644:
2551:, 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.
31:
657:
1315:
760:. 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".
1948:
723:. 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
1118:, 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.
1802:
1002:
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
2528:
1372:
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
1298:
771:. 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
2184:
1492:
2542:
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
880:
1600:
1161:. 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
1943:{\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}}}
2736:
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).
2301:
2095:
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:
3231:
2427:
1993:
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.
2373:
1738:
1116:
1076:
2594:
1199:
1159:
2415:
1362:
2586:. 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.
1381:
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 (
2601:(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
2222:
2597:(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.
1211:
2066:
2033:
1984:
2102:
1036:
914:
796:
2093:
3228:
947:
719:. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the
1794:
1641:
1121:
The state of the nanoparticle (superparamagnetic or blocked) depends on the measurement time. A transition between superparamagnetism and blocked state occurs when
1774:
1667:
1408:
804:
1519:
688:
2229:
2523:{\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}
1078:, the nanoparticle magnetization will flip several times during the measurement, then the measured magnetization will average to zero. If
979:
associated with the magnetization moving from its initial easy axis direction, through a “hard plane”, to the other easy axis direction.
2969:"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"
3262:
2308:
681:
3175:
2719:
749:. Superparamagnetism is different from this standard transition since it occurs below the Curie temperature of the material.
2953:
2698:
Néel, L. (1949). "Théorie du traînage magnétique des ferromagnétiques en grains fins avec applications aux terres cuites".
1674:
1081:
1041:
3024:
Shiroishi, Y.; Fukuda, K.; Tagawa, I.; Iwasaki, H.; Takenoiri, S.; Tanaka, H.; Mutoh, H.; Yoshikawa, N. (October 2009).
2739:"The Origin of Magnetic Anisotropy and Single-Molecule Magnet Behavior in Chromium(II)-Based Extended Metal Atom Chains"
3148:
1164:
1124:
2421:
From this frequency-dependent susceptibility, the time-dependence of the magnetization for low-fields can be derived:
1306:
Equivalently, blocking temperature is the temperature below which a material shows slow relaxation of magnetization.
916:
is thus the average length of time that it takes for the nanoparticle’s magnetization to randomly flip as a result of
2937:
2380:
674:
661:
3223:
1321:
3026:"Y. Shiroishi et al., "Future Options for HDD Storage", IEEE Trans. Magn., Vol. 45, No. 10, pp. 3816-22, Sep. 2009"
2590:
2564:
1303:
For typical laboratory measurements, the value of the logarithm in the previous equation is in the order of 20–25.
643:
2802:
Gittleman, J. I.; Abeles, B.; Bozowski, S. (1974). "Superparamagnetism and relaxation effects in granular Ni-SiO
3410:
3187:
1011:
Let us imagine that the magnetization of a single superparamagnetic nanoparticle is measured and let us define
745:
Normally, any ferromagnetic or ferrimagnetic material undergoes a transition to a paramagnetic state above its
436:
3255:
1293:{\displaystyle T_{\text{B}}={\frac {KV}{k_{\text{B}}\ln \left({\frac {\tau _{\text{m}}}{\tau _{0}}}\right)}}}
3350:
767:, the magnetic moment has usually only two stable orientations antiparallel to each other, separated by an
611:
91:
2195:
2179:{\displaystyle \chi (\omega )={\frac {\chi _{\text{sp}}+i\omega \tau \chi _{\text{b}}}{1+i\omega \tau }}}
3149:"Théorie du traînage magnétique des ferromagnétiques en grains fins avec applications aux terres cuites"
3405:
2638:
2038:
2005:
2002:
There is no time-dependence of the magnetization when the nanoparticles are either completely blocked (
1956:
616:
241:
1014:
892:
774:
506:
181:
1817:
740:
720:
3248:
2668:
753:
501:
496:
22:
2071:
586:
3307:
2598:
2583:
2539:
728:
191:
596:
3185:
Weller, D.; Moser, A. (1999). "Thermal Effect Limits in
Ultrahigh Density Magnetic Recording".
2673:
2648:
2576:
925:
581:
521:
491:
441:
161:
51:
2922:
Magnetics
Conference, 2000. INTERMAG 2000 Digest of Technical Papers. 2000 IEEE International
2652:
1644:
621:
236:
221:
2547:, there will be a different magnetic response than when the frequency is much lower than 1/Ď„
3196:
3100:
2890:
2825:
1779:
917:
211:
101:
1750:
1619:
1487:{\displaystyle M(H)\approx n\mu \tanh \left({\frac {\mu _{0}H\mu }{k_{\text{B}}T}}\right)}
8:
3345:
1374:
764:
451:
261:
111:
3200:
3104:
2894:
2829:
3330:
3064:
3045:
2779:
989:
875:{\displaystyle \tau _{\text{N}}=\tau _{0}\exp \left({\frac {KV}{k_{\text{B}}T}}\right)}
591:
566:
314:
1652:
3290:
3171:
3124:
3116:
2933:
2878:
2816:
2784:
2766:
2715:
1741:
1595:{\displaystyle M(H)\approx n\mu L\left({\frac {\mu _{0}H\mu }{k_{\text{B}}T}}\right)}
746:
561:
406:
296:
216:
3049:
3377:
3204:
3108:
3091:
Fert, Albert; Cros, Vincent; Sampaio, JoĂŁo (2013-03-01). "Skyrmions on the track".
3037:
2980:
2925:
2898:
2833:
2774:
2758:
2750:
266:
231:
226:
186:
156:
126:
86:
46:
2852:
2754:
3235:
2634:
2560:
757:
576:
526:
396:
151:
63:
2998:
2738:
3367:
3340:
3335:
3325:
3025:
2999:"Hitachi achieves nanotechnology milestone for quadrupling terabyte hard drive"
2929:
2656:
976:
768:
648:
626:
606:
601:
556:
476:
411:
309:
196:
41:
3041:
2968:
3399:
3362:
3357:
3297:
3120:
2954:"Computer History Museum: HDD Areal Density reaches 1 terabitper square inch"
2770:
716:
713:
709:
337:
318:
300:
201:
121:
2837:
531:
3285:
3128:
2788:
1989:
It can be seen from these equations that large nanoparticles have a larger
551:
541:
511:
471:
466:
446:
291:
271:
131:
3112:
2296:{\textstyle \chi _{\text{sp}}={\frac {n\mu _{0}\mu ^{2}}{3k_{\text{B}}T}}}
3069:
2762:
571:
546:
516:
461:
456:
388:
30:
3372:
2879:"Magneto-optical harmonic susceptometry of superparamagnetic materials"
2620:
1499:
If all the particles are identical and the temperature is high enough (
734:
724:
481:
323:
116:
3208:
2984:
2902:
3271:
2563:
due to the minimum size of particles that can be used. This limit on
705:
536:
486:
359:
206:
106:
1314:
3382:
2602:
96:
2644:
Magnetic separation: cell-, DNA-, protein- separation, RNA fishing
3002:
416:
401:
364:
355:
350:
2589:
Future hard disk technologies currently in development include:
1377:. This function is quite complicated but for some simple cases:
949:
is a length of time, characteristic of the material, called the
3065:"Will Toshiba's Bit-Patterned Drives Change the HDD Landscape?"
369:
345:
76:
2368:{\textstyle \chi _{\text{b}}={\frac {n\mu _{0}\mu ^{2}}{3KV}}}
1986:
if the easy axes of the nanoparticles are randomly oriented.
1953:
The latter susceptibility is also valid for all temperatures
967:
is the nanoparticle’s magnetic anisotropy energy density and
374:
71:
3240:
3023:
1514:), then, irrespective of the orientations of the easy axes:
1936:
2559:
Superparamagnetism sets a limit on the storage density of
2735:
81:
2801:
1997:
798:
and is given by the following Néel–Arrhenius equation:
2383:
2311:
2232:
2198:
1776:
function is the magnetic susceptibility of the sample
1733:{\textstyle L(x)={\frac {1}{\tanh(x)}}-{\frac {1}{x}}}
1677:
1655:
1622:
1324:
2918:
Magnetic recording beyond the superparamagnetic limit
2430:
2105:
2074:
2041:
2008:
1959:
1877:
1820:
1805:
1782:
1753:
1522:
1411:
1214:
1167:
1127:
1084:
1044:
1017:
928:
895:
807:
777:
752:
Superparamagnetism occurs in nanoparticles which are
3229:
2303:
is the susceptibility in the superparamagnetic state
1111:{\displaystyle \tau _{\text{m}}\ll \tau _{\text{N}}}
1071:{\displaystyle \tau _{\text{m}}\gg \tau _{\text{N}}}
735:
The NĂ©el relaxation in the absence of magnetic field
2708:(in French; an English translation is available in
2579:. It has an estimated limit of 100 to 200 Gbit/in.
2522:
2409:
2367:
2295:
2216:
2178:
2087:
2060:
2027:
1978:
1942:
1788:
1768:
1732:
1661:
1635:
1594:
1486:
1356:
1292:
1193:
1153:
1110:
1070:
1030:
941:
908:
874:
790:
3170:. New York: Gordon and Breach. pp. 407–427.
1194:{\displaystyle \tau _{\text{m}}=\tau _{\text{N}}}
1154:{\displaystyle \tau _{\text{m}}=\tau _{\text{N}}}
961:); its typical value is between 10 and 10 second.
3397:
2538:A superparamagnetic system can be measured with
2410:{\textstyle \tau ={\frac {\tau _{\text{N}}}{2}}}
3090:
2876:
1357:{\textstyle \tanh \left({\frac {1}{3}}x\right)}
3224:Superparamagnetism of Co-Ferrite Nanoparticles
2877:Vandendriessche, Stefaan; et al. (2013).
1403:)), then the magnetization of the assembly is
3256:
2068:). There is, however, a narrow window around
1614:is the density of nanoparticles in the sample
1309:
682:
1318:Langevin function (red line), compared with
3184:
3263:
3249:
2627:
2375:is the susceptibility in the blocked state
689:
675:
29:
2778:
731:is much larger than that of paramagnets.
2554:
1669:is the magnetic moment of a nanoparticle
1313:
3164:An English translation is available in
2714:. Gordon and Breach. pp. 407–427.
2614:
1006:
3398:
3062:
2915:
2417:is the relaxation time of the assembly
3244:
3165:
2709:
2691:
2595:microwave-assisted magnetic recording
2224:is the frequency of the applied field
2217:{\textstyle {\frac {\omega }{2\pi }}}
3146:
2966:
2853:"Introduction to: AC susceptibility"
2697:
1998:Time dependence of the magnetization
2850:
2035:) or completely superparamagnetic (
13:
2582:Current hard disk technology uses
2494:
2484:
2448:
2438:
14:
3422:
3217:
2061:{\displaystyle T\gg T_{\text{B}}}
2028:{\displaystyle T\ll T_{\text{B}}}
1979:{\displaystyle T>T_{\text{B}}}
2591:heat-assisted magnetic recording
2575:Older hard disk technology uses
1368:When an external magnetic field
1031:{\displaystyle \tau _{\text{m}}}
909:{\displaystyle \tau _{\text{N}}}
791:{\displaystyle \tau _{\text{N}}}
656:
655:
642:
3084:
3056:
3017:
2609:
2533:
3188:IEEE Transactions on Magnetics
3063:Murray, Matthew (2010-08-19).
3030:IEEE Transactions on Magnetics
2991:
2973:IEEE Transactions on Magnetics
2960:
2946:
2909:
2870:
2844:
2795:
2729:
2115:
2109:
1763:
1757:
1711:
1705:
1687:
1681:
1532:
1526:
1421:
1415:
957:(its reciprocal is called the
763:Because of the nanoparticle’s
1:
3270:
2755:10.1021/acs.inorgchem.9b02994
2679:
3351:ferromagnetic superconductor
3168:Selected Works of Louis NĂ©el
2712:Selected Works of Louis NĂ©el
2088:{\displaystyle T_{\text{B}}}
1038:as the measurement time. If
756:, i.e. composed of a single
7:
2662:
10:
3427:
3139:
2930:10.1109/INTMAG.2000.872350
2639:magnetic resonance imaging
1310:Effect of a magnetic field
738:
242:Spin gapless semiconductor
3318:
3278:
3042:10.1109/TMAG.2009.2024879
2967:Wood, R. (January 2000).
1747:The initial slope of the
942:{\displaystyle \tau _{0}}
182:Electronic band structure
2684:
2669:Iron oxide nanoparticles
1607:In the above equations:
92:Bose–Einstein condensate
23:Condensed matter physics
3308:Van Vleck paramagnetism
3166:Kurti, N., ed. (1988).
2883:Applied Physics Letters
2838:10.1103/PhysRevB.9.3891
2710:Kurti, N., ed. (1988).
2628:Biomedical applications
2599:Bit-patterned recording
2584:perpendicular recording
2569:superparamagnetic limit
729:magnetic susceptibility
708:which appears in small
2916:Kryder, M. H. (2000).
2674:Single-molecule magnet
2649:targeted drug delivery
2577:longitudinal recording
2524:
2411:
2369:
2297:
2218:
2180:
2089:
2062:
2029:
1980:
1944:
1790:
1770:
1734:
1663:
1637:
1596:
1488:
1365:
1358:
1294:
1195:
1155:
1112:
1072:
1032:
943:
910:
876:
792:
741:NĂ©el relaxation theory
3411:Statistical mechanics
3113:10.1038/nnano.2013.29
3093:Nature Nanotechnology
2653:magnetic hyperthermia
2605:, have been proposed.
2555:Effect on hard drives
2525:
2412:
2370:
2298:
2219:
2181:
2090:
2063:
2030:
1981:
1945:
1791:
1789:{\displaystyle \chi }
1771:
1735:
1664:
1645:magnetic permeability
1638:
1636:{\textstyle \mu _{0}}
1597:
1489:
1359:
1317:
1295:
1196:
1156:
1113:
1073:
1033:
944:
911:
877:
793:
237:Topological insulator
2615:General applications
2428:
2381:
2309:
2230:
2196:
2103:
2072:
2039:
2006:
1957:
1803:
1780:
1769:{\displaystyle M(H)}
1751:
1675:
1653:
1620:
1520:
1409:
1322:
1212:
1203:blocking temperature
1165:
1125:
1082:
1042:
1015:
1007:Blocking temperature
926:
918:thermal fluctuations
893:
805:
775:
721:NĂ©el relaxation time
255:Electronic phenomena
102:Fermionic condensate
3378:amorphous magnetism
3346:superferromagnetism
3201:1999ITM....35.4423W
3105:2013NatNa...8..152F
2895:2013ApPhL.102p1903V
2830:1974PhRvB...9.3891G
2743:Inorganic Chemistry
2623:: tunable viscosity
1375:increasing function
998:is the temperature.
765:magnetic anisotropy
262:Quantum Hall effect
3331:antiferromagnetism
3303:superparamagnetism
3234:2008-12-03 at the
3005:. October 15, 2007
2520:
2407:
2365:
2293:
2214:
2176:
2085:
2058:
2025:
1976:
1940:
1935:
1925:
1865:
1786:
1766:
1730:
1659:
1633:
1592:
1484:
1366:
1354:
1290:
1191:
1151:
1108:
1068:
1028:
990:Boltzmann constant
939:
906:
872:
788:
702:Superparamagnetism
649:Physics portal
3406:Magnetic ordering
3393:
3392:
3291:superdiamagnetism
3279:Magnetic response
3209:10.1109/20.809134
3177:978-2-88124-300-4
3147:NĂ©el, L. (1949).
3036:(10): 3816–3822.
3001:(Press release).
2985:10.1109/20.824422
2903:10.1063/1.4801837
2851:Martien, Dinesh.
2817:Physical Review B
2721:978-2-88124-300-4
2540:AC susceptibility
2514:
2502:
2477:
2456:
2405:
2399:
2363:
2319:
2291:
2284:
2240:
2212:
2174:
2153:
2131:
2082:
2055:
2022:
1973:
1931:
1923:
1916:
1871:
1863:
1856:
1742:Langevin function
1728:
1715:
1662:{\textstyle \mu }
1586:
1579:
1478:
1471:
1344:
1288:
1281:
1268:
1246:
1222:
1188:
1175:
1148:
1135:
1105:
1092:
1065:
1052:
1025:
975:is therefore the
959:attempt frequency
903:
866:
859:
815:
785:
747:Curie temperature
727:. However, their
699:
698:
407:Granular material
175:Electronic phases
16:Form of magnetism
3418:
3265:
3258:
3251:
3242:
3241:
3212:
3195:(6): 4423–4439.
3181:
3163:
3153:
3133:
3132:
3088:
3082:
3081:
3079:
3077:
3060:
3054:
3053:
3021:
3015:
3014:
3012:
3010:
2995:
2989:
2988:
2964:
2958:
2957:
2950:
2944:
2943:
2913:
2907:
2906:
2889:(16): 161903–5.
2874:
2868:
2867:
2865:
2863:
2858:. Quantum Design
2857:
2848:
2842:
2841:
2824:(9): 3891–3897.
2799:
2793:
2792:
2782:
2749:(3): 1763–1777.
2733:
2727:
2725:
2707:
2695:
2567:is known as the
2561:hard disk drives
2529:
2527:
2526:
2521:
2516:
2515:
2512:
2503:
2501:
2497:
2491:
2487:
2481:
2479:
2478:
2475:
2457:
2455:
2451:
2445:
2441:
2435:
2416:
2414:
2413:
2408:
2406:
2401:
2400:
2397:
2391:
2374:
2372:
2371:
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2364:
2362:
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2349:
2340:
2339:
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2321:
2320:
2317:
2302:
2300:
2299:
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2292:
2290:
2286:
2285:
2282:
2272:
2271:
2270:
2261:
2260:
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2241:
2238:
2223:
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2220:
2215:
2213:
2211:
2200:
2185:
2183:
2182:
2177:
2175:
2173:
2156:
2155:
2154:
2151:
2133:
2132:
2129:
2122:
2094:
2092:
2091:
2086:
2084:
2083:
2080:
2067:
2065:
2064:
2059:
2057:
2056:
2053:
2034:
2032:
2031:
2026:
2024:
2023:
2020:
1985:
1983:
1982:
1977:
1975:
1974:
1971:
1949:
1947:
1946:
1941:
1939:
1938:
1932:
1930:for the 2nd case
1929:
1924:
1922:
1918:
1917:
1914:
1904:
1903:
1902:
1893:
1892:
1879:
1872:
1870:for the 1st case
1869:
1864:
1862:
1858:
1857:
1854:
1847:
1846:
1845:
1836:
1835:
1822:
1795:
1793:
1792:
1787:
1775:
1773:
1772:
1767:
1739:
1737:
1736:
1731:
1729:
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1668:
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1642:
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1591:
1587:
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1577:
1570:
1563:
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1552:
1493:
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1490:
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1479:
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1473:
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1469:
1462:
1455:
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1444:
1363:
1361:
1360:
1355:
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1337:
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1198:
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1103:
1094:
1093:
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1077:
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1069:
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1063:
1054:
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1050:
1037:
1035:
1034:
1029:
1027:
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1023:
948:
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789:
787:
786:
783:
691:
684:
677:
664:
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658:
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267:Spin Hall effect
157:Phase transition
127:Luttinger liquid
64:States of matter
47:Phase transition
33:
19:
18:
3426:
3425:
3421:
3420:
3419:
3417:
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3319:Magnetic states
3314:
3274:
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3236:Wayback Machine
3220:
3215:
3178:
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2947:
2940:
2924:. p. 575.
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2849:
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2813:
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2692:
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2682:
2665:
2635:contrast agents
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2199:
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2019:
2015:
2007:
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1966:
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1928:
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1128:
1126:
1123:
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1016:
1013:
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1009:
1003:nanoparticles.
987:
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890:
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851:
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837:
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821:
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802:
782:
778:
776:
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758:magnetic domain
743:
737:
695:
654:
641:
640:
633:
632:
631:
431:
423:
422:
421:
397:Amorphous solid
391:
381:
380:
379:
358:
340:
330:
329:
328:
317:
315:Antiferromagnet
308:
306:Superparamagnet
299:
286:
285:Magnetic phases
278:
277:
276:
256:
248:
247:
246:
176:
168:
167:
166:
152:Order parameter
146:
145:Phase phenomena
138:
137:
136:
66:
56:
17:
12:
11:
5:
3424:
3414:
3413:
3408:
3391:
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3388:
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3386:
3385:
3380:
3370:
3368:mictomagnetism
3365:
3360:
3355:
3354:
3353:
3348:
3341:ferromagnetism
3338:
3336:ferrimagnetism
3333:
3328:
3326:altermagnetism
3322:
3320:
3316:
3315:
3313:
3312:
3311:
3310:
3305:
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3293:
3282:
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3275:
3268:
3267:
3260:
3253:
3245:
3239:
3238:
3226:
3219:
3218:External links
3216:
3214:
3213:
3182:
3176:
3143:
3141:
3138:
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3134:
3099:(3): 152–156.
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2657:magnetofection
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2051:
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2018:
2014:
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1218:
1201:is called the
1184:
1180:
1171:
1144:
1140:
1131:
1101:
1097:
1088:
1061:
1057:
1048:
1021:
1008:
1005:
1000:
999:
993:
985:
980:
977:energy barrier
962:
955:attempt period
936:
932:
921:
899:
884:
883:
870:
864:
855:
849:
846:
840:
836:
833:
828:
824:
820:
811:
781:
769:energy barrier
739:Main article:
736:
733:
697:
696:
694:
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686:
679:
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652:
635:
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459:
454:
449:
444:
439:
433:
432:
429:
428:
425:
424:
420:
419:
414:
412:Liquid crystal
409:
404:
399:
393:
392:
387:
386:
383:
382:
378:
377:
372:
367:
362:
353:
348:
342:
341:
338:Quasiparticles
336:
335:
332:
331:
327:
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321:
312:
303:
297:Superdiamagnet
294:
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269:
264:
258:
257:
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222:Thermoelectric
219:
217:Superconductor
214:
209:
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197:Mott insulator
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55:
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49:
44:
38:
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26:
25:
15:
9:
6:
4:
3:
2:
3423:
3412:
3409:
3407:
3404:
3403:
3401:
3384:
3381:
3379:
3376:
3375:
3374:
3371:
3369:
3366:
3364:
3363:metamagnetism
3361:
3359:
3358:helimagnetism
3356:
3352:
3349:
3347:
3344:
3343:
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3329:
3327:
3324:
3323:
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3317:
3309:
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3304:
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3300:
3299:
3298:paramagnetism
3296:
3292:
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3266:
3261:
3259:
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3206:
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3179:
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3169:
3161:
3158:(in French).
3157:
3156:Ann. GĂ©ophys.
3150:
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2763:11380/1197352
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2565:areal-density
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754:single-domain
750:
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742:
732:
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726:
722:
718:
717:nanoparticles
715:
714:ferrimagnetic
711:
710:ferromagnetic
707:
704:is a form of
703:
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3286:diamagnetism
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3086:
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3068:
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2993:
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2700:Ann. GĂ©ophys
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2647:Treatments:
2610:Applications
2568:
2558:
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2534:Measurements
2420:
2188:
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1990:
1988:
1952:
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567:von Klitzing
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272:Kondo effect
132:Time crystal
112:Fermi liquid
3070:PC Magazine
2593:(HAMR) and
389:Soft matter
310:Ferromagnet
3400:Categories
3373:spin glass
2680:References
2621:Ferrofluid
725:paramagnet
532:Louis NĂ©el
522:Schrieffer
430:Scientists
324:Spin glass
319:Metamagnet
301:Paramagnet
117:Supersolid
3272:Magnetism
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3121:1748-3387
2806:and Ni-Al
2771:0020-1669
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2603:skyrmions
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2472:χ
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2333:μ
2314:χ
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2254:μ
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2202:ω
2171:τ
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1100:τ
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1060:τ
1056:≫
1047:τ
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931:τ
898:τ
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823:τ
810:τ
780:τ
706:magnetism
612:Abrikosov
527:Josephson
497:Van Vleck
487:Luttinger
360:Polariton
292:Diamagnet
212:Conductor
207:Semimetal
192:Insulator
107:Fermi gas
3383:spin ice
3232:Archived
3129:23459548
3050:24634675
2814:films".
2789:31967457
2663:See also
662:Category
617:Ginzburg
592:Laughlin
552:Kadanoff
507:Shockley
492:Anderson
447:von Laue
97:Bose gas
3197:Bibcode
3140:Sources
3101:Bibcode
3003:Hitachi
2891:Bibcode
2826:Bibcode
2780:7901656
1740:is the
1643:is the
988:is the
886:where:
622:Leggett
597:Störmer
582:Bednorz
542:Giaever
512:Bardeen
502:Hubbard
477:Peierls
467:Onsager
417:Polymer
402:Colloid
365:Polaron
356:Plasmon
351:Exciton
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587:MĂĽller
577:Rohrer
572:Binnig
562:Wilson
557:Fisher
517:Cooper
482:Landau
370:Magnon
346:Phonon
187:Plasma
87:Plasma
77:Liquid
42:Phases
3152:(PDF)
3046:S2CID
3009:1 Sep
2856:(PDF)
2685:Notes
2641:(MRI)
1396:/(10
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537:Esaki
462:Bloch
457:Debye
452:Bragg
442:Onnes
375:Roton
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3172:ISBN
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