteristics and inability to detect the polarity of a magnetic field, the following structure is used for sensors. It consists of stripes of aluminum or gold placed on a thin film of
1059:
827:), for electric current measuring (by measuring the magnetic field created around the conductor), for traffic detection and for linear position and angle sensing. The biggest AMR sensor manufacturers are
491:, an example of a high mobility semiconductor, could have an electron mobility above 4 m·V·s at 300 K. So in a 0.25 T field, for example the magnetoresistance increase would be 100%.
852:
1213:
changes sign upon magnetic field reversal and it is an orbital effect (unrelated to spin) due to the
Lorentz force. Transversal AMR (planar Hall effect) does not change sign and it is caused by
1698:
Kokado, Satoshi; Tsunoda, Masakiyo; Harigaya, Kikuo; Sakuma, Akimasa (2012). "Anisotropic
Magnetoresistance Effects in Fe, Co, Ni, Fe4N, and Half-Metallic Ferromagnet: A Systematic Analysis".
511:
Thomson's experiments are an example of AMR, a property of a material in which a dependence of electrical resistance on the angle between the direction of electric current and direction of
704:
1011:
553:
94:
1126:
806:
757:
730:
560:
34:. There are a variety of effects that can be called magnetoresistance. Some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance,
1166:
86:
nickel and found that it was affected in the same way but the magnitude of the effect was greater. This effect is referred to as anisotropic magnetoresistance (AMR).
1146:
119:
drives a circular component of current, and the resistance between the inner and outer rims goes up. This increase in resistance due to the magnetic field is called
1751:
Kokado, Satoshi; Tsunoda, Masakiyo (2013). "Anisotropic
Magnetoresistance Effect: General Expression of AMR Ratio and Intuitive Explanation for Sign of AMR Ratio".
780:
667:
1099:
1079:
1487:
165:
1312:
Thomson, W. (18 June 1857), "On the
Electro-Dynamic Qualities of Metals:—Effects of Magnetization on the Electric Conductivity of Nickel and of Iron",
555:
between the magnetization and current direction and (as long as the resistivity of the material can be described by a rank-two tensor), it must follow
148:
field perpendicular to the plane of the annulus is applied, (either into or out of the page) a circular component of current flows as well, due to
1245:
1197:
61:, better known as Lord Kelvin, but he was unable to lower the electrical resistance of anything by more than 5%. Today, systems including
82:
58:
1016:
1192:
66:
51:
940:{\displaystyle {\frac {\Delta \rho }{\rho }}={\frac {\rho _{\parallel }-\rho _{\perp }}{\rho _{\perp }}}=\gamma (\alpha -1),}
759:, respectively. Associated with longitudinal resistivity, there is also transversal resistivity dubbed (somewhat confusingly
155:
In a simple model, supposing the response to the
Lorentz force is the same as for an electric field, the carrier velocity
35:
152:. Initial interest in this problem began with Boltzmann in 1886, and independently was re-examined by Corbino in 1911.
1877:
1214:
516:
1528:
Wiśniewski, P. (2007). "Giant anisotropic magnetoresistance and magnetothermopower in cubic 3:4 uranium pnictides".
1887:
1872:
1187:
47:
1882:
1182:
676:
71:
43:
1177:
952:
526:
136:
103:
39:
1663:
Campbell, I. A.; Fert, A.; Jaoul, O. (1970). "The spontaneous resistivity anisotropy in Ni-based alloys".
823:
The AMR effect is used in a wide array of sensors for measurement of Earth's magnetic field (electronic
27:
1892:
1826:
1766:
1717:
1672:
1630:
1576:
1537:
1502:
1442:
1382:
1270:
1104:
1563:
Yang, Huali (2021). "Colossal angular magnetoresistance in the antiferromagnetic semiconductor EuTe
785:
640:{\displaystyle \rho (\varphi )=\rho _{\perp }+(\rho _{\parallel }-\rho _{\perp })\cos ^{2}\varphi }
1340:
1295:
1850:
1816:
1782:
1778:
1756:
1733:
1707:
1646:
1620:
1592:
1432:
1398:
1372:
836:
832:
735:
709:
515:
is observed. The effect arises in most cases from the simultaneous action of magnetization and
1842:
1468:
1241:
488:
476:
132:
1151:
70:
magnetoresistance) and those where it does so indirectly through magnetization (e.g. AMR and
1834:
1774:
1725:
1680:
1638:
1584:
1545:
1510:
1458:
1450:
1390:
1321:
1278:
1131:
1801:
765:
652:
1830:
1770:
1721:
1676:
1642:
1634:
1580:
1541:
1506:
1463:
1446:
1420:
1386:
1274:
1084:
1064:
31:
23:
1866:
1737:
1684:
1650:
1596:
471:
with a single carrier type, the magnetoresistance is proportional to (1 + (
468:
149:
116:
1786:
1402:
1854:
1394:
484:
1838:
218:{\displaystyle \mathbf {v} =\mu \left(\mathbf {E} +\mathbf {v\times B} \right),\ }
1235:
523:
In polycrystalline ferromagnetic materials, the AMR can only depend on the angle
1588:
1210:
817:
670:
128:
499:
1514:
1261:
Coleman, R.V.; Isin, A. (1966), "Magnetoresistance in Iron Single
Crystals",
1800:
Tang, H. X.; Kawakami, R. K.; Awschalom, D. D.; Roukes, M. L. (March 2003),
828:
813:
504:
62:
1846:
1729:
1472:
1326:
507:
film is shown here as a function of the angle of an applied external field.
110:
1821:
1454:
824:
1549:
1282:
228:
where ÎĽ is the carrier mobility. Solving for the velocity, we find:
1437:
1421:"Anisotropic magnetoresistance: Materials, models and applications"
1377:
1761:
1712:
1625:
1363:
G Giuliani (2008). "A general law for electromagnetic induction".
88:
1054:{\displaystyle \alpha =\rho _{\downarrow }/\rho _{\uparrow }}
57:
The first magnetoresistive effect was discovered in 1856 by
1488:"Anisotropic magnetoresistance in ferromagnetic 3d alloys"
840:
135:
were jointly awarded the Nobel Prize for the discovery of
1802:"Giant Planar Hall Effect in Epitaxial (Ga,Mn)As Devices"
762:) the planar Hall effect. In monocrystals, resistivity
1154:
1134:
1107:
1087:
1067:
1019:
955:
855:
788:
768:
738:
712:
679:
655:
563:
529:
460:
where the effective reduction in mobility due to the
237:
168:
102:Animation about graphs related to the discovery of
1160:
1140:
1120:
1093:
1073:
1053:
1005:
939:
800:
774:
751:
724:
698:
661:
639:
547:
449:
217:
1148:), an exchange field, and a resistivity for spin
1128:are a spin-orbit coupling constant (so-called
8:
1419:Ritzinger, Philipp; Vyborny, Karel (2023).
1414:
1412:
1779:10.4028/www.scientific.net/AMR.750-752.978
1820:
1760:
1711:
1624:
1462:
1436:
1376:
1325:
1153:
1133:
1112:
1106:
1086:
1066:
1045:
1036:
1030:
1018:
997:
985:
968:
954:
905:
894:
881:
874:
856:
854:
787:
767:
743:
737:
711:
699:{\displaystyle \rho _{\parallel ,\perp }}
684:
678:
654:
625:
612:
599:
583:
562:
528:
435:
430:
407:
395:
390:
375:
350:
337:
323:
314:
296:
285:
271:
246:
238:
236:
193:
185:
169:
167:
1307:
1305:
498:
109:
1226:
1006:{\displaystyle \gamma =(3/4)(A/H)^{2}}
548:{\displaystyle \varphi =\psi -\theta }
16:Magnetically-induced resistance change
1198:Magnetoresistive random-access memory
22:is the tendency of a material (often
7:
495:Anisotropic magnetoresistance (AMR)
859:
14:
1486:McGuire, T.; Potter, R. (1975).
431:
414:
408:
391:
338:
330:
324:
303:
297:
286:
239:
200:
194:
186:
170:
1342:The Nobel Prize in Physics 2007
1296:"Unstoppable Magnetoresistance"
1193:Extraordinary magnetoresistance
1121:{\displaystyle \rho _{\sigma }}
52:extraordinary magnetoresistance
1495:IEEE Transactions on Magnetics
1240:. Cambridge University Press.
1046:
1031:
994:
979:
976:
962:
931:
919:
760:
685:
618:
592:
573:
567:
372:
362:
334:
320:
268:
258:
36:Shubnikov–de Haas oscillations
1:
1839:10.1103/PhysRevLett.90.107201
1643:10.1088/1367-2630/10/6/065003
801:{\displaystyle \psi ,\theta }
483:is the magnetic field (units
143:Geometrical magnetoresistance
83:William Thomson (Lord Kelvin)
26:) to change the value of its
1345:, Nobel Media AB, 9 Oct 2007
1753:Advanced Materials Research
1589:10.1103/PhysRevB.104.214419
1237:Magnetoresistance in Metals
752:{\displaystyle 90^{\circ }}
1909:
1685:10.1088/0022-3719/3/1S/310
1425:Royal Society Open Science
1395:10.1209/0295-5075/81/60002
1263:Journal of Applied Physics
1188:Colossal magnetoresistance
725:{\displaystyle \varphi =0}
706:are the resistivities for
48:colossal magnetoresistance
1515:10.1109/TMAG.1975.1058782
503:The resistance of a thin
30:in an externally-applied
1183:Tunnel magnetoresistance
44:tunnel magnetoresistance
1530:Applied Physics Letters
1178:Giant magnetoresistance
1161:{\displaystyle \sigma }
479:(units m·V·s or T) and
137:giant magnetoresistance
104:giant magnetoresistance
54:(EMR) can be observed.
40:giant magnetoresistance
1730:10.1143/JPSJ.81.024705
1327:10.1098/rspl.1856.0144
1234:Pippard, A.B. (1989).
1215:spin-orbit interaction
1162:
1142:
1141:{\displaystyle \zeta }
1122:
1095:
1075:
1055:
1007:
941:
802:
776:
753:
726:
700:
669:is the (longitudinal)
663:
641:
549:
517:spin-orbit interaction
508:
477:semiconductor mobility
451:
219:
124:
107:
1163:
1143:
1123:
1096:
1076:
1056:
1008:
942:
803:
777:
775:{\displaystyle \rho }
754:
727:
701:
664:
662:{\displaystyle \rho }
642:
550:
502:
452:
220:
113:
101:
28:electrical resistance
1755:. 750–752: 978–982.
1152:
1132:
1105:
1085:
1065:
1017:
953:
853:
786:
766:
736:
710:
677:
653:
561:
527:
235:
166:
65:and concentric ring
1831:2003PhRvL..90j7201T
1771:2013arXiv1305.3517K
1722:2012JPSJ...81b4705K
1677:1970JPhC....3S..95C
1635:2008NJPh...10f5003D
1581:2021PhRvB.104u4419Y
1542:2007ApPhL..90s2106W
1507:1975ITM....11.1018M
1455:10.1098/rsos.230564
1447:2023RSOS...1030564R
1387:2008EL.....8160002G
1314:Proc. R. Soc. Lond.
1275:1966JAP....37.1028C
475:)), where ÎĽ is the
1878:1856 introductions
1706:(2): 024705–1–17.
1209:1. The (ordinary)
1158:
1138:
1118:
1091:
1071:
1051:
1003:
937:
837:STMicroelectronics
833:NXP Semiconductors
798:
772:
749:
722:
696:
659:
637:
545:
509:
447:
215:
125:
108:
1888:Magnetic ordering
1873:Magnetoresistance
1700:J. Phys. Soc. Jpn
1550:10.1063/1.2737904
1283:10.1063/1.1708320
1247:978-0-521-32660-5
1094:{\displaystyle H}
1074:{\displaystyle A}
911:
869:
673:of the film and
489:Indium antimonide
446:
382:
278:
214:
121:magnetoresistance
99:
20:Magnetoresistance
1900:
1858:
1857:
1824:
1822:cond-mat/0210118
1809:Phys. Rev. Lett.
1806:
1797:
1791:
1790:
1764:
1748:
1742:
1741:
1715:
1695:
1689:
1688:
1671:(1S): S95–S101.
1660:
1654:
1653:
1628:
1607:
1601:
1600:
1560:
1554:
1553:
1525:
1519:
1518:
1492:
1483:
1477:
1476:
1466:
1440:
1416:
1407:
1406:
1380:
1360:
1354:
1353:
1352:
1350:
1337:
1331:
1330:
1329:
1309:
1300:
1299:
1292:
1286:
1285:
1258:
1252:
1251:
1231:
1167:
1165:
1164:
1159:
1147:
1145:
1144:
1139:
1127:
1125:
1124:
1119:
1117:
1116:
1100:
1098:
1097:
1092:
1080:
1078:
1077:
1072:
1060:
1058:
1057:
1052:
1050:
1049:
1040:
1035:
1034:
1012:
1010:
1009:
1004:
1002:
1001:
989:
972:
946:
944:
943:
938:
912:
910:
909:
900:
899:
898:
886:
885:
875:
870:
865:
857:
807:
805:
804:
799:
782:depends also on
781:
779:
778:
773:
758:
756:
755:
750:
748:
747:
731:
729:
728:
723:
705:
703:
702:
697:
695:
694:
668:
666:
665:
660:
646:
644:
643:
638:
630:
629:
617:
616:
604:
603:
588:
587:
554:
552:
551:
546:
456:
454:
453:
448:
444:
440:
439:
434:
422:
418:
417:
400:
399:
394:
383:
381:
380:
379:
351:
346:
342:
341:
333:
319:
318:
306:
289:
279:
277:
276:
275:
247:
242:
224:
222:
221:
216:
212:
208:
204:
203:
189:
173:
100:
1908:
1907:
1903:
1902:
1901:
1899:
1898:
1897:
1883:1856 in science
1863:
1862:
1861:
1804:
1799:
1798:
1794:
1750:
1749:
1745:
1697:
1696:
1692:
1662:
1661:
1657:
1609:
1608:
1604:
1566:
1562:
1561:
1557:
1527:
1526:
1522:
1490:
1485:
1484:
1480:
1418:
1417:
1410:
1362:
1361:
1357:
1348:
1346:
1339:
1338:
1334:
1311:
1310:
1303:
1294:
1293:
1289:
1260:
1259:
1255:
1248:
1233:
1232:
1228:
1224:
1206:
1174:
1150:
1149:
1130:
1129:
1108:
1103:
1102:
1083:
1082:
1063:
1062:
1041:
1026:
1015:
1014:
993:
951:
950:
901:
890:
877:
876:
858:
851:
850:
784:
783:
764:
763:
739:
734:
733:
708:
707:
680:
675:
674:
651:
650:
621:
608:
595:
579:
559:
558:
525:
524:
522:
497:
429:
389:
388:
384:
371:
355:
310:
284:
280:
267:
251:
233:
232:
184:
180:
164:
163:
145:
89:
80:
59:William Thomson
17:
12:
11:
5:
1906:
1904:
1896:
1895:
1890:
1885:
1880:
1875:
1865:
1864:
1860:
1859:
1815:(10): 107201,
1792:
1743:
1690:
1655:
1602:
1575:(21): 214419.
1564:
1555:
1536:(19): 192106.
1520:
1501:(4): 1018–38.
1478:
1408:
1355:
1332:
1301:
1287:
1253:
1246:
1225:
1223:
1220:
1219:
1218:
1205:
1202:
1201:
1200:
1195:
1190:
1185:
1180:
1173:
1170:
1157:
1137:
1115:
1111:
1090:
1070:
1048:
1044:
1039:
1033:
1029:
1025:
1022:
1000:
996:
992:
988:
984:
981:
978:
975:
971:
967:
964:
961:
958:
936:
933:
930:
927:
924:
921:
918:
915:
908:
904:
897:
893:
889:
884:
880:
873:
868:
864:
861:
808:individually.
797:
794:
791:
771:
746:
742:
721:
718:
715:
693:
690:
687:
683:
658:
636:
633:
628:
624:
620:
615:
611:
607:
602:
598:
594:
591:
586:
582:
578:
575:
572:
569:
566:
544:
541:
538:
535:
532:
496:
493:
458:
457:
443:
438:
433:
428:
425:
421:
416:
413:
410:
406:
403:
398:
393:
387:
378:
374:
370:
367:
364:
361:
358:
354:
349:
345:
340:
336:
332:
329:
326:
322:
317:
313:
309:
305:
302:
299:
295:
292:
288:
283:
274:
270:
266:
263:
260:
257:
254:
250:
245:
241:
226:
225:
211:
207:
202:
199:
196:
192:
188:
183:
179:
176:
172:
144:
141:
133:Peter GrĂĽnberg
79:
76:
32:magnetic field
15:
13:
10:
9:
6:
4:
3:
2:
1905:
1894:
1891:
1889:
1886:
1884:
1881:
1879:
1876:
1874:
1871:
1870:
1868:
1856:
1852:
1848:
1844:
1840:
1836:
1832:
1828:
1823:
1818:
1814:
1810:
1803:
1796:
1793:
1788:
1784:
1780:
1776:
1772:
1768:
1763:
1758:
1754:
1747:
1744:
1739:
1735:
1731:
1727:
1723:
1719:
1714:
1709:
1705:
1701:
1694:
1691:
1686:
1682:
1678:
1674:
1670:
1666:
1659:
1656:
1652:
1648:
1644:
1640:
1636:
1632:
1627:
1622:
1619:(6): 065003,
1618:
1614:
1606:
1603:
1598:
1594:
1590:
1586:
1582:
1578:
1574:
1570:
1559:
1556:
1551:
1547:
1543:
1539:
1535:
1531:
1524:
1521:
1516:
1512:
1508:
1504:
1500:
1496:
1489:
1482:
1479:
1474:
1470:
1465:
1460:
1456:
1452:
1448:
1444:
1439:
1434:
1430:
1426:
1422:
1415:
1413:
1409:
1404:
1400:
1396:
1392:
1388:
1384:
1379:
1374:
1370:
1366:
1359:
1356:
1344:
1343:
1336:
1333:
1328:
1323:
1319:
1315:
1308:
1306:
1302:
1297:
1291:
1288:
1284:
1280:
1276:
1272:
1269:(3): 1028–9,
1268:
1264:
1257:
1254:
1249:
1243:
1239:
1238:
1230:
1227:
1221:
1216:
1212:
1208:
1207:
1203:
1199:
1196:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1175:
1171:
1169:
1155:
1135:
1113:
1109:
1088:
1068:
1042:
1037:
1027:
1023:
1020:
998:
990:
986:
982:
973:
969:
965:
959:
956:
947:
934:
928:
925:
922:
916:
913:
906:
902:
895:
891:
887:
882:
878:
871:
866:
862:
848:
847:expressed as
844:
842:
841:Sensitec GmbH
838:
834:
830:
826:
821:
819:
815:
809:
795:
792:
789:
769:
761:
744:
740:
719:
716:
713:
691:
688:
681:
672:
656:
647:
634:
631:
626:
622:
613:
609:
605:
600:
596:
589:
584:
580:
576:
570:
564:
556:
542:
539:
536:
533:
530:
520:
518:
514:
513:magnetization
506:
501:
494:
492:
490:
486:
482:
478:
474:
470:
469:semiconductor
465:
463:
441:
436:
426:
423:
419:
411:
404:
401:
396:
385:
376:
368:
365:
359:
356:
352:
347:
343:
327:
315:
311:
307:
300:
293:
290:
281:
272:
264:
261:
255:
252:
248:
243:
231:
230:
229:
209:
205:
197:
190:
181:
177:
174:
162:
161:
160:
159:is given by:
158:
153:
151:
150:Lorentz force
142:
140:
138:
134:
130:
122:
118:
117:Lorentz force
112:
105:
87:
84:
77:
75:
73:
68:
64:
60:
55:
53:
49:
45:
41:
37:
33:
29:
25:
24:ferromagnetic
21:
1812:
1808:
1795:
1752:
1746:
1703:
1699:
1693:
1668:
1664:
1658:
1616:
1613:New J. Phys.
1612:
1605:
1572:
1569:Phys. Rev. B
1568:
1558:
1533:
1529:
1523:
1498:
1494:
1481:
1428:
1424:
1371:(6): 60002.
1368:
1364:
1358:
1347:, retrieved
1341:
1335:
1317:
1313:
1290:
1266:
1262:
1256:
1236:
1229:
948:
849:
845:
822:
810:
648:
557:
521:
512:
510:
480:
472:
466:
461:
459:
227:
156:
154:
146:
126:
120:
81:
56:
19:
18:
1893:Spintronics
1320:: 546–550,
1211:Hall effect
818:barber pole
671:resistivity
129:Albert Fert
50:(CMR), and
1867:Categories
1665:J. Phys. C
1438:2212.03700
1378:1502.00502
1222:References
63:semimetals
1762:1305.3517
1738:100002412
1713:1111.4864
1651:119291699
1626:0802.3344
1597:245189642
1204:Footnotes
1156:σ
1136:ζ
1114:σ
1110:ρ
1047:↑
1043:ρ
1032:↓
1028:ρ
1021:α
957:γ
926:−
923:α
917:γ
907:⊥
903:ρ
896:⊥
892:ρ
888:−
883:∥
879:ρ
867:ρ
863:ρ
860:Δ
829:Honeywell
814:permalloy
796:θ
790:ψ
770:ρ
745:∘
714:φ
692:⊥
686:∥
682:ρ
657:ρ
635:φ
632:
614:⊥
610:ρ
606:−
601:∥
597:ρ
585:⊥
581:ρ
571:φ
565:ρ
543:θ
540:−
537:ψ
531:φ
505:Permalloy
437:∥
427:μ
412:×
405:μ
397:⊥
366:μ
353:μ
328:⋅
312:μ
301:×
294:μ
262:μ
249:μ
198:×
178:μ
127:In 2007,
78:Discovery
1847:12689027
1787:35733115
1473:37859834
1464:10582618
1403:14917438
1172:See also
1061:, where
1855:1485882
1827:Bibcode
1767:Bibcode
1718:Bibcode
1673:Bibcode
1631:Bibcode
1577:Bibcode
1538:Bibcode
1503:Bibcode
1443:Bibcode
1383:Bibcode
1271:Bibcode
825:compass
46:(TMR),
42:(GMR),
1853:
1845:
1785:
1736:
1649:
1595:
1471:
1461:
1431:(10).
1401:
1349:25 Jun
1244:
1101:, and
839:, and
649:where
485:teslas
445:
213:
1851:S2CID
1817:arXiv
1805:(PDF)
1783:S2CID
1757:arXiv
1734:S2CID
1708:arXiv
1647:S2CID
1621:arXiv
1593:S2CID
1491:(PDF)
1433:arXiv
1399:S2CID
1373:arXiv
949:with
467:In a
1843:PMID
1469:PMID
1351:2014
1242:ISBN
1013:and
732:and
131:and
1835:doi
1775:doi
1726:doi
1681:doi
1639:doi
1585:doi
1573:104
1567:".
1546:doi
1511:doi
1459:PMC
1451:doi
1391:doi
1365:EPL
1322:doi
1279:doi
820:'.
623:cos
487:).
74:).
72:TMR
67:EMR
1869::
1849:,
1841:,
1833:,
1825:,
1813:90
1811:,
1807:,
1781:.
1773:.
1765:.
1732:.
1724:.
1716:.
1704:81
1702:.
1679:.
1667:.
1645:,
1637:,
1629:,
1617:10
1615:,
1591:.
1583:.
1571:.
1544:.
1534:90
1532:.
1509:.
1499:11
1497:.
1493:.
1467:.
1457:.
1449:.
1441:.
1429:10
1427:.
1423:.
1411:^
1397:.
1389:.
1381:.
1369:81
1367:.
1316:,
1304:^
1277:,
1267:37
1265:,
1081:,
843:.
835:,
831:,
741:90
473:ÎĽB
139:.
1837::
1829::
1819::
1789:.
1777::
1769::
1759::
1740:.
1728::
1720::
1710::
1687:.
1683::
1675::
1669:3
1641::
1633::
1623::
1599:.
1587::
1579::
1565:2
1552:.
1548::
1540::
1517:.
1513::
1505::
1475:.
1453::
1445::
1435::
1405:.
1393::
1385::
1375::
1324::
1318:8
1298:.
1281::
1273::
1250:.
1217:.
1089:H
1069:A
1038:/
1024:=
999:2
995:)
991:H
987:/
983:A
980:(
977:)
974:4
970:/
966:3
963:(
960:=
935:,
932:)
929:1
920:(
914:=
872:=
793:,
720:0
717:=
689:,
627:2
619:)
593:(
590:+
577:=
574:)
568:(
534:=
481:B
462:B
442:,
432:E
424:+
420:)
415:B
409:E
402:+
392:E
386:(
377:2
373:)
369:B
363:(
360:+
357:1
348:=
344:)
339:B
335:)
331:E
325:B
321:(
316:2
308:+
304:B
298:E
291:+
287:E
282:(
273:2
269:)
265:B
259:(
256:+
253:1
244:=
240:v
210:,
206:)
201:B
195:v
191:+
187:E
182:(
175:=
171:v
157:v
123:.
106:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
