1429:
1147:
1424:{\displaystyle \mathbf {M} _{\rm {orb}}={\frac {e}{2\hbar }}\sum _{n}\int _{\rm {BZ}}{\frac {1}{(2\pi )^{3}}}\,f_{n\mathbf {k} }\;\operatorname {Im} \;\left\langle {\frac {\partial u_{n\mathbf {k} }}{\partial {\mathbf {k} }}}\right|\times \left(H_{\mathbf {k} }+E_{n\mathbf {k} }-2\mu \right)\left|{\frac {\partial u_{n\mathbf {k} }}{\partial {\mathbf {k} }}}\right\rangle \,d^{3}k\,,}
1064:
701:
However, real crystals are made up out of atomic or molecular constituents whose charge clouds overlap, so that the above formula cannot be taken as a fundamental definition of orbital magnetization. Only recently have theoretical developments led to a proper theory of orbital magnetization in
875:
1121:) inside each sphere, and summing the contributions. This approximation neglects the contributions from currents in the interstitial regions between the atomic spheres. Nevertheless, it is often a good approximation because the orbital currents associated with partially filled
529:
823:
1761:
182:
1658:
318:
1547:
696:
1899:
1059:{\displaystyle \mathbf {M} _{\rm {orb}}={\frac {-e}{2m_{e}}}\sum _{n}\int _{\rm {BZ}}{\frac {1}{(2\pi )^{3}}}\,\langle \psi _{n\mathbf {k} }\vert \mathbf {r} \times \mathbf {p} \vert \psi _{n\mathbf {k} }\rangle \,d^{3}k\,,}
422:
433:
721:
1669:
92:
1137:
A general and exact formulation of the theory of orbital magnetization was developed in the mid-2000s by several authors, first based on a semiclassical approach, then on a derivation from the
836:
in the integrand, the integral has contributions from surface currents that cannot be neglected, and as a result the above equation does not lead to a bulk definition of orbital magnetization.
1565:
233:
1797:, i.e., the ratio between the magnetic dipole moment of a body and its angular momentum. The gyromagnetic ratio is related to the spin and orbital magnetization according to
1468:
839:
Another way to see that there is a difficulty is to try to write down the quantum-mechanical expression for the orbital magnetization in terms of the occupied single-particle
603:
1803:
2190:
Ceresoli, D.; Thonhauser, T.; Vanderbilt, D.; Resta, R. (2006). "Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals".
356:
1105:
In practice, orbital magnetization is often computed by decomposing space into non-overlapping spheres centered on atoms (similar in spirit to the
2246:
Shi, Junren; Vignale, G.; Niu, Qian (November 2007), "Quantum Theory of
Orbital Magnetization and Its Generalization to Interacting Systems",
2467:
1141:, and finally from a long-wavelength expansion. The resulting formula for the orbital magnetization, specialized to zero temperature, is
58:, to the total magnetization. A nonzero orbital magnetization requires broken time-reversal symmetry, which can occur spontaneously in
1937:
524:{\displaystyle \mathbf {m} _{\rm {spin}}={\frac {-g_{s}\mu _{\rm {B}}}{\hbar }}\,\langle \Psi \vert \mathbf {S} \vert \Psi \rangle }
818:{\displaystyle \mathbf {M} _{\rm {orb}}={\frac {1}{2V}}\int _{V}\mathbf {r} \times \mathbf {J} (\mathbf {r} )\ d^{3}\mathbf {r} }
1756:{\displaystyle H_{\mathbf {k} }\left|u_{n\mathbf {k} }\right\rangle =E_{n\mathbf {k} }\left|u_{n\mathbf {k} }\right\rangle \;.}
1779:
1782:. Results computed using the above formula have appeared in the literature. A recent review summarizes these developments.
177:{\displaystyle \mathbf {m} _{\rm {orb}}={\frac {1}{2}}\int \mathbf {r} \times \mathbf {J} (\mathbf {r} )\ d^{3}\mathbf {r} }
2035:
Todorova, M.; Sandratskii, M.; Kubler, J. (January 2001), "Current-determined orbital magnetization in a metallic magnet",
2306:
Ceresoli, D.; Gerstmann, U.; Seitsonen, A.P.; Mauri, F. (Feb 2010). "First-principles theory of orbital magnetization".
1909:
1653:{\displaystyle u_{n\mathbf {k} }(\mathbf {r} )=e^{-i\mathbf {k} \cdot \mathbf {r} }\psi _{n\mathbf {k} }(\mathbf {r} )}
2069:
Xiao, Di; Shi, Junren; Niu, Qian (September 2005), "Berry Phase
Correction to Electron Density of States in Solids",
1129:
shells are typically strongly localized inside these atomic spheres. It remains, however, an approximate approach.
2462:
2457:
2129:
Thonhauser, T.; Ceresoli, D.; Vanderbilt, D.; Resta, R. (2005). "Orbital magnetization in periodic insulators".
1106:
313:{\displaystyle \mathbf {m} _{\rm {orb}}={\frac {-e}{2m_{e}}}\langle \Psi \vert \mathbf {L} \vert \Psi \rangle }
36:
1093:(BZ). However, because the Bloch functions are extended, the matrix element of a quantity containing the
1542:{\displaystyle H_{\mathbf {k} }=e^{-i\mathbf {k} \cdot \mathbf {r} }He^{i\mathbf {k} \cdot \mathbf {r} }}
579:
is defined as the orbital moment density; i.e., orbital moment per unit volume. For a crystal of volume
1766:
A generalization to finite temperature is also available. Note that the term involving the band energy
2421:
2378:
2325:
2265:
2209:
2148:
2088:
2044:
1994:
1961:
691:{\displaystyle \mathbf {M} _{\rm {orb}}={\frac {1}{V}}\sum _{j\in V}\mathbf {m} _{{\rm {orb}},j}\;.}
1989:
Resta, Raffaele (2010), "Electrical polarization and orbital magnetization: the modern theories",
2452:
2412:
Meyer, A.J.P.; Asch, G. (1961). "Experimental g' and g values for Fe, Co, Ni, and their alloys".
2394:
2368:
2341:
2315:
2289:
2255:
2225:
2199:
2172:
2138:
2112:
2078:
2018:
1791:
542:
1894:{\displaystyle \gamma =1+{\frac {M_{\mathrm {orb} }}{(M_{\mathrm {spin} }+M_{\mathrm {orb} })}}}
840:
2281:
2164:
2104:
2010:
1933:
1074:
224:
67:
17:
2429:
2386:
2333:
2273:
2217:
2156:
2096:
2052:
2002:
1969:
1138:
863:
347:
40:
561:
196:
83:
2006:
2425:
2382:
2329:
2269:
2213:
2152:
2092:
2048:
1998:
1965:
51:. The term "orbital" distinguishes it from the contribution of spin degrees of freedom,
1905:
1090:
569:
220:
208:
71:
63:
59:
1790:
The orbital magnetization of a material can be determined accurately by measuring the
2446:
2398:
2345:
2116:
553:
339:
32:
2176:
2022:
2293:
2277:
2229:
2160:
2100:
427:
where the spin contribution is intrinsically quantum-mechanical and is given by
2337:
2221:
2056:
1956:
Hirst, L. L. (1997), "The microscopic magnetization: concept and application",
417:{\displaystyle \mathbf {m} =\mathbf {m} _{\rm {orb}}+\mathbf {m} _{\rm {spin}}}
2390:
1973:
1553:
2285:
2168:
2108:
2014:
2204:
2143:
2083:
1912:. Experimental data for Fe, Co, Ni, and their alloys have been compiled.
335:
204:
44:
2359:
Thonhauser, T. (May 2011). "Theory of
Orbital Magnetization in Solids".
1778:
in this formula is really just an integral of the band energy times the
2433:
583:
composed of isolated entities (e.g., molecules) labelled by an index
1097:
operator is ill-defined, and this formula is actually ill-defined.
2373:
2320:
2260:
48:
832:
of the system becomes large. However, because of the factor of
86:
of a finite system, such as a molecule, is given classically by
1904:
The two main experimental techniques are based either on the
715:
For a magnetic crystal, it is tempting to try to define
711:
Difficulties in the definition of orbital magnetization
1806:
1672:
1568:
1471:
1150:
878:
724:
606:
436:
359:
236:
95:
1893:
1755:
1652:
1541:
1423:
1058:
817:
690:
523:
416:
312:
176:
1663:is the cell-periodic Bloch function satisfying
1960:, vol. 69, no. 2, pp. 607–628,
1993:, vol. 22, no. 12, p. 123201,
8:
1035:
1017:
1001:
983:
518:
512:
504:
498:
307:
301:
293:
287:
1749:
1446:is 0 or 1 respectively as the band energy
1262:
1258:
684:
2372:
2319:
2259:
2254:(19), American Physical Society: 197202,
2203:
2142:
2082:
1872:
1871:
1848:
1847:
1826:
1825:
1819:
1805:
1738:
1734:
1719:
1715:
1697:
1693:
1678:
1677:
1671:
1642:
1632:
1628:
1617:
1609:
1602:
1587:
1577:
1573:
1567:
1532:
1524:
1520:
1506:
1498:
1491:
1477:
1476:
1470:
1417:
1408:
1403:
1390:
1389:
1377:
1373:
1363:
1338:
1334:
1320:
1319:
1294:
1293:
1281:
1277:
1267:
1251:
1247:
1242:
1233:
1214:
1204:
1203:
1193:
1174:
1158:
1157:
1152:
1149:
1089:, and the integral is evaluated over the
1052:
1043:
1038:
1028:
1024:
1012:
1004:
994:
990:
982:
973:
954:
944:
943:
933:
920:
902:
886:
885:
880:
877:
810:
804:
789:
781:
773:
767:
748:
732:
731:
726:
723:
664:
663:
662:
657:
644:
630:
614:
613:
608:
605:
507:
497:
484:
483:
473:
463:
444:
443:
438:
435:
398:
397:
392:
375:
374:
369:
360:
358:
296:
278:
260:
244:
243:
238:
235:
169:
163:
148:
140:
132:
119:
103:
102:
97:
94:
2043:(5), American Physical Society: 052408,
350:operator. The total magnetic moment is
1984:
1982:
1951:
1949:
1920:
1183:
828:where the limit is taken as the volume
492:
1458:falls above or below the Fermi energy
1133:Modern theory of orbital magnetization
66:materials, or can be induced in a non-
2241:
2239:
227:context, this can also be written as
7:
1991:Journal of Physics: Condensed Matter
1930:Classical Electrodynamics (3rd ed.)
1879:
1876:
1873:
1858:
1855:
1852:
1849:
1833:
1830:
1827:
1386:
1366:
1290:
1270:
1208:
1205:
1165:
1162:
1159:
948:
945:
893:
890:
887:
739:
736:
733:
671:
668:
665:
621:
618:
615:
515:
501:
485:
454:
451:
448:
445:
408:
405:
402:
399:
382:
379:
376:
304:
290:
251:
248:
245:
110:
107:
104:
14:
1739:
1720:
1698:
1679:
1643:
1633:
1618:
1610:
1588:
1578:
1552:is the effective Hamiltonian at
1533:
1525:
1507:
1499:
1478:
1391:
1378:
1339:
1321:
1295:
1282:
1252:
1153:
1029:
1013:
1005:
995:
881:
811:
790:
782:
774:
727:
658:
609:
508:
439:
393:
370:
361:
297:
239:
170:
149:
141:
133:
98:
334:are the charge and mass of the
2007:10.1088/0953-8984/22/12/123201
1885:
1840:
1647:
1639:
1592:
1584:
1230:
1220:
970:
960:
794:
786:
702:crystals, as explained below.
153:
145:
1:
2278:10.1103/PhysRevLett.99.197202
2161:10.1103/PhysRevLett.95.137205
2101:10.1103/PhysRevLett.95.137204
1109:), computing the integral of
2468:Electronic structure methods
211:, the prefactor would be 1/2
1101:Atomic sphere approximation
2484:
2338:10.1103/PhysRevB.81.060409
2222:10.1103/PhysRevB.74.024408
2057:10.1103/PhysRevB.63.052408
575:The orbital magnetization
2391:10.1142/S0217979211058912
1974:10.1103/RevModPhys.69.607
1958:Reviews of Modern Physics
1928:Jackson, John D. (1998).
2314:(6): 060409 of 4 pages.
1107:muffin-tin approximation
587:having magnetic moments
338:, Ψ is the ground-state
1910:Einstein–de Haas effect
562:reduced Planck constant
1895:
1757:
1654:
1543:
1425:
1139:Wannier representation
1060:
819:
692:
543:electron spin g-factor
525:
418:
314:
178:
1896:
1758:
1655:
1544:
1426:
1061:
820:
693:
526:
419:
315:
179:
22:orbital magnetization
2361:Int. J. Mod. Phys. B
1804:
1670:
1566:
1469:
1148:
876:
722:
604:
434:
357:
234:
93:
2426:1961JAP....32S.330M
2383:2011IJMPB..25.1429T
2330:2010PhRvB..81f0409C
2270:2007PhRvL..99s7202S
2214:2006PhRvB..74b4408C
2153:2005PhRvL..95m7205T
2093:2005PhRvL..95m7204X
2049:2001PhRvB..63e2408T
1999:2010JPCM...22l3201R
1966:1997RvMP...69..607H
1891:
1792:gyromagnetic ratio
1753:
1650:
1539:
1421:
1198:
1056:
938:
815:
688:
655:
521:
414:
310:
225:quantum-mechanical
174:
2463:Quantum mechanics
2434:10.1063/1.2000457
2367:(11): 1429–1458.
2037:Physical Review B
1889:
1397:
1301:
1240:
1189:
1187:
1075:momentum operator
980:
929:
927:
799:
761:
640:
638:
495:
285:
158:
127:
68:magnetic material
41:charged particles
18:quantum mechanics
2475:
2458:Electromagnetism
2438:
2437:
2409:
2403:
2402:
2376:
2356:
2350:
2349:
2323:
2303:
2297:
2296:
2263:
2248:Phys. Rev. Lett.
2243:
2234:
2233:
2207:
2205:cond-mat/0512142
2187:
2181:
2180:
2146:
2144:cond-mat/0505518
2126:
2120:
2119:
2086:
2084:cond-mat/0502340
2071:Phys. Rev. Lett.
2066:
2060:
2059:
2032:
2026:
2025:
1986:
1977:
1976:
1953:
1944:
1943:
1925:
1900:
1898:
1897:
1892:
1890:
1888:
1884:
1883:
1882:
1863:
1862:
1861:
1838:
1837:
1836:
1820:
1762:
1760:
1759:
1754:
1748:
1744:
1743:
1742:
1725:
1724:
1723:
1707:
1703:
1702:
1701:
1684:
1683:
1682:
1659:
1657:
1656:
1651:
1646:
1638:
1637:
1636:
1623:
1622:
1621:
1613:
1591:
1583:
1582:
1581:
1548:
1546:
1545:
1540:
1538:
1537:
1536:
1528:
1512:
1511:
1510:
1502:
1483:
1482:
1481:
1430:
1428:
1427:
1422:
1413:
1412:
1402:
1398:
1396:
1395:
1394:
1384:
1383:
1382:
1381:
1364:
1358:
1354:
1344:
1343:
1342:
1326:
1325:
1324:
1306:
1302:
1300:
1299:
1298:
1288:
1287:
1286:
1285:
1268:
1257:
1256:
1255:
1241:
1239:
1238:
1237:
1215:
1213:
1212:
1211:
1197:
1188:
1186:
1175:
1170:
1169:
1168:
1156:
1065:
1063:
1062:
1057:
1048:
1047:
1034:
1033:
1032:
1016:
1008:
1000:
999:
998:
981:
979:
978:
977:
955:
953:
952:
951:
937:
928:
926:
925:
924:
911:
903:
898:
897:
896:
884:
864:crystal momentum
857:
824:
822:
821:
816:
814:
809:
808:
797:
793:
785:
777:
772:
771:
762:
760:
749:
744:
743:
742:
730:
697:
695:
694:
689:
683:
682:
675:
674:
661:
654:
639:
631:
626:
625:
624:
612:
568:is the electron
530:
528:
527:
522:
511:
496:
491:
490:
489:
488:
478:
477:
464:
459:
458:
457:
442:
423:
421:
420:
415:
413:
412:
411:
396:
387:
386:
385:
373:
364:
348:angular momentum
319:
317:
316:
311:
300:
286:
284:
283:
282:
269:
261:
256:
255:
254:
242:
183:
181:
180:
175:
173:
168:
167:
156:
152:
144:
136:
128:
120:
115:
114:
113:
101:
31:, refers to the
2483:
2482:
2478:
2477:
2476:
2474:
2473:
2472:
2443:
2442:
2441:
2411:
2410:
2406:
2358:
2357:
2353:
2305:
2304:
2300:
2245:
2244:
2237:
2189:
2188:
2184:
2131:Phys. Rev. Lett
2128:
2127:
2123:
2068:
2067:
2063:
2034:
2033:
2029:
1988:
1987:
1980:
1955:
1954:
1947:
1940:
1927:
1926:
1922:
1918:
1867:
1843:
1839:
1821:
1802:
1801:
1788:
1780:Berry curvature
1777:
1730:
1726:
1711:
1689:
1685:
1673:
1668:
1667:
1624:
1598:
1569:
1564:
1563:
1516:
1487:
1472:
1467:
1466:
1457:
1445:
1404:
1385:
1369:
1365:
1359:
1330:
1315:
1314:
1310:
1289:
1273:
1269:
1263:
1243:
1229:
1219:
1199:
1179:
1151:
1146:
1145:
1135:
1103:
1039:
1020:
986:
969:
959:
939:
916:
912:
904:
879:
874:
873:
855:
843:
841:Bloch functions
800:
763:
753:
725:
720:
719:
713:
708:
656:
607:
602:
601:
596:
550:
539:
479:
469:
465:
437:
432:
431:
391:
368:
355:
354:
332:
274:
270:
262:
237:
232:
231:
215:instead, where
197:current density
159:
96:
91:
90:
84:magnetic moment
80:
57:
30:
12:
11:
5:
2481:
2479:
2471:
2470:
2465:
2460:
2455:
2445:
2444:
2440:
2439:
2404:
2351:
2298:
2235:
2182:
2137:(13): 137205.
2121:
2077:(13): 137204,
2061:
2027:
1978:
1945:
1938:
1919:
1917:
1914:
1906:Barnett effect
1902:
1901:
1887:
1881:
1878:
1875:
1870:
1866:
1860:
1857:
1854:
1851:
1846:
1842:
1835:
1832:
1829:
1824:
1818:
1815:
1812:
1809:
1787:
1784:
1770:
1764:
1763:
1752:
1747:
1741:
1737:
1733:
1729:
1722:
1718:
1714:
1710:
1706:
1700:
1696:
1692:
1688:
1681:
1676:
1661:
1660:
1649:
1645:
1641:
1635:
1631:
1627:
1620:
1616:
1612:
1608:
1605:
1601:
1597:
1594:
1590:
1586:
1580:
1576:
1572:
1550:
1549:
1535:
1531:
1527:
1523:
1519:
1515:
1509:
1505:
1501:
1497:
1494:
1490:
1486:
1480:
1475:
1450:
1438:
1432:
1431:
1420:
1416:
1411:
1407:
1401:
1393:
1388:
1380:
1376:
1372:
1368:
1362:
1357:
1353:
1350:
1347:
1341:
1337:
1333:
1329:
1323:
1318:
1313:
1309:
1305:
1297:
1292:
1284:
1280:
1276:
1272:
1266:
1261:
1254:
1250:
1246:
1236:
1232:
1228:
1225:
1222:
1218:
1210:
1207:
1202:
1196:
1192:
1185:
1182:
1178:
1173:
1167:
1164:
1161:
1155:
1134:
1131:
1102:
1099:
1091:Brillouin zone
1067:
1066:
1055:
1051:
1046:
1042:
1037:
1031:
1027:
1023:
1019:
1015:
1011:
1007:
1003:
997:
993:
989:
985:
976:
972:
968:
965:
962:
958:
950:
947:
942:
936:
932:
923:
919:
915:
910:
907:
901:
895:
892:
889:
883:
848:
826:
825:
813:
807:
803:
796:
792:
788:
784:
780:
776:
770:
766:
759:
756:
752:
747:
741:
738:
735:
729:
712:
709:
707:
704:
699:
698:
687:
681:
678:
673:
670:
667:
660:
653:
650:
647:
643:
637:
634:
629:
623:
620:
617:
611:
591:
548:
537:
532:
531:
520:
517:
514:
510:
506:
503:
500:
494:
487:
482:
476:
472:
468:
462:
456:
453:
450:
447:
441:
425:
424:
410:
407:
404:
401:
395:
390:
384:
381:
378:
372:
367:
363:
330:
321:
320:
309:
306:
303:
299:
295:
292:
289:
281:
277:
273:
268:
265:
259:
253:
250:
247:
241:
221:speed of light
209:Gaussian units
185:
184:
172:
166:
162:
155:
151:
147:
143:
139:
135:
131:
126:
123:
118:
112:
109:
106:
100:
79:
76:
72:magnetic field
70:by an applied
55:
37:orbital motion
28:
13:
10:
9:
6:
4:
3:
2:
2480:
2469:
2466:
2464:
2461:
2459:
2456:
2454:
2451:
2450:
2448:
2435:
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2427:
2423:
2419:
2415:
2414:J. Appl. Phys
2408:
2405:
2400:
2396:
2392:
2388:
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2317:
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2291:
2287:
2283:
2279:
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2227:
2223:
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2198:(2): 024408.
2197:
2193:
2186:
2183:
2178:
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2170:
2166:
2162:
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2154:
2150:
2145:
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2125:
2122:
2118:
2114:
2110:
2106:
2102:
2098:
2094:
2090:
2085:
2080:
2076:
2072:
2065:
2062:
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2050:
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2042:
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2024:
2020:
2016:
2012:
2008:
2004:
2000:
1996:
1992:
1985:
1983:
1979:
1975:
1971:
1967:
1963:
1959:
1952:
1950:
1946:
1941:
1939:7-04-014432-8
1935:
1931:
1924:
1921:
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1911:
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1868:
1864:
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1810:
1807:
1800:
1799:
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645:
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582:
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573:
571:
570:spin operator
567:
563:
559:
555:
554:Bohr magneton
551:
544:
540:
480:
474:
470:
466:
460:
430:
429:
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388:
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353:
352:
351:
349:
345:
341:
340:wave function
337:
333:
326:
279:
275:
271:
266:
263:
257:
230:
229:
228:
226:
222:
218:
214:
210:
207:are used; in
206:
202:
198:
194:
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164:
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129:
124:
121:
116:
89:
88:
87:
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75:
73:
69:
65:
64:ferrimagnetic
61:
60:ferromagnetic
54:
50:
46:
42:
38:
34:
33:magnetization
27:
23:
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2354:
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2308:Phys. Rev. B
2307:
2301:
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2247:
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2192:Phys. Rev. B
2191:
2185:
2134:
2130:
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2074:
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1990:
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82:The orbital
81:
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1786:Experiments
78:Definitions
35:induced by
2447:Categories
1916:References
1554:wavevector
597:, this is
43:, usually
2453:Magnetism
2399:119292686
2374:1105.5251
2346:118625623
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2261:0704.3824
2117:119017032
1932:. Wiley.
1808:γ
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1615:⋅
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1530:⋅
1504:⋅
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1387:∂
1367:∂
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1308:×
1291:∂
1271:∂
1227:π
1201:∫
1191:∑
1184:ℏ
1036:⟩
1022:ψ
1010:×
988:ψ
984:⟨
967:π
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931:∑
906:−
779:×
765:∫
649:∈
642:∑
519:⟩
516:Ψ
502:Ψ
499:⟨
493:ℏ
481:μ
467:−
308:⟩
305:Ψ
291:Ψ
288:⟨
264:−
223:.) In a
199:at point
195:) is the
138:×
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45:electrons
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1746:⟩
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858:of band
856:⟩
336:electron
205:SI units
203:. (Here
2422:Bibcode
2379:Bibcode
2326:Bibcode
2294:7942622
2266:Bibcode
2210:Bibcode
2149:Bibcode
2089:Bibcode
2045:Bibcode
1995:Bibcode
1962:Bibcode
1908:or the
1559:, and
1073:is the
560:is the
552:is the
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346:is the
323:where −
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564:, and
534:where
342:, and
187:where
157:
49:solids
2395:S2CID
2369:arXiv
2342:S2CID
2316:arXiv
2290:S2CID
2256:arXiv
2226:S2CID
2200:arXiv
2173:S2CID
2139:arXiv
2113:S2CID
2079:arXiv
2019:S2CID
592:orb,
2282:PMID
2165:PMID
2105:PMID
2011:PMID
1934:ISBN
1125:and
862:and
327:and
62:and
56:spin
2430:doi
2387:doi
2334:doi
2274:doi
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2157:doi
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2053:doi
2003:doi
1970:doi
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556:,
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1972::
1964::
1942:.
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1127:f
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1115:J
1111:r
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957:1
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680:j
677:,
672:b
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622:b
619:r
616:o
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594:j
589:m
585:j
581:V
577:M
566:S
558:ħ
549:B
547:μ
538:s
536:g
513:|
509:S
505:|
486:B
475:s
471:g
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455:n
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440:m
409:n
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389:+
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362:m
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298:L
294:|
280:e
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142:J
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53:M
26:M
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