1296:
2080:
3407:
2522:
1096:
714:
1845:
3129:
2994:
2282:
1291:{\displaystyle \Delta E^{(1)}=\mu _{0}{\frac {\mu _{\rm {B}}}{\hbar }}\langle \mathrm {g} |(\mathbf {L} +g\mathbf {S} )\cdot \mathbf {H} |\mathrm {g} \rangle =g_{J}\mu _{0}{\frac {\mu _{\rm {B}}}{\hbar }}\langle \mathrm {g} |\mathbf {J} \cdot \mathbf {H} |\mathrm {g} \rangle }
542:
2075:{\displaystyle \Delta E^{\rm {(2)}}=\left({\frac {\mu _{0}\mu _{\rm {B}}}{\hbar }}\right)^{2}\sum _{i}{\frac {|\langle \mathrm {g} |(\mathbf {L} +g\mathbf {S} )\cdot \mathbf {H} |\mathrm {e} _{i}\rangle |^{2}}{E_{\mathrm {g} }^{(0)}-E_{\mathrm {e} ,i}^{(0)}}}}
79:, Van Vleck discovered an additional paramagnetic contribution of the same order as Langevin's diamagnetism. Van Vleck contribution is usually important for systems with one electron short of being half filled and this contribution vanishes for elements with
3120:
3402:{\displaystyle W_{i}^{\rm {(2)}}={\frac {1}{\hbar ^{2}}}\sum _{k(k\neq i)}{\frac {|\langle \mathrm {e} _{i}|L_{z}+gS_{z}|\mathrm {e} _{k}\rangle |^{2}}{\delta E_{i,k}}}\;;\;\delta E_{i,k}=E_{\mathrm {e} ,i}^{(0)}-E_{\mathrm {e} ,k}^{(0)}}
2724:
2517:{\displaystyle \chi _{\rm {VV}}=2n\mu _{0}\left({\frac {\mu _{\rm {B}}}{\hbar }}\right)^{2}\sum _{i(i\neq 0)}{\frac {g_{j}^{2}|\langle \mathrm {g} |L_{z}+gS_{z}|\mathrm {e} _{i}\rangle |^{2}}{E_{\mathrm {e} ,i}-E_{\rm {g}}}},}
2681:
1659:
2271:
2192:
1478:
306:
1398:
709:{\displaystyle {\mathcal {H}}={\mathcal {H}}_{0}+\mu _{0}{\frac {\mu _{\rm {B}}}{\hbar }}(\mathbf {L} +g\mathbf {S} )\cdot \mathbf {H} +\mu _{0}^{2}{\frac {e^{2}}{8m_{\rm {e}}}}r_{\perp }^{2}H^{2}}
3940:
3853:
3673:
3521:
151:
3606:
2120:
1742:
1329:
1542:
1052:
972:
3792:
3757:
3722:
374:
777:
500:
467:
3005:
994:
910:
884:
534:
115:
3550:
3449:
858:
407:
937:
238:
208:
2708:
434:
744:
4108:
4569:
2603:
2576:
1817:
1689:
1576:
1356:
1021:
174:
2989:{\displaystyle \chi _{\rm {para}}=\mu _{0}\mu _{\rm {B}}^{2}{\frac {n}{\sum _{i}p_{i}}}\sum _{i}p_{i}\left\;;\;p_{i}=\exp \left(-{\frac {E_{i}^{(0)}}{kT}}\right),}
4134:
4073:
2218:
1752:
While Curie and Larmor susceptibilities were well understood from experimental measurements, J.H. Van Vleck noticed that the calculation above was incomplete. If
3960:
3873:
2545:
1837:
1790:
1770:
1709:
1502:
1088:
825:
801:
330:
2718:
For a more general system (molecules, complex systems), the paramagnetic susceptibility for an ensemble of independent magnetic moments can be written as
4421:
4136:
is very close to the ground state at 330 K and contributes through second order corrections as showed by Van Vleck. A similar effect is observed in
4574:
1055:
4387:
4357:
4327:
2611:
4377:
1412:
paramagnetism), that leads to a positive magnetic susceptibility. For sufficiently large temperatures, this contribution is described by
1588:
2223:
2125:
4218:"On Dielectric Constants and Magnetic Susceptibilities in the New Quantum Mechanics Part III—Application to Dia- and Paramagnetism"
1422:
249:
1409:
511:
4347:
1365:
4297:
4414:
3881:
243:
Experimental measurements show that most non-magnetic materials have a susceptibility that behaves in the following way:
4509:
1772:
is taken as the perturbation parameter, the calculation must include all orders of perturbation up to the same power of
3797:
3614:
3462:
1578:), leads to a negative response (magnetization that opposes the magnetic field). Usually known as Larmor or Langenvin
123:
3559:
2605:
are the projection of the spin and orbital angular momentum in the direction of the magnetic field, respectively.
1401:
887:
333:
4407:
4047:
2088:
48:
1548:. If the ground state has no total angular momentum there is no Curie contribution and other terms dominate.
4564:
1744:
is the mean squared radius of the atom. Note that Larmor susceptibility does not depend on the temperature.
177:
36:
2276:
In this way, Van Vleck susceptibility comes from the second order energy correction, and can be written as
1714:
1304:
80:
4002:
to be in case (d) and obtained a more precise prediction of its susceptibility using the formula above.
1507:
1026:
946:
3762:
3727:
3681:
2194:
are the energies of the excited states and the ground state, respectively, the sum excludes the state
4229:
3115:{\displaystyle W_{i}^{(1)}=g_{J}^{(i)}\langle \mathrm {e} _{i}|J_{z}|\mathrm {e} _{i}\rangle /\hbar }
339:
211:
753:
472:
439:
4504:
4011:
1059:
747:
977:
893:
867:
517:
98:
4489:
4461:
3553:
3526:
3416:
861:
834:
804:
379:
44:
4267:
3455:. Van Vleck summarizes the results of this formula in four cases, depending on the temperature:
915:
217:
187:
2686:
412:
4449:
4383:
4353:
4323:
4245:
1359:
940:
828:
722:
4078:
974:
is the unperturbed
Hamiltonian without the magnetic field, the second one is proportional to
4536:
4237:
20:
2581:
2554:
1795:
1667:
1554:
1334:
999:
159:
4113:
4052:
4035:) salts where there are six 4f electrons in trivalent europium ions. The ground state of
2197:
436:
can be positive, negative or null. Van Vleck paramagnetism often refers to systems where
4233:
4526:
4499:
4494:
4484:
3945:
3858:
2548:
2530:
2273:. Historically, J.H. Van Vleck called this term the "high frequency matrix elements".
1822:
1775:
1755:
1694:
1545:
1487:
1413:
1073:
1070:
First order perturbation theory on the second term of the
Hamiltonian (proportional to
810:
786:
315:
72:
24:
4558:
4521:
4516:
4456:
1405:
780:
181:
92:
68:
64:
40:
1551:
The first perturbation theory on the third term of the
Hamiltonian (proportional to
4444:
1579:
76:
52:
4217:
2683:, as the signs of Larmor and Van Vleck susceptibilities are opposite, the sign of
4317:
1090:) for electrons bound to an atom, gives a positive correction to energy given by
943:
orthogonal to the magnetic field. The
Hamiltonian has three terms, the first one
32:
4531:
60:
4249:
4430:
51:
between the 1920s and the 1930s to explain the magnetic response of gaseous
4241:
4541:
4152:
4137:
2676:{\displaystyle \chi _{0}\approx \chi _{\rm {VV}}+\chi _{\rm {Larmor}}}
1792:. As Larmor diamagnetism comes from first order perturbation of the
1484:
a susceptibility that is inversely proportional to the temperature
1023:. In order to obtain the ground state of the system, one can treat
184:
material, its magnetization is parallel to the magnetic field and
1654:{\displaystyle \chi _{\rm {Larmor}}=-C_{2}\langle r^{2}\rangle }
4403:
2266:{\displaystyle |\mathrm {e} _{0}\rangle =|\mathrm {g} \rangle }
2187:{\displaystyle E_{\mathrm {e} ,i}^{(0)},E_{\mathrm {g} }^{(0)}}
1473:{\displaystyle \chi _{\rm {Curie}}\approx {\frac {C_{1}}{T}}}
4399:
1054:
exactly, and treat the magnetic field dependent terms using
1033:
953:
559:
548:
301:{\displaystyle \chi (T)\approx {\frac {C_{0}}{T}}+\chi _{0}}
39:
of a material, derived from second order corrections to the
3998:, deviates slightly from it. In 1927, Van Vleck considered
3675:, the susceptibility is independent of the temperature;
514:
for an electron in a static homogeneous magnetic field
2085:
where the sum goes over all excited degenerate states
1819:, one must calculate second order perturbation of the
1404:). This correction leads to what is known as Langevin
1393:{\displaystyle \mathbf {J} =\mathbf {L} +\mathbf {S} }
4116:
4081:
4055:
3948:
3884:
3861:
3800:
3765:
3730:
3684:
3617:
3562:
3529:
3465:
3419:
3132:
3008:
2727:
2689:
2614:
2584:
2557:
2533:
2285:
2226:
2200:
2128:
2091:
1848:
1825:
1798:
1778:
1758:
1717:
1697:
1670:
1591:
1557:
1510:
1490:
1425:
1368:
1337:
1307:
1099:
1076:
1029:
1002:
980:
949:
918:
896:
870:
837:
813:
789:
756:
725:
545:
520:
475:
442:
415:
382:
342:
318:
252:
220:
190:
162:
126:
101:
95:
of a material under an external small magnetic field
4346:
Nolting, Wolfgang; Ramakanth, Anupuru (2009-10-03).
4200:
The Theory of
Electric and Magnetic Susceptibilities
4010:
The standard example of Van Vleck paramagnetism are
3935:{\displaystyle |\delta E_{i,k}|\approx k_{\rm {B}}T}
2710:
depends on the specific properties of the material.
4477:
4437:
4128:
4102:
4067:
3954:
3934:
3867:
3847:
3786:
3751:
3716:
3667:
3600:
3544:
3515:
3443:
3401:
3114:
2988:
2702:
2675:
2597:
2570:
2539:
2516:
2265:
2212:
2186:
2114:
2074:
1831:
1811:
1784:
1764:
1736:
1703:
1683:
1653:
1570:
1536:
1496:
1472:
1392:
1350:
1323:
1290:
1082:
1046:
1015:
988:
966:
931:
904:
878:
852:
819:
795:
771:
738:
708:
528:
494:
461:
428:
401:
368:
324:
300:
232:
202:
168:
145:
109:
3848:{\displaystyle \chi _{\rm {para}}\propto 1/T+c,}
3668:{\displaystyle |\delta E_{i,k}|\gg k_{\rm {B}}T}
3516:{\displaystyle |\delta E_{i,k}|\ll k_{\rm {B}}T}
4305:. Washington D.C: National Academy of Sciences.
4155:, Van Vleck paramagnetism is also important in
3794:, the susceptibility has a mixed behavior and
536:in an atom is usually composed of three terms
146:{\displaystyle \mathbf {M} =\chi \mathbf {H} }
4415:
3601:{\displaystyle \chi _{\rm {para}}\propto 1/T}
63:salts. Alongside other magnetic effects like
8:
3272:
3209:
3101:
3054:
2458:
2402:
2260:
2244:
2109:
1997:
1937:
1731:
1718:
1648:
1635:
1400:is the total angular momentum operator (see
1318:
1285:
1249:
1204:
1151:
214:, the magnetization opposes the field, and
4110:) vanishes, the first excited state with
4422:
4408:
4400:
3315:
3311:
2917:
2913:
4382:. Cambridge: Cambridge University Press.
4352:. Springer Science & Business Media.
4115:
4092:
4086:
4080:
4054:
3947:
3922:
3921:
3909:
3897:
3885:
3883:
3860:
3828:
3806:
3805:
3799:
3774:
3773:
3764:
3739:
3738:
3729:
3709:
3697:
3685:
3683:
3655:
3654:
3642:
3630:
3618:
3616:
3590:
3568:
3567:
3561:
3556:, the susceptibility follows Curie law:
3535:
3534:
3528:
3503:
3502:
3490:
3478:
3466:
3464:
3429:
3424:
3418:
3387:
3375:
3374:
3355:
3343:
3342:
3323:
3296:
3281:
3276:
3266:
3261:
3255:
3249:
3233:
3224:
3218:
3213:
3204:
3201:
3180:
3168:
3159:
3143:
3142:
3137:
3131:
3104:
3095:
3090:
3084:
3078:
3069:
3063:
3058:
3042:
3037:
3018:
3013:
3007:
2956:
2951:
2945:
2922:
2896:
2891:
2865:
2849:
2844:
2833:
2822:
2812:
2799:
2789:
2779:
2773:
2767:
2766:
2756:
2733:
2732:
2726:
2694:
2688:
2651:
2650:
2633:
2632:
2619:
2613:
2589:
2583:
2562:
2556:
2532:
2501:
2500:
2480:
2479:
2467:
2462:
2452:
2447:
2441:
2435:
2419:
2410:
2405:
2397:
2391:
2386:
2379:
2358:
2348:
2332:
2331:
2325:
2314:
2291:
2290:
2284:
2255:
2250:
2238:
2233:
2227:
2225:
2199:
2172:
2166:
2165:
2146:
2134:
2133:
2127:
2115:{\displaystyle |\mathrm {e} _{i}\rangle }
2103:
2098:
2092:
2090:
2057:
2045:
2044:
2025:
2019:
2018:
2006:
2001:
1991:
1986:
1980:
1975:
1964:
1953:
1945:
1940:
1932:
1929:
1923:
1913:
1896:
1895:
1885:
1878:
1857:
1856:
1847:
1824:
1803:
1797:
1777:
1757:
1725:
1716:
1711:the number of atoms per unit volume, and
1696:
1675:
1669:
1642:
1629:
1597:
1596:
1590:
1562:
1556:
1528:
1515:
1509:
1489:
1459:
1453:
1431:
1430:
1424:
1385:
1377:
1369:
1367:
1342:
1336:
1313:
1308:
1306:
1280:
1275:
1270:
1262:
1257:
1252:
1237:
1236:
1230:
1224:
1214:
1199:
1194:
1189:
1178:
1167:
1159:
1154:
1139:
1138:
1132:
1126:
1107:
1098:
1075:
1038:
1032:
1031:
1028:
1007:
1001:
981:
979:
958:
952:
951:
948:
923:
917:
897:
895:
871:
869:
843:
842:
836:
812:
788:
762:
761:
755:
730:
724:
700:
690:
685:
671:
670:
656:
650:
644:
639:
627:
616:
605:
590:
589:
583:
577:
564:
558:
557:
547:
546:
544:
521:
519:
480:
474:
447:
441:
420:
414:
387:
381:
360:
347:
341:
317:
292:
274:
268:
251:
219:
189:
161:
138:
127:
125:
102:
100:
3994:follows Curie law as in case (a), while
1408:(the quantum theory is sometimes called
180:. When a magnetic field is applied to a
4190:
3165:
3109:
2339:
1904:
1244:
1146:
996:, and the third one is proportional to
597:
4570:Electric and magnetic fields in matter
2714:General formula and Van Vleck criteria
1748:Second order: Van Vleck susceptibility
1058:Note that for strong magnetic fields,
1737:{\displaystyle \langle r^{2}\rangle }
1324:{\displaystyle |\mathrm {g} \rangle }
7:
4371:
4369:
4341:
4339:
4291:
4289:
4287:
4261:
4259:
4211:
4209:
1691:is another constant proportional to
3942:, there is no simple dependence on
4198:Van Vleck, John Hasbrouck (1932).
3923:
3816:
3813:
3810:
3807:
3775:
3740:
3656:
3578:
3575:
3572:
3569:
3536:
3504:
3376:
3344:
3262:
3214:
3091:
3059:
2768:
2743:
2740:
2737:
2734:
2667:
2664:
2661:
2658:
2655:
2652:
2637:
2634:
2502:
2481:
2448:
2406:
2333:
2295:
2292:
2256:
2234:
2167:
2135:
2099:
2046:
2020:
1987:
1941:
1897:
1849:
1613:
1610:
1607:
1604:
1601:
1598:
1537:{\displaystyle C_{0}\approx C_{1}}
1444:
1441:
1438:
1435:
1432:
1314:
1281:
1253:
1238:
1200:
1155:
1140:
1100:
1047:{\displaystyle {\mathcal {H}}_{0}}
967:{\displaystyle {\mathcal {H}}_{0}}
844:
763:
672:
591:
14:
4316:Marder, Michael P. (2010-11-17).
4268:"John H. van Vleck Nobel Lecture"
35:-independent contribution to the
4379:Magnetism and Magnetic Materials
3982:are similar paramagnetic gases,
3787:{\displaystyle \ll k_{\rm {B}}T}
3752:{\displaystyle \gg k_{\rm {B}}T}
3717:{\displaystyle |\delta E_{i,k}|}
1976:
1965:
1954:
1386:
1378:
1370:
1271:
1263:
1190:
1179:
1168:
982:
898:
872:
628:
617:
606:
522:
139:
128:
103:
4216:Van Vleck, J. H. (1928-04-01).
3451:is the Landé g-factor of state
1066:First order perturbation theory
369:{\displaystyle C_{0},\chi _{0}}
117:is approximately described by
4575:Eponymous equations of physics
3910:
3886:
3710:
3686:
3643:
3619:
3491:
3467:
3436:
3430:
3394:
3388:
3362:
3356:
3277:
3256:
3225:
3205:
3196:
3184:
3150:
3144:
3085:
3070:
3049:
3043:
3025:
3019:
2963:
2957:
2903:
2897:
2856:
2850:
2463:
2442:
2411:
2398:
2374:
2362:
2251:
2228:
2179:
2173:
2153:
2147:
2093:
2064:
2058:
2032:
2026:
2002:
1981:
1969:
1950:
1946:
1933:
1864:
1858:
1309:
1276:
1258:
1195:
1183:
1164:
1160:
1114:
1108:
772:{\displaystyle \mu _{\rm {B}}}
621:
602:
495:{\displaystyle \chi _{0}>0}
462:{\displaystyle C_{0}\approx 0}
262:
256:
1:
4510:ferromagnetic superconductor
4296:Anderson, Philip W. (1987).
989:{\displaystyle \mathbf {H} }
905:{\displaystyle \mathbf {S} }
879:{\displaystyle \mathbf {L} }
529:{\displaystyle \mathbf {H} }
110:{\displaystyle \mathbf {H} }
4349:Quantum Theory of Magnetism
4266:van Vleck, John H. (1977).
3545:{\displaystyle k_{\rm {B}}}
3444:{\displaystyle g_{J}^{(i)}}
853:{\displaystyle m_{\rm {e}}}
402:{\displaystyle C_{0}\geq 0}
4591:
4075:and Curie's contribution (
1544:is the material dependent
932:{\displaystyle r_{\perp }}
233:{\displaystyle \chi <0}
203:{\displaystyle \chi >0}
4322:. John Wiley & Sons.
4177:which have a localized 5f
2703:{\displaystyle \chi _{0}}
888:angular momentum operator
429:{\displaystyle \chi _{0}}
31:refers to a positive and
4319:Condensed Matter Physics
4299:John Hasbrouck Van Vleck
4048:azimuthal quantum number
1362:of the ground state and
939:is the component of the
739:{\displaystyle \mu _{0}}
49:John Hasbrouck Van Vleck
47:theory was developed by
4467:Van Vleck paramagnetism
4376:Coey, J. M. D. (2010).
4103:{\displaystyle C_{0}/T}
3966:While molecular oxygen
178:magnetic susceptibility
37:magnetic susceptibility
29:Van Vleck paramagnetism
4242:10.1103/PhysRev.31.587
4130:
4104:
4069:
3956:
3936:
3869:
3849:
3788:
3753:
3718:
3669:
3602:
3546:
3517:
3457:
3445:
3403:
3116:
2990:
2704:
2677:
2599:
2572:
2541:
2518:
2267:
2214:
2188:
2116:
2076:
1833:
1813:
1786:
1766:
1738:
1705:
1685:
1655:
1572:
1538:
1498:
1474:
1394:
1352:
1325:
1292:
1084:
1048:
1017:
990:
968:
933:
906:
880:
854:
821:
797:
773:
740:
710:
530:
496:
463:
430:
403:
370:
326:
302:
234:
204:
170:
147:
111:
4131:
4105:
4070:
3957:
3937:
3870:
3850:
3789:
3754:
3719:
3670:
3603:
3547:
3518:
3446:
3404:
3117:
2991:
2705:
2678:
2600:
2598:{\displaystyle L_{z}}
2573:
2571:{\displaystyle S_{z}}
2542:
2519:
2268:
2215:
2189:
2117:
2077:
1834:
1814:
1812:{\displaystyle H^{2}}
1787:
1767:
1739:
1706:
1686:
1684:{\displaystyle C_{2}}
1656:
1573:
1571:{\displaystyle H^{2}}
1539:
1499:
1475:
1402:Wigner–Eckart theorem
1395:
1353:
1351:{\displaystyle g_{J}}
1331:is the ground state,
1326:
1293:
1085:
1049:
1018:
1016:{\displaystyle H^{2}}
991:
969:
934:
907:
881:
855:
822:
798:
774:
741:
711:
531:
497:
464:
431:
404:
371:
327:
303:
235:
205:
171:
169:{\displaystyle \chi }
148:
112:
4114:
4079:
4053:
3946:
3882:
3859:
3798:
3763:
3728:
3682:
3615:
3560:
3527:
3463:
3417:
3130:
3006:
2725:
2687:
2612:
2582:
2555:
2531:
2283:
2224:
2198:
2126:
2089:
1846:
1823:
1796:
1776:
1756:
1715:
1695:
1668:
1589:
1555:
1508:
1488:
1423:
1366:
1335:
1305:
1097:
1074:
1056:perturbation theory.
1027:
1000:
978:
947:
916:
894:
868:
835:
811:
787:
754:
723:
543:
518:
473:
440:
413:
380:
340:
316:
250:
218:
212:diamagnetic material
188:
160:
124:
99:
4537:amorphous magnetism
4505:superferromagnetism
4234:1928PhRv...31..587V
4129:{\displaystyle j=1}
4068:{\displaystyle j=0}
4012:europium(III) oxide
4006:Systems of interest
3440:
3398:
3366:
3155:
3053:
3029:
2967:
2907:
2860:
2778:
2396:
2213:{\displaystyle i=0}
2183:
2157:
2068:
2036:
1060:Paschen-Back effect
748:vacuum permeability
695:
649:
4490:antiferromagnetism
4462:superparamagnetism
4202:. Clarendon Press.
4126:
4100:
4065:
3952:
3932:
3865:
3845:
3784:
3749:
3714:
3665:
3598:
3554:Boltzmann constant
3542:
3513:
3441:
3420:
3399:
3370:
3338:
3200:
3133:
3112:
3033:
3009:
2986:
2947:
2887:
2840:
2817:
2794:
2762:
2700:
2673:
2595:
2568:
2537:
2514:
2382:
2378:
2263:
2210:
2184:
2161:
2129:
2112:
2072:
2040:
2014:
1928:
1829:
1809:
1782:
1762:
1734:
1701:
1681:
1651:
1568:
1534:
1494:
1470:
1390:
1348:
1321:
1288:
1080:
1044:
1013:
986:
964:
929:
902:
876:
850:
817:
793:
769:
736:
706:
681:
635:
526:
492:
459:
426:
399:
376:are constant, and
366:
322:
298:
230:
200:
166:
143:
107:
45:quantum mechanical
41:Zeeman interaction
4552:
4551:
4450:superdiamagnetism
4438:Magnetic response
4389:978-0-521-81614-4
4359:978-3-540-85416-6
4329:978-0-470-94994-8
4046:that has a total
3978:and nitric oxide
3955:{\displaystyle T}
3868:{\displaystyle c}
3309:
3176:
3174:
2976:
2879:
2808:
2806:
2785:
2540:{\displaystyle n}
2509:
2354:
2342:
2070:
1919:
1907:
1832:{\displaystyle B}
1785:{\displaystyle H}
1765:{\displaystyle H}
1704:{\displaystyle n}
1497:{\displaystyle T}
1468:
1247:
1149:
1083:{\displaystyle H}
941:position operator
829:elementary charge
820:{\displaystyle e}
796:{\displaystyle g}
679:
600:
325:{\displaystyle T}
283:
16:Magnetic property
4582:
4424:
4417:
4410:
4401:
4394:
4393:
4373:
4364:
4363:
4343:
4334:
4333:
4313:
4307:
4306:
4304:
4293:
4282:
4281:
4279:
4278:
4263:
4254:
4253:
4213:
4204:
4203:
4195:
4176:
4175:
4174:
4165:
4164:
4163:
4150:
4149:
4148:
4135:
4133:
4132:
4127:
4109:
4107:
4106:
4101:
4096:
4091:
4090:
4074:
4072:
4071:
4066:
4045:
4044:
4043:
4034:
4033:
4032:
4024:
4023:
4001:
3997:
3993:
3992:
3991:
3981:
3977:
3976:
3975:
3961:
3959:
3958:
3953:
3941:
3939:
3938:
3933:
3928:
3927:
3926:
3913:
3908:
3907:
3889:
3874:
3872:
3871:
3866:
3854:
3852:
3851:
3846:
3832:
3821:
3820:
3819:
3793:
3791:
3790:
3785:
3780:
3779:
3778:
3758:
3756:
3755:
3750:
3745:
3744:
3743:
3723:
3721:
3720:
3715:
3713:
3708:
3707:
3689:
3674:
3672:
3671:
3666:
3661:
3660:
3659:
3646:
3641:
3640:
3622:
3607:
3605:
3604:
3599:
3594:
3583:
3582:
3581:
3551:
3549:
3548:
3543:
3541:
3540:
3539:
3522:
3520:
3519:
3514:
3509:
3508:
3507:
3494:
3489:
3488:
3470:
3450:
3448:
3447:
3442:
3439:
3428:
3408:
3406:
3405:
3400:
3397:
3386:
3379:
3365:
3354:
3347:
3334:
3333:
3310:
3308:
3307:
3306:
3287:
3286:
3285:
3280:
3271:
3270:
3265:
3259:
3254:
3253:
3238:
3237:
3228:
3223:
3222:
3217:
3208:
3202:
3199:
3175:
3173:
3172:
3160:
3154:
3153:
3141:
3121:
3119:
3118:
3113:
3108:
3100:
3099:
3094:
3088:
3083:
3082:
3073:
3068:
3067:
3062:
3052:
3041:
3028:
3017:
2995:
2993:
2992:
2987:
2982:
2978:
2977:
2975:
2966:
2955:
2946:
2927:
2926:
2912:
2908:
2906:
2895:
2880:
2878:
2870:
2869:
2864:
2859:
2848:
2834:
2827:
2826:
2816:
2807:
2805:
2804:
2803:
2793:
2780:
2777:
2772:
2771:
2761:
2760:
2748:
2747:
2746:
2709:
2707:
2706:
2701:
2699:
2698:
2682:
2680:
2679:
2674:
2672:
2671:
2670:
2642:
2641:
2640:
2624:
2623:
2604:
2602:
2601:
2596:
2594:
2593:
2577:
2575:
2574:
2569:
2567:
2566:
2546:
2544:
2543:
2538:
2523:
2521:
2520:
2515:
2510:
2508:
2507:
2506:
2505:
2492:
2491:
2484:
2473:
2472:
2471:
2466:
2457:
2456:
2451:
2445:
2440:
2439:
2424:
2423:
2414:
2409:
2401:
2395:
2390:
2380:
2377:
2353:
2352:
2347:
2343:
2338:
2337:
2336:
2326:
2319:
2318:
2300:
2299:
2298:
2272:
2270:
2269:
2264:
2259:
2254:
2243:
2242:
2237:
2231:
2219:
2217:
2216:
2211:
2193:
2191:
2190:
2185:
2182:
2171:
2170:
2156:
2145:
2138:
2121:
2119:
2118:
2113:
2108:
2107:
2102:
2096:
2081:
2079:
2078:
2073:
2071:
2069:
2067:
2056:
2049:
2035:
2024:
2023:
2012:
2011:
2010:
2005:
1996:
1995:
1990:
1984:
1979:
1968:
1957:
1949:
1944:
1936:
1930:
1927:
1918:
1917:
1912:
1908:
1903:
1902:
1901:
1900:
1890:
1889:
1879:
1869:
1868:
1867:
1838:
1836:
1835:
1830:
1818:
1816:
1815:
1810:
1808:
1807:
1791:
1789:
1788:
1783:
1771:
1769:
1768:
1763:
1743:
1741:
1740:
1735:
1730:
1729:
1710:
1708:
1707:
1702:
1690:
1688:
1687:
1682:
1680:
1679:
1660:
1658:
1657:
1652:
1647:
1646:
1634:
1633:
1618:
1617:
1616:
1577:
1575:
1574:
1569:
1567:
1566:
1543:
1541:
1540:
1535:
1533:
1532:
1520:
1519:
1503:
1501:
1500:
1495:
1479:
1477:
1476:
1471:
1469:
1464:
1463:
1454:
1449:
1448:
1447:
1399:
1397:
1396:
1391:
1389:
1381:
1373:
1357:
1355:
1354:
1349:
1347:
1346:
1330:
1328:
1327:
1322:
1317:
1312:
1297:
1295:
1294:
1289:
1284:
1279:
1274:
1266:
1261:
1256:
1248:
1243:
1242:
1241:
1231:
1229:
1228:
1219:
1218:
1203:
1198:
1193:
1182:
1171:
1163:
1158:
1150:
1145:
1144:
1143:
1133:
1131:
1130:
1118:
1117:
1089:
1087:
1086:
1081:
1053:
1051:
1050:
1045:
1043:
1042:
1037:
1036:
1022:
1020:
1019:
1014:
1012:
1011:
995:
993:
992:
987:
985:
973:
971:
970:
965:
963:
962:
957:
956:
938:
936:
935:
930:
928:
927:
911:
909:
908:
903:
901:
885:
883:
882:
877:
875:
859:
857:
856:
851:
849:
848:
847:
826:
824:
823:
818:
802:
800:
799:
794:
778:
776:
775:
770:
768:
767:
766:
745:
743:
742:
737:
735:
734:
715:
713:
712:
707:
705:
704:
694:
689:
680:
678:
677:
676:
675:
661:
660:
651:
648:
643:
631:
620:
609:
601:
596:
595:
594:
584:
582:
581:
569:
568:
563:
562:
552:
551:
535:
533:
532:
527:
525:
501:
499:
498:
493:
485:
484:
468:
466:
465:
460:
452:
451:
435:
433:
432:
427:
425:
424:
408:
406:
405:
400:
392:
391:
375:
373:
372:
367:
365:
364:
352:
351:
332:is the absolute
331:
329:
328:
323:
307:
305:
304:
299:
297:
296:
284:
279:
278:
269:
239:
237:
236:
231:
209:
207:
206:
201:
175:
173:
172:
167:
152:
150:
149:
144:
142:
131:
116:
114:
113:
108:
106:
67:'s formulas for
58:
21:condensed matter
4590:
4589:
4585:
4584:
4583:
4581:
4580:
4579:
4555:
4554:
4553:
4548:
4478:Magnetic states
4473:
4433:
4428:
4398:
4397:
4390:
4375:
4374:
4367:
4360:
4345:
4344:
4337:
4330:
4315:
4314:
4310:
4302:
4295:
4294:
4285:
4276:
4274:
4265:
4264:
4257:
4222:Physical Review
4215:
4214:
4207:
4197:
4196:
4192:
4187:
4181:configuration.
4180:
4173:
4171:
4170:
4169:
4167:
4162:
4160:
4159:
4158:
4156:
4147:
4145:
4144:
4143:
4141:
4112:
4111:
4082:
4077:
4076:
4051:
4050:
4042:
4040:
4039:
4038:
4036:
4031:
4028:
4027:
4026:
4022:
4019:
4018:
4017:
4015:
4008:
3999:
3995:
3990:
3987:
3986:
3985:
3983:
3979:
3974:
3971:
3970:
3969:
3967:
3944:
3943:
3917:
3893:
3880:
3879:
3857:
3856:
3801:
3796:
3795:
3769:
3761:
3760:
3734:
3726:
3725:
3693:
3680:
3679:
3650:
3626:
3613:
3612:
3563:
3558:
3557:
3530:
3525:
3524:
3498:
3474:
3461:
3460:
3415:
3414:
3319:
3292:
3288:
3275:
3260:
3245:
3229:
3212:
3203:
3164:
3128:
3127:
3089:
3074:
3057:
3004:
3003:
2968:
2941:
2937:
2918:
2871:
2836:
2835:
2832:
2828:
2818:
2795:
2784:
2752:
2728:
2723:
2722:
2716:
2690:
2685:
2684:
2646:
2628:
2615:
2610:
2609:
2585:
2580:
2579:
2558:
2553:
2552:
2529:
2528:
2496:
2475:
2474:
2461:
2446:
2431:
2415:
2381:
2327:
2321:
2320:
2310:
2286:
2281:
2280:
2232:
2222:
2221:
2196:
2195:
2124:
2123:
2097:
2087:
2086:
2013:
2000:
1985:
1931:
1891:
1881:
1880:
1874:
1873:
1852:
1844:
1843:
1821:
1820:
1799:
1794:
1793:
1774:
1773:
1754:
1753:
1750:
1721:
1713:
1712:
1693:
1692:
1671:
1666:
1665:
1638:
1625:
1592:
1587:
1586:
1558:
1553:
1552:
1524:
1511:
1506:
1505:
1486:
1485:
1455:
1426:
1421:
1420:
1364:
1363:
1338:
1333:
1332:
1303:
1302:
1232:
1220:
1210:
1134:
1122:
1103:
1095:
1094:
1072:
1071:
1068:
1030:
1025:
1024:
1003:
998:
997:
976:
975:
950:
945:
944:
919:
914:
913:
912:the spin and
892:
891:
886:is the orbital
866:
865:
838:
833:
832:
809:
808:
785:
784:
757:
752:
751:
726:
721:
720:
696:
666:
662:
652:
585:
573:
556:
541:
540:
516:
515:
508:
476:
471:
470:
443:
438:
437:
416:
411:
410:
383:
378:
377:
356:
343:
338:
337:
314:
313:
288:
270:
248:
247:
216:
215:
186:
185:
158:
157:
122:
121:
97:
96:
89:
56:
17:
12:
11:
5:
4588:
4586:
4578:
4577:
4572:
4567:
4565:Atomic physics
4557:
4556:
4550:
4549:
4547:
4546:
4545:
4544:
4539:
4529:
4527:mictomagnetism
4524:
4519:
4514:
4513:
4512:
4507:
4500:ferromagnetism
4497:
4495:ferrimagnetism
4492:
4487:
4485:altermagnetism
4481:
4479:
4475:
4474:
4472:
4471:
4470:
4469:
4464:
4454:
4453:
4452:
4441:
4439:
4435:
4434:
4429:
4427:
4426:
4419:
4412:
4404:
4396:
4395:
4388:
4365:
4358:
4335:
4328:
4308:
4283:
4255:
4228:(4): 587–613.
4205:
4189:
4188:
4186:
4183:
4178:
4172:
4161:
4151:ions). In the
4146:
4125:
4122:
4119:
4099:
4095:
4089:
4085:
4064:
4061:
4058:
4041:
4029:
4020:
4007:
4004:
3988:
3972:
3964:
3963:
3951:
3931:
3925:
3920:
3916:
3912:
3906:
3903:
3900:
3896:
3892:
3888:
3876:
3875:is a constant;
3864:
3844:
3841:
3838:
3835:
3831:
3827:
3824:
3818:
3815:
3812:
3809:
3804:
3783:
3777:
3772:
3768:
3748:
3742:
3737:
3733:
3712:
3706:
3703:
3700:
3696:
3692:
3688:
3676:
3664:
3658:
3653:
3649:
3645:
3639:
3636:
3633:
3629:
3625:
3621:
3609:
3597:
3593:
3589:
3586:
3580:
3577:
3574:
3571:
3566:
3538:
3533:
3512:
3506:
3501:
3497:
3493:
3487:
3484:
3481:
3477:
3473:
3469:
3438:
3435:
3432:
3427:
3423:
3411:
3410:
3396:
3393:
3390:
3385:
3382:
3378:
3373:
3369:
3364:
3361:
3358:
3353:
3350:
3346:
3341:
3337:
3332:
3329:
3326:
3322:
3318:
3314:
3305:
3302:
3299:
3295:
3291:
3284:
3279:
3274:
3269:
3264:
3258:
3252:
3248:
3244:
3241:
3236:
3232:
3227:
3221:
3216:
3211:
3207:
3198:
3195:
3192:
3189:
3186:
3183:
3179:
3171:
3167:
3163:
3158:
3152:
3149:
3146:
3140:
3136:
3124:
3123:
3111:
3107:
3103:
3098:
3093:
3087:
3081:
3077:
3072:
3066:
3061:
3056:
3051:
3048:
3045:
3040:
3036:
3032:
3027:
3024:
3021:
3016:
3012:
2997:
2996:
2985:
2981:
2974:
2971:
2965:
2962:
2959:
2954:
2950:
2944:
2940:
2936:
2933:
2930:
2925:
2921:
2916:
2911:
2905:
2902:
2899:
2894:
2890:
2886:
2883:
2877:
2874:
2868:
2863:
2858:
2855:
2852:
2847:
2843:
2839:
2831:
2825:
2821:
2815:
2811:
2802:
2798:
2792:
2788:
2783:
2776:
2770:
2765:
2759:
2755:
2751:
2745:
2742:
2739:
2736:
2731:
2715:
2712:
2697:
2693:
2669:
2666:
2663:
2660:
2657:
2654:
2649:
2645:
2639:
2636:
2631:
2627:
2622:
2618:
2592:
2588:
2565:
2561:
2549:number density
2536:
2525:
2524:
2513:
2504:
2499:
2495:
2490:
2487:
2483:
2478:
2470:
2465:
2460:
2455:
2450:
2444:
2438:
2434:
2430:
2427:
2422:
2418:
2413:
2408:
2404:
2400:
2394:
2389:
2385:
2376:
2373:
2370:
2367:
2364:
2361:
2357:
2351:
2346:
2341:
2335:
2330:
2324:
2317:
2313:
2309:
2306:
2303:
2297:
2294:
2289:
2262:
2258:
2253:
2249:
2246:
2241:
2236:
2230:
2209:
2206:
2203:
2181:
2178:
2175:
2169:
2164:
2160:
2155:
2152:
2149:
2144:
2141:
2137:
2132:
2111:
2106:
2101:
2095:
2083:
2082:
2066:
2063:
2060:
2055:
2052:
2048:
2043:
2039:
2034:
2031:
2028:
2022:
2017:
2009:
2004:
1999:
1994:
1989:
1983:
1978:
1974:
1971:
1967:
1963:
1960:
1956:
1952:
1948:
1943:
1939:
1935:
1926:
1922:
1916:
1911:
1906:
1899:
1894:
1888:
1884:
1877:
1872:
1866:
1863:
1860:
1855:
1851:
1828:
1806:
1802:
1781:
1761:
1749:
1746:
1733:
1728:
1724:
1720:
1700:
1678:
1674:
1662:
1661:
1650:
1645:
1641:
1637:
1632:
1628:
1624:
1621:
1615:
1612:
1609:
1606:
1603:
1600:
1595:
1565:
1561:
1546:Curie constant
1531:
1527:
1523:
1518:
1514:
1493:
1482:
1481:
1467:
1462:
1458:
1452:
1446:
1443:
1440:
1437:
1434:
1429:
1388:
1384:
1380:
1376:
1372:
1360:Landé g-factor
1345:
1341:
1320:
1316:
1311:
1299:
1298:
1287:
1283:
1278:
1273:
1269:
1265:
1260:
1255:
1251:
1246:
1240:
1235:
1227:
1223:
1217:
1213:
1209:
1206:
1202:
1197:
1192:
1188:
1185:
1181:
1177:
1174:
1170:
1166:
1162:
1157:
1153:
1148:
1142:
1137:
1129:
1125:
1121:
1116:
1113:
1110:
1106:
1102:
1079:
1067:
1064:
1041:
1035:
1010:
1006:
984:
961:
955:
926:
922:
900:
874:
846:
841:
816:
792:
765:
760:
733:
729:
717:
716:
703:
699:
693:
688:
684:
674:
669:
665:
659:
655:
647:
642:
638:
634:
630:
626:
623:
619:
615:
612:
608:
604:
599:
593:
588:
580:
576:
572:
567:
561:
555:
550:
524:
507:
504:
491:
488:
483:
479:
458:
455:
450:
446:
423:
419:
398:
395:
390:
386:
363:
359:
355:
350:
346:
321:
310:
309:
295:
291:
287:
282:
277:
273:
267:
264:
261:
258:
255:
229:
226:
223:
199:
196:
193:
165:
154:
153:
141:
137:
134:
130:
105:
88:
85:
25:atomic physics
15:
13:
10:
9:
6:
4:
3:
2:
4587:
4576:
4573:
4571:
4568:
4566:
4563:
4562:
4560:
4543:
4540:
4538:
4535:
4534:
4533:
4530:
4528:
4525:
4523:
4522:metamagnetism
4520:
4518:
4517:helimagnetism
4515:
4511:
4508:
4506:
4503:
4502:
4501:
4498:
4496:
4493:
4491:
4488:
4486:
4483:
4482:
4480:
4476:
4468:
4465:
4463:
4460:
4459:
4458:
4457:paramagnetism
4455:
4451:
4448:
4447:
4446:
4443:
4442:
4440:
4436:
4432:
4425:
4420:
4418:
4413:
4411:
4406:
4405:
4402:
4391:
4385:
4381:
4380:
4372:
4370:
4366:
4361:
4355:
4351:
4350:
4342:
4340:
4336:
4331:
4325:
4321:
4320:
4312:
4309:
4301:
4300:
4292:
4290:
4288:
4284:
4273:
4269:
4262:
4260:
4256:
4251:
4247:
4243:
4239:
4235:
4231:
4227:
4223:
4219:
4212:
4210:
4206:
4201:
4194:
4191:
4184:
4182:
4154:
4139:
4123:
4120:
4117:
4097:
4093:
4087:
4083:
4062:
4059:
4056:
4049:
4013:
4005:
4003:
3949:
3929:
3918:
3914:
3904:
3901:
3898:
3894:
3890:
3877:
3862:
3842:
3839:
3836:
3833:
3829:
3825:
3822:
3802:
3781:
3770:
3766:
3746:
3735:
3731:
3704:
3701:
3698:
3694:
3690:
3677:
3662:
3651:
3647:
3637:
3634:
3631:
3627:
3623:
3610:
3595:
3591:
3587:
3584:
3564:
3555:
3531:
3510:
3499:
3495:
3485:
3482:
3479:
3475:
3471:
3458:
3456:
3454:
3433:
3425:
3421:
3391:
3383:
3380:
3371:
3367:
3359:
3351:
3348:
3339:
3335:
3330:
3327:
3324:
3320:
3316:
3312:
3303:
3300:
3297:
3293:
3289:
3282:
3267:
3250:
3246:
3242:
3239:
3234:
3230:
3219:
3193:
3190:
3187:
3181:
3177:
3169:
3161:
3156:
3147:
3138:
3134:
3126:
3125:
3105:
3096:
3079:
3075:
3064:
3046:
3038:
3034:
3030:
3022:
3014:
3010:
3002:
3001:
3000:
2983:
2979:
2972:
2969:
2960:
2952:
2948:
2942:
2938:
2934:
2931:
2928:
2923:
2919:
2914:
2909:
2900:
2892:
2888:
2884:
2881:
2875:
2872:
2866:
2861:
2853:
2845:
2841:
2837:
2829:
2823:
2819:
2813:
2809:
2800:
2796:
2790:
2786:
2781:
2774:
2763:
2757:
2753:
2749:
2729:
2721:
2720:
2719:
2713:
2711:
2695:
2691:
2647:
2643:
2629:
2625:
2620:
2616:
2608:In this way,
2606:
2590:
2586:
2563:
2559:
2550:
2534:
2511:
2497:
2493:
2488:
2485:
2476:
2468:
2453:
2436:
2432:
2428:
2425:
2420:
2416:
2392:
2387:
2383:
2371:
2368:
2365:
2359:
2355:
2349:
2344:
2328:
2322:
2315:
2311:
2307:
2304:
2301:
2287:
2279:
2278:
2277:
2274:
2247:
2239:
2207:
2204:
2201:
2176:
2162:
2158:
2150:
2142:
2139:
2130:
2104:
2061:
2053:
2050:
2041:
2037:
2029:
2015:
2007:
1992:
1972:
1961:
1958:
1924:
1920:
1914:
1909:
1892:
1886:
1882:
1875:
1870:
1861:
1853:
1842:
1841:
1840:
1826:
1804:
1800:
1779:
1759:
1747:
1745:
1726:
1722:
1698:
1676:
1672:
1643:
1639:
1630:
1626:
1622:
1619:
1593:
1585:
1584:
1583:
1581:
1563:
1559:
1549:
1547:
1529:
1525:
1521:
1516:
1512:
1491:
1465:
1460:
1456:
1450:
1427:
1419:
1418:
1417:
1415:
1411:
1407:
1406:paramagnetism
1403:
1382:
1374:
1361:
1343:
1339:
1267:
1233:
1225:
1221:
1215:
1211:
1207:
1186:
1175:
1172:
1135:
1127:
1123:
1119:
1111:
1104:
1093:
1092:
1091:
1077:
1065:
1063:
1061:
1057:
1039:
1008:
1004:
959:
942:
924:
920:
889:
863:
862:electron mass
839:
830:
814:
806:
790:
782:
781:Bohr magneton
758:
749:
731:
727:
701:
697:
691:
686:
682:
667:
663:
657:
653:
645:
640:
636:
632:
624:
613:
610:
586:
578:
574:
570:
565:
553:
539:
538:
537:
513:
505:
503:
489:
486:
481:
477:
456:
453:
448:
444:
421:
417:
396:
393:
388:
384:
361:
357:
353:
348:
344:
335:
319:
293:
289:
285:
280:
275:
271:
265:
259:
253:
246:
245:
244:
241:
227:
224:
221:
213:
197:
194:
191:
183:
179:
163:
135:
132:
120:
119:
118:
94:
93:magnetization
86:
84:
82:
81:closed shells
78:
74:
70:
69:paramagnetism
66:
65:Paul Langevin
62:
54:
50:
46:
42:
38:
34:
30:
26:
22:
4466:
4445:diamagnetism
4378:
4348:
4318:
4311:
4298:
4275:. Retrieved
4271:
4225:
4221:
4199:
4193:
4009:
3965:
3452:
3412:
2998:
2717:
2607:
2526:
2275:
2084:
1751:
1663:
1580:diamagnetism
1550:
1483:
1300:
1069:
718:
509:
311:
242:
182:paramagnetic
155:
90:
77:diamagnetism
53:nitric oxide
28:
18:
4272:Nobel Prize
1414:Curie's law
1062:dominates.
512:Hamiltonian
334:temperature
87:Description
73:Curie's law
33:temperature
4559:Categories
4532:spin glass
4277:2020-10-18
4185:References
3724:is either
506:Derivation
61:rare-earth
4431:Magnetism
4250:0031-899X
4153:actinides
3915:≈
3891:δ
3823:∝
3803:χ
3767:≪
3732:≫
3691:δ
3648:≫
3624:δ
3585:∝
3565:χ
3496:≪
3472:δ
3368:−
3317:δ
3290:δ
3273:⟩
3210:⟨
3191:≠
3178:∑
3166:ℏ
3110:ℏ
3102:⟩
3055:⟨
2943:−
2935:
2882:−
2810:∑
2787:∑
2764:μ
2754:μ
2730:χ
2692:χ
2648:χ
2630:χ
2626:≈
2617:χ
2494:−
2459:⟩
2403:⟨
2369:≠
2356:∑
2340:ℏ
2329:μ
2312:μ
2288:χ
2261:⟩
2245:⟩
2110:⟩
2038:−
1998:⟩
1973:⋅
1938:⟨
1921:∑
1905:ℏ
1893:μ
1883:μ
1850:Δ
1732:⟩
1719:⟨
1649:⟩
1636:⟨
1623:−
1594:χ
1522:≈
1451:≈
1428:χ
1410:Brillouin
1319:⟩
1286:⟩
1268:⋅
1250:⟨
1245:ℏ
1234:μ
1222:μ
1205:⟩
1187:⋅
1152:⟨
1147:ℏ
1136:μ
1124:μ
1101:Δ
925:⊥
759:μ
728:μ
687:⊥
637:μ
625:⋅
598:ℏ
587:μ
575:μ
478:χ
454:≈
418:χ
394:≥
358:χ
290:χ
266:≈
254:χ
222:χ
210:. For a
192:χ
164:χ
136:χ
59:) and of
4542:spin ice
4138:samarium
3523:, where
2220:, where
1504:, where
805:g-factor
409:, while
4230:Bibcode
4140:salts (
3878:if all
3678:if all
3611:if all
3459:if all
2999:where
2547:is the
1358:is the
860:is the
827:is the
803:is the
779:is the
746:is the
176:is the
4386:
4356:
4326:
4248:
3855:where
2551:, and
2527:where
2122:, and
1839:term:
1664:where
1301:where
719:where
312:where
156:where
75:) and
43:. The
4303:(PDF)
4384:ISBN
4354:ISBN
4324:ISBN
4246:ISSN
4166:and
3413:and
2578:and
510:The
487:>
469:and
225:<
195:>
91:The
23:and
4238:doi
3759:or
3552:is
2932:exp
831:,
19:In
4561::
4368:^
4338:^
4286:^
4270:.
4258:^
4244:.
4236:.
4226:31
4224:.
4220:.
4208:^
4168:Cm
4157:Bk
4142:Sm
4037:Eu
4016:Eu
4000:NO
3996:NO
3980:NO
1582::
1416::
890:,
864:,
807:,
783:,
750:,
502:.
336:;
240:.
83:.
57:NO
27:,
4423:e
4416:t
4409:v
4392:.
4362:.
4332:.
4280:.
4252:.
4240::
4232::
4179:6
4124:1
4121:=
4118:j
4098:T
4094:/
4088:0
4084:C
4063:0
4060:=
4057:j
4030:3
4025:O
4021:2
4014:(
3989:2
3984:O
3973:2
3968:O
3962:.
3950:T
3930:T
3924:B
3919:k
3911:|
3905:k
3902:,
3899:i
3895:E
3887:|
3863:c
3843:,
3840:c
3837:+
3834:T
3830:/
3826:1
3817:a
3814:r
3811:a
3808:p
3782:T
3776:B
3771:k
3747:T
3741:B
3736:k
3711:|
3705:k
3702:,
3699:i
3695:E
3687:|
3663:T
3657:B
3652:k
3644:|
3638:k
3635:,
3632:i
3628:E
3620:|
3608:;
3596:T
3592:/
3588:1
3579:a
3576:r
3573:a
3570:p
3537:B
3532:k
3511:T
3505:B
3500:k
3492:|
3486:k
3483:,
3480:i
3476:E
3468:|
3453:i
3437:)
3434:i
3431:(
3426:J
3422:g
3409:,
3395:)
3392:0
3389:(
3384:k
3381:,
3377:e
3372:E
3363:)
3360:0
3357:(
3352:i
3349:,
3345:e
3340:E
3336:=
3331:k
3328:,
3325:i
3321:E
3313:;
3304:k
3301:,
3298:i
3294:E
3283:2
3278:|
3268:k
3263:e
3257:|
3251:z
3247:S
3243:g
3240:+
3235:z
3231:L
3226:|
3220:i
3215:e
3206:|
3197:)
3194:i
3188:k
3185:(
3182:k
3170:2
3162:1
3157:=
3151:)
3148:2
3145:(
3139:i
3135:W
3122:,
3106:/
3097:i
3092:e
3086:|
3080:z
3076:J
3071:|
3065:i
3060:e
3050:)
3047:i
3044:(
3039:J
3035:g
3031:=
3026:)
3023:1
3020:(
3015:i
3011:W
2984:,
2980:)
2973:T
2970:k
2964:)
2961:0
2958:(
2953:i
2949:E
2939:(
2929:=
2924:i
2920:p
2915:;
2910:]
2904:)
2901:2
2898:(
2893:i
2889:W
2885:2
2876:T
2873:k
2867:2
2862:)
2857:)
2854:1
2851:(
2846:i
2842:W
2838:(
2830:[
2824:i
2820:p
2814:i
2801:i
2797:p
2791:i
2782:n
2775:2
2769:B
2758:0
2750:=
2744:a
2741:r
2738:a
2735:p
2696:0
2668:r
2665:o
2662:m
2659:r
2656:a
2653:L
2644:+
2638:V
2635:V
2621:0
2591:z
2587:L
2564:z
2560:S
2535:n
2512:,
2503:g
2498:E
2489:i
2486:,
2482:e
2477:E
2469:2
2464:|
2454:i
2449:e
2443:|
2437:z
2433:S
2429:g
2426:+
2421:z
2417:L
2412:|
2407:g
2399:|
2393:2
2388:j
2384:g
2375:)
2372:0
2366:i
2363:(
2360:i
2350:2
2345:)
2334:B
2323:(
2316:0
2308:n
2305:2
2302:=
2296:V
2293:V
2257:g
2252:|
2248:=
2240:0
2235:e
2229:|
2208:0
2205:=
2202:i
2180:)
2177:0
2174:(
2168:g
2163:E
2159:,
2154:)
2151:0
2148:(
2143:i
2140:,
2136:e
2131:E
2105:i
2100:e
2094:|
2065:)
2062:0
2059:(
2054:i
2051:,
2047:e
2042:E
2033:)
2030:0
2027:(
2021:g
2016:E
2008:2
2003:|
1993:i
1988:e
1982:|
1977:H
1970:)
1966:S
1962:g
1959:+
1955:L
1951:(
1947:|
1942:g
1934:|
1925:i
1915:2
1910:)
1898:B
1887:0
1876:(
1871:=
1865:)
1862:2
1859:(
1854:E
1827:B
1805:2
1801:H
1780:H
1760:H
1727:2
1723:r
1699:n
1677:2
1673:C
1644:2
1640:r
1631:2
1627:C
1620:=
1614:r
1611:o
1608:m
1605:r
1602:a
1599:L
1564:2
1560:H
1530:1
1526:C
1517:0
1513:C
1492:T
1480:,
1466:T
1461:1
1457:C
1445:e
1442:i
1439:r
1436:u
1433:C
1387:S
1383:+
1379:L
1375:=
1371:J
1344:J
1340:g
1315:g
1310:|
1282:g
1277:|
1272:H
1264:J
1259:|
1254:g
1239:B
1226:0
1216:J
1212:g
1208:=
1201:g
1196:|
1191:H
1184:)
1180:S
1176:g
1173:+
1169:L
1165:(
1161:|
1156:g
1141:B
1128:0
1120:=
1115:)
1112:1
1109:(
1105:E
1078:H
1040:0
1034:H
1009:2
1005:H
983:H
960:0
954:H
921:r
899:S
873:L
845:e
840:m
815:e
791:g
764:B
732:0
702:2
698:H
692:2
683:r
673:e
668:m
664:8
658:2
654:e
646:2
641:0
633:+
629:H
622:)
618:S
614:g
611:+
607:L
603:(
592:B
579:0
571:+
566:0
560:H
554:=
549:H
523:H
490:0
482:0
457:0
449:0
445:C
422:0
397:0
389:0
385:C
362:0
354:,
349:0
345:C
320:T
308:,
294:0
286:+
281:T
276:0
272:C
263:)
260:T
257:(
228:0
198:0
140:H
133:=
129:M
104:H
71:(
55:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.