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833:
31:
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56:
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852:) are so much stronger such that, when different forms of magnetism are present in a material, the diamagnetic contribution is usually negligible. Substances where the diamagnetic behaviour is the strongest effect are termed diamagnetic materials, or diamagnets. Diamagnetic materials are those that some people generally think of as
1898:
1745:
1287:
The electrons in a material generally settle in orbitals, with effectively zero resistance and act like current loops. Thus it might be imagined that diamagnetism effects in general would be common, since any applied magnetic field would generate currents in these loops that would oppose the change,
1239:
seems to preclude the possibility of static magnetic levitation. However, Earnshaw's theorem applies only to objects with positive susceptibilities, such as ferromagnets (which have a permanent positive moment) and paramagnets (which induce a positive moment). These are attracted to field maxima,
823:
is used in chemistry to determine whether a particle (atom, ion, or molecule) is paramagnetic or diamagnetic: If all electrons in the particle are paired, then the substance made of this particle is diamagnetic; If it has unpaired electrons, then the substance is paramagnetic.
2562:
1787:
1634:
2588:
Suzuki, Motohiro; Kawamura, Naomi; Miyagawa, hayato; Garitaonandia, Jose S.; Yamamoto, Yoshiyuki; Hori, Hidenobu (24 January 2012). "Measurement of a Pauli and
Orbital Paramagnetic State in Bulk Gold Using X-Ray Magnetic Circular Dichroism Spectroscopy".
1197:) is covered with a layer of water (that is thin compared to the diameter of the magnet) then the field of the magnet significantly repels the water. This causes a slight dimple in the water's surface that may be seen by a reflection in its surface.
923:. This means that diamagnetic materials are repelled by magnetic fields. However, since diamagnetism is such a weak property, its effects are not observable in everyday life. For example, the magnetic susceptibility of diamagnets such as water is
2038:
1299:
proves that there cannot be any diamagnetism or paramagnetism in a purely classical system. However, the classical theory of
Langevin for diamagnetism gives the same prediction as the quantum theory. The classical theory is given below.
749:
effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances, the weak diamagnetic force is overcome by the attractive force of
2180:
840:. On keeping diamagnetic materials in a magnetic field, the electron orbital motion changes in such a way that magnetic dipole moments are induced on the atoms / molecules in the direction opposite to the external magnetic field
1616:
1491:
1528:
1782:
2292:
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in a similar way to superconductors, which are essentially perfect diamagnets. However, since the electrons are rigidly held in orbitals by the charge of the protons and are further constrained by the
2079:, an effect associated with the polarization of delocalized electrons' spins. For the bulk case of a 3D system and low magnetic fields, the (volume) diamagnetic susceptibility can be calculated using
1893:{\displaystyle \scriptstyle \left\langle \rho ^{2}\right\rangle \;=\;\left\langle x^{2}\right\rangle \;+\;\left\langle y^{2}\right\rangle \;=\;{\frac {2}{3}}\left\langle r^{2}\right\rangle }
1273:, an important step forward since mice are closer biologically to humans than frogs. JPL said it hopes to perform experiments regarding the effects of microgravity on bone and muscle mass.
1438:
2422:
of the charge carriers differing from the electron mass in vacuum, increasing the diamagnetic contribution. The formula presented here only applies for the bulk; in confined systems like
1740:{\displaystyle \scriptstyle \left\langle x^{2}\right\rangle \;=\;\left\langle y^{2}\right\rangle \;=\;\left\langle z^{2}\right\rangle \;=\;{\frac {1}{3}}\left\langle r^{2}\right\rangle }
792:
demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field. On a suggestion by
2372:
844:
Diamagnetism is a property of all materials, and always makes a weak contribution to the material's response to a magnetic field. However, other forms of magnetism (such as
37:
has one of the largest diamagnetic constants of any room temperature material. Here a pyrolytic carbon sheet is levitated by its repulsion from the strong magnetic field of
1930:
2212:
889:
2405:
1276:
Recent experiments studying the growth of protein crystals have led to a technique using powerful magnets to allow growth in ways that counteract Earth's gravity.
2430:. Additionally, for strong magnetic fields, the susceptibility of delocalized electrons oscillates as a function of the field strength, a phenomenon known as the
1251:
permanent magnets. This can be done with all components at room temperature, making a visually effective and relatively convenient demonstration of diamagnetism.
2323:
1918:
2089:
1240:
which do not exist in free space. Diamagnets (which induce a negative moment) are attracted to field minima, and there can be a field minimum in free space.
2658:
713:
1262:, has conducted experiments where water and other substances were successfully levitated. Most spectacularly, a live frog (see figure) was levitated.
902:
Diamagnetic materials, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1, and therefore a
1279:
A simple homemade device for demonstration can be constructed out of bismuth plates and a few permanent magnets that levitate a permanent magnet.
3385:
2738:
982:
in one plane. Nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets. Because
3059:
1546:
1456:
1496:
996:, which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully with
3240:
2812:
Liu, Yuanming; Zhu, Da-Ming; Strayer, Donald M.; Israelsson, Ulf E. (2010). "Magnetic levitation of large water droplets and mice".
2411:(number of states per energy per volume). This formula takes into account the spin degeneracy of the carriers (spin-1/2 electrons).
1750:
2876:
2221:
1628:
706:
3145:
Richter, Klaus; Ullmo, Denis; Jalabert, Rodolfo A. (1996). "Orbital magnetism in the ballistic regime: geometrical effects".
2950:
2419:
2903:
3013:
2937:
769:. In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but a
3022:
2071:, and instead considers the weak counteracting field that forms when the electrons' trajectories are curved due to the
2670:
997:
699:
686:
1247:, which is an unusually strongly diamagnetic material, can be stably floated in a magnetic field, such as that from
1381:
668:
992:
In rare cases, the diamagnetic contribution can be stronger than paramagnetic contribution. This is the case for
755:
1206:
2328:
461:
3233:
3207:
3037:
Landau, L. D. "Diamagnetismus der metalle." Zeitschrift für Physik A Hadrons and Nuclei 64.9 (1930): 629-637.
2431:
1447:
of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with the
989:
is derived from the ratio of the internal magnetic field to the applied field, it is a dimensionless value.
3390:
3328:
1296:
1000:, has an extremely weak paramagnetic contribution that is overcome by a stronger diamagnetic contribution.
636:
116:
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1255:
1228:
17:
2814:
641:
266:
2752:
2033:{\displaystyle \chi ={\frac {\mu _{0}n\mu }{B}}=-{\frac {\mu _{0}e^{2}Zn}{6m}}\langle r^{2}\rangle .}
1289:
1266:
832:
531:
206:
3226:
2427:
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521:
47:
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1235:
Diamagnets may be levitated in stable equilibrium in a magnetic field, with no power consumption.
611:
3285:
2633:
2461: – Mathematical inequality relating the derivative of a function to its covariant derivative
2188:
2076:
2044:
1921:
1144:
903:
216:
1621:
If the distribution of charge is spherically symmetric, we can suppose that the distribution of
773:
acts as a strong diamagnet because it entirely expels any magnetic field from its interior (the
621:
3110:
Lévy, L. P.; Reich, D. H.; Pfeiffer, L.; West, K. (1993). "Aharonov-Bohm ballistic billiards".
3085:
2458:
2415:
1311:'s theory of diamagnetism (1905) applies to materials containing atoms with closed shells (see
1292:, many materials exhibit diamagnetism, but typically respond very little to the applied field.
1270:
734:
606:
546:
516:
466:
186:
76:
3048:
1236:
885:
646:
261:
246:
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because there are also non-localized electrons. The theory that describes diamagnetism in a
3164:
3119:
2942:
2823:
2598:
236:
126:
2381:
8:
3323:
2782:
2175:{\displaystyle \chi =-\mu _{0}{\frac {e^{2}}{12\pi ^{2}m\hbar }}{\sqrt {2mE_{\rm {F}}}},}
2080:
759:
476:
286:
136:
3168:
3123:
2827:
2602:
864:, most organic compounds such as petroleum and some plastics, and many metals including
3395:
3308:
3280:
3180:
3154:
2986:
2524:
2499:
2443:
1903:
1244:
857:
746:
616:
591:
339:
330:
2297:
1176:), because they expel all magnetic fields (except in a thin surface layer) due to the
3268:
3184:
3176:
3131:
3018:
2990:
2946:
2732:
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2614:
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2408:
1338:
1248:
1163:
1159:
1148:
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873:
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586:
431:
321:
241:
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3172:
3127:
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2519:
2511:
2448:
1269:(JPL) in Pasadena, California announced it had successfully levitated mice using a
1033:
962:
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111:
71:
38:
34:
30:
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2713:
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421:
176:
88:
3345:
3318:
3313:
3303:
3008:
2932:
2907:
1152:
894:
884:. The magnetic susceptibility values of various molecular fragments are called
869:
845:
837:
781:
730:
673:
651:
631:
626:
581:
501:
436:
334:
221:
66:
2835:
1211:
3379:
3340:
3335:
3275:
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2480:
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1308:
849:
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742:
362:
343:
325:
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146:
556:
2618:
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2453:
2215:
1224:
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in them in the opposite direction, causing a repulsive force. In contrast,
576:
566:
536:
496:
491:
471:
296:
156:
2418:
the ratio between Landau and Pauli susceptibilities may change due to the
1784:
is the mean square distance of the electrons from the nucleus. Therefore,
3159:
2423:
1312:
1259:
1219:
levitates inside a 32 mm (1.26 in) diameter vertical bore of a
1194:
596:
571:
541:
486:
481:
413:
55:
3350:
3214:
The
Feynman Lectures on Physics Vol. II Ch. 34: The Magnetism of Matter
2068:
2043:
In atoms, Langevin susceptibility is of the same order of magnitude as
506:
348:
141:
3249:
2060:
1611:{\displaystyle \mu =-{\frac {Ze^{2}B}{4m}}\langle \rho ^{2}\rangle .}
1531:
1486:{\displaystyle \scriptstyle \pi \left\langle \rho ^{2}\right\rangle }
561:
511:
384:
231:
131:
2970:
3360:
2587:
1372:
1322:
1103:
121:
1523:{\displaystyle \scriptstyle \left\langle \rho ^{2}\right\rangle }
1083:
1043:
941:
881:
785:
441:
426:
389:
380:
375:
3202:
2688:"Neodymium supermagnets: Some demonstrations—Diamagnetic water"
2056:
1155:
expels the magnetic field and then acts as a perfect diamagnet.
1113:
1073:
865:
745:
materials are attracted by a magnetic field. Diamagnetism is a
394:
370:
101:
1777:{\displaystyle \scriptstyle \left\langle r^{2}\right\rangle }
1123:
399:
96:
3218:
1139:
906:
less than or equal to 0, since susceptibility is defined as
2287:{\displaystyle -\mu _{0}\mu _{\rm {B}}^{2}g(E_{\rm {F}})/3}
1216:
1093:
1053:
993:
877:
861:
2075:. Landau diamagnetism, however, should be contrasted with
106:
2811:
2665:(2nd ed.). Amsterdam: Academic Press. p. 23.
3011:(2005). "Chapter 14: Diamagnetism and Paramagnetism".
2300:
1791:
1754:
1638:
1500:
1460:
3109:
2481:"Diamagnetic Levitation – Historical Milestones"
2384:
2331:
2224:
2191:
2092:
1933:
1906:
1790:
1753:
1637:
1549:
1499:
1459:
1384:
3144:
2500:"John Tyndall and the Early History of Diamagnetism"
729:
is the property of materials that are repelled by a
1920:is the number of atoms per unit volume, the volume
2399:
2366:
2317:
2286:
2206:
2174:
2032:
1912:
1892:
1776:
1739:
1610:
1522:
1485:
1432:
3084:Drakos, Nikos; Moore, Ross; Young, Peter (2002).
1207:Magnetic levitation § Diamagnetic levitation
3377:
3083:
2434:, also first described theoretically by Landau.
2055:The Langevin theory is not the full picture for
2877:"Magnetic gravity trick grows perfect crystals"
2325:times Pauli paramagnetic susceptibility, where
796:, Faraday first referred to the phenomenon as
3234:
2906:. ForceField. 2 December 2008. Archived from
2485:Rev. Roum. Sci. Techn. Électrotechn. Et Énerg
1433:{\displaystyle I=-{\frac {Ze^{2}B}{4\pi m}}.}
707:
2024:
2011:
1602:
1589:
1453:axis. The average loop area can be given as
1355:. The number of revolutions per unit time is
940:. The most strongly diamagnetic material is
2737:: CS1 maint: numeric names: authors list (
3241:
3227:
2975:Journal de Physique Théorique et Appliquée
1860:
1856:
1837:
1833:
1814:
1810:
1707:
1703:
1684:
1680:
1661:
1657:
788:was repelled by magnetic fields. In 1845,
758:of diamagnetic materials is less than the
714:
700:
54:
3158:
2927:
2925:
2523:
2367:{\displaystyle \mu _{\rm {B}}=e\hbar /2m}
1188:
2965:
1303:
1210:
1138:
868:, particularly the heavy ones with many
831:
29:
2874:
2711:
2497:
2478:
1629:independent and identically distributed
1540:axis. The magnetic moment is therefore
780:Diamagnetism was first discovered when
733:; an applied magnetic field creates an
27:Magnetic property of ordinary materials
14:
3386:Electric and magnetic fields in matter
3378:
3007:
2931:
2922:
2685:
3222:
3017:(8 ed.). John Wiley & Sons.
2849:Choi, Charles Q. (9 September 2009).
2657:
2551:. Oxford University Press. June 2017.
2045:Van Vleck paramagnetic susceptibility
1229:Nijmegen High Field Magnet Laboratory
3040:
2848:
2625:
2426:, the description is altered due to
836:Diamagnetic material interaction in
3014:Introduction to Solid State Physics
2938:Introduction to Solid State Physics
1530:is the mean square distance of the
24:
2338:
2267:
2244:
2198:
2161:
1365:, so the current for an atom with
1134:
25:
3407:
3195:
3046:
2904:"Fun with diamagnetic levitation"
2350:
2141:
1183:
998:X-ray magnetic circular dichroism
3201:
3049:"Diamagnetism and paramagnetism"
2987:10.1051/jphystap:019050040067800
2875:Kleiner, Kurt (10 August 2007).
2631:
2498:Jackson, Roland (21 July 2014).
1223:in a magnetic field of about 16
1193:If a powerful magnet (such as a
1151:(right). At the transition, the
681:
680:
667:
3138:
3103:
3077:
3065:from the original on 4 May 2006
3031:
3001:
2959:
2896:
2868:
2842:
2805:
2775:
2745:
2634:"Magnetic Properties of Solids"
2971:"Sur la théorie du magnétisme"
2705:
2679:
2651:
2611:10.1103/PhysRevLett.108.047201
2581:
2555:
2540:
2491:
2472:
2394:
2388:
2273:
2258:
1007:Notable diamagnetic materials
13:
1:
3248:
3090:Electrons in a magnetic field
2465:
1200:
965:may have a susceptibility of
3329:ferromagnetic superconductor
3177:10.1016/0370-1573(96)00010-5
3132:10.1016/0921-4526(93)90161-x
2516:10.1080/00033790.2014.929743
2050:
827:
812:), then later changed it to
7:
3112:Physica B: Condensed Matter
2791:Radboud University Nijmegen
2761:Radboud University Nijmegen
2547:"diamagnetic, adj. and n".
2437:
2207:{\displaystyle E_{\rm {F}}}
1256:Radboud University Nijmegen
10:
3412:
2815:Advances in Space Research
1922:diamagnetic susceptibility
1315:). A field with intensity
1265:In September 2009, NASA's
1204:
267:Spin gapless semiconductor
3296:
3256:
2836:10.1016/j.asr.2009.08.033
2432:De Haas–Van Alphen effect
1290:Pauli exclusion principle
1282:
1267:Jet Propulsion Laboratory
1143:Transition from ordinary
207:Electronic band structure
2753:"Diamagnetic Levitation"
2479:Küstler, Gerald (2007).
2218:. This is equivalent to
1297:Bohr–Van Leeuwen theorem
117:Bose–Einstein condensate
48:Condensed matter physics
3286:Van Vleck paramagnetism
2851:"Mice levitated in lab"
2591:Physical Review Letters
2083:, which in SI units is
904:magnetic susceptibility
2714:"Diamagnetism Gallery"
2459:Diamagnetic inequality
2401:
2368:
2319:
2288:
2208:
2176:
2034:
1914:
1894:
1778:
1741:
1612:
1524:
1487:
1434:
1271:superconducting magnet
1232:
1189:Curving water surfaces
1156:
841:
784:observed in 1778 that
760:permeability of vacuum
735:induced magnetic field
41:
3086:"Landau diamagnetism"
2943:John Wiley & Sons
2787:High Field Laboratory
2783:"The Real Levitation"
2757:High Field Laboratory
2686:Beatty, Bill (2005).
2659:Poole, Charles P. Jr.
2563:"Magnetic Properties"
2402:
2369:
2320:
2289:
2209:
2177:
2035:
1915:
1895:
1779:
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1534:perpendicular to the
1525:
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1435:
1304:Langevin diamagnetism
1214:
1142:
835:
756:magnetic permeability
754:in the material. The
262:Topological insulator
33:
3210:at Wikimedia Commons
2945:. pp. 299–302.
2567:Chemistry LibreTexts
2416:doped semiconductors
2400:{\displaystyle g(E)}
2382:
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2298:
2222:
2189:
2090:
1931:
1904:
1788:
1751:
1635:
1547:
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1457:
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280:Electronic phenomena
127:Fermionic condensate
3391:Magnetic levitation
3356:amorphous magnetism
3324:superferromagnetism
3169:1996PhR...276....1R
3124:1993PhyB..189..204L
2910:on 12 February 2008
2828:2010AdSpR..45..208L
2603:2012PhRvL.108d7201S
2428:quantum confinement
2254:
2081:Landau quantization
2077:Pauli paramagnetism
2065:Landau diamagnetism
1008:
287:Quantum Hall effect
3309:antiferromagnetism
3281:superparamagnetism
3056:NTNU lecture notes
2444:Antiferromagnetism
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1245:pyrolytic graphite
1237:Earnshaw's theorem
1233:
1164:perfect diamagnets
1162:may be considered
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1006:
886:Pascal's constants
842:
747:quantum mechanical
674:Physics portal
42:
3371:
3370:
3269:superdiamagnetism
3257:Magnetic response
3206:Media related to
2952:978-0-471-87474-4
2663:Superconductivity
2504:Annals of Science
2487:. 52, 3: 265–282.
2409:density of states
2318:{\textstyle -1/3}
2167:
2145:
2061:free electron gas
2009:
1963:
1913:{\displaystyle n}
1869:
1716:
1587:
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1371:electrons is (in
1339:Larmor precession
1149:superconductivity
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432:Granular material
200:Electronic phases
39:neodymium magnets
16:(Redirected from
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2941:(6th ed.).
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2569:. 2 October 2013
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1698:
1697:
1679:
1675:
1674:
1656:
1652:
1651:
1627:coordinates are
1626:
1617:
1615:
1614:
1609:
1601:
1600:
1588:
1586:
1578:
1574:
1573:
1560:
1539:
1529:
1527:
1526:
1521:
1518:
1514:
1513:
1492:
1490:
1489:
1484:
1481:
1477:
1476:
1452:
1439:
1437:
1436:
1431:
1426:
1424:
1413:
1409:
1408:
1395:
1370:
1364:
1363:
1354:
1337:, gives rise to
1336:
1330:
1321:, applied to an
1320:
1243:A thin slice of
1175:
1084:Carbon (diamond)
1034:Pyrolytic carbon
1009:
1005:
981:
980:
978:
963:pyrolytic carbon
960:
959:
957:
939:
938:
936:
922:
898:
752:magnetic dipoles
716:
709:
702:
689:
684:
683:
676:
672:
671:
292:Spin Hall effect
182:Phase transition
152:Luttinger liquid
89:States of matter
72:Phase transition
58:
44:
43:
35:Pyrolytic carbon
21:
3411:
3410:
3406:
3405:
3404:
3402:
3401:
3400:
3376:
3375:
3372:
3367:
3297:Magnetic states
3292:
3252:
3247:
3198:
3193:
3192:
3147:Physics Reports
3143:
3139:
3108:
3104:
3094:
3092:
3082:
3078:
3068:
3066:
3062:
3051:
3045:
3041:
3036:
3032:
3025:
3009:Kittel, Charles
3006:
3002:
2964:
2960:
2953:
2933:Kittel, Charles
2930:
2923:
2913:
2911:
2902:
2901:
2897:
2887:
2885:
2873:
2869:
2859:
2857:
2847:
2843:
2810:
2806:
2796:
2794:
2781:
2780:
2776:
2766:
2764:
2751:
2750:
2746:
2730:
2729:
2722:
2720:
2710:
2706:
2696:
2694:
2684:
2680:
2673:
2656:
2652:
2642:
2640:
2630:
2626:
2586:
2582:
2572:
2570:
2561:
2560:
2556:
2546:
2545:
2541:
2496:
2492:
2477:
2473:
2468:
2440:
2383:
2380:
2379:
2353:
2337:
2336:
2332:
2330:
2327:
2326:
2307:
2299:
2296:
2295:
2276:
2266:
2265:
2261:
2249:
2243:
2242:
2232:
2228:
2223:
2220:
2219:
2197:
2196:
2192:
2190:
2187:
2186:
2160:
2159:
2155:
2147:
2132:
2128:
2124:
2118:
2114:
2112:
2106:
2102:
2091:
2088:
2087:
2053:
2018:
2014:
2001:
1988:
1984:
1978:
1974:
1973:
1971:
1947:
1943:
1942:
1940:
1932:
1929:
1928:
1924:in SI units is
1905:
1902:
1901:
1879:
1875:
1871:
1861:
1846:
1842:
1838:
1823:
1819:
1815:
1800:
1796:
1792:
1789:
1786:
1785:
1763:
1759:
1755:
1752:
1749:
1748:
1726:
1722:
1718:
1708:
1693:
1689:
1685:
1670:
1666:
1662:
1647:
1643:
1639:
1636:
1633:
1632:
1625:
1622:
1596:
1592:
1579:
1569:
1565:
1561:
1559:
1548:
1545:
1544:
1538:
1535:
1509:
1505:
1501:
1498:
1495:
1494:
1472:
1468:
1464:
1458:
1455:
1454:
1451:
1448:
1445:magnetic moment
1414:
1404:
1400:
1396:
1394:
1383:
1380:
1379:
1369:
1366:
1361:
1359:
1356:
1353:
1349:
1345:
1342:
1341:with frequency
1335:
1332:
1329:
1326:
1319:
1316:
1306:
1285:
1221:Bitter solenoid
1209:
1203:
1191:
1186:
1178:Meissner effect
1173:
1167:
1160:Superconductors
1137:
1135:Superconductors
1025:Superconductor
1020:
1003:
988:
976:
974:
972:
966:
955:
953:
951:
945:
934:
932:
930:
924:
920:
913:
907:
892:
830:
794:William Whewell
790:Michael Faraday
775:Meissner effect
768:
720:
679:
666:
665:
658:
657:
656:
456:
448:
447:
446:
422:Amorphous solid
416:
406:
405:
404:
383:
365:
355:
354:
353:
342:
340:Antiferromagnet
333:
331:Superparamagnet
324:
311:
310:Magnetic phases
303:
302:
301:
281:
273:
272:
271:
201:
193:
192:
191:
177:Order parameter
171:
170:Phase phenomena
163:
162:
161:
91:
81:
28:
23:
22:
15:
12:
11:
5:
3409:
3399:
3398:
3393:
3388:
3369:
3368:
3366:
3365:
3364:
3363:
3358:
3348:
3346:mictomagnetism
3343:
3338:
3333:
3332:
3331:
3326:
3319:ferromagnetism
3316:
3314:ferrimagnetism
3311:
3306:
3304:altermagnetism
3300:
3298:
3294:
3293:
3291:
3290:
3289:
3288:
3283:
3273:
3272:
3271:
3260:
3258:
3254:
3253:
3246:
3245:
3238:
3231:
3223:
3217:
3216:
3211:
3197:
3196:External links
3194:
3191:
3190:
3137:
3102:
3076:
3039:
3030:
3024:978-0471415268
3023:
3000:
2981:(1): 678–693.
2967:Langevin, Paul
2958:
2951:
2921:
2895:
2867:
2841:
2822:(1): 208–213.
2804:
2774:
2744:
2704:
2678:
2671:
2650:
2632:Nave, Carl L.
2624:
2580:
2554:
2539:
2510:(4): 435–489.
2490:
2470:
2469:
2467:
2464:
2463:
2462:
2456:
2451:
2446:
2439:
2436:
2420:effective mass
2396:
2393:
2390:
2387:
2363:
2360:
2356:
2352:
2349:
2346:
2340:
2335:
2314:
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2241:
2235:
2231:
2227:
2200:
2195:
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2171:
2163:
2158:
2154:
2151:
2143:
2140:
2135:
2131:
2127:
2121:
2117:
2109:
2105:
2101:
2098:
2095:
2067:, named after
2052:
2049:
2041:
2040:
2029:
2026:
2021:
2017:
2013:
2007:
2004:
1999:
1996:
1991:
1987:
1981:
1977:
1970:
1967:
1962:
1958:
1955:
1950:
1946:
1939:
1936:
1909:
1887:
1882:
1878:
1874:
1868:
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1859:
1854:
1849:
1845:
1841:
1836:
1831:
1826:
1822:
1818:
1813:
1808:
1803:
1799:
1795:
1771:
1766:
1762:
1758:
1734:
1729:
1725:
1721:
1715:
1712:
1706:
1701:
1696:
1692:
1688:
1683:
1678:
1673:
1669:
1665:
1660:
1655:
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1646:
1642:
1623:
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1618:
1607:
1604:
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1582:
1577:
1572:
1568:
1564:
1558:
1555:
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1517:
1512:
1508:
1504:
1480:
1475:
1471:
1467:
1463:
1449:
1441:
1440:
1429:
1423:
1420:
1417:
1412:
1407:
1403:
1399:
1393:
1390:
1387:
1367:
1357:
1351:
1347:
1343:
1333:
1327:
1317:
1305:
1302:
1284:
1281:
1205:Main article:
1202:
1199:
1190:
1187:
1185:
1184:Demonstrations
1182:
1171:
1153:superconductor
1136:
1133:
1130:
1129:
1126:
1120:
1119:
1116:
1110:
1109:
1106:
1100:
1099:
1096:
1090:
1089:
1086:
1080:
1079:
1076:
1070:
1069:
1066:
1060:
1059:
1056:
1050:
1049:
1046:
1040:
1039:
1036:
1030:
1029:
1026:
1022:
1021:
1018:
1013:
986:
970:
949:
928:
918:
911:
870:core electrons
856:, and include
846:ferromagnetism
838:magnetic field
829:
826:
782:Anton Brugmans
771:superconductor
766:
731:magnetic field
722:
721:
719:
718:
711:
704:
696:
693:
692:
691:
690:
677:
660:
659:
655:
654:
649:
644:
639:
634:
629:
624:
619:
614:
609:
604:
599:
594:
589:
584:
579:
574:
569:
564:
559:
554:
549:
544:
539:
534:
529:
524:
519:
514:
509:
504:
499:
494:
489:
484:
479:
474:
469:
464:
458:
457:
454:
453:
450:
449:
445:
444:
439:
437:Liquid crystal
434:
429:
424:
418:
417:
412:
411:
408:
407:
403:
402:
397:
392:
387:
378:
373:
367:
366:
363:Quasiparticles
361:
360:
357:
356:
352:
351:
346:
337:
328:
322:Superdiamagnet
319:
313:
312:
309:
308:
305:
304:
300:
299:
294:
289:
283:
282:
279:
278:
275:
274:
270:
269:
264:
259:
254:
249:
247:Thermoelectric
244:
242:Superconductor
239:
234:
229:
224:
222:Mott insulator
219:
214:
209:
203:
202:
199:
198:
195:
194:
190:
189:
184:
179:
173:
172:
169:
168:
165:
164:
160:
159:
154:
149:
144:
139:
134:
129:
124:
119:
114:
109:
104:
99:
93:
92:
87:
86:
83:
82:
80:
79:
74:
69:
63:
60:
59:
51:
50:
26:
9:
6:
4:
3:
2:
3408:
3397:
3394:
3392:
3389:
3387:
3384:
3383:
3381:
3374:
3362:
3359:
3357:
3354:
3353:
3352:
3349:
3347:
3344:
3342:
3341:metamagnetism
3339:
3337:
3336:helimagnetism
3334:
3330:
3327:
3325:
3322:
3321:
3320:
3317:
3315:
3312:
3310:
3307:
3305:
3302:
3301:
3299:
3295:
3287:
3284:
3282:
3279:
3278:
3277:
3276:paramagnetism
3274:
3270:
3267:
3266:
3265:
3262:
3261:
3259:
3255:
3251:
3244:
3239:
3237:
3232:
3230:
3225:
3224:
3221:
3215:
3212:
3209:
3204:
3200:
3199:
3186:
3182:
3178:
3174:
3170:
3166:
3161:
3156:
3152:
3148:
3141:
3133:
3129:
3125:
3121:
3117:
3113:
3106:
3091:
3087:
3080:
3061:
3057:
3050:
3047:Chang, M. C.
3043:
3034:
3026:
3020:
3016:
3015:
3010:
3004:
2996:
2992:
2988:
2984:
2980:
2977:(in French).
2976:
2972:
2968:
2962:
2954:
2948:
2944:
2940:
2939:
2934:
2928:
2926:
2909:
2905:
2899:
2884:
2883:
2882:New Scientist
2878:
2871:
2856:
2852:
2845:
2837:
2833:
2829:
2825:
2821:
2817:
2816:
2808:
2792:
2788:
2784:
2778:
2762:
2758:
2754:
2748:
2740:
2734:
2719:
2715:
2708:
2693:
2689:
2682:
2674:
2672:9780080550480
2668:
2664:
2660:
2654:
2639:
2638:Hyper Physics
2635:
2628:
2620:
2616:
2612:
2608:
2604:
2600:
2597:(4): 047201.
2596:
2592:
2584:
2568:
2564:
2558:
2550:
2543:
2535:
2531:
2526:
2521:
2517:
2513:
2509:
2505:
2501:
2494:
2486:
2482:
2475:
2471:
2460:
2457:
2455:
2452:
2450:
2447:
2445:
2442:
2441:
2435:
2433:
2429:
2425:
2421:
2417:
2412:
2410:
2391:
2385:
2377:
2376:Bohr magneton
2361:
2358:
2354:
2347:
2344:
2333:
2312:
2308:
2304:
2301:
2281:
2277:
2262:
2255:
2250:
2239:
2233:
2229:
2225:
2217:
2193:
2169:
2156:
2152:
2149:
2138:
2133:
2129:
2125:
2119:
2115:
2107:
2103:
2099:
2096:
2093:
2086:
2085:
2084:
2082:
2078:
2074:
2073:Lorentz force
2070:
2066:
2062:
2058:
2048:
2046:
2027:
2019:
2015:
2005:
2002:
1997:
1994:
1989:
1985:
1979:
1975:
1968:
1965:
1960:
1956:
1953:
1948:
1944:
1937:
1934:
1927:
1926:
1925:
1923:
1907:
1885:
1880:
1876:
1872:
1866:
1863:
1857:
1852:
1847:
1843:
1839:
1834:
1829:
1824:
1820:
1816:
1811:
1806:
1801:
1797:
1793:
1769:
1764:
1760:
1756:
1732:
1727:
1723:
1719:
1713:
1710:
1704:
1699:
1694:
1690:
1686:
1681:
1676:
1671:
1667:
1663:
1658:
1653:
1648:
1644:
1640:
1630:
1605:
1597:
1593:
1583:
1580:
1575:
1570:
1566:
1562:
1556:
1553:
1550:
1543:
1542:
1541:
1533:
1515:
1510:
1506:
1502:
1478:
1473:
1469:
1465:
1461:
1446:
1427:
1421:
1418:
1415:
1410:
1405:
1401:
1397:
1391:
1388:
1385:
1378:
1377:
1376:
1374:
1340:
1324:
1314:
1310:
1309:Paul Langevin
1301:
1298:
1293:
1291:
1280:
1277:
1274:
1272:
1268:
1263:
1261:
1257:
1252:
1250:
1246:
1241:
1238:
1230:
1226:
1222:
1218:
1213:
1208:
1198:
1196:
1181:
1179:
1170:
1165:
1161:
1154:
1150:
1146:
1141:
1127:
1125:
1122:
1121:
1117:
1115:
1112:
1111:
1107:
1105:
1102:
1101:
1097:
1095:
1092:
1091:
1087:
1085:
1082:
1081:
1077:
1075:
1072:
1071:
1067:
1065:
1062:
1061:
1057:
1055:
1052:
1051:
1047:
1045:
1042:
1041:
1037:
1035:
1032:
1031:
1027:
1024:
1023:
1017:
1014:
1011:
1010:
1004:
1001:
999:
995:
990:
985:
969:
964:
948:
943:
927:
917:
910:
905:
900:
896:
891:
888:(named after
887:
883:
879:
875:
871:
867:
863:
859:
855:
851:
850:paramagnetism
847:
839:
834:
825:
822:
821:rule of thumb
817:
815:
811:
807:
803:
799:
795:
791:
787:
783:
778:
776:
772:
765:
761:
757:
753:
748:
744:
743:ferromagnetic
740:
736:
732:
728:
717:
712:
710:
705:
703:
698:
697:
695:
694:
688:
678:
675:
670:
664:
663:
662:
661:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
623:
620:
618:
615:
613:
610:
608:
605:
603:
600:
598:
595:
593:
590:
588:
585:
583:
580:
578:
575:
573:
570:
568:
565:
563:
560:
558:
555:
553:
550:
548:
545:
543:
540:
538:
535:
533:
530:
528:
525:
523:
520:
518:
515:
513:
510:
508:
505:
503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
475:
473:
470:
468:
465:
463:
462:Van der Waals
460:
459:
452:
451:
443:
440:
438:
435:
433:
430:
428:
425:
423:
420:
419:
415:
410:
409:
401:
398:
396:
393:
391:
388:
386:
382:
379:
377:
374:
372:
369:
368:
364:
359:
358:
350:
347:
345:
341:
338:
336:
332:
329:
327:
323:
320:
318:
315:
314:
307:
306:
298:
295:
293:
290:
288:
285:
284:
277:
276:
268:
265:
263:
260:
258:
257:Ferroelectric
255:
253:
252:Piezoelectric
250:
248:
245:
243:
240:
238:
235:
233:
230:
228:
227:Semiconductor
225:
223:
220:
218:
215:
213:
210:
208:
205:
204:
197:
196:
188:
185:
183:
180:
178:
175:
174:
167:
166:
158:
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153:
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147:Superfluidity
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3208:Diamagnetism
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3093:. Retrieved
3089:
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3067:. Retrieved
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2961:
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2912:. Retrieved
2908:the original
2898:
2888:26 September
2886:. Retrieved
2880:
2870:
2860:26 September
2858:. Retrieved
2855:Live Science
2854:
2844:
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2807:
2797:26 September
2795:. Retrieved
2786:
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2767:26 September
2765:. Retrieved
2756:
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2723:26 September
2721:. Retrieved
2717:
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2695:. Retrieved
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2566:
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2454:Moses effect
2424:quantum dots
2413:
2216:Fermi energy
2184:
2064:
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1442:
1325:with charge
1307:
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854:non-magnetic
853:
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818:
814:diamagnetism
813:
809:
805:
801:
800:(the prefix
797:
779:
763:
739:paramagnetic
727:Diamagnetism
726:
725:
592:von Klitzing
316:
297:Kondo effect
157:Time crystal
137:Fermi liquid
3153:(1): 1–83.
3095:27 November
3069:24 February
1313:dielectrics
1260:Netherlands
1195:supermagnet
961:, although
893: [
890:Paul Pascal
798:diamagnetic
414:Soft matter
335:Ferromagnet
18:Diamagnetic
3380:Categories
3351:spin glass
2718:DeviantART
2643:9 November
2573:21 January
2549:OED Online
2466:References
2294:, exactly
2069:Lev Landau
2063:is called
1249:rare earth
1201:Levitation
1147:(left) to
872:, such as
557:Louis Néel
547:Schrieffer
455:Scientists
349:Spin glass
344:Metamagnet
326:Paramagnet
142:Supersolid
3396:Magnetism
3250:Magnetism
3185:119330207
2995:0368-3893
2351:ℏ
2334:μ
2302:−
2240:μ
2230:μ
2226:−
2142:ℏ
2130:π
2104:μ
2100:−
2094:χ
2051:In metals
2025:⟩
2012:⟨
1976:μ
1969:−
1957:μ
1945:μ
1935:χ
1798:ρ
1603:⟩
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1590:⟨
1557:−
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1532:electrons
1507:ρ
1470:ρ
1462:π
1419:π
1392:−
1331:and mass
828:Materials
819:A simple
637:Abrikosov
552:Josephson
522:Van Vleck
512:Luttinger
385:Polariton
317:Diamagnet
237:Conductor
232:Semimetal
217:Insulator
132:Fermi gas
3361:spin ice
3060:Archived
2969:(1905).
2935:(1986).
2733:cite web
2661:(2007).
2619:22400883
2534:26221835
2438:See also
1886:⟩
1873:⟨
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1770:⟩
1757:⟨
1747:, where
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1687:⟨
1677:⟩
1664:⟨
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1641:⟨
1516:⟩
1503:⟨
1493:, where
1479:⟩
1466:⟨
1373:SI units
1323:electron
1012:Material
804:meaning
687:Category
642:Ginzburg
617:Laughlin
577:Kadanoff
532:Shockley
517:Anderson
472:von Laue
122:Bose gas
3165:Bibcode
3120:Bibcode
2824:Bibcode
2599:Bibcode
2525:4524391
2407:is the
2374:is the
2214:is the
1631:. Then
1227:at the
1215:A live
1064:Mercury
1044:Bismuth
942:bismuth
882:bismuth
874:mercury
806:through
786:bismuth
647:Leggett
622:Störmer
607:Bednorz
567:Giaever
537:Bardeen
527:Hubbard
502:Peierls
492:Onsager
442:Polymer
427:Colloid
390:Polaron
381:Plasmon
376:Exciton
3183:
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2993:
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2793:. 2011
2763:. 2011
2669:
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2522:
2185:where
2057:metals
1283:Theory
1258:, the
1225:teslas
1128:−0.91
1114:Copper
1074:Silver
1058:−6.74
1048:−16.6
1038:−40.9
866:copper
810:across
685:
652:Parisi
612:Müller
602:Rohrer
597:Binnig
587:Wilson
582:Fisher
542:Cooper
507:Landau
395:Magnon
371:Phonon
212:Plasma
112:Plasma
102:Liquid
67:Phases
3181:S2CID
3155:arXiv
3063:(PDF)
3052:(PDF)
1900:. If
1624:x,y,z
1124:Water
1118:−1.0
1108:−1.6
1098:−1.8
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1078:−2.6
1068:−2.9
975:−4.00
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487:Bloch
482:Debye
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467:Onnes
400:Roton
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3097:2012
3071:2011
3019:ISBN
2991:ISSN
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2890:2011
2862:2011
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2769:2020
2739:link
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