655:
2562:, since in the latter case, but not the former, the ferromagnetic clusters will have time to respond to the field by flipping their magnetization. The precise dependence can be calculated from the Néel–Arrhenius equation, assuming that the neighboring clusters behave independently of one another (if clusters interact, their behavior becomes more complicated). It is also possible to perform magneto-optical AC susceptibility measurements with magneto-optically active superparamagnetic materials such as iron oxide nanoparticles in the visible wavelength range.
42:
668:
1326:
771:. This is possible when their diameter is below 3–50 nm, depending on the materials. In this condition, it is considered that the magnetization of the nanoparticles is a single giant magnetic moment, sum of all the individual magnetic moments carried by the atoms of the nanoparticle. Those in the field of superparamagnetism call this "macro-spin approximation".
1959:
734:. In the absence of an external magnetic field, when the time used to measure the magnetization of the nanoparticles is much longer than the NĂ©el relaxation time, their magnetization appears to be on average zero; they are said to be in the superparamagnetic state. In this state, an external magnetic field is able to magnetize the nanoparticles, similarly to a
1129:, the magnetization will not flip during the measurement, so the measured magnetization will be what the instantaneous magnetization was at the beginning of the measurement. In the former case, the nanoparticle will appear to be in the superparamagnetic state whereas in the latter case it will appear to be “blocked” in its initial state.
1813:
1013:
This length of time can be anywhere from a few nanoseconds to years or much longer. In particular, it can be seen that the NĂ©el relaxation time is an exponential function of the grain volume, which explains why the flipping probability becomes rapidly negligible for bulk materials or large
2539:
1383:
is applied to an assembly of superparamagnetic nanoparticles, their magnetic moments tend to align along the applied field, leading to a net magnetization. The magnetization curve of the assembly, i.e. the magnetization as a function of the applied field, is a reversible S-shaped
1309:
782:. The stable orientations define the nanoparticle’s so called “easy axis”. At finite temperature, there is a finite probability for the magnetization to flip and reverse its direction. The mean time between two flips is called the Néel relaxation time
2195:
1503:
2553:
measurements, where an applied magnetic field varies in time, and the magnetic response of the system is measured. A superparamagnetic system will show a characteristic frequency dependence: When the frequency is much higher than
891:
1611:
1172:. In several experiments, the measurement time is kept constant but the temperature is varied, so the transition between superparamagnetism and blocked state is seen as a function of the temperature. The temperature for which
1954:{\displaystyle \chi ={\begin{cases}\displaystyle {\frac {n\mu _{0}\mu ^{2}}{k_{\text{B}}T}}&{\text{for the 1st case}}\\\displaystyle {\frac {n\mu _{0}\mu ^{2}}{3k_{\text{B}}T}}&{\text{for the 2nd case}}\end{cases}}}
2747:
Cornia, Andrea; Barra, Anne-Laure; Bulicanu, Vladimir; Clérac, Rodolphe; Cortijo, Miguel; Hillard, Elizabeth A.; Galavotti, Rita; Lunghi, Alessandro; Nicolini, Alessio; Rouzières, Mathieu; Sorace, Lorenzo (2020-02-03).
2312:
2106:
where the measurement time and the relaxation time have comparable magnitude. In this case, a frequency-dependence of the susceptibility can be observed. For a randomly oriented sample, the complex susceptibility is:
3242:
2438:
2004:
and so a larger susceptibility. This explains why superparamagnetic nanoparticles have a much larger susceptibility than standard paramagnets: they behave exactly as a paramagnet with a huge magnetic moment.
2384:
1749:
1127:
1087:
2605:
1210:
1170:
2426:
1373:
2597:. As of July 2020 drives with densities of approximately 1 Tbit/in are available commercially. This is at the limit for conventional magnetic recording that was predicted in 1999.
1392:
If all the particles are identical (same energy barrier and same magnetic moment), their easy axes are all oriented parallel to the applied field and the temperature is low enough (
2612:(BPR) avoids the use of fine-grained media and is another possibility. In addition, magnetic recording technologies based on topological distortions of the magnetization, known as
2233:
2608:(MAMR), which use materials that are stable at much smaller sizes. They require localized heating or microwave excitation before the magnetic orientation of a bit can be changed.
1222:
2077:
2044:
1995:
2113:
1047:
925:
807:
2104:
3239:
958:
730:. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the
1805:
1652:
1132:
The state of the nanoparticle (superparamagnetic or blocked) depends on the measurement time. A transition between superparamagnetism and blocked state occurs when
1785:
1678:
1419:
815:
1530:
699:
2240:
2534:{\displaystyle \tau {\frac {\mathrm {d} M}{\mathrm {d} t}}+M=\tau \chi _{\text{b}}{\frac {\mathrm {d} H}{\mathrm {d} t}}+\chi _{\text{sp}}H}
1089:, the nanoparticle magnetization will flip several times during the measurement, then the measured magnetization will average to zero. If
990:
associated with the magnetization moving from its initial easy axis direction, through a “hard plane”, to the other easy axis direction.
2980:"R. Wood, "The feasibility of magnetic recording at 1 Terabit per square inch", IEEE Trans. Magn., Vol. 36, No. 1, pp. 36-42, Jan 2000"
3273:
2319:
692:
3186:
2730:
760:. Superparamagnetism is different from this standard transition since it occurs below the Curie temperature of the material.
2964:
2709:
Néel, L. (1949). "Théorie du traînage magnétique des ferromagnétiques en grains fins avec applications aux terres cuites".
1685:
1092:
1052:
3035:
Shiroishi, Y.; Fukuda, K.; Tagawa, I.; Iwasaki, H.; Takenoiri, S.; Tanaka, H.; Mutoh, H.; Yoshikawa, N. (October 2009).
2750:"The Origin of Magnetic Anisotropy and Single-Molecule Magnet Behavior in Chromium(II)-Based Extended Metal Atom Chains"
3159:
1175:
1135:
2432:
From this frequency-dependent susceptibility, the time-dependence of the magnetization for low-fields can be derived:
1317:
Equivalently, blocking temperature is the temperature below which a material shows slow relaxation of magnetization.
927:
is thus the average length of time that it takes for the nanoparticle’s magnetization to randomly flip as a result of
2948:
2391:
685:
672:
17:
3234:
1332:
3037:"Y. Shiroishi et al., "Future Options for HDD Storage", IEEE Trans. Magn., Vol. 45, No. 10, pp. 3816-22, Sep. 2009"
2601:
2575:
1314:
For typical laboratory measurements, the value of the logarithm in the previous equation is in the order of 20–25.
654:
2813:
Gittleman, J. I.; Abeles, B.; Bozowski, S. (1974). "Superparamagnetism and relaxation effects in granular Ni-SiO
3421:
3198:
1022:
Let us imagine that the magnetization of a single superparamagnetic nanoparticle is measured and let us define
756:
Normally, any ferromagnetic or ferrimagnetic material undergoes a transition to a paramagnetic state above its
447:
3266:
1304:{\displaystyle T_{\text{B}}={\frac {KV}{k_{\text{B}}\ln \left({\frac {\tau _{\text{m}}}{\tau _{0}}}\right)}}}
3361:
778:, the magnetic moment has usually only two stable orientations antiparallel to each other, separated by an
622:
102:
2206:
2190:{\displaystyle \chi (\omega )={\frac {\chi _{\text{sp}}+i\omega \tau \chi _{\text{b}}}{1+i\omega \tau }}}
3160:"Théorie du traînage magnétique des ferromagnétiques en grains fins avec applications aux terres cuites"
3416:
2649:
2049:
2016:
2013:
There is no time-dependence of the magnetization when the nanoparticles are either completely blocked (
1967:
627:
252:
1025:
903:
785:
517:
192:
1828:
751:
731:
3259:
2679:
764:
512:
507:
33:
2082:
597:
3318:
2609:
2594:
2550:
739:
202:
607:
3196:
Weller, D.; Moser, A. (1999). "Thermal Effect Limits in
Ultrahigh Density Magnetic Recording".
2684:
2659:
2587:
936:
592:
532:
502:
452:
172:
62:
2933:
Magnetics
Conference, 2000. INTERMAG 2000 Digest of Technical Papers. 2000 IEEE International
2663:
1655:
632:
247:
232:
2558:, there will be a different magnetic response than when the frequency is much lower than 1/Ď„
3207:
3111:
2901:
2836:
1790:
928:
222:
112:
1761:
1630:
1498:{\displaystyle M(H)\approx n\mu \tanh \left({\frac {\mu _{0}H\mu }{k_{\text{B}}T}}\right)}
8:
3356:
1385:
775:
462:
272:
122:
3211:
3115:
2905:
2840:
3341:
3075:
3056:
2790:
1000:
886:{\displaystyle \tau _{\text{N}}=\tau _{0}\exp \left({\frac {KV}{k_{\text{B}}T}}\right)}
602:
577:
325:
1663:
3301:
3182:
3135:
3127:
2944:
2889:
2827:
2795:
2777:
2726:
1752:
1606:{\displaystyle M(H)\approx n\mu L\left({\frac {\mu _{0}H\mu }{k_{\text{B}}T}}\right)}
757:
572:
417:
307:
227:
3060:
3388:
3215:
3119:
3102:
Fert, Albert; Cros, Vincent; Sampaio, JoĂŁo (2013-03-01). "Skyrmions on the track".
3048:
2991:
2936:
2909:
2844:
2785:
2769:
2761:
277:
242:
237:
197:
167:
137:
97:
57:
2863:
2765:
3246:
2645:
2571:
768:
587:
537:
407:
162:
74:
3009:
2749:
3378:
3351:
3346:
3336:
3036:
3010:"Hitachi achieves nanotechnology milestone for quadrupling terabyte hard drive"
2940:
2667:
987:
779:
659:
637:
617:
612:
567:
487:
422:
320:
207:
52:
3052:
2979:
3410:
3373:
3368:
3308:
3131:
2965:"Computer History Museum: HDD Areal Density reaches 1 terabitper square inch"
2781:
727:
724:
720:
348:
329:
311:
212:
132:
2848:
542:
3296:
3139:
2799:
2000:
It can be seen from these equations that large nanoparticles have a larger
562:
552:
522:
482:
477:
457:
302:
282:
142:
3123:
2307:{\textstyle \chi _{\text{sp}}={\frac {n\mu _{0}\mu ^{2}}{3k_{\text{B}}T}}}
3080:
2773:
582:
557:
527:
472:
467:
399:
41:
3383:
2890:"Magneto-optical harmonic susceptometry of superparamagnetic materials"
2631:
1510:
If all the particles are identical and the temperature is high enough (
745:
735:
492:
334:
127:
3219:
2995:
2913:
3282:
2574:
due to the minimum size of particles that can be used. This limit on
716:
547:
497:
370:
217:
117:
1325:
3393:
2613:
107:
2655:
Magnetic separation: cell-, DNA-, protein- separation, RNA fishing
3013:
427:
412:
375:
366:
361:
2600:
Future hard disk technologies currently in development include:
1388:. This function is quite complicated but for some simple cases:
960:
is a length of time, characteristic of the material, called the
3076:"Will Toshiba's Bit-Patterned Drives Change the HDD Landscape?"
380:
356:
87:
2379:{\textstyle \chi _{\text{b}}={\frac {n\mu _{0}\mu ^{2}}{3KV}}}
1997:
if the easy axes of the nanoparticles are randomly oriented.
1964:
The latter susceptibility is also valid for all temperatures
978:
is the nanoparticle’s magnetic anisotropy energy density and
385:
82:
3251:
3034:
1525:), then, irrespective of the orientations of the easy axes:
1947:
2570:
Superparamagnetism sets a limit on the storage density of
2746:
92:
2812:
2008:
809:
and is given by the following Néel–Arrhenius equation:
2394:
2322:
2243:
2209:
1787:
function is the magnetic susceptibility of the sample
1744:{\textstyle L(x)={\frac {1}{\tanh(x)}}-{\frac {1}{x}}}
1688:
1666:
1633:
1335:
2929:
Magnetic recording beyond the superparamagnetic limit
2441:
2116:
2085:
2052:
2019:
1970:
1888:
1831:
1816:
1793:
1764:
1533:
1422:
1225:
1178:
1138:
1095:
1055:
1028:
939:
906:
818:
788:
763:
Superparamagnetism occurs in nanoparticles which are
3240:
2314:
is the susceptibility in the superparamagnetic state
1122:{\displaystyle \tau _{\text{m}}\ll \tau _{\text{N}}}
1082:{\displaystyle \tau _{\text{m}}\gg \tau _{\text{N}}}
746:
The NĂ©el relaxation in the absence of magnetic field
2719:(in French; an English translation is available in
2590:. It has an estimated limit of 100 to 200 Gbit/in.
2533:
2420:
2378:
2306:
2227:
2189:
2098:
2071:
2038:
1989:
1953:
1799:
1779:
1743:
1672:
1646:
1605:
1497:
1367:
1303:
1204:
1164:
1121:
1081:
1041:
952:
919:
885:
801:
3181:. New York: Gordon and Breach. pp. 407–427.
1205:{\displaystyle \tau _{\text{m}}=\tau _{\text{N}}}
1165:{\displaystyle \tau _{\text{m}}=\tau _{\text{N}}}
972:); its typical value is between 10 and 10 second.
3408:
2549:A superparamagnetic system can be measured with
2421:{\textstyle \tau ={\frac {\tau _{\text{N}}}{2}}}
3101:
2887:
1368:{\textstyle \tanh \left({\frac {1}{3}}x\right)}
3235:Superparamagnetism of Co-Ferrite Nanoparticles
2888:Vandendriessche, Stefaan; et al. (2013).
1414:)), then the magnetization of the assembly is
3267:
2079:). There is, however, a narrow window around
1625:is the density of nanoparticles in the sample
1320:
693:
1329:Langevin function (red line), compared with
3195:
3274:
3260:
2638:
2386:is the susceptibility in the blocked state
700:
686:
40:
2789:
742:is much larger than that of paramagnets.
2565:
1680:is the magnetic moment of a nanoparticle
1324:
3175:An English translation is available in
2725:. Gordon and Breach. pp. 407–427.
2625:
1017:
14:
3409:
3073:
2926:
2428:is the relaxation time of the assembly
3255:
3176:
2720:
2702:
2606:microwave-assisted magnetic recording
2235:is the frequency of the applied field
2228:{\textstyle {\frac {\omega }{2\pi }}}
3157:
2977:
2864:"Introduction to: AC susceptibility"
2708:
2009:Time dependence of the magnetization
2861:
2046:) or completely superparamagnetic (
24:
2593:Current hard disk technology uses
2505:
2495:
2459:
2449:
25:
3433:
3228:
2072:{\displaystyle T\gg T_{\text{B}}}
2039:{\displaystyle T\ll T_{\text{B}}}
1990:{\displaystyle T>T_{\text{B}}}
2602:heat-assisted magnetic recording
2586:Older hard disk technology uses
1379:When an external magnetic field
1042:{\displaystyle \tau _{\text{m}}}
920:{\displaystyle \tau _{\text{N}}}
802:{\displaystyle \tau _{\text{N}}}
667:
666:
653:
3095:
3067:
3028:
2620:
2544:
3199:IEEE Transactions on Magnetics
3074:Murray, Matthew (2010-08-19).
3041:IEEE Transactions on Magnetics
3002:
2984:IEEE Transactions on Magnetics
2971:
2957:
2920:
2881:
2855:
2806:
2740:
2126:
2120:
1774:
1768:
1722:
1716:
1698:
1692:
1543:
1537:
1432:
1426:
968:(its reciprocal is called the
774:Because of the nanoparticle’s
13:
1:
3281:
2766:10.1021/acs.inorgchem.9b02994
2690:
3362:ferromagnetic superconductor
3179:Selected Works of Louis NĂ©el
2723:Selected Works of Louis NĂ©el
2099:{\displaystyle T_{\text{B}}}
1049:as the measurement time. If
767:, i.e. composed of a single
7:
2673:
10:
3438:
3150:
2941:10.1109/INTMAG.2000.872350
2650:magnetic resonance imaging
1321:Effect of a magnetic field
749:
253:Spin gapless semiconductor
3329:
3289:
3053:10.1109/TMAG.2009.2024879
2978:Wood, R. (January 2000).
1758:The initial slope of the
953:{\displaystyle \tau _{0}}
193:Electronic band structure
2695:
2680:Iron oxide nanoparticles
1618:In the above equations:
103:Bose–Einstein condensate
34:Condensed matter physics
3319:Van Vleck paramagnetism
3177:Kurti, N., ed. (1988).
2894:Applied Physics Letters
2849:10.1103/PhysRevB.9.3891
2721:Kurti, N., ed. (1988).
2639:Biomedical applications
2610:Bit-patterned recording
2595:perpendicular recording
2580:superparamagnetic limit
740:magnetic susceptibility
719:which appears in small
2927:Kryder, M. H. (2000).
2685:Single-molecule magnet
2660:targeted drug delivery
2588:longitudinal recording
2535:
2422:
2380:
2308:
2229:
2191:
2100:
2073:
2040:
1991:
1955:
1801:
1781:
1745:
1674:
1648:
1607:
1499:
1376:
1369:
1305:
1206:
1166:
1123:
1083:
1043:
954:
921:
887:
803:
752:NĂ©el relaxation theory
3422:Statistical mechanics
3124:10.1038/nnano.2013.29
3104:Nature Nanotechnology
2664:magnetic hyperthermia
2616:, have been proposed.
2566:Effect on hard drives
2536:
2423:
2381:
2309:
2230:
2192:
2101:
2074:
2041:
1992:
1956:
1802:
1800:{\displaystyle \chi }
1782:
1746:
1675:
1656:magnetic permeability
1649:
1647:{\textstyle \mu _{0}}
1608:
1500:
1370:
1328:
1306:
1207:
1167:
1124:
1084:
1044:
955:
922:
888:
804:
248:Topological insulator
2626:General applications
2439:
2392:
2320:
2241:
2207:
2114:
2083:
2050:
2017:
1968:
1814:
1791:
1780:{\displaystyle M(H)}
1762:
1686:
1664:
1631:
1531:
1420:
1333:
1223:
1214:blocking temperature
1176:
1136:
1093:
1053:
1026:
1018:Blocking temperature
937:
929:thermal fluctuations
904:
816:
786:
732:NĂ©el relaxation time
266:Electronic phenomena
113:Fermionic condensate
3389:amorphous magnetism
3357:superferromagnetism
3212:1999ITM....35.4423W
3116:2013NatNa...8..152F
2906:2013ApPhL.102p1903V
2841:1974PhRvB...9.3891G
2754:Inorganic Chemistry
2634:: tunable viscosity
1386:increasing function
1009:is the temperature.
776:magnetic anisotropy
273:Quantum Hall effect
3342:antiferromagnetism
3314:superparamagnetism
3245:2008-12-03 at the
3016:. October 15, 2007
2531:
2418:
2376:
2304:
2225:
2187:
2096:
2069:
2036:
1987:
1951:
1946:
1936:
1876:
1797:
1777:
1741:
1670:
1644:
1603:
1495:
1377:
1365:
1301:
1202:
1162:
1119:
1079:
1039:
1001:Boltzmann constant
950:
917:
883:
799:
713:Superparamagnetism
660:Physics portal
3417:Magnetic ordering
3404:
3403:
3302:superdiamagnetism
3290:Magnetic response
3220:10.1109/20.809134
3188:978-2-88124-300-4
3158:NĂ©el, L. (1949).
3047:(10): 3816–3822.
3012:(Press release).
2996:10.1109/20.824422
2914:10.1063/1.4801837
2862:Martien, Dinesh.
2828:Physical Review B
2732:978-2-88124-300-4
2551:AC susceptibility
2525:
2513:
2488:
2467:
2416:
2410:
2374:
2330:
2302:
2295:
2251:
2223:
2185:
2164:
2142:
2093:
2066:
2033:
1984:
1942:
1934:
1927:
1882:
1874:
1867:
1753:Langevin function
1739:
1726:
1673:{\textstyle \mu }
1597:
1590:
1489:
1482:
1355:
1299:
1292:
1279:
1257:
1233:
1199:
1186:
1159:
1146:
1116:
1103:
1076:
1063:
1036:
986:is therefore the
970:attempt frequency
914:
877:
870:
826:
796:
758:Curie temperature
738:. However, their
710:
709:
418:Granular material
186:Electronic phases
27:Form of magnetism
18:Superparamagnetic
16:(Redirected from
3429:
3276:
3269:
3262:
3253:
3252:
3223:
3206:(6): 4423–4439.
3192:
3174:
3164:
3144:
3143:
3099:
3093:
3092:
3090:
3088:
3071:
3065:
3064:
3032:
3026:
3025:
3023:
3021:
3006:
3000:
2999:
2975:
2969:
2968:
2961:
2955:
2954:
2924:
2918:
2917:
2900:(16): 161903–5.
2885:
2879:
2878:
2876:
2874:
2869:. Quantum Design
2868:
2859:
2853:
2852:
2835:(9): 3891–3897.
2810:
2804:
2803:
2793:
2760:(3): 1763–1777.
2744:
2738:
2736:
2718:
2706:
2578:is known as the
2572:hard disk drives
2540:
2538:
2537:
2532:
2527:
2526:
2523:
2514:
2512:
2508:
2502:
2498:
2492:
2490:
2489:
2486:
2468:
2466:
2462:
2456:
2452:
2446:
2427:
2425:
2424:
2419:
2417:
2412:
2411:
2408:
2402:
2385:
2383:
2382:
2377:
2375:
2373:
2362:
2361:
2360:
2351:
2350:
2337:
2332:
2331:
2328:
2313:
2311:
2310:
2305:
2303:
2301:
2297:
2296:
2293:
2283:
2282:
2281:
2272:
2271:
2258:
2253:
2252:
2249:
2234:
2232:
2231:
2226:
2224:
2222:
2211:
2196:
2194:
2193:
2188:
2186:
2184:
2167:
2166:
2165:
2162:
2144:
2143:
2140:
2133:
2105:
2103:
2102:
2097:
2095:
2094:
2091:
2078:
2076:
2075:
2070:
2068:
2067:
2064:
2045:
2043:
2042:
2037:
2035:
2034:
2031:
1996:
1994:
1993:
1988:
1986:
1985:
1982:
1960:
1958:
1957:
1952:
1950:
1949:
1943:
1941:for the 2nd case
1940:
1935:
1933:
1929:
1928:
1925:
1915:
1914:
1913:
1904:
1903:
1890:
1883:
1881:for the 1st case
1880:
1875:
1873:
1869:
1868:
1865:
1858:
1857:
1856:
1847:
1846:
1833:
1806:
1804:
1803:
1798:
1786:
1784:
1783:
1778:
1750:
1748:
1747:
1742:
1740:
1732:
1727:
1725:
1705:
1679:
1677:
1676:
1671:
1653:
1651:
1650:
1645:
1643:
1642:
1612:
1610:
1609:
1604:
1602:
1598:
1596:
1592:
1591:
1588:
1581:
1574:
1573:
1563:
1504:
1502:
1501:
1496:
1494:
1490:
1488:
1484:
1483:
1480:
1473:
1466:
1465:
1455:
1374:
1372:
1371:
1366:
1364:
1360:
1356:
1348:
1310:
1308:
1307:
1302:
1300:
1298:
1297:
1293:
1291:
1290:
1281:
1280:
1277:
1271:
1259:
1258:
1255:
1248:
1240:
1235:
1234:
1231:
1211:
1209:
1208:
1203:
1201:
1200:
1197:
1188:
1187:
1184:
1171:
1169:
1168:
1163:
1161:
1160:
1157:
1148:
1147:
1144:
1128:
1126:
1125:
1120:
1118:
1117:
1114:
1105:
1104:
1101:
1088:
1086:
1085:
1080:
1078:
1077:
1074:
1065:
1064:
1061:
1048:
1046:
1045:
1040:
1038:
1037:
1034:
959:
957:
956:
951:
949:
948:
926:
924:
923:
918:
916:
915:
912:
892:
890:
889:
884:
882:
878:
876:
872:
871:
868:
861:
853:
841:
840:
828:
827:
824:
808:
806:
805:
800:
798:
797:
794:
702:
695:
688:
675:
670:
669:
662:
658:
657:
278:Spin Hall effect
168:Phase transition
138:Luttinger liquid
75:States of matter
58:Phase transition
44:
30:
29:
21:
3437:
3436:
3432:
3431:
3430:
3428:
3427:
3426:
3407:
3406:
3405:
3400:
3330:Magnetic states
3325:
3285:
3280:
3247:Wayback Machine
3231:
3226:
3189:
3162:
3153:
3148:
3147:
3100:
3096:
3086:
3084:
3072:
3068:
3033:
3029:
3019:
3017:
3008:
3007:
3003:
2976:
2972:
2963:
2962:
2958:
2951:
2935:. p. 575.
2925:
2921:
2886:
2882:
2872:
2870:
2866:
2860:
2856:
2824:
2820:
2816:
2811:
2807:
2745:
2741:
2733:
2707:
2703:
2698:
2693:
2676:
2646:contrast agents
2641:
2628:
2623:
2568:
2561:
2557:
2547:
2522:
2518:
2504:
2503:
2494:
2493:
2491:
2485:
2481:
2458:
2457:
2448:
2447:
2445:
2440:
2437:
2436:
2407:
2403:
2401:
2393:
2390:
2389:
2363:
2356:
2352:
2346:
2342:
2338:
2336:
2327:
2323:
2321:
2318:
2317:
2292:
2288:
2284:
2277:
2273:
2267:
2263:
2259:
2257:
2248:
2244:
2242:
2239:
2238:
2215:
2210:
2208:
2205:
2204:
2168:
2161:
2157:
2139:
2135:
2134:
2132:
2115:
2112:
2111:
2090:
2086:
2084:
2081:
2080:
2063:
2059:
2051:
2048:
2047:
2030:
2026:
2018:
2015:
2014:
2011:
1981:
1977:
1969:
1966:
1965:
1945:
1944:
1939:
1937:
1924:
1920:
1916:
1909:
1905:
1899:
1895:
1891:
1889:
1885:
1884:
1879:
1877:
1864:
1860:
1859:
1852:
1848:
1842:
1838:
1834:
1832:
1824:
1823:
1815:
1812:
1811:
1792:
1789:
1788:
1763:
1760:
1759:
1731:
1709:
1704:
1687:
1684:
1683:
1665:
1662:
1661:
1638:
1634:
1632:
1629:
1628:
1587:
1583:
1582:
1569:
1565:
1564:
1562:
1558:
1532:
1529:
1528:
1524:
1479:
1475:
1474:
1461:
1457:
1456:
1454:
1450:
1421:
1418:
1417:
1413:
1398:
1347:
1346:
1342:
1334:
1331:
1330:
1323:
1286:
1282:
1276:
1272:
1270:
1266:
1254:
1250:
1249:
1241:
1239:
1230:
1226:
1224:
1221:
1220:
1196:
1192:
1183:
1179:
1177:
1174:
1173:
1156:
1152:
1143:
1139:
1137:
1134:
1133:
1113:
1109:
1100:
1096:
1094:
1091:
1090:
1073:
1069:
1060:
1056:
1054:
1051:
1050:
1033:
1029:
1027:
1024:
1023:
1020:
1014:nanoparticles.
998:
944:
940:
938:
935:
934:
911:
907:
905:
902:
901:
867:
863:
862:
854:
852:
848:
836:
832:
823:
819:
817:
814:
813:
793:
789:
787:
784:
783:
769:magnetic domain
754:
748:
706:
665:
652:
651:
644:
643:
642:
442:
434:
433:
432:
408:Amorphous solid
402:
392:
391:
390:
369:
351:
341:
340:
339:
328:
326:Antiferromagnet
319:
317:Superparamagnet
310:
297:
296:Magnetic phases
289:
288:
287:
267:
259:
258:
257:
187:
179:
178:
177:
163:Order parameter
157:
156:Phase phenomena
149:
148:
147:
77:
67:
28:
23:
22:
15:
12:
11:
5:
3435:
3425:
3424:
3419:
3402:
3401:
3399:
3398:
3397:
3396:
3391:
3381:
3379:mictomagnetism
3376:
3371:
3366:
3365:
3364:
3359:
3352:ferromagnetism
3349:
3347:ferrimagnetism
3344:
3339:
3337:altermagnetism
3333:
3331:
3327:
3326:
3324:
3323:
3322:
3321:
3316:
3306:
3305:
3304:
3293:
3291:
3287:
3286:
3279:
3278:
3271:
3264:
3256:
3250:
3249:
3237:
3230:
3229:External links
3227:
3225:
3224:
3193:
3187:
3154:
3152:
3149:
3146:
3145:
3110:(3): 152–156.
3094:
3066:
3027:
3001:
2970:
2956:
2949:
2919:
2880:
2854:
2822:
2818:
2814:
2805:
2739:
2731:
2700:
2699:
2697:
2694:
2692:
2689:
2688:
2687:
2682:
2675:
2672:
2671:
2670:
2668:magnetofection
2656:
2653:
2640:
2637:
2636:
2635:
2627:
2624:
2622:
2619:
2618:
2617:
2598:
2591:
2567:
2564:
2559:
2555:
2546:
2543:
2542:
2541:
2530:
2521:
2517:
2511:
2507:
2501:
2497:
2484:
2480:
2477:
2474:
2471:
2465:
2461:
2455:
2451:
2444:
2430:
2429:
2415:
2406:
2400:
2397:
2387:
2372:
2369:
2366:
2359:
2355:
2349:
2345:
2341:
2335:
2326:
2315:
2300:
2291:
2287:
2280:
2276:
2270:
2266:
2262:
2256:
2247:
2236:
2221:
2218:
2214:
2198:
2197:
2183:
2180:
2177:
2174:
2171:
2160:
2156:
2153:
2150:
2147:
2138:
2131:
2128:
2125:
2122:
2119:
2089:
2062:
2058:
2055:
2029:
2025:
2022:
2010:
2007:
1980:
1976:
1973:
1962:
1961:
1948:
1938:
1932:
1923:
1919:
1912:
1908:
1902:
1898:
1894:
1887:
1886:
1878:
1872:
1863:
1855:
1851:
1845:
1841:
1837:
1830:
1829:
1827:
1822:
1819:
1796:
1776:
1773:
1770:
1767:
1756:
1755:
1738:
1735:
1730:
1724:
1721:
1718:
1715:
1712:
1708:
1703:
1700:
1697:
1694:
1691:
1681:
1669:
1659:
1641:
1637:
1626:
1616:
1615:
1614:
1613:
1601:
1595:
1586:
1580:
1577:
1572:
1568:
1561:
1557:
1554:
1551:
1548:
1545:
1542:
1539:
1536:
1522:
1508:
1507:
1506:
1493:
1487:
1478:
1472:
1469:
1464:
1460:
1453:
1449:
1446:
1443:
1440:
1437:
1434:
1431:
1428:
1425:
1411:
1396:
1363:
1359:
1354:
1351:
1345:
1341:
1338:
1322:
1319:
1312:
1311:
1296:
1289:
1285:
1275:
1269:
1265:
1262:
1253:
1247:
1244:
1238:
1229:
1212:is called the
1195:
1191:
1182:
1155:
1151:
1142:
1112:
1108:
1099:
1072:
1068:
1059:
1032:
1019:
1016:
1011:
1010:
1004:
996:
991:
988:energy barrier
973:
966:attempt period
947:
943:
932:
910:
895:
894:
881:
875:
866:
860:
857:
851:
847:
844:
839:
835:
831:
822:
792:
780:energy barrier
750:Main article:
747:
744:
708:
707:
705:
704:
697:
690:
682:
679:
678:
677:
676:
663:
646:
645:
641:
640:
635:
630:
625:
620:
615:
610:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
555:
550:
545:
540:
535:
530:
525:
520:
515:
510:
505:
500:
495:
490:
485:
480:
475:
470:
465:
460:
455:
450:
444:
443:
440:
439:
436:
435:
431:
430:
425:
423:Liquid crystal
420:
415:
410:
404:
403:
398:
397:
394:
393:
389:
388:
383:
378:
373:
364:
359:
353:
352:
349:Quasiparticles
347:
346:
343:
342:
338:
337:
332:
323:
314:
308:Superdiamagnet
305:
299:
298:
295:
294:
291:
290:
286:
285:
280:
275:
269:
268:
265:
264:
261:
260:
256:
255:
250:
245:
240:
235:
233:Thermoelectric
230:
228:Superconductor
225:
220:
215:
210:
208:Mott insulator
205:
200:
195:
189:
188:
185:
184:
181:
180:
176:
175:
170:
165:
159:
158:
155:
154:
151:
150:
146:
145:
140:
135:
130:
125:
120:
115:
110:
105:
100:
95:
90:
85:
79:
78:
73:
72:
69:
68:
66:
65:
60:
55:
49:
46:
45:
37:
36:
26:
9:
6:
4:
3:
2:
3434:
3423:
3420:
3418:
3415:
3414:
3412:
3395:
3392:
3390:
3387:
3386:
3385:
3382:
3380:
3377:
3375:
3374:metamagnetism
3372:
3370:
3369:helimagnetism
3367:
3363:
3360:
3358:
3355:
3354:
3353:
3350:
3348:
3345:
3343:
3340:
3338:
3335:
3334:
3332:
3328:
3320:
3317:
3315:
3312:
3311:
3310:
3309:paramagnetism
3307:
3303:
3300:
3299:
3298:
3295:
3294:
3292:
3288:
3284:
3277:
3272:
3270:
3265:
3263:
3258:
3257:
3254:
3248:
3244:
3241:
3238:
3236:
3233:
3232:
3221:
3217:
3213:
3209:
3205:
3201:
3200:
3194:
3190:
3184:
3180:
3172:
3169:(in French).
3168:
3167:Ann. GĂ©ophys.
3161:
3156:
3155:
3141:
3137:
3133:
3129:
3125:
3121:
3117:
3113:
3109:
3105:
3098:
3083:
3082:
3077:
3070:
3062:
3058:
3054:
3050:
3046:
3042:
3038:
3031:
3015:
3011:
3005:
2997:
2993:
2989:
2985:
2981:
2974:
2966:
2960:
2952:
2950:0-7803-5943-7
2946:
2942:
2938:
2934:
2930:
2923:
2915:
2911:
2907:
2903:
2899:
2895:
2891:
2884:
2865:
2858:
2850:
2846:
2842:
2838:
2834:
2830:
2829:
2809:
2801:
2797:
2792:
2787:
2783:
2779:
2775:
2774:11380/1197352
2771:
2767:
2763:
2759:
2755:
2751:
2743:
2734:
2728:
2724:
2716:
2712:
2705:
2701:
2686:
2683:
2681:
2678:
2677:
2669:
2665:
2661:
2657:
2654:
2651:
2647:
2643:
2642:
2633:
2630:
2629:
2615:
2611:
2607:
2603:
2599:
2596:
2592:
2589:
2585:
2584:
2583:
2581:
2577:
2576:areal-density
2573:
2563:
2552:
2528:
2519:
2515:
2509:
2499:
2482:
2478:
2475:
2472:
2469:
2463:
2453:
2442:
2435:
2434:
2433:
2413:
2404:
2398:
2395:
2388:
2370:
2367:
2364:
2357:
2353:
2347:
2343:
2339:
2333:
2324:
2316:
2298:
2289:
2285:
2278:
2274:
2268:
2264:
2260:
2254:
2245:
2237:
2219:
2216:
2212:
2203:
2202:
2201:
2181:
2178:
2175:
2172:
2169:
2158:
2154:
2151:
2148:
2145:
2136:
2129:
2123:
2117:
2110:
2109:
2108:
2087:
2060:
2056:
2053:
2027:
2023:
2020:
2006:
2003:
1998:
1978:
1974:
1971:
1930:
1921:
1917:
1910:
1906:
1900:
1896:
1892:
1870:
1861:
1853:
1849:
1843:
1839:
1835:
1825:
1820:
1817:
1810:
1809:
1808:
1794:
1771:
1765:
1754:
1736:
1733:
1728:
1719:
1713:
1710:
1706:
1701:
1695:
1689:
1682:
1667:
1660:
1657:
1639:
1635:
1627:
1624:
1621:
1620:
1619:
1599:
1593:
1584:
1578:
1575:
1570:
1566:
1559:
1555:
1552:
1549:
1546:
1540:
1534:
1527:
1526:
1521:
1517:
1513:
1509:
1491:
1485:
1476:
1470:
1467:
1462:
1458:
1451:
1447:
1444:
1441:
1438:
1435:
1429:
1423:
1416:
1415:
1410:
1406:
1402:
1395:
1391:
1390:
1389:
1387:
1382:
1361:
1357:
1352:
1349:
1343:
1339:
1336:
1327:
1318:
1315:
1294:
1287:
1283:
1273:
1267:
1263:
1260:
1251:
1245:
1242:
1236:
1227:
1219:
1218:
1217:
1215:
1193:
1189:
1180:
1153:
1149:
1140:
1130:
1110:
1106:
1097:
1070:
1066:
1057:
1030:
1015:
1008:
1005:
1002:
995:
992:
989:
985:
981:
977:
974:
971:
967:
963:
945:
941:
933:
930:
908:
900:
899:
898:
879:
873:
864:
858:
855:
849:
845:
842:
837:
833:
829:
820:
812:
811:
810:
790:
781:
777:
772:
770:
766:
765:single-domain
761:
759:
753:
743:
741:
737:
733:
729:
728:nanoparticles
726:
725:ferrimagnetic
722:
721:ferromagnetic
718:
715:is a form of
714:
703:
698:
696:
691:
689:
684:
683:
681:
680:
674:
664:
661:
656:
650:
649:
648:
647:
639:
636:
634:
631:
629:
626:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
534:
531:
529:
526:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
459:
456:
454:
451:
449:
448:Van der Waals
446:
445:
438:
437:
429:
426:
424:
421:
419:
416:
414:
411:
409:
406:
405:
401:
396:
395:
387:
384:
382:
379:
377:
374:
372:
368:
365:
363:
360:
358:
355:
354:
350:
345:
344:
336:
333:
331:
327:
324:
322:
318:
315:
313:
309:
306:
304:
301:
300:
293:
292:
284:
281:
279:
276:
274:
271:
270:
263:
262:
254:
251:
249:
246:
244:
243:Ferroelectric
241:
239:
238:Piezoelectric
236:
234:
231:
229:
226:
224:
221:
219:
216:
214:
213:Semiconductor
211:
209:
206:
204:
201:
199:
196:
194:
191:
190:
183:
182:
174:
171:
169:
166:
164:
161:
160:
153:
152:
144:
141:
139:
136:
134:
133:Superfluidity
131:
129:
126:
124:
121:
119:
116:
114:
111:
109:
106:
104:
101:
99:
96:
94:
91:
89:
86:
84:
81:
80:
76:
71:
70:
64:
61:
59:
56:
54:
51:
50:
48:
47:
43:
39:
38:
35:
32:
31:
19:
3313:
3297:diamagnetism
3203:
3197:
3178:
3170:
3166:
3107:
3103:
3097:
3085:. Retrieved
3079:
3069:
3044:
3040:
3030:
3018:. Retrieved
3004:
2990:(1): 36–42.
2987:
2983:
2973:
2959:
2932:
2928:
2922:
2897:
2893:
2883:
2871:. Retrieved
2857:
2832:
2826:
2808:
2757:
2753:
2742:
2722:
2714:
2711:Ann. GĂ©ophys
2710:
2704:
2658:Treatments:
2621:Applications
2579:
2569:
2548:
2545:Measurements
2431:
2199:
2012:
2001:
1999:
1963:
1757:
1622:
1617:
1519:
1515:
1511:
1408:
1404:
1400:
1393:
1380:
1378:
1375:(blue line).
1316:
1313:
1213:
1131:
1021:
1012:
1006:
993:
983:
982:its volume.
979:
975:
969:
965:
962:attempt time
961:
896:
773:
762:
755:
712:
711:
578:von Klitzing
316:
283:Kondo effect
143:Time crystal
123:Fermi liquid
3081:PC Magazine
2604:(HAMR) and
400:Soft matter
321:Ferromagnet
3411:Categories
3384:spin glass
2691:References
2632:Ferrofluid
736:paramagnet
543:Louis NĂ©el
533:Schrieffer
441:Scientists
335:Spin glass
330:Metamagnet
312:Paramagnet
128:Supersolid
3283:Magnetism
3173:: 99–136.
3132:1748-3387
2817:and Ni-Al
2782:0020-1669
2717:: 99–136.
2644:Imaging:
2614:skyrmions
2520:χ
2483:χ
2479:τ
2443:τ
2405:τ
2396:τ
2354:μ
2344:μ
2325:χ
2275:μ
2265:μ
2246:χ
2220:π
2213:ω
2182:τ
2179:ω
2159:χ
2155:τ
2152:ω
2137:χ
2124:ω
2118:χ
2057:≫
2024:≪
1907:μ
1897:μ
1850:μ
1840:μ
1818:χ
1795:χ
1729:−
1714:
1668:μ
1658:of vacuum
1636:μ
1579:μ
1567:μ
1553:μ
1547:≈
1471:μ
1459:μ
1448:
1442:μ
1436:≈
1340:
1284:τ
1274:τ
1264:
1194:τ
1181:τ
1154:τ
1141:τ
1111:τ
1107:≪
1098:τ
1071:τ
1067:≫
1058:τ
1031:τ
942:τ
909:τ
846:
834:τ
821:τ
791:τ
717:magnetism
623:Abrikosov
538:Josephson
508:Van Vleck
498:Luttinger
371:Polariton
303:Diamagnet
223:Conductor
218:Semimetal
203:Insulator
118:Fermi gas
3394:spin ice
3243:Archived
3140:23459548
3061:24634675
2825:films".
2800:31967457
2674:See also
673:Category
628:Ginzburg
603:Laughlin
563:Kadanoff
518:Shockley
503:Anderson
458:von Laue
108:Bose gas
3208:Bibcode
3151:Sources
3112:Bibcode
3014:Hitachi
2902:Bibcode
2837:Bibcode
2791:7901656
1751:is the
1654:is the
999:is the
897:where:
633:Leggett
608:Störmer
593:Bednorz
553:Giaever
523:Bardeen
513:Hubbard
488:Peierls
478:Onsager
428:Polymer
413:Colloid
376:Polaron
367:Plasmon
362:Exciton
3185:
3138:
3130:
3087:21 Aug
3059:
2947:
2873:15 Apr
2798:
2788:
2780:
2729:
2200:where
671:
638:Parisi
598:MĂĽller
588:Rohrer
583:Binnig
573:Wilson
568:Fisher
528:Cooper
493:Landau
381:Magnon
357:Phonon
198:Plasma
98:Plasma
88:Liquid
53:Phases
3163:(PDF)
3057:S2CID
3020:1 Sep
2867:(PDF)
2696:Notes
2652:(MRI)
1407:/(10
1399:<
548:Esaki
473:Bloch
468:Debye
463:Bragg
453:Onnes
386:Roton
83:Solid
3183:ISBN
3136:PMID
3128:ISSN
3089:2010
3022:2011
2945:ISBN
2875:2017
2796:PMID
2778:ISSN
2727:ISBN
1975:>
1711:tanh
1445:tanh
1337:tanh
618:Tsui
613:Yang
558:Kohn
483:Mott
3216:doi
3120:doi
3049:doi
2992:doi
2937:doi
2910:doi
2898:102
2845:doi
2786:PMC
2770:hdl
2762:doi
2648:in
2554:1/Ď„
964:or
843:exp
723:or
173:QCP
93:Gas
63:QCP
3413::
3214:.
3204:35
3202:.
3165:.
3134:.
3126:.
3118:.
3106:.
3078:.
3055:.
3045:45
3043:.
3039:.
2988:36
2986:.
2982:.
2943:.
2931:.
2908:.
2896:.
2892:.
2843:.
2831:.
2794:.
2784:.
2776:.
2768:.
2758:59
2756:.
2752:.
2737:).
2713:.
2666:,
2662:,
2582:.
2524:sp
2250:sp
2141:sp
1807::
1516:KV
1514:≳
1405:KV
1403:≲
1261:ln
1216::
984:KV
3275:e
3268:t
3261:v
3222:.
3218::
3210::
3191:.
3171:5
3142:.
3122::
3114::
3108:8
3091:.
3063:.
3051::
3024:.
2998:.
2994::
2967:.
2953:.
2939::
2916:.
2912::
2904::
2877:.
2851:.
2847::
2839::
2833:9
2823:3
2821:O
2819:2
2815:2
2802:.
2772::
2764::
2735:.
2715:5
2560:N
2556:N
2529:H
2516:+
2510:t
2506:d
2500:H
2496:d
2487:b
2476:=
2473:M
2470:+
2464:t
2460:d
2454:M
2450:d
2414:2
2409:N
2399:=
2371:V
2368:K
2365:3
2358:2
2348:0
2340:n
2334:=
2329:b
2299:T
2294:B
2290:k
2286:3
2279:2
2269:0
2261:n
2255:=
2217:2
2176:i
2173:+
2170:1
2163:b
2149:i
2146:+
2130:=
2127:)
2121:(
2092:B
2088:T
2065:B
2061:T
2054:T
2032:B
2028:T
2021:T
2002:ÎĽ
1983:B
1979:T
1972:T
1931:T
1926:B
1922:k
1918:3
1911:2
1901:0
1893:n
1871:T
1866:B
1862:k
1854:2
1844:0
1836:n
1826:{
1821:=
1775:)
1772:H
1769:(
1766:M
1737:x
1734:1
1723:)
1720:x
1717:(
1707:1
1702:=
1699:)
1696:x
1693:(
1690:L
1640:0
1623:n
1600:)
1594:T
1589:B
1585:k
1576:H
1571:0
1560:(
1556:L
1550:n
1544:)
1541:H
1538:(
1535:M
1523:B
1520:k
1518:/
1512:T
1505:.
1492:)
1486:T
1481:B
1477:k
1468:H
1463:0
1452:(
1439:n
1433:)
1430:H
1427:(
1424:M
1412:B
1409:k
1401:T
1397:B
1394:T
1381:H
1362:)
1358:x
1353:3
1350:1
1344:(
1295:)
1288:0
1278:m
1268:(
1256:B
1252:k
1246:V
1243:K
1237:=
1232:B
1228:T
1198:N
1190:=
1185:m
1158:N
1150:=
1145:m
1115:N
1102:m
1075:N
1062:m
1035:m
1007:T
1003:.
997:B
994:k
980:V
976:K
946:0
931:.
913:N
893:,
880:)
874:T
869:B
865:k
859:V
856:K
850:(
838:0
830:=
825:N
795:N
701:e
694:t
687:v
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
