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867:) 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
1913:
1760:
1302:
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,
1254:
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,
838:
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.
2577:
1802:
1649:
2603:
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".
1212:) 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.
938:. 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
2053:
1314:
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.
764:
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
2195:
855:. 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
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1303:
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
2094:, 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
1908:{\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 }
1288:, 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.
1453:
2437:
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
1755:{\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 }
807:
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
2387:
859:
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
1945:
728:
2227:
3400:
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1291:
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.
2445:. Additionally, for strong magnetic fields, the susceptibility of delocalized electrons oscillates as a function of the field strength, a phenomenon known as the
1266:
permanent magnets. This can be done with all components at room temperature, making a visually effective and relatively convenient demonstration of diamagnetism.
2338:
1933:
2104:
1255:
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.
3255:
1277:, has conducted experiments where water and other substances were successfully levitated. Most spectacularly, a live frog (see figure) was levitated.
917:
Diamagnetic materials, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1, and therefore a
1643:
1294:
A simple homemade device for demonstration can be constructed out of bismuth plates and a few permanent magnets that levitate a permanent magnet.
997:
in one plane. Nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets. Because
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1011:, which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully with
3037:
2827:
Liu, Yuanming; Zhu, Da-Ming; Strayer, Donald M.; Israelsson, Ulf E. (2010). "Magnetic levitation of large water droplets and mice".
2685:
2426:(number of states per energy per volume). This formula takes into account the spin degeneracy of the carriers (spin-1/2 electrons).
1012:
714:
701:
1765:
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2236:
770:
3160:
Richter, Klaus; Ullmo, Denis; Jalabert, Rodolfo A. (1996). "Orbital magnetism in the ballistic regime: geometrical effects".
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784:. In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but a
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2086:, and instead considers the weak counteracting field that forms when the electrons' trajectories are curved due to the
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1262:, which is an unusually strongly diamagnetic material, can be stably floated in a magnetic field, such as that from
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In rare cases, the diamagnetic contribution can be stronger than paramagnetic contribution. This is the case for
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Landau, L. D. "Diamagnetismus der metalle." Zeitschrift für Physik A Hadrons and Nuclei 64.9 (1930): 629-637.
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1936:
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of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with the
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is derived from the ratio of the internal magnetic field to the applied field, it is a dimensionless value.
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621:
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1015:, has an extremely weak paramagnetic contribution that is overcome by a stronger diamagnetic contribution.
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2048:{\displaystyle \chi ={\frac {\mu _{0}n\mu }{B}}=-{\frac {\mu _{0}e^{2}Zn}{6m}}\langle r^{2}\rangle .}
236:
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Diamagnets may be levitated in stable equilibrium in a magnetic field, with no power consumption.
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2648:
2476: – Mathematical inequality relating the derivative of a function to its covariant derivative
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339:
330:
1636:
If the distribution of charge is spherically symmetric, we can suppose that the distribution of
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acts as a strong diamagnet because it entirely expels any magnetic field from its interior (the
3125:
Lévy, L. P.; Reich, D. H.; Pfeiffer, L.; West, K. (1993). "Aharonov-Bohm ballistic billiards".
3100:
1326:'s theory of diamagnetism (1905) applies to materials containing atoms with closed shells (see
1307:, many materials exhibit diamagnetism, but typically respond very little to the applied field.
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because there are also non-localized electrons. The theory that describes diamagnetism in a
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2190:{\displaystyle \chi =-\mu _{0}{\frac {e^{2}}{12\pi ^{2}m\hbar }}{\sqrt {2mE_{\rm {F}}}},}
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3138:
2842:
2617:
879:, most organic compounds such as petroleum and some plastics, and many metals including
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1191:), because they expel all magnetic fields (except in a thin surface layer) due to the
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1284:(JPL) in Pasadena, California announced it had successfully levitated mice using a
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909:
899:. The magnetic susceptibility values of various molecular fragments are called
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in them in the opposite direction, causing a repulsive force. In contrast,
17:
3217:
2433:
the ratio between Landau and Pauli susceptibilities may change due to the
1799:
is the mean square distance of the electrons from the nucleus. Therefore,
3375:
3174:
1387:
1337:
1234:
levitates inside a 32 mm (1.26 in) diameter vertical bore of a
1118:
121:
3229:
The
Feynman Lectures on Physics Vol. II Ch. 34: The Magnetism of Matter
2058:
In atoms, Langevin susceptibility is of the same order of magnitude as
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956:
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800:
441:
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389:
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375:
1154:
2071:
1626:{\displaystyle \mu =-{\frac {Ze^{2}B}{4m}}\langle \rho ^{2}\rangle .}
1501:{\displaystyle \scriptstyle \pi \left\langle \rho ^{2}\right\rangle }
1128:
1088:
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394:
370:
101:
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1153:
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96:
29:
1538:{\displaystyle \scriptstyle \left\langle \rho ^{2}\right\rangle }
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1108:
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1008:
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876:
3237:
2703:"Neodymium supermagnets: Some demonstrations—Diamagnetic water"
1170:
expels the magnetic field and then acts as a perfect diamagnet.
760:
materials are attracted by a magnetic field. Diamagnetism is a
106:
1792:{\displaystyle \scriptstyle \left\langle r^{2}\right\rangle }
3233:
921:
less than or equal to 0, since susceptibility is defined as
2302:{\displaystyle -\mu _{0}\mu _{\rm {B}}^{2}g(E_{\rm {F}})/3}
2090:. Landau diamagnetism, however, should be contrasted with
2680:(2nd ed.). Amsterdam: Academic Press. p. 23.
3026:(2005). "Chapter 14: Diamagnetism and Paramagnetism".
2315:
1806:
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1653:
1515:
1475:
2496:"Diamagnetic Levitation – Historical Milestones"
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1948:
1921:
1805:
1768:
1652:
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1514:
1474:
1399:
2515:"John Tyndall and the Early History of Diamagnetism"
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is the property of materials that are repelled by a
3311:
3271:
1935:is the number of atoms per unit volume, the volume
2414:
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2332:
2301:
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2189:
2047:
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1907:
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1500:
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3099:Drakos, Nikos; Moore, Ross; Young, Peter (2002).
1222:Magnetic levitation § Diamagnetic levitation
2449:, also first described theoretically by Landau.
2070:The Langevin theory is not the full picture for
2892:"Magnetic gravity trick grows perfect crystals"
2340:times Pauli paramagnetic susceptibility, where
811:, Faraday first referred to the phenomenon as
3249:
2921:. ForceField. 2 December 2008. Archived from
2500:Rev. Roum. Sci. Techn. Électrotechn. Et Énerg
1448:{\displaystyle I=-{\frac {Ze^{2}B}{4\pi m}}.}
722:
8:
2039:
2026:
1617:
1604:
1468:axis. The average loop area can be given as
1370:. The number of revolutions per unit time is
955:. The most strongly diamagnetic material is
2752:: CS1 maint: numeric names: authors list (
3256:
3242:
3234:
2990:Journal de Physique Théorique et Appliquée
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1825:
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803:was repelled by magnetic fields. In 1845,
773:of diamagnetic materials is less than the
729:
715:
54:
43:
3173:
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2382:{\displaystyle \mu _{\rm {B}}=e\hbar /2m}
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883:, particularly the heavy ones with many
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1644:independent and identically distributed
1555:axis. The magnetic moment is therefore
795:Diamagnetism was first discovered when
748:; an applied magnetic field creates an
46:
27:Magnetic property of ordinary materials
3401:Electric and magnetic fields in matter
2745:
3032:(8 ed.). John Wiley & Sons.
2864:Choi, Charles Q. (9 September 2009).
2566:. Oxford University Press. June 2017.
2060:Van Vleck paramagnetic susceptibility
1244:Nijmegen High Field Magnet Laboratory
7:
2441:, the description is altered due to
851:Diamagnetic material interaction in
3029:Introduction to Solid State Physics
2953:Introduction to Solid State Physics
1545:is the mean square distance of the
2353:
2282:
2259:
2213:
2176:
1380:, so the current for an atom with
25:
2919:"Fun with diamagnetic levitation"
1013:X-ray magnetic circular dichroism
3216:
3064:"Diamagnetism and paramagnetism"
3002:10.1051/jphystap:019050040067800
2890:Kleiner, Kurt (10 August 2007).
2513:Jackson, Roland (21 July 2014).
1238:in a magnetic field of about 16
1208:If a powerful magnet (such as a
1166:(right). At the transition, the
696:
695:
682:
3080:from the original on 4 May 2006
2649:"Magnetic Properties of Solids"
2986:"Sur la théorie du magnétisme"
2626:10.1103/PhysRevLett.108.047201
2409:
2403:
2288:
2273:
1022:Notable diamagnetic materials
1:
3105:Electrons in a magnetic field
980:may have a susceptibility of
3344:ferromagnetic superconductor
3192:10.1016/0370-1573(96)00010-5
3147:10.1016/0921-4526(93)90161-x
2531:10.1080/00033790.2014.929743
827:), then later changed it to
3127:Physica B: Condensed Matter
2806:Radboud University Nijmegen
2776:Radboud University Nijmegen
2562:"diamagnetic, adj. and n".
2222:{\displaystyle E_{\rm {F}}}
1271:Radboud University Nijmegen
3427:
2830:Advances in Space Research
1937:diamagnetic susceptibility
1330:). A field with intensity
1280:In September 2009, NASA's
1219:
267:Spin gapless semiconductor
2851:10.1016/j.asr.2009.08.033
2447:De Haas–Van Alphen effect
1305:Pauli exclusion principle
1282:Jet Propulsion Laboratory
1158:Transition from ordinary
207:Electronic band structure
2768:"Diamagnetic Levitation"
2494:Küstler, Gerald (2007).
2233:. This is equivalent to
1312:Bohr–Van Leeuwen theorem
117:Bose–Einstein condensate
48:Condensed matter physics
3301:Van Vleck paramagnetism
2866:"Mice levitated in lab"
2606:Physical Review Letters
2098:, which in SI units is
919:magnetic susceptibility
2729:"Diamagnetism Gallery"
2474:Diamagnetic inequality
2416:
2383:
2334:
2303:
2223:
2191:
2049:
1929:
1909:
1793:
1756:
1627:
1539:
1502:
1449:
1286:superconducting magnet
1247:
1204:Curving water surfaces
1171:
856:
799:observed in 1778 that
775:permeability of vacuum
750:induced magnetic field
41:
3101:"Landau diamagnetism"
2958:John Wiley & Sons
2802:High Field Laboratory
2798:"The Real Levitation"
2772:High Field Laboratory
2701:Beatty, Bill (2005).
2674:Poole, Charles P. Jr.
2578:"Magnetic Properties"
2417:
2384:
2335:
2304:
2224:
2192:
2050:
1930:
1910:
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1549:perpendicular to the
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1319:Langevin diamagnetism
1229:
1157:
850:
771:magnetic permeability
769:in the material. The
262:Topological insulator
33:
3225:at Wikimedia Commons
2960:. pp. 299–302.
2582:Chemistry LibreTexts
2431:doped semiconductors
2415:{\displaystyle g(E)}
2397:
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2313:
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2105:
1946:
1919:
1803:
1766:
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280:Electronic phenomena
127:Fermionic condensate
3406:Magnetic levitation
3371:amorphous magnetism
3339:superferromagnetism
3184:1996PhR...276....1R
3139:1993PhyB..189..204L
2925:on 12 February 2008
2843:2010AdSpR..45..208L
2618:2012PhRvL.108d7201S
2443:quantum confinement
2269:
2096:Landau quantization
2092:Pauli paramagnetism
2080:Landau diamagnetism
1023:
287:Quantum Hall effect
3324:antiferromagnetism
3296:superparamagnetism
3071:NTNU lecture notes
2459:Antiferromagnetism
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1260:pyrolytic graphite
1252:Earnshaw's theorem
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1179:perfect diamagnets
1177:may be considered
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1021:
901:Pascal's constants
857:
762:quantum mechanical
689:Physics portal
42:
3386:
3385:
3284:superdiamagnetism
3272:Magnetic response
3221:Media related to
2967:978-0-471-87474-4
2678:Superconductivity
2519:Annals of Science
2502:. 52, 3: 265–282.
2424:density of states
2333:{\textstyle -1/3}
2182:
2160:
2076:free electron gas
2024:
1978:
1928:{\displaystyle n}
1884:
1731:
1602:
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1386:electrons is (in
1354:Larmor precession
1164:superconductivity
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1119:Carbon (graphite)
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432:Granular material
200:Electronic phases
39:neodymium magnets
16:(Redirected from
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3133:(1–4): 204–209.
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2956:(6th ed.).
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2584:. 2 October 2013
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1746:
1745:
1732:
1724:
1717:
1713:
1712:
1694:
1690:
1689:
1671:
1667:
1666:
1642:coordinates are
1641:
1632:
1630:
1629:
1624:
1616:
1615:
1603:
1601:
1593:
1589:
1588:
1575:
1554:
1544:
1542:
1541:
1536:
1533:
1529:
1528:
1507:
1505:
1504:
1499:
1496:
1492:
1491:
1467:
1454:
1452:
1451:
1446:
1441:
1439:
1428:
1424:
1423:
1410:
1385:
1379:
1378:
1369:
1352:, gives rise to
1351:
1345:
1336:, applied to an
1335:
1258:A thin slice of
1190:
1099:Carbon (diamond)
1049:Pyrolytic carbon
1024:
996:
995:
993:
978:pyrolytic carbon
975:
974:
972:
954:
953:
951:
937:
913:
767:magnetic dipoles
731:
724:
717:
704:
699:
698:
691:
687:
686:
292:Spin Hall effect
182:Phase transition
152:Luttinger liquid
89:States of matter
72:Phase transition
58:
44:
35:Pyrolytic carbon
21:
3426:
3425:
3421:
3420:
3419:
3417:
3416:
3415:
3391:
3390:
3387:
3382:
3312:Magnetic states
3307:
3267:
3262:
3213:
3208:
3207:
3162:Physics Reports
3159:
3158:
3154:
3124:
3123:
3119:
3109:
3107:
3098:
3097:
3093:
3083:
3081:
3077:
3066:
3061:
3060:
3056:
3051:
3047:
3040:
3024:Kittel, Charles
3022:
3021:
3017:
2980:
2979:
2975:
2968:
2948:Kittel, Charles
2946:
2945:
2938:
2928:
2926:
2917:
2916:
2912:
2902:
2900:
2889:
2888:
2884:
2874:
2872:
2863:
2862:
2858:
2826:
2825:
2821:
2811:
2809:
2796:
2795:
2791:
2781:
2779:
2766:
2765:
2761:
2744:
2737:
2735:
2726:
2725:
2721:
2711:
2709:
2700:
2699:
2695:
2688:
2672:
2671:
2667:
2657:
2655:
2646:
2645:
2641:
2602:
2601:
2597:
2587:
2585:
2576:
2575:
2571:
2561:
2560:
2556:
2512:
2511:
2507:
2493:
2492:
2488:
2483:
2455:
2395:
2394:
2347:
2342:
2341:
2311:
2310:
2276:
2243:
2235:
2234:
2207:
2202:
2201:
2170:
2143:
2139:
2129:
2117:
2103:
2102:
2068:
2029:
2016:
1999:
1989:
1988:
1958:
1957:
1944:
1943:
1939:in SI units is
1917:
1916:
1890:
1886:
1857:
1853:
1834:
1830:
1811:
1807:
1801:
1800:
1774:
1770:
1764:
1763:
1737:
1733:
1704:
1700:
1681:
1677:
1658:
1654:
1648:
1647:
1640:
1637:
1607:
1594:
1580:
1576:
1560:
1559:
1553:
1550:
1520:
1516:
1510:
1509:
1483:
1479:
1470:
1469:
1466:
1463:
1460:magnetic moment
1429:
1415:
1411:
1395:
1394:
1384:
1381:
1376:
1374:
1371:
1368:
1364:
1360:
1357:
1356:with frequency
1350:
1347:
1344:
1341:
1334:
1331:
1321:
1300:
1236:Bitter solenoid
1224:
1218:
1206:
1201:
1193:Meissner effect
1188:
1182:
1175:Superconductors
1152:
1150:Superconductors
1040:Superconductor
1035:
1018:
1003:
991:
989:
987:
981:
970:
968:
966:
960:
949:
947:
945:
939:
935:
928:
922:
907:
845:
809:William Whewell
805:Michael Faraday
790:Meissner effect
783:
735:
694:
681:
680:
673:
672:
671:
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:
3424:
3422:
3414:
3413:
3408:
3403:
3393:
3392:
3384:
3383:
3381:
3380:
3379:
3378:
3373:
3363:
3361:mictomagnetism
3358:
3353:
3348:
3347:
3346:
3341:
3334:ferromagnetism
3331:
3329:ferrimagnetism
3326:
3321:
3319:altermagnetism
3315:
3313:
3309:
3308:
3306:
3305:
3304:
3303:
3298:
3288:
3287:
3286:
3275:
3273:
3269:
3268:
3263:
3261:
3260:
3253:
3246:
3238:
3232:
3231:
3226:
3212:
3211:External links
3209:
3206:
3205:
3152:
3117:
3091:
3054:
3045:
3039:978-0471415268
3038:
3015:
2996:(1): 678–693.
2982:Langevin, Paul
2973:
2966:
2936:
2910:
2882:
2856:
2837:(1): 208–213.
2819:
2789:
2759:
2719:
2693:
2686:
2665:
2647:Nave, Carl L.
2639:
2595:
2569:
2554:
2525:(4): 435–489.
2505:
2485:
2484:
2482:
2479:
2478:
2477:
2471:
2466:
2461:
2454:
2451:
2435:effective mass
2411:
2408:
2405:
2402:
2378:
2375:
2371:
2367:
2364:
2361:
2355:
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2329:
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2250:
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2158:
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2116:
2113:
2110:
2082:, named after
2067:
2064:
2056:
2055:
2044:
2041:
2036:
2032:
2028:
2022:
2019:
2014:
2011:
2006:
2002:
1996:
1992:
1985:
1982:
1977:
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1970:
1965:
1961:
1954:
1951:
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1902:
1897:
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1427:
1422:
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1362:
1358:
1348:
1342:
1332:
1320:
1317:
1299:
1296:
1220:Main article:
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1214:
1205:
1202:
1200:
1199:Demonstrations
1197:
1186:
1168:superconductor
1151:
1148:
1145:
1144:
1141:
1135:
1134:
1131:
1125:
1124:
1121:
1115:
1114:
1111:
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1095:
1094:
1091:
1085:
1084:
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1075:
1074:
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1061:
1055:
1054:
1051:
1045:
1044:
1041:
1037:
1036:
1033:
1028:
1001:
985:
964:
943:
933:
926:
885:core electrons
871:, and include
861:ferromagnetism
853:magnetic field
844:
841:
797:Anton Brugmans
786:superconductor
781:
746:magnetic field
737:
736:
734:
733:
726:
719:
711:
708:
707:
706:
705:
692:
675:
674:
670:
669:
664:
659:
654:
649:
644:
639:
634:
629:
624:
619:
614:
609:
604:
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579:
574:
569:
564:
559:
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539:
534:
529:
524:
519:
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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
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242:Superconductor
239:
234:
229:
224:
222:Mott insulator
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202:
199:
198:
195:
194:
190:
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173:
172:
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149:
144:
139:
134:
129:
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119:
114:
109:
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99:
93:
92:
87:
86:
83:
82:
80:
79:
74:
69:
63:
60:
59:
51:
50:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3423:
3412:
3409:
3407:
3404:
3402:
3399:
3398:
3396:
3389:
3377:
3374:
3372:
3369:
3368:
3367:
3364:
3362:
3359:
3357:
3356:metamagnetism
3354:
3352:
3351:helimagnetism
3349:
3345:
3342:
3340:
3337:
3336:
3335:
3332:
3330:
3327:
3325:
3322:
3320:
3317:
3316:
3314:
3310:
3302:
3299:
3297:
3294:
3293:
3292:
3291:paramagnetism
3289:
3285:
3282:
3281:
3280:
3277:
3276:
3274:
3270:
3266:
3259:
3254:
3252:
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3230:
3227:
3224:
3219:
3215:
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3193:
3189:
3185:
3181:
3176:
3171:
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3163:
3156:
3153:
3148:
3144:
3140:
3136:
3132:
3128:
3121:
3118:
3106:
3102:
3095:
3092:
3076:
3072:
3065:
3062:Chang, M. C.
3058:
3055:
3049:
3046:
3041:
3035:
3031:
3030:
3025:
3019:
3016:
3011:
3007:
3003:
2999:
2995:
2992:(in French).
2991:
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2897:New Scientist
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2799:
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2720:
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2704:
2697:
2694:
2689:
2687:9780080550480
2683:
2679:
2675:
2669:
2666:
2654:
2653:Hyper Physics
2650:
2643:
2640:
2635:
2631:
2627:
2623:
2619:
2615:
2612:(4): 047201.
2611:
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2406:
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2391:Bohr magneton
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2100:
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2089:
2088:Lorentz force
2085:
2081:
2077:
2073:
2065:
2063:
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2042:
2034:
2030:
2020:
2017:
2012:
2009:
2004:
2000:
1994:
1990:
1983:
1980:
1975:
1971:
1968:
1963:
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1949:
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1941:
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1938:
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1400:
1393:
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1389:
1355:
1339:
1329:
1325:
1324:Paul Langevin
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1120:
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1067:
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1062:
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1050:
1047:
1046:
1042:
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1038:
1032:
1029:
1026:
1025:
1019:
1016:
1014:
1010:
1005:
1000:
984:
979:
963:
958:
942:
932:
925:
920:
915:
911:
906:
903:(named after
902:
898:
894:
890:
886:
882:
878:
874:
870:
866:
865:paramagnetism
862:
854:
849:
842:
840:
837:
836:rule of thumb
832:
830:
826:
822:
818:
814:
810:
806:
802:
798:
793:
791:
787:
780:
776:
772:
768:
763:
759:
758:ferromagnetic
755:
751:
747:
743:
732:
727:
725:
720:
718:
713:
712:
710:
709:
703:
693:
690:
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462:Van der Waals
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459:
452:
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443:
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428:
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257:Ferroelectric
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252:Piezoelectric
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227:Semiconductor
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2923:the original
2913:
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2895:
2885:
2875:26 September
2873:. Retrieved
2870:Live Science
2869:
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2812:26 September
2810:. Retrieved
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2581:
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2469:Moses effect
2439:quantum dots
2428:
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2199:
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1340:with charge
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828:
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816:
815:(the prefix
812:
794:
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754:paramagnetic
742:Diamagnetism
741:
740:
592:von Klitzing
316:
297:Kondo effect
157:Time crystal
137:Fermi liquid
3168:(1): 1–83.
3110:27 November
3084:24 February
1328:dielectrics
1275:Netherlands
1210:supermagnet
976:, although
908: [
905:Paul Pascal
813:diamagnetic
414:Soft matter
335:Ferromagnet
18:Diamagnetic
3395:Categories
3366:spin glass
2733:DeviantART
2658:9 November
2588:21 January
2564:OED Online
2481:References
2309:, exactly
2084:Lev Landau
2078:is called
1264:rare earth
1216:Levitation
1162:(left) to
887:, such as
667:Polchinski
557:Louis Néel
547:Schrieffer
455:Scientists
349:Spin glass
344:Metamagnet
326:Paramagnet
142:Supersolid
3411:Magnetism
3265:Magnetism
3200:119330207
3010:0368-3893
2366:ℏ
2349:μ
2317:−
2255:μ
2245:μ
2241:−
2157:ℏ
2145:π
2119:μ
2115:−
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2066:In metals
2040:⟩
2027:⟨
1991:μ
1984:−
1972:μ
1960:μ
1950:χ
1813:ρ
1618:⟩
1609:ρ
1605:⟨
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1547:electrons
1522:ρ
1485:ρ
1477:π
1434:π
1407:−
1346:and mass
843:Materials
834:A simple
657:Wetterich
637:Abrikosov
552:Josephson
522:Van Vleck
512:Luttinger
385:Polariton
317:Diamagnet
237:Conductor
232:Semimetal
217:Insulator
132:Fermi gas
3376:spin ice
3075:Archived
2984:(1905).
2950:(1986).
2748:cite web
2676:(2007).
2634:22400883
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1785:⟩
1772:⟨
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1656:⟨
1531:⟩
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1508:, where
1494:⟩
1481:⟨
1388:SI units
1338:electron
1027:Material
819:meaning
702:Category
642:Ginzburg
617:Laughlin
577:Kadanoff
532:Shockley
517:Anderson
472:von Laue
122:Bose gas
3180:Bibcode
3135:Bibcode
2839:Bibcode
2614:Bibcode
2540:4524391
2422:is the
2389:is the
2229:is the
1646:. Then
1242:at the
1230:A live
1079:Mercury
1059:Bismuth
957:bismuth
897:bismuth
889:mercury
821:through
801: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
3198:
3036:
3008:
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2778:. 2011
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2072:metals
1298:Theory
1273:, the
1240:teslas
1143:−0.91
1129:Copper
1089:Silver
1073:−6.74
1063:−16.6
1053:−40.9
881:copper
825:across
700:
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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
3196:S2CID
3170:arXiv
3078:(PDF)
3067:(PDF)
1915:. If
1639:x,y,z
1139:Water
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1123:−1.6
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467:Onnes
400:Roton
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3112:2012
3086:2011
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