179:
3359:; this magnetization is reached when the external field is strong enough to make all the moments align in the same direction. When this point is reached, the magnetization cannot increase, as there are no more moments to align. When the external field is removed, the magnetization of the ferrimagnet does not disappear, but a nonzero magnetization remains. This effect is often used in applications of magnets. If an external field in the opposite direction is applied subsequently, the magnet will demagnetize further until it eventually reaches a magnetization of
3266:
40:
67:
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206:. An example of this can be seen in the figure above. Here the atoms with a smaller magnetic moment point in the opposite direction of the larger moments. This arrangement is similar to that present in antiferromagnetic materials, but in ferrimagnetic materials the net moment is nonzero because the opposed moments differ in magnitude.
3182:
165:
Sb, French physicist
Charles Guillaud discovered that the current theories on magnetism were not adequate to explain the behavior of the material, and made a model to explain the behavior. In 1948, Néel published a paper about a third type of cooperative magnetism, based on the assumptions in
3212:
Unlike ferromagnetism, the magnetization curves of ferrimagnetism can take many different shapes depending on the strength of the interactions and the relative abundance of atoms. The most notable instances of this property are that the direction of magnetization can reverse while heating a
3253:, but at which the opposing magnetic moments are equal (resulting in a net magnetic moment of zero) is called a magnetization compensation point. This compensation point is observed easily in garnets and rare-earth–transition-metal alloys (RE-TM). Furthermore, ferrimagnets may also have an
2867:
3012:
2337:
2174:
3217:
to its critical temperature, and that strength of magnetization can increase while heating a ferrimagnetic material to the critical temperature, both of which cannot occur for ferromagnetic materials. These temperature dependencies have also been experimentally observed in
843:
48:
3441:; when it is polarized in the opposite direction, the interaction is very low. When the interaction is strong, the microwave signal can pass through the material. This directional property is used in the construction of microwave devices like
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2020:
182:➀ Below the magnetization compensation point, ferrimagnetic material is magnetic. ➁ At the compensation point, the magnetic components cancel each other, and the total magnetic moment is zero. ➂ Above the
1086:{\displaystyle {\vec {H}}_{aa}=\gamma _{aa}{\vec {M}},\quad {\vec {H}}_{ab}=\gamma _{ab}{\vec {M}}_{b},\quad {\vec {H}}_{ba}=\gamma _{ba}{\vec {M}}_{a},\quad {\vec {H}}_{bb}=\gamma _{bb}{\vec {M}}_{b}.}
310:
3646:
221:, and the system can no longer maintain a spontaneous magnetization. This is because at higher temperatures the thermal motion is strong enough that it exceeds the tendency of the dipoles to align.
1787:
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446:
4080:
Sessoli, Roberta; Tsai, Hui Lien; Schake, Ann R.; Wang, Sheyi; Vincent, John B.; Folting, Kirsten; Gatteschi, Dante; Christou, George; Hendrickson, David N. (1993). "High-spin molecules: ".
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is actually induced by an external applied field. When this applied field aligns with the magnetic dipoles, it causes a net magnetic dipole moment and causes the magnetic dipoles to
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compensation point, at which the net angular momentum vanishes. This compensation point is crucial for achieving fast magnetization reversal in magnetic-memory devices.
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2008:
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3461:. Ferrimagnetic minerals in various rock types are used to study ancient geomagnetic properties of Earth and other planets. That field of study is known as
4040:"Natural Magnetite for thermal energy storage: Excellent thermophysical properties, reversible latent heat transition and controlled thermal conductivity"
198:. In ferrimagnetic materials the magnetization is also caused by a combination of dipole–dipole interactions and exchange interactions resulting from the
3177:{\displaystyle F(\lambda ,\alpha ,\beta )={\frac {1}{2}}\left(\lambda \alpha +\mu \beta +{\sqrt {(\lambda \alpha -\mu \beta )^{2}+4\lambda \mu }}\right)}
4144:
2862:{\displaystyle \lambda \sigma _{a}={\frac {\tau F(\lambda ,\alpha ,\beta )}{\alpha \beta -1}}(\beta \tanh ^{-1}\sigma _{a}+\tanh ^{-1}\sigma _{b}),}
1795:
3007:{\displaystyle \mu \sigma _{b}={\frac {\tau F(\lambda ,\alpha ,\beta )}{\alpha \beta -1}}(\tanh ^{-1}\sigma _{a}+\alpha \tanh ^{-1}\sigma _{b})}
2456:
2348:
52:
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3995:
Soler, M. A. G.; Paterno, L. G. (2017-01-01), Da Róz, Alessandra L.; Ferreira, Marystela; de Lima Leite, Fábio; Oliveira, Osvaldo N. (eds.),
3877:
3830:
3621:
1891:
178:
2332:{\displaystyle {\vec {H}}_{b}={\vec {H}}_{0}+Ng\mu _{B}S_{b}\gamma _{ab}(-\lambda {\vec {\sigma }}_{a}+\mu \beta {\vec {\sigma }}_{b}).}
2169:{\displaystyle {\vec {H}}_{a}={\vec {H}}_{0}+Ng\mu _{B}S_{a}\gamma _{ab}(\lambda \alpha {\vec {\sigma }}_{a}-\mu {\vec {\sigma }}_{b}),}
3184:. These equations do not have a known analytical solution, so they must be solved numerically to find the temperature dependence of
161:
published a paper proposing the existence of a new form of cooperative magnetism he called antiferromagnetism. While working with Mn
2600:
239:
141:
discovered ferrimagnetism in 1948. Since the discovery, numerous uses have been found for ferrimagnetic materials, such as
4137:
3571: = 10 derived from antiferromagnetic interaction on Mn(IV) metal centers with Mn(III) and Mn(II) metal centers.
218:
4232:
1735:
1681:
394:
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which give the ratio between the strengths of the interactions. At last we will introduce the reduced magnetizations
1145:
4287:
4116:
199:
95:
4130:
1099:
202:. The main difference is that in ferrimagnetic materials there are different types of atoms in the material's
3332:, where magnetic behavior depends on the history of the magnet. They also exhibit a saturation magnetization
4292:
4189:
166:
Guillaud's model. He called it ferrimagnetism. In 1970, Néel was awarded for his work in magnetism with the
157:
Until the twentieth century, all naturally occurring magnetic substances were called ferromagnets. In 1936,
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1668:{\displaystyle {\vec {H}}_{b}={\vec {H}}_{0}+\gamma _{bb}{\vec {M}}_{b}-\gamma _{ab}{\vec {M}}_{a}.}
1536:{\displaystyle {\vec {H}}_{a}={\vec {H}}_{0}+\gamma _{aa}{\vec {M}}_{a}-\gamma _{ab}{\vec {M}}_{b},}
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as a positive quantity and write the minus sign explicitly in front of it. For the total fields on
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sites of its crystal structure exhibit opposite spin. Other known ferrimagnetic materials include
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4184:
3848:
3685:
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195:
91:
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3705:"Propriétés magnétiques de l'état métallique et énergie d'interaction entre atomes magnétiques"
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122:
71:
4038:
Grosu, Yaroslav; Faik, Abdessamad; Ortega-Fernández, Iñigo; D'Aguanno, Bruno (March 2017).
1986:
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142:
87:
3328:
When ferrimagnets are exposed to an external magnetic field, they display what is called
3965:
3918:
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3665:
3265:
661:{\displaystyle {\vec {H}}_{i}={\vec {H}}_{0}+\sum _{k=1}^{n}\gamma _{ik}{\vec {M}}_{k},}
391:
is field caused by the interactions between the atoms. The following assumption then is
4249:
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191:
39:
31:
3950:"Reversal of Spontaneous Magnetization as a Function of Temperature in LiFeCr Spinels"
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210:
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3647:"Propriétés magnétiques des ferrites ; ferrimagnétisme et antiferromagnétisme"
3290:. The downward curve after saturation, along with the lower return curve, form the
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3728:
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4056:
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3704:
3402:
146:
749:-th substructures. For a diatomic lattice we can designate two types of sites,
229:
There are various ways to describe ferrimagnets, the simplest of which is with
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remains. This can for example occur when the populations consist of different
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1880:{\displaystyle {\vec {\sigma }}_{a}={\vec {M}}_{a}/\lambda Ng\mu _{B}S_{a},}
548:
to be position- and orientation-dependent, we can then write it in the form
203:
126:
4111:
3902:
4264:
3926:
3502:
2553:{\displaystyle \sigma _{b}=B_{S_{b}}(g\mu _{b}S_{b}H_{b}/k_{\text{B}}T).}
2445:{\displaystyle \sigma _{a}=B_{S_{a}}(g\mu _{b}S_{a}H_{a}/k_{\text{B}}T),}
78:
compound, is one of the most common examples of a ferrimagnetic material.
4093:
4070:
Klein, C. and Dutrow, B., Mineral
Science, 23rd ed., Wiley, p. 243.
3521:; and hexagonal or spinel type ferrites, including rhenium ferrite, ReFe
3450:
1973:{\displaystyle {\vec {\sigma }}_{b}={\vec {M}}_{b}/\mu Ng\mu _{B}S_{b}}
233:. In mean-field theory the field acting on the atoms can be written as
75:
62:
Magnetic orders: comparison between ferro, antiferro and ferrimagnetism
3775:
3903:"Magnetic Properties of Ferrite-Chromite Series of Nickel and Cobalt"
3510:
3506:
3437:
in the same direction as this precession strongly interacts with the
114:
86:
material is a material that has populations of atoms with opposing
3264:
2342:
The solutions to these equations (omitted here) are then given by
177:
65:
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38:
209:
Ferrimagnets have a critical temperature above which they become
3518:
137:), is ferrimagnetic, but was classified as a ferromagnet before
99:
4126:
103:
4122:
3465:. In addition, it has been shown that ferrimagnets such as
305:{\displaystyle {\vec {H}}={\vec {H}}_{0}+{\vec {H}}_{m},}
213:
just as ferromagnets do. At this temperature (called the
3616:(2nd ed.). Cambridge: Cambridge University Press.
3614:
Magnetic materials : fundamentals and applications
3417:
at a frequency controlled by the applied field, called
113:
substances, ferrimagnetic substances are attracted by
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favors an anti-parallel alignment. For ferrimagnets,
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Pages displaying wikidata descriptions as a fallback
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3453:. Ferrimagnetic materials are also used to produce
2719:, this then gives the following pair of equations:
94:, but these moments are unequal in magnitude, so a
3868:Blundell, Stephen; Blundell, Katherine M. (2010).
3381:
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3286:. Starting at the origin, the upward curve is the
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3872:(2nd ed.). Oxford: Oxford University Press.
1782:{\displaystyle \beta =\gamma _{bb}/\gamma _{ab},}
1725:{\displaystyle \alpha =\gamma _{aa}/\gamma _{ab}}
479:is the average magnetization of the lattice, and
441:{\displaystyle {\vec {H}}_{m}=\gamma {\vec {M}}.}
190:Ferrimagnetism has the same physical origins as
4003:, William Andrew Publishing, pp. 147–186,
741:is the molecular field coefficient between the
1678:Furthermore, we will introduce the parameters
1184:{\displaystyle \gamma _{aa}\neq \gamma _{bb},}
4138:
3948:Gorter, E. W.; Schulkes, J. A. (1953-05-01).
2014:-th element. This then gives for the fields:
777:the number of magnetic ions per unit volume,
8:
3389:. This behavior results in what is called a
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3853:: CS1 maint: location missing publisher (
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3997:"Chapter 6. Magnetic Nanomaterials"
3907:Journal of the Physical Society of Japan
125:. The oldest known magnetic substance,
3601:
3563:. A classic example is a dodecanuclear
4044:Solar Energy Materials and Solar Cells
3846:
3583: – energy in a specific direction
1191:unless the structures are identical.
7:
3485:, is a ferrimagnetic substance. The
3481:The oldest known magnetic material,
3051:{\displaystyle \tau =T/T_{\text{c}}}
2603:. The simplest case to solve now is
3752:"The Néel Theory of Ferrimagnetism"
3750:Smart, J. Samuel (September 1955).
2712:{\displaystyle B_{1/2}(x)=\tanh(x)}
1371:, so it will be convenient to take
4009:10.1016/b978-0-323-49782-4.00006-1
3497:(YIG); cubic ferrites composed of
3401:Ferrimagnetic materials have high
25:
3901:Tsushima, Tachiro (August 1963).
3821:Simon, Steven H. (21 June 2013).
3798:"The Nobel Prize in Physics 1970"
3559:Ferrimagnetism can also occur in
1364:{\displaystyle \gamma _{ab}<0}
1328:{\displaystyle \gamma _{ab}<0}
1220:{\displaystyle \gamma _{ab}>0}
4110:
3567:molecule with an effective spin
2650:{\displaystyle S_{a}=S_{b}=1/2}
1227:favors a parallel alignment of
1022:
961:
900:
826:{\displaystyle \mu =1-\lambda }
186:, the material loses magnetism.
3382:{\displaystyle -M_{\text{rs}}}
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3127:
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1292:{\displaystyle {\vec {M}}_{b}}
1277:
1256:{\displaystyle {\vec {M}}_{a}}
1241:
1068:
1030:
1007:
969:
946:
908:
891:
854:
700:{\displaystyle {\vec {H}}_{i}}
685:
643:
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429:
405:
384:{\displaystyle {\vec {H}}_{m}}
369:
344:{\displaystyle {\vec {H}}_{0}}
329:
287:
265:
249:
1:
3823:The Oxford Solid State Basics
3429:. As a particular example, a
3352:{\displaystyle M_{\text{rs}}}
3249:A temperature lower than the
219:second-order phase transition
4233:ferromagnetic superconductor
4057:10.1016/j.solmat.2016.12.006
3501:with other elements such as
3213:ferrimagnetic material from
1394:{\displaystyle \gamma _{ab}}
734:{\displaystyle \gamma _{ik}}
3870:Concepts in thermal physics
3756:American Journal of Physics
3729:10.1051/anphys/193611050232
3674:10.1051/anphys/194812030137
3288:initial magnetization curve
707:is the field acting on the
27:Type of magnetic phenomenon
4309:
521:{\displaystyle {\vec {M}}}
472:{\displaystyle {\vec {M}}}
29:
3261:Effect of external fields
200:Pauli exclusion principle
96:spontaneous magnetization
3974:10.1103/physrev.90.487.2
3825:(1st ed.). Oxford.
2592:{\displaystyle B_{J}(x)}
790:{\displaystyle \lambda }
30:Not to be confused with
4190:Van Vleck paramagnetism
3645:Néel, M. Louis (1948).
3561:single-molecule magnets
3439:magnetic dipole moments
837:sites. This then gives
541:{\displaystyle \gamma }
492:{\displaystyle \gamma }
3471:thermal energy storage
3383:
3353:
3325:
3208:Effects of temperature
3198:
3178:
3052:
3008:
2863:
2713:
2651:
2593:
2554:
2446:
2333:
2170:
2004:
1974:
1881:
1783:
1726:
1669:
1537:
1395:
1365:
1329:
1293:
1257:
1221:
1185:
1136:
1087:
827:
791:
771:
735:
711:-th substructure, and
701:
662:
622:
542:
522:
493:
473:
442:
385:
353:applied magnetic field
345:
306:
187:
168:Nobel Prize in Physics
79:
63:
44:
43:Ferrimagnetic ordering
3590:Orbital magnetization
3384:
3354:
3268:
3199:
3179:
3053:
3009:
2864:
2714:
2652:
2594:
2555:
2447:
2334:
2171:
2005:
2003:{\displaystyle S_{i}}
1975:
1882:
1784:
1727:
1670:
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1396:
1366:
1330:
1294:
1258:
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1096:It can be shown that
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772:
736:
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523:
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106:(such as Fe and Fe).
69:
61:
42:
4119:at Wikimedia Commons
3927:10.1143/jpsj.18.1162
3703:Néel, Louis (1936).
3435:circularly polarized
3426:precession frequency
3363:
3336:
3321:saturation remanence
3197:{\displaystyle \mu }
3188:
3062:
3021:
2874:
2726:
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2607:
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2457:
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833:the fraction on the
805:
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454:
395:
359:
319:
240:
4260:amorphous magnetism
4228:superferromagnetism
4094:10.1021/ja00058a027
3966:1953PhRv...90..487G
3919:1963JPSJ...18.1162T
3768:1955AmJPh..23..356S
3721:1936AnPh...11..232N
3709:Annales de Physique
3666:1948AnPh...12..137N
3654:Annales de Physique
3495:yttrium iron garnet
3397:Properties and uses
3330:magnetic hysteresis
757:. We can designate
4213:antiferromagnetism
4185:superparamagnetism
3610:Spaldin, Nicola A.
3379:
3349:
3326:
3194:
3174:
3048:
3004:
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2709:
2647:
2601:Brillouin function
2589:
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823:
787:
767:
731:
697:
658:
538:
518:
489:
469:
438:
381:
341:
302:
196:antiferromagnetism
188:
92:antiferromagnetism
80:
70:Ferrite magnets.
64:
45:
4288:Magnetic ordering
4275:
4274:
4173:superdiamagnetism
4161:Magnetic response
4115:Media related to
4018:978-0-323-49782-4
3879:978-0-19-956209-1
3832:978-0-19-150210-1
3776:10.1119/1.1934006
3623:978-0-521-88669-7
3581:Anisotropy energy
3455:optical isolators
3376:
3346:
3294:. The intercepts
3270:Theoretical model
3251:Curie temperature
3167:
3100:
3045:
2938:
2790:
2538:
2430:
2314:
2286:
2216:
2194:
2151:
2126:
2056:
2034:
1927:
1905:
1831:
1809:
1653:
1618:
1583:
1561:
1521:
1486:
1451:
1429:
1280:
1244:
1071:
1033:
1010:
972:
949:
911:
894:
857:
770:{\displaystyle N}
688:
646:
590:
568:
515:
466:
432:
408:
372:
332:
290:
268:
252:
231:mean-field theory
215:Curie temperature
184:Curie temperature
123:permanent magnets
59:
16:(Redirected from
4300:
4147:
4140:
4133:
4124:
4114:
4098:
4097:
4088:(5): 1804–1816.
4082:J. Am. Chem. Soc
4077:
4071:
4068:
4062:
4061:
4059:
4035:
4029:
4027:
4026:
4025:
3992:
3986:
3985:
3945:
3939:
3938:
3913:(8): 1162–1166.
3898:
3892:
3891:
3865:
3859:
3858:
3852:
3844:
3818:
3812:
3811:
3809:
3808:
3794:
3788:
3787:
3747:
3741:
3740:
3700:
3694:
3693:
3651:
3642:
3636:
3635:
3606:
3586:
3469:can be used for
3409:properties. The
3388:
3386:
3385:
3380:
3378:
3377:
3374:
3358:
3356:
3355:
3350:
3348:
3347:
3344:
3311:
3302:
3285:
3278:
3255:angular momentum
3203:
3201:
3200:
3195:
3183:
3181:
3180:
3175:
3173:
3169:
3168:
3154:
3153:
3126:
3101:
3093:
3057:
3055:
3054:
3049:
3047:
3046:
3043:
3037:
3013:
3011:
3010:
3005:
3000:
2999:
2987:
2986:
2968:
2967:
2955:
2954:
2939:
2937:
2923:
2894:
2889:
2888:
2868:
2866:
2865:
2860:
2852:
2851:
2839:
2838:
2823:
2822:
2810:
2809:
2791:
2789:
2775:
2746:
2741:
2740:
2718:
2716:
2715:
2710:
2681:
2680:
2676:
2656:
2654:
2653:
2648:
2643:
2632:
2631:
2619:
2618:
2598:
2596:
2595:
2590:
2579:
2578:
2559:
2557:
2556:
2551:
2540:
2539:
2536:
2530:
2525:
2524:
2515:
2514:
2505:
2504:
2489:
2488:
2487:
2486:
2469:
2468:
2451:
2449:
2448:
2443:
2432:
2431:
2428:
2422:
2417:
2416:
2407:
2406:
2397:
2396:
2381:
2380:
2379:
2378:
2361:
2360:
2338:
2336:
2335:
2330:
2322:
2321:
2316:
2315:
2307:
2294:
2293:
2288:
2287:
2279:
2266:
2265:
2253:
2252:
2243:
2242:
2224:
2223:
2218:
2217:
2209:
2202:
2201:
2196:
2195:
2187:
2175:
2173:
2172:
2167:
2159:
2158:
2153:
2152:
2144:
2134:
2133:
2128:
2127:
2119:
2106:
2105:
2093:
2092:
2083:
2082:
2064:
2063:
2058:
2057:
2049:
2042:
2041:
2036:
2035:
2027:
2010:the spin of the
2009:
2007:
2006:
2001:
1999:
1998:
1979:
1977:
1976:
1971:
1969:
1968:
1959:
1958:
1940:
1935:
1934:
1929:
1928:
1920:
1913:
1912:
1907:
1906:
1898:
1886:
1884:
1883:
1878:
1873:
1872:
1863:
1862:
1844:
1839:
1838:
1833:
1832:
1824:
1817:
1816:
1811:
1810:
1802:
1788:
1786:
1785:
1780:
1775:
1774:
1762:
1757:
1756:
1731:
1729:
1728:
1723:
1721:
1720:
1708:
1703:
1702:
1674:
1672:
1671:
1666:
1661:
1660:
1655:
1654:
1646:
1642:
1641:
1626:
1625:
1620:
1619:
1611:
1607:
1606:
1591:
1590:
1585:
1584:
1576:
1569:
1568:
1563:
1562:
1554:
1542:
1540:
1539:
1534:
1529:
1528:
1523:
1522:
1514:
1510:
1509:
1494:
1493:
1488:
1487:
1479:
1475:
1474:
1459:
1458:
1453:
1452:
1444:
1437:
1436:
1431:
1430:
1422:
1409:this then gives
1400:
1398:
1397:
1392:
1390:
1389:
1370:
1368:
1367:
1362:
1354:
1353:
1334:
1332:
1331:
1326:
1318:
1317:
1298:
1296:
1295:
1290:
1288:
1287:
1282:
1281:
1273:
1262:
1260:
1259:
1254:
1252:
1251:
1246:
1245:
1237:
1226:
1224:
1223:
1218:
1210:
1209:
1190:
1188:
1187:
1182:
1177:
1176:
1161:
1160:
1141:
1139:
1138:
1133:
1131:
1130:
1115:
1114:
1092:
1090:
1089:
1084:
1079:
1078:
1073:
1072:
1064:
1060:
1059:
1044:
1043:
1035:
1034:
1026:
1018:
1017:
1012:
1011:
1003:
999:
998:
983:
982:
974:
973:
965:
957:
956:
951:
950:
942:
938:
937:
922:
921:
913:
912:
904:
896:
895:
887:
884:
883:
868:
867:
859:
858:
850:
832:
830:
829:
824:
796:
794:
793:
788:
776:
774:
773:
768:
740:
738:
737:
732:
730:
729:
706:
704:
703:
698:
696:
695:
690:
689:
681:
667:
665:
664:
659:
654:
653:
648:
647:
639:
635:
634:
621:
616:
598:
597:
592:
591:
583:
576:
575:
570:
569:
561:
547:
545:
544:
539:
527:
525:
524:
519:
517:
516:
508:
498:
496:
495:
490:
478:
476:
475:
470:
468:
467:
459:
447:
445:
444:
439:
434:
433:
425:
416:
415:
410:
409:
401:
390:
388:
387:
382:
380:
379:
374:
373:
365:
350:
348:
347:
342:
340:
339:
334:
333:
325:
311:
309:
308:
303:
298:
297:
292:
291:
283:
276:
275:
270:
269:
261:
254:
253:
245:
88:magnetic moments
60:
21:
4308:
4307:
4303:
4302:
4301:
4299:
4298:
4297:
4278:
4277:
4276:
4271:
4201:Magnetic states
4196:
4156:
4151:
4107:
4102:
4101:
4079:
4078:
4074:
4069:
4065:
4037:
4036:
4032:
4023:
4021:
4019:
3994:
3993:
3989:
3954:Physical Review
3947:
3946:
3942:
3900:
3899:
3895:
3880:
3867:
3866:
3862:
3845:
3833:
3820:
3819:
3815:
3806:
3804:
3796:
3795:
3791:
3749:
3748:
3744:
3702:
3701:
3697:
3649:
3644:
3643:
3639:
3624:
3608:
3607:
3603:
3598:
3584:
3577:
3555:
3544:
3540:
3536:
3532:
3528:
3524:
3479:
3399:
3391:hysteresis loop
3369:
3361:
3360:
3339:
3334:
3333:
3310:
3307:
3304:
3301:
3298:
3295:
3283:
3276:
3263:
3245:
3241:
3237:
3233:
3229:
3225:
3221:
3210:
3186:
3185:
3145:
3106:
3102:
3060:
3059:
3038:
3019:
3018:
2991:
2975:
2959:
2943:
2924:
2895:
2880:
2872:
2871:
2843:
2827:
2814:
2798:
2776:
2747:
2732:
2724:
2723:
2664:
2659:
2658:
2623:
2610:
2605:
2604:
2570:
2565:
2564:
2531:
2516:
2506:
2496:
2478:
2473:
2460:
2455:
2454:
2423:
2408:
2398:
2388:
2370:
2365:
2352:
2347:
2346:
2304:
2276:
2254:
2244:
2234:
2206:
2184:
2179:
2178:
2141:
2116:
2094:
2084:
2074:
2046:
2024:
2019:
2018:
1990:
1985:
1984:
1960:
1950:
1917:
1895:
1890:
1889:
1864:
1854:
1821:
1799:
1794:
1793:
1763:
1745:
1734:
1733:
1709:
1691:
1680:
1679:
1643:
1630:
1608:
1595:
1573:
1551:
1546:
1545:
1511:
1498:
1476:
1463:
1441:
1419:
1414:
1413:
1378:
1373:
1372:
1342:
1337:
1336:
1306:
1301:
1300:
1270:
1265:
1264:
1234:
1229:
1228:
1198:
1193:
1192:
1165:
1149:
1144:
1143:
1119:
1103:
1098:
1097:
1061:
1048:
1023:
1000:
987:
962:
939:
926:
901:
872:
847:
842:
841:
803:
802:
779:
778:
759:
758:
718:
713:
712:
678:
673:
672:
636:
623:
580:
558:
553:
552:
530:
529:
501:
500:
481:
480:
452:
451:
398:
393:
392:
362:
357:
356:
322:
317:
316:
280:
258:
238:
237:
227:
176:
174:Physical origin
164:
155:
136:
132:
47:
35:
28:
23:
22:
15:
12:
11:
5:
4306:
4304:
4296:
4295:
4293:Quantum phases
4290:
4280:
4279:
4273:
4272:
4270:
4269:
4268:
4267:
4262:
4252:
4250:mictomagnetism
4247:
4242:
4237:
4236:
4235:
4230:
4223:ferromagnetism
4220:
4218:ferrimagnetism
4215:
4210:
4208:altermagnetism
4204:
4202:
4198:
4197:
4195:
4194:
4193:
4192:
4187:
4177:
4176:
4175:
4164:
4162:
4158:
4157:
4152:
4150:
4149:
4142:
4135:
4127:
4121:
4120:
4117:Ferrimagnetism
4106:
4105:External links
4103:
4100:
4099:
4072:
4063:
4030:
4017:
4001:Nanostructures
3987:
3960:(3): 487–488.
3940:
3893:
3878:
3860:
3831:
3813:
3802:NobelPrize.org
3789:
3762:(6): 356–370.
3742:
3715:(5): 232–279.
3695:
3660:(3): 137–198.
3637:
3622:
3600:
3599:
3597:
3594:
3593:
3592:
3587:
3576:
3573:
3550:
3542:
3538:
3534:
3530:
3526:
3522:
3478:
3475:
3463:paleomagnetism
3398:
3395:
3372:
3368:
3342:
3308:
3305:
3299:
3296:
3281:magnetic field
3262:
3259:
3243:
3239:
3235:
3231:
3227:
3223:
3219:
3209:
3206:
3193:
3172:
3166:
3163:
3160:
3157:
3152:
3148:
3144:
3141:
3138:
3135:
3132:
3129:
3124:
3121:
3118:
3115:
3112:
3109:
3105:
3099:
3096:
3091:
3088:
3085:
3082:
3079:
3076:
3073:
3070:
3067:
3041:
3036:
3032:
3029:
3026:
3015:
3014:
3003:
2998:
2994:
2990:
2985:
2982:
2978:
2974:
2971:
2966:
2962:
2958:
2953:
2950:
2946:
2942:
2936:
2933:
2930:
2927:
2922:
2919:
2916:
2913:
2910:
2907:
2904:
2901:
2898:
2892:
2887:
2883:
2879:
2869:
2858:
2855:
2850:
2846:
2842:
2837:
2834:
2830:
2826:
2821:
2817:
2813:
2808:
2805:
2801:
2797:
2794:
2788:
2785:
2782:
2779:
2774:
2771:
2768:
2765:
2762:
2759:
2756:
2753:
2750:
2744:
2739:
2735:
2731:
2708:
2705:
2702:
2699:
2696:
2693:
2690:
2687:
2684:
2679:
2675:
2671:
2667:
2646:
2642:
2638:
2635:
2630:
2626:
2622:
2617:
2613:
2588:
2585:
2582:
2577:
2573:
2561:
2560:
2549:
2546:
2543:
2534:
2529:
2523:
2519:
2513:
2509:
2503:
2499:
2495:
2492:
2485:
2481:
2476:
2472:
2467:
2463:
2452:
2441:
2438:
2435:
2426:
2421:
2415:
2411:
2405:
2401:
2395:
2391:
2387:
2384:
2377:
2373:
2368:
2364:
2359:
2355:
2340:
2339:
2328:
2325:
2320:
2313:
2310:
2303:
2300:
2297:
2292:
2285:
2282:
2275:
2272:
2269:
2264:
2261:
2257:
2251:
2247:
2241:
2237:
2233:
2230:
2227:
2222:
2215:
2212:
2205:
2200:
2193:
2190:
2176:
2165:
2162:
2157:
2150:
2147:
2140:
2137:
2132:
2125:
2122:
2115:
2112:
2109:
2104:
2101:
2097:
2091:
2087:
2081:
2077:
2073:
2070:
2067:
2062:
2055:
2052:
2045:
2040:
2033:
2030:
1997:
1993:
1981:
1980:
1967:
1963:
1957:
1953:
1949:
1946:
1943:
1939:
1933:
1926:
1923:
1916:
1911:
1904:
1901:
1887:
1876:
1871:
1867:
1861:
1857:
1853:
1850:
1847:
1843:
1837:
1830:
1827:
1820:
1815:
1808:
1805:
1778:
1773:
1770:
1766:
1761:
1755:
1752:
1748:
1744:
1741:
1719:
1716:
1712:
1707:
1701:
1698:
1694:
1690:
1687:
1676:
1675:
1664:
1659:
1652:
1649:
1640:
1637:
1633:
1629:
1624:
1617:
1614:
1605:
1602:
1598:
1594:
1589:
1582:
1579:
1572:
1567:
1560:
1557:
1543:
1532:
1527:
1520:
1517:
1508:
1505:
1501:
1497:
1492:
1485:
1482:
1473:
1470:
1466:
1462:
1457:
1450:
1447:
1440:
1435:
1428:
1425:
1388:
1385:
1381:
1360:
1357:
1352:
1349:
1345:
1324:
1321:
1316:
1313:
1309:
1286:
1279:
1276:
1250:
1243:
1240:
1216:
1213:
1208:
1205:
1201:
1180:
1175:
1172:
1168:
1164:
1159:
1156:
1152:
1129:
1126:
1122:
1118:
1113:
1110:
1106:
1094:
1093:
1082:
1077:
1070:
1067:
1058:
1055:
1051:
1047:
1042:
1039:
1032:
1029:
1021:
1016:
1009:
1006:
997:
994:
990:
986:
981:
978:
971:
968:
960:
955:
948:
945:
936:
933:
929:
925:
920:
917:
910:
907:
899:
893:
890:
882:
879:
875:
871:
866:
863:
856:
853:
822:
819:
816:
813:
810:
786:
766:
728:
725:
721:
694:
687:
684:
669:
668:
657:
652:
645:
642:
633:
630:
626:
620:
615:
612:
609:
605:
601:
596:
589:
586:
579:
574:
567:
564:
537:
514:
511:
488:
465:
462:
437:
431:
428:
422:
419:
414:
407:
404:
378:
371:
368:
338:
331:
328:
313:
312:
301:
296:
289:
286:
279:
274:
267:
264:
257:
251:
248:
226:
223:
192:ferromagnetism
175:
172:
162:
154:
151:
149:applications.
134:
130:
32:Ferromagnetism
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4305:
4294:
4291:
4289:
4286:
4285:
4283:
4266:
4263:
4261:
4258:
4257:
4256:
4253:
4251:
4248:
4246:
4245:metamagnetism
4243:
4241:
4240:helimagnetism
4238:
4234:
4231:
4229:
4226:
4225:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4205:
4203:
4199:
4191:
4188:
4186:
4183:
4182:
4181:
4180:paramagnetism
4178:
4174:
4171:
4170:
4169:
4166:
4165:
4163:
4159:
4155:
4148:
4143:
4141:
4136:
4134:
4129:
4128:
4125:
4118:
4113:
4109:
4108:
4104:
4095:
4091:
4087:
4083:
4076:
4073:
4067:
4064:
4058:
4053:
4049:
4045:
4041:
4034:
4031:
4020:
4014:
4010:
4006:
4002:
3998:
3991:
3988:
3983:
3979:
3975:
3971:
3967:
3963:
3959:
3955:
3951:
3944:
3941:
3936:
3932:
3928:
3924:
3920:
3916:
3912:
3908:
3904:
3897:
3894:
3889:
3885:
3881:
3875:
3871:
3864:
3861:
3856:
3850:
3842:
3838:
3834:
3828:
3824:
3817:
3814:
3803:
3799:
3793:
3790:
3785:
3781:
3777:
3773:
3769:
3765:
3761:
3757:
3753:
3746:
3743:
3738:
3734:
3730:
3726:
3722:
3718:
3714:
3710:
3706:
3699:
3696:
3691:
3687:
3683:
3679:
3675:
3671:
3667:
3663:
3659:
3655:
3648:
3641:
3638:
3633:
3629:
3625:
3619:
3615:
3611:
3605:
3602:
3595:
3591:
3588:
3582:
3579:
3578:
3574:
3572:
3570:
3566:
3562:
3557:
3554:
3548:
3520:
3516:
3512:
3508:
3504:
3500:
3496:
3492:
3488:
3484:
3476:
3474:
3472:
3468:
3464:
3460:
3456:
3452:
3448:
3444:
3440:
3436:
3432:
3428:
3427:
3422:
3421:
3416:
3412:
3408:
3404:
3396:
3394:
3392:
3370:
3366:
3340:
3331:
3323:
3322:
3317:
3316:
3293:
3289:
3282:
3275:
3274:magnetization
3271:
3267:
3260:
3258:
3256:
3252:
3247:
3216:
3215:absolute zero
3207:
3205:
3191:
3170:
3164:
3161:
3158:
3155:
3150:
3142:
3139:
3136:
3133:
3130:
3122:
3119:
3116:
3113:
3110:
3107:
3103:
3097:
3094:
3089:
3083:
3080:
3077:
3074:
3071:
3065:
3039:
3034:
3030:
3027:
3024:
2996:
2992:
2988:
2983:
2980:
2976:
2972:
2969:
2964:
2960:
2956:
2951:
2948:
2944:
2934:
2931:
2928:
2925:
2917:
2914:
2911:
2908:
2905:
2899:
2896:
2890:
2885:
2881:
2877:
2870:
2856:
2848:
2844:
2840:
2835:
2832:
2828:
2824:
2819:
2815:
2811:
2806:
2803:
2799:
2795:
2786:
2783:
2780:
2777:
2769:
2766:
2763:
2760:
2757:
2751:
2748:
2742:
2737:
2733:
2729:
2722:
2721:
2720:
2703:
2697:
2694:
2691:
2685:
2677:
2673:
2669:
2665:
2644:
2640:
2636:
2633:
2628:
2624:
2620:
2615:
2611:
2602:
2583:
2575:
2571:
2547:
2541:
2532:
2527:
2521:
2517:
2511:
2507:
2501:
2497:
2493:
2483:
2479:
2474:
2470:
2465:
2461:
2453:
2439:
2433:
2424:
2419:
2413:
2409:
2403:
2399:
2393:
2389:
2385:
2375:
2371:
2366:
2362:
2357:
2353:
2345:
2344:
2343:
2326:
2318:
2308:
2301:
2298:
2295:
2290:
2280:
2273:
2270:
2262:
2259:
2255:
2249:
2245:
2239:
2235:
2231:
2228:
2225:
2220:
2210:
2203:
2198:
2188:
2177:
2163:
2155:
2145:
2138:
2135:
2130:
2120:
2113:
2110:
2102:
2099:
2095:
2089:
2085:
2079:
2075:
2071:
2068:
2065:
2060:
2050:
2043:
2038:
2028:
2017:
2016:
2015:
2013:
1995:
1991:
1965:
1961:
1955:
1951:
1947:
1944:
1941:
1937:
1931:
1921:
1914:
1909:
1899:
1888:
1874:
1869:
1865:
1859:
1855:
1851:
1848:
1845:
1841:
1835:
1825:
1818:
1813:
1803:
1792:
1791:
1790:
1776:
1771:
1768:
1764:
1759:
1753:
1750:
1746:
1742:
1739:
1717:
1714:
1710:
1705:
1699:
1696:
1692:
1688:
1685:
1662:
1657:
1647:
1638:
1635:
1631:
1627:
1622:
1612:
1603:
1600:
1596:
1592:
1587:
1577:
1570:
1565:
1555:
1544:
1530:
1525:
1515:
1506:
1503:
1499:
1495:
1490:
1480:
1471:
1468:
1464:
1460:
1455:
1445:
1438:
1433:
1423:
1412:
1411:
1410:
1408:
1404:
1386:
1383:
1379:
1358:
1355:
1350:
1347:
1343:
1322:
1319:
1314:
1311:
1307:
1284:
1274:
1248:
1238:
1214:
1211:
1206:
1203:
1199:
1178:
1173:
1170:
1166:
1162:
1157:
1154:
1150:
1127:
1124:
1120:
1116:
1111:
1108:
1104:
1080:
1075:
1065:
1056:
1053:
1049:
1045:
1040:
1037:
1027:
1019:
1014:
1004:
995:
992:
988:
984:
979:
976:
966:
958:
953:
943:
934:
931:
927:
923:
918:
915:
905:
897:
888:
880:
877:
873:
869:
864:
861:
851:
840:
839:
838:
836:
820:
817:
814:
811:
808:
800:
784:
764:
756:
752:
748:
744:
726:
723:
719:
710:
692:
682:
655:
650:
640:
631:
628:
624:
618:
613:
610:
607:
603:
599:
594:
584:
577:
572:
562:
551:
550:
549:
535:
509:
486:
460:
448:
435:
426:
420:
417:
412:
402:
376:
366:
354:
336:
326:
299:
294:
284:
277:
272:
262:
255:
246:
236:
235:
234:
232:
224:
222:
220:
217:) there is a
216:
212:
207:
205:
201:
197:
193:
185:
180:
173:
171:
169:
160:
152:
150:
148:
145:platters and
144:
140:
128:
124:
120:
116:
112:
111:ferromagnetic
107:
105:
101:
97:
93:
89:
85:
84:ferrimagnetic
77:
73:
68:
41:
37:
33:
19:
18:Ferrimagnetic
4217:
4168:diamagnetism
4085:
4081:
4075:
4066:
4047:
4043:
4033:
4022:, retrieved
4000:
3990:
3957:
3953:
3943:
3910:
3906:
3896:
3869:
3863:
3822:
3816:
3805:. Retrieved
3801:
3792:
3759:
3755:
3745:
3712:
3708:
3698:
3657:
3653:
3640:
3613:
3604:
3568:
3558:
3552:
3480:
3424:
3418:
3400:
3390:
3327:
3319:
3313:
3291:
3287:
3248:
3211:
3016:
2562:
2341:
2011:
1982:
1677:
1406:
1402:
1095:
834:
798:
754:
750:
746:
742:
708:
670:
449:
314:
228:
211:paramagnetic
208:
189:
156:
108:
83:
81:
36:
4050:: 170–176.
3499:iron oxides
3487:tetrahedral
3459:circulators
3447:circulators
3407:anisotropic
3403:resistivity
801:sites, and
117:and can be
4282:Categories
4255:spin glass
4024:2021-01-25
3807:2021-01-26
3596:References
3547:pyrrhotite
3491:octahedral
3411:anisotropy
3315:coercivity
225:Derivation
159:Louis Néel
147:biomedical
143:hard-drive
139:Louis Néel
119:magnetized
4154:Magnetism
3982:0031-899X
3935:0031-9015
3888:607907330
3849:cite book
3841:851099021
3784:0002-9505
3737:0003-4169
3690:126111103
3682:0003-4169
3632:607986416
3565:manganese
3515:manganese
3483:magnetite
3467:magnetite
3443:isolators
3431:microwave
3405:and have
3367:−
3292:main loop
3192:μ
3165:μ
3162:λ
3143:β
3140:μ
3137:−
3134:α
3131:λ
3120:β
3117:μ
3111:α
3108:λ
3084:β
3078:α
3072:λ
3025:τ
2993:σ
2989:
2981:−
2973:α
2961:σ
2957:
2949:−
2932:−
2929:β
2926:α
2918:β
2912:α
2906:λ
2897:τ
2882:σ
2878:μ
2845:σ
2841:
2833:−
2816:σ
2812:
2804:−
2796:β
2784:−
2781:β
2778:α
2770:β
2764:α
2758:λ
2749:τ
2734:σ
2730:λ
2698:
2498:μ
2462:σ
2390:μ
2354:σ
2312:→
2309:σ
2302:β
2299:μ
2284:→
2281:σ
2274:λ
2271:−
2256:γ
2236:μ
2214:→
2192:→
2149:→
2146:σ
2139:μ
2136:−
2124:→
2121:σ
2114:α
2111:λ
2096:γ
2076:μ
2054:→
2032:→
1952:μ
1942:μ
1925:→
1903:→
1900:σ
1856:μ
1846:λ
1829:→
1807:→
1804:σ
1765:γ
1747:γ
1740:β
1711:γ
1693:γ
1686:α
1651:→
1632:γ
1628:−
1616:→
1597:γ
1581:→
1559:→
1519:→
1500:γ
1496:−
1484:→
1465:γ
1449:→
1427:→
1380:γ
1344:γ
1308:γ
1278:→
1242:→
1200:γ
1167:γ
1163:≠
1151:γ
1142:and that
1121:γ
1105:γ
1069:→
1050:γ
1031:→
1008:→
989:γ
970:→
947:→
928:γ
909:→
892:→
874:γ
855:→
821:λ
818:−
809:μ
785:λ
720:γ
686:→
644:→
625:γ
604:∑
588:→
566:→
536:γ
513:→
487:γ
464:→
430:→
421:γ
406:→
370:→
330:→
288:→
266:→
250:→
204:unit cell
127:magnetite
4265:spin ice
3612:(2011).
3575:See also
3537:and BaFe
3503:aluminum
3477:Examples
3451:gyrators
3312:are the
3279:against
2657:. Since
1299:, while
745:-th and
121:to make
90:, as in
3962:Bibcode
3915:Bibcode
3764:Bibcode
3717:Bibcode
3662:Bibcode
3433:signal
3415:precess
2599:is the
351:is the
153:History
115:magnets
76:ceramic
72:Ferrite
4015:
3980:
3933:
3886:
3876:
3839:
3829:
3782:
3735:
3688:
3680:
3630:
3620:
3529:, PbFe
3517:, and
3511:nickel
3507:cobalt
3449:, and
3420:Larmor
3230:and Li
2563:where
671:where
355:, and
315:where
3686:S2CID
3650:(PDF)
3017:with
1983:with
450:Here
109:Like
100:atoms
4013:ISBN
3978:ISSN
3931:ISSN
3884:OCLC
3874:ISBN
3855:link
3837:OCLC
3827:ISBN
3780:ISSN
3733:ISSN
3678:ISSN
3628:OCLC
3618:ISBN
3549:, Fe
3545:and
3519:zinc
3489:and
3457:and
3318:and
3303:and
3218:NiFe
3058:and
2977:tanh
2945:tanh
2829:tanh
2800:tanh
2695:tanh
1732:and
1405:and
1356:<
1320:<
1263:and
1212:>
753:and
528:and
194:and
104:ions
74:, a
4090:doi
4086:115
4052:doi
4048:161
4005:doi
3970:doi
3923:doi
3772:doi
3725:doi
3670:doi
3556:S.
3423:or
3272:of
3240:5/4
3236:5/4
3232:1/2
3224:8/5
3220:2/5
129:(Fe
102:or
4284::
4084:.
4046:.
4042:.
4011:,
3999:,
3976:.
3968:.
3958:90
3956:.
3952:.
3929:.
3921:.
3911:18
3909:.
3905:.
3882:.
3851:}}
3847:{{
3835:.
3800:.
3778:.
3770:.
3760:23
3758:.
3754:.
3731:.
3723:.
3713:11
3711:.
3707:.
3684:.
3676:.
3668:.
3658:12
3656:.
3652:.
3626:.
3551:1−
3543:19
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3535:19
3531:12
3513:,
3509:,
3505:,
3473:.
3445:,
3393:.
3375:rs
3345:rs
3309:rs
3246:.
3238:Ce
3234:Fe
3222:Cr
3204:.
170:.
82:A
4146:e
4139:t
4132:v
4096:.
4092::
4060:.
4054::
4028:.
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3984:.
3972::
3964::
3937:.
3925::
3917::
3890:.
3857:)
3843:.
3810:.
3786:.
3774::
3766::
3739:.
3727::
3719::
3692:.
3672::
3664::
3634:.
3569:S
3553:x
3541:O
3533:O
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3523:2
3371:M
3341:M
3324:.
3306:m
3300:c
3297:h
3284:h
3277:m
3244:4
3242:O
3228:4
3226:O
3171:)
3159:4
3156:+
3151:2
3147:)
3128:(
3123:+
3114:+
3104:(
3098:2
3095:1
3090:=
3087:)
3081:,
3075:,
3069:(
3066:F
3044:c
3040:T
3035:/
3031:T
3028:=
3002:)
2997:b
2984:1
2970:+
2965:a
2952:1
2941:(
2935:1
2921:)
2915:,
2909:,
2903:(
2900:F
2891:=
2886:b
2857:,
2854:)
2849:b
2836:1
2825:+
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2807:1
2793:(
2787:1
2773:)
2767:,
2761:,
2755:(
2752:F
2743:=
2738:a
2707:)
2704:x
2701:(
2692:=
2689:)
2686:x
2683:(
2678:2
2674:/
2670:1
2666:B
2645:2
2641:/
2637:1
2634:=
2629:b
2625:S
2621:=
2616:a
2612:S
2587:)
2584:x
2581:(
2576:J
2572:B
2548:.
2545:)
2542:T
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2533:k
2528:/
2522:b
2518:H
2512:b
2508:S
2502:b
2494:g
2491:(
2484:b
2480:S
2475:B
2471:=
2466:b
2440:,
2437:)
2434:T
2429:B
2425:k
2420:/
2414:a
2410:H
2404:a
2400:S
2394:b
2386:g
2383:(
2376:a
2372:S
2367:B
2363:=
2358:a
2327:.
2324:)
2319:b
2296:+
2291:a
2268:(
2263:b
2260:a
2250:b
2246:S
2240:B
2232:g
2229:N
2226:+
2221:0
2211:H
2204:=
2199:b
2189:H
2164:,
2161:)
2156:b
2131:a
2108:(
2103:b
2100:a
2090:a
2086:S
2080:B
2072:g
2069:N
2066:+
2061:0
2051:H
2044:=
2039:a
2029:H
2012:i
1996:i
1992:S
1966:b
1962:S
1956:B
1948:g
1945:N
1938:/
1932:b
1922:M
1915:=
1910:b
1875:,
1870:a
1866:S
1860:B
1852:g
1849:N
1842:/
1836:a
1826:M
1819:=
1814:a
1777:,
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1760:/
1754:b
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1706:/
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1689:=
1663:.
1658:a
1648:M
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1636:a
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1571:=
1566:b
1556:H
1531:,
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1516:M
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1504:a
1491:a
1481:M
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1469:a
1461:+
1456:0
1446:H
1439:=
1434:a
1424:H
1407:b
1403:a
1387:b
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1359:0
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1323:0
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1275:M
1249:a
1239:M
1215:0
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1125:b
1117:=
1112:b
1109:a
1081:.
1076:b
1066:M
1057:b
1054:b
1046:=
1041:b
1038:b
1028:H
1020:,
1015:a
1005:M
996:a
993:b
985:=
980:a
977:b
967:H
959:,
954:b
944:M
935:b
932:a
924:=
919:b
916:a
906:H
898:,
889:M
881:a
878:a
870:=
865:a
862:a
852:H
835:b
815:1
812:=
799:a
765:N
755:b
751:a
747:k
743:i
727:k
724:i
709:i
693:i
683:H
656:,
651:k
641:M
632:k
629:i
619:n
614:1
611:=
608:k
600:+
595:0
585:H
578:=
573:i
563:H
510:M
461:M
436:.
427:M
418:=
413:m
403:H
377:m
367:H
337:0
327:H
300:,
295:m
285:H
278:+
273:0
263:H
256:=
247:H
163:2
135:4
133:O
131:3
34:.
20:)
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