812:(MgO), amorphous aluminum oxide was used as the tunnel barrier of the MTJ, and typical room temperature TMR was in the range of tens of percent. MgO barriers increased TMR to hundreds of percent. This large increase reflects a synergetic combination of electrode and barrier electronic structures, which in turn reflects the achievement of structurally ordered junctions. Indeed, MgO filters the tunneling transmission of electrons with a particular symmetry that are fully spin-polarized within the current flowing across
839:
vacancies in the MgO tunnel barrier. Extensive solid-state tunnelling spectroscopy experiments across MgO MTJs revealed in 2014 that the electronic retention on the ground and excited states of an oxygen vacancy, which is temperature-dependent, determines the tunnelling barrier height for electrons of a given symmetry, and thus crafts the effective TMR ratio and its temperature dependence. This low barrier height in turn enables the high current densities required for spin-transfer torque, discussed hereafter.
31:
243:
608:
1399:
2462:
Schleicher, F.; Halisdemir, U.; Lacour, D.; Gallart, M.; Boukari, S.; Schmerber, G.; Davesne, V.; Panissod, P.; Halley, D.; Majjad, H.; Henry, Y.; Leconte, B.; Boulard, A.; Spor, D.; Beyer, N.; Kieber, C.; Sternitzky, E.; Cregut, O.; Ziegler, M.; Montaigne, F.; Beaurepaire, E.; Gilliot, P.; Hehn, M.;
1904:
In addition to grain boundaries, point defects such as boron interstitial and oxygen vacancies could be significantly altering the tunnelling magneto-resistance. Recent theoretical calculations have revealed that boron interstitials introduce defect states in the band gap potentially reducing the TMR
193:
as the insulator, the tunnel magnetoresistance can reach several thousand percent. The same year, Bowen et al. were the first to report experiments showing a significant TMR in a MgO based magnetic tunnel junction . In 2004, Parkin and Yuasa were able to make Fe/MgO/Fe junctions that reach over 200%
851:
has been studied and applied widely in MTJs, where there is a tunnelling barrier sandwiched between a set of two ferromagnetic electrodes such that there is (free) magnetization of the right electrode, while assuming that the left electrode (with fixed magnetization) acts as spin-polarizer. This may
816:
Fe-based electrodes. Thus, in the MTJ's parallel (P) state of electrode magnetization, electrons of this symmetry dominate the junction current. In contrast, in the MTJ's antiparallel (AP) state, this channel is blocked, such that electrons with the next most favorable symmetry to transmit dominate
1892:
could be affecting the insulating properties of the MgO barrier; however, the structure of films in buried stack structures is difficult to determine. The grain boundaries may act as short circuit conduction paths through the material, reducing the resistance of the device. Recently, using new
838:
While theory, first formulated in 2001, predicts large TMR values associated with a 4eV barrier height in the MTJ's P state and 12eV in the MTJ's AP state, experiments reveal barrier heights as low as 0.4eV. This contradiction is lifted if one takes into account the localized states of oxygen
1537:
1468:
448:
2627:
Matsumoto, Rie; Fukushima, Akio; Yakushiji, Kay; Nishioka, Shingo; Nagahama, Taro; Katayama, Toshikazu; Suzuki, Yoshishige; Ando, Koji; Yuasa, Shinji (2009). "Spin-dependent tunneling in epitaxial Fe/Cr/MgO/Fe magnetic tunnel junctions with an ultrathin Cr(001) spacer layer".
612:
The spin-up electrons are those with spin orientation parallel to the external magnetic field, whereas the spin-down electrons have anti-parallel alignment with the external field. The relative resistance change is now given by the spin polarizations of the two ferromagnets,
2310:
Ikeda, S.; Hayakawa, J.; Ashizawa, Y.; Lee, Y. M.; Miura, K.; Hasegawa, H.; Tsunoda, M.; Matsukura, F.; Ohno, H. (25 August 2008). "Tunnel magnetoresistance of 604% at 300K by suppression of Ta diffusion in CoFeB/MgO/CoFeB pseudo-spin-valves annealed at high temperature".
1300:
764:
equal 1, i.e. if both electrodes have 100% spin polarization. In this case the magnetic tunnel junction becomes a switch, that switches magnetically between low resistance and infinite resistance. Materials that come into consideration for this are called
731:
during tunneling, the current can be described in a two-current model. The total current is split in two partial currents, one for the spin-up electrons and another for the spin-down electrons. These vary depending on the magnetic state of the junctions.
218:. The 1st generation technologies relied on creating cross-point magnetic fields on each bit to write the data on it, although this approach has a scaling limit at around 90–130 nm. There are two 2nd generation techniques currently being developed:
229:
Magnetic tunnel junctions are also used for sensing applications. Today they are commonly used for position sensors and current sensors in various automotive, industrial and consumer applications. These higher performance sensors are replacing
1876:) should consist of the tunnel barrier + the right ferromagnetic layer of finite thickness (as in realistic devices). The active region is attached to the left ferromagnetic electrode (modeled as semi-infinite tight-binding chain with non-zero
1151:
777:) but its experimental confirmation has been the subject of subtle debate. Nevertheless, if one considers only those electrons that enter into transport, measurements by Bowen et al. of up to 99.6% spin polarization at the interface between La
1239:
330:
2831:
Ikeda, S.; Hayakawa, J.; Ashizawa, Y.; Lee, Y.M.; Miura, K.; Hasegawa, H.; et al. (2008). "Tunnel magnetoresistance of 604% at 300 K by suppression of Ta diffusion in CoFeBMgOCoFeB pseudo-spin-valves annealed at high temperature".
2567:
Greullet, F.; Tiusan, C.; Montaigne, F.; Hehn, M.; Halley, D.; Bengone, O.; Bowen, M.; Weber, W. (November 2007). "Evidence of a
Symmetry-Dependent Metallic Barrier in Fully Epitaxial MgO Based Magnetic Tunnel Junctions".
1665:
603:{\displaystyle P={\frac {{\mathcal {D}}_{\uparrow }(E_{\mathrm {F} })-{\mathcal {D}}_{\downarrow }(E_{\mathrm {F} })}{{\mathcal {D}}_{\uparrow }(E_{\mathrm {F} })+{\mathcal {D}}_{\downarrow }(E_{\mathrm {F} })}}}
1474:
1405:
715:
194:
TMR at room temperature. In 2008, effects of up to 604% at room temperature and more than 1100% at 4.2 K were observed in junctions of CoFeB/MgO/CoFeB by S. Ikeda, H. Ohno group of Tohoku
University in Japan.
1738:
1905:
further These theoretical calculations have also been backed up by experimental evidence showing the nature of boron within the MgO layer between two different systems and how the TMR is different.
1394:{\displaystyle ({\boldsymbol {\sigma }}\cdot \mathbf {p} )({\boldsymbol {\sigma }}\cdot \mathbf {q} )=\mathbf {p} \cdot \mathbf {q} +i(\mathbf {p} \times \mathbf {q} )\cdot {\boldsymbol {\sigma }}}
1784:
In symmetric MTJs (made of electrodes with the same geometry and exchange splitting), the spin-transfer torque vector has only one active component, as the perpendicular component disappears:
3027:
Xu, X.D.; Mukaiyama, K.; Kasai, S.; Ohkubo, T.; Hono, K. (2018). "Impact of boron diffusion at MgO grain boundaries on magneto-transport properties of MgO/CoFeB/W magnetic tunnel junctions".
989:
2663:
Mahfouzi, F.; Nagaosa, N.; Nikolić, B.K. (2012). "Spin-Orbit
Coupling Induced Spin-Transfer Torque and Current Polarization in Topological-Insulator/Ferromagnet Vertical Heterostructures".
943:
1293:
1869:
needs to be plotted at the site of the right electrode to characterise tunnelling in symmetric MTJs, making them appealing for production and characterisation at an industrial scale.
1570:
1028:
1598:
1817:
800:
excitations and interactions with magnons, as well as due to tunnelling with respect to localized states induced by oxygen vacancies (see
Symmetry Filtering section hereafter).
365:
1780:
824:
has been indirectly confirmed by engineering the junction's potential landscape for electrons of a given symmetry. This was first achieved by examining how the electrons of a
394:
1847:
437:
132:
will tunnel through the insulating film than if they are in the oppositional (antiparallel) orientation. Consequently, such a junction can be switched between two states of
2408:
Bowen, M; Barthélémy, A; Bibes, M; Jacquet, E; Contour, J P; Fert, A; Wortmann, D; Blügel, S (2005-10-19). "Half-metallicity proven using fully spin-polarized tunnelling".
1263:
1035:
835:
tunnel barrier. The conceptually simpler experiment of inserting an appropriate metal spacer at the junction interface during sample growth was also later demonstrated .
1867:
175:
found 11.8% in junctions with electrodes of CoFe and Co. The highest effects observed at this time with aluminum oxide insulators was around 70% at room temperature.
3075:
1160:
256:
1888:
Theoretical tunnelling magneto-resistance ratios of 10000% have been predicted. However, the largest that have been observed are only 604%. One suggestion is that
2205:
S Yuasa; T Nagahama; A Fukushima; Y Suzuki & K Ando (2004). "Giant room-temperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel junctions".
1901:
calculations to be performed on structural units that are present in real films. Such calculations have shown that the band gap can be reduced by as much as 45%.
1894:
1603:
105:
1880:) and the right N electrode (semi-infinite tight-binding chain without any Zeeman splitting), as encoded by the corresponding self-energy terms.
1873:
2151:
2875:
Benedetti, S.; Torelli, P.; Valeri, S.; Benia, H.M.; Nilius, N.; Renaud, G. (2008). "Structure and morphology of thin MgO films on Mo(001)".
853:
1532:{\displaystyle {\boldsymbol {\sigma }}({\boldsymbol {\sigma }}\cdot \mathbf {q} )=\mathbf {q} +i\mathbf {q} \times {\boldsymbol {\sigma }}}
1463:{\displaystyle ({\boldsymbol {\sigma }}\cdot \mathbf {p} ){\boldsymbol {\sigma }}=\mathbf {p} +i{\boldsymbol {\sigma }}\times \mathbf {p} }
863:
The spin-transfer torque vector, driven by the linear response voltage, can be computed from the expectation value of the torque operator:
2360:
632:
160:-junctions at 4.2 K. The relative change of resistance was around 14%, and did not attract much attention. In 1991 Terunobu Miyazaki (
77:
from one ferromagnet into the other. Since this process is forbidden in classical physics, the tunnel magnetoresistance is a strictly
2377:
769:. Their conduction electrons are fully spin-polarized. This property is theoretically predicted for a number of materials (e.g. CrO
1676:
2256:
S. S. P. Parkin; et al. (2004). "Giant tunnelling magnetoresistance at room temperature with MgO (100) tunnel barriers".
2027:
J. S. Moodera; et al. (1995). "Large
Magnetoresistance at Room Temperature in Ferromagnetic Thin Film Tunnel Junctions".
1897:
techniques, the grain boundaries within FeCoB/MgO/FeCoB MTJs have been atomically resolved. This has allowed first principles
817:
the junction current. Since those electrons tunnel with respect to a larger barrier height, this results in the sizeable TMR.
210:
work on the basis of magnetic tunnel junctions. TMR, or more specifically the magnetic tunnel junction, is also the basis of
164:, Japan) found a change of 2.7% at room temperature. Later, in 1994, Miyazaki found 18% in junctions of iron separated by an
825:
739:(by using different materials or different film thicknesses). And second, one of the ferromagnets can be coupled with an
2520:
Bowen, M.; Barthélémy, A.; Bellini, V.; Bibes, M.; Seneor, P.; Jacquet, E.; Contour, J.-P.; Dederichs, P. (April 2006).
820:
Beyond these large values of TMR across MgO-based MTJs, this impact of the barrier's electronic structure on tunnelling
796:
The TMR decreases with both increasing temperature and increasing bias voltage. Both can be understood in principle by
999:
for the steady-state transport, in the zero-temperature limit, in the linear-response regime, and the torque operator
185:(MgO) have been under development. In 2001 Butler and Mathon independently made the theoretical prediction that using
2115:
J. Mathon & A. Umerski (2001). "Theory of tunneling magnetoresistance of an epitaxial Fe/MgO/Fe (001) junction".
950:
735:
There are two possibilities to obtain a defined anti-parallel state. First, one can use ferromagnets with different
3085:
728:
219:
2522:"Observation of Fowler–Nordheim hole tunneling across an electron tunnel junction due to total symmetry filtering"
2465:"Localized states in advanced dielectrics from the vantage of spin- and symmetry-polarized tunnelling across MgO"
1898:
2729:
Bias-voltage dependence of perpendicular spin-transfer torque in a symmetric MgO-based magnetic tunnel junctions
868:
1268:
203:
1924:
1670:
The spin-transfer torque vector in general MTJs has two components: a parallel and perpendicular component:
101:
2922:"Atomic structure and electronic properties of MgO grain boundaries in tunnelling magnetoresistive devices"
1544:
1002:
1575:
831:
electrode with both full spin (P=+1 ) and symmetry polarization tunnel across an electrically biased SrTiO
97:
62:
1789:
133:
338:
1745:
723:
is applied to the junction, electrons tunnel in both directions with equal rates. With a bias voltage
370:
3080:
3036:
2993:
2933:
2884:
2841:
2771:
2682:
2637:
2577:
2533:
2476:
2417:
2320:
2265:
2214:
2166:
2124:
2086:
2036:
2001:
1958:
1930:
848:
813:
223:
211:
1872:
Note: In these calculations the active region (for which it is necessary to calculate the retarded
1825:
1146:{\displaystyle {\hat {\mathbf {T} }}={\frac {d{\hat {\mathbf {S} }}}{dt}}=-{\frac {i}{\hbar }}\left}
418:
2979:"Stability of point defects near MgO grain boundaries in FeCoB/MgO/FeCoB magnetic tunnel junctions"
215:
1246:
144:
The effect was originally discovered in 1975 by Michel Jullière (University of Rennes, France) in
3052:
3009:
2857:
2813:
2761:
2706:
2672:
2609:
2441:
2336:
2289:
2238:
1914:
231:
93:
2736:
2959:
2805:
2787:
2698:
2601:
2593:
2549:
2521:
2502:
2494:
2433:
2357:
2281:
2230:
2052:
1919:
1234:{\displaystyle {\hat {H}}={\hat {H}}_{0}-\Delta ({\boldsymbol {\sigma }}\cdot \mathbf {m} )/2}
727:, electrons tunnel preferentially to the positive electrode. With the assumption that spin is
412:
400:
325:{\displaystyle \mathrm {TMR} :={\frac {R_{\mathrm {ap} }-R_{\mathrm {p} }}{R_{\mathrm {p} }}}}
172:
161:
78:
74:
46:
1852:
3044:
3001:
2949:
2941:
2900:
2892:
2849:
2795:
2779:
2690:
2645:
2585:
2541:
2484:
2425:
2328:
2273:
2222:
2182:
2174:
2132:
2094:
2044:
2009:
1966:
1889:
109:
2905:
2364:
857:
809:
740:
207:
182:
30:
3040:
2997:
2937:
2888:
2845:
2775:
2748:
de Sousa, D. J. P.; Ascencio, C. O.; Haney, P. M.; Wang, J. P.; Low, Tony (2021-07-01).
2686:
2641:
2581:
2537:
2480:
2421:
2324:
2269:
2218:
2170:
2128:
2090:
2040:
2005:
1962:
17:
2954:
2921:
2800:
2749:
996:
408:
168:
125:
3005:
2429:
3069:
3056:
3013:
2861:
2817:
2445:
2340:
2152:"Large magnetoresistance in Fe/MgO/FeCo(001) epitaxial tunnel junctions on GaAs(001)"
2013:
1970:
1877:
774:
744:
121:
2978:
2710:
2613:
2293:
2242:
2694:
992:
440:
3048:
2750:"Gigantic tunneling magnetoresistance in magnetic Weyl semimetal tunnel junctions"
2589:
2783:
2048:
821:
246:
Two-current model for parallel and anti-parallel alignment of the magnetizations
179:
82:
58:
2896:
2649:
2545:
2136:
2098:
242:
828:
736:
2791:
2597:
2553:
2498:
2437:
1984:
T. Miyazaki & N. Tezuka (1995). "Giant magnetic tunneling effect in Fe/Al
1660:{\displaystyle {\boldsymbol {\sigma }}=(\sigma _{x},\sigma _{y},\sigma _{z})}
747:). In this case the magnetization of the uncoupled electrode remains "free".
128:. If the magnetizations are in a parallel orientation it is more likely that
165:
149:
92:
technology. On an industrial scale the film deposition is done by magnetron
89:
66:
2963:
2809:
2702:
2605:
2506:
2285:
2234:
2056:
2073:
W. H. Butler; X.-G. Zhang; T. C. Schulthess & J. M. MacLaren (2001).
1265:
and the Pauli matrices properties involving arbitrary classical vectors
129:
70:
2489:
2464:
720:
124:
of the ferromagnetic films can be switched individually by an external
2945:
2853:
2332:
2187:
2178:
2277:
2226:
797:
157:
153:
2074:
2766:
2677:
1243:
where total magnetization (as macrospin) is along the unit vector
710:{\displaystyle \mathrm {TMR} ={\frac {2P_{1}P_{2}}{1-P_{1}P_{2}}}}
241:
29:
1541:
it is then possible to first obtain an analytical expression for
367:
is the electrical resistance in the anti-parallel state, whereas
250:
The relative resistance change—or effect amplitude—is defined as
186:
145:
2920:
Bean, J.J.; Saito, M.; Fukami, S.; Sato, H.; Ikeda, S. (2017).
2075:"Spin-dependent tunneling conductance of Fe/MgO/Fe sandwiches"
190:
1949:
M. Julliere (1975). "Tunneling between ferromagnetic films".
793:
pragmatically amount to experimental proof of this property.
1733:{\displaystyle T_{\parallel }={\sqrt {T_{x}^{2}+T_{z}^{2}}}}
568:
533:
499:
464:
424:
1030:
is obtained from the time derivative of the spin operator:
1155:
Using the general form of a 1D tight-binding
Hamiltonian:
65:. If the insulating layer is thin enough (typically a few
843:
Spin-transfer torque in magnetic tunnel junctions (MTJs)
234:
in many applications due to their improved performance.
403:
of the ferromagnetic electrodes. The spin polarization
1855:
1828:
1792:
1748:
1679:
1606:
1578:
1547:
1477:
1408:
1303:
1271:
1249:
1163:
1038:
1005:
953:
871:
635:
451:
421:
373:
341:
259:
2457:
2455:
1861:
1841:
1811:
1774:
1732:
1659:
1592:
1564:
1531:
1462:
1393:
1287:
1257:
1233:
1145:
1022:
983:
937:
709:
602:
431:
399:The TMR effect was explained by Jullière with the
388:
359:
324:
136:, one with low and one with very high resistance.
27:Magnetic effect in insulators between ferromagnets
852:then be pinned to some selecting transistor in a
108:are also utilized. The junctions are prepared by
2403:
2401:
2110:
2108:
2068:
2066:
1572:(which can be expressed in compact form using
984:{\displaystyle {\hat {\rho }}_{\mathrm {neq} }}
2352:
2350:
2305:
2303:
88:Magnetic tunnel junctions are manufactured in
2200:
2198:
8:
856:device, or connected to a preamplifier in a
938:{\displaystyle \mathbf {T} =\mathrm {Tr} }
57:), which is a component consisting of two
2953:
2904:
2799:
2765:
2676:
2488:
2186:
1895:scanning transmission electron microscopy
1884:Discrepancy between theory and experiment
1854:
1833:
1827:
1797:
1791:
1766:
1753:
1747:
1722:
1717:
1704:
1699:
1693:
1684:
1678:
1648:
1635:
1622:
1607:
1605:
1585:
1577:
1551:
1549:
1548:
1546:
1524:
1516:
1505:
1494:
1486:
1478:
1476:
1455:
1447:
1436:
1428:
1420:
1412:
1407:
1386:
1375:
1367:
1353:
1345:
1334:
1326:
1315:
1307:
1302:
1288:{\displaystyle \mathbf {p} ,\mathbf {q} }
1280:
1272:
1270:
1250:
1248:
1223:
1215:
1207:
1192:
1181:
1180:
1165:
1164:
1162:
1127:
1126:
1118:
1108:
1093:
1065:
1063:
1062:
1056:
1042:
1040:
1039:
1037:
1009:
1007:
1006:
1004:
968:
967:
956:
955:
952:
919:
918:
907:
906:
894:
892:
891:
880:
872:
870:
698:
688:
670:
660:
650:
636:
634:
587:
586:
573:
567:
566:
552:
551:
538:
532:
531:
518:
517:
504:
498:
497:
483:
482:
469:
463:
462:
458:
450:
423:
422:
420:
396:is the resistance in the parallel state.
379:
378:
372:
347:
346:
340:
313:
312:
300:
299:
282:
281:
274:
260:
258:
1600:, and the vector of Pauli spin matrices
178:Since the year 2000, tunnel barriers of
1941:
1608:
1525:
1487:
1479:
1448:
1429:
1413:
1387:
1327:
1308:
1208:
1119:
1110:
1098:
808:Prior to the introduction of epitaxial
106:electron beam physical vapor deposition
3076:Electric and magnetic fields in matter
1565:{\displaystyle {\hat {\mathbf {T} }}}
1023:{\displaystyle {\hat {\mathbf {T} }}}
854:magnetoresistive random-access memory
804:Symmetry-filtering in tunnel barriers
81:phenomenon, and lies in the study of
7:
2410:Journal of Physics: Condensed Matter
1593:{\displaystyle \Delta ,\mathbf {m} }
34:Magnetic tunnel junction (schematic)
2977:Bean, J.J.; McKenna, K.P. (2018).
1812:{\displaystyle T_{\perp }\equiv 0}
1579:
1201:
975:
972:
969:
926:
923:
920:
884:
881:
643:
640:
637:
588:
553:
519:
484:
380:
351:
348:
314:
301:
286:
283:
267:
264:
261:
25:
3006:10.1103/PhysRevMaterials.2.125002
360:{\displaystyle R_{\mathrm {ap} }}
1775:{\displaystyle T_{\perp }=T_{y}}
1586:
1552:
1517:
1506:
1495:
1456:
1437:
1421:
1376:
1368:
1354:
1346:
1335:
1316:
1281:
1273:
1251:
1216:
1066:
1043:
1010:
895:
873:
389:{\displaystyle R_{\mathrm {p} }}
2358:The Emergence of Practical MRAM
1742:And a perpendicular component:
2906:11858/00-001M-0000-0010-FF18-5
2695:10.1103/PhysRevLett.109.166602
2150:M. Bowen; et al. (2001).
1842:{\displaystyle T_{\parallel }}
1654:
1615:
1556:
1499:
1483:
1425:
1409:
1380:
1364:
1339:
1323:
1320:
1304:
1220:
1204:
1186:
1170:
1132:
1070:
1047:
1014:
961:
932:
912:
899:
888:
594:
579:
574:
559:
544:
539:
525:
510:
505:
490:
475:
470:
432:{\displaystyle {\mathcal {D}}}
1:
3049:10.1016/j.actamat.2018.09.028
2590:10.1103/PhysRevLett.99.187202
826:lanthanum strontium manganite
2784:10.1103/physrevb.104.l041401
2014:10.1016/0304-8853(95)90001-2
1971:10.1016/0375-9601(75)90174-7
1258:{\displaystyle \mathbf {m} }
750:The TMR becomes infinite if
116:Phenomenological description
2430:10.1088/0953-8984/17/41/L02
2049:10.1103/PhysRevLett.74.3273
3102:
2897:10.1103/PhysRevB.78.195411
2650:10.1103/PhysRevB.79.174436
2546:10.1103/PhysRevB.73.140408
2137:10.1103/PhysRevB.63.220403
2099:10.1103/PhysRevB.63.054416
220:Thermal Assisted Switching
2986:Physical Review Materials
2671:(16): 166602 See Eq. 13.
2378:"From Hall Effect to TMR"
1899:density functional theory
767:ferromagnetic half-metals
120:The direction of the two
2463:Bowen, M. (2014-08-04).
96:; on a laboratory scale
51:magnetic tunnel junction
39:Tunnel magnetoresistance
18:Magnetic tunnel junction
2834:Applied Physics Letters
2570:Physical Review Letters
2313:Applied Physics Letters
1925:Giant Magnetoresistance
1862:{\displaystyle \theta }
407:is calculated from the
189:as the ferromagnet and
102:pulsed laser deposition
47:magnetoresistive effect
1863:
1843:
1813:
1776:
1734:
1673:A parallel component:
1661:
1594:
1566:
1533:
1464:
1395:
1289:
1259:
1235:
1147:
1024:
985:
939:
711:
604:
433:
390:
361:
326:
247:
98:molecular beam epitaxy
35:
2469:Nature Communications
2367:. Crocus Technologies
1864:
1844:
1814:
1777:
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1290:
1260:
1236:
1148:
1025:
986:
940:
712:
605:
434:
391:
362:
327:
245:
134:electrical resistance
33:
1994:J. Magn. Magn. Mater
1931:Spin-transfer torque
1853:
1826:
1790:
1746:
1677:
1604:
1576:
1545:
1475:
1406:
1301:
1269:
1247:
1161:
1036:
1003:
951:
869:
849:spin-transfer torque
633:
449:
419:
371:
339:
257:
238:Physical explanation
224:Spin-transfer torque
61:separated by a thin
3041:2018AcMat.161..360X
2998:2018PhRvM...2l5002B
2938:2017NatSR...745594B
2889:2008PhRvB..78s5411B
2846:2008ApPhL..93h2508I
2776:2021PhRvB.104d1401D
2687:2012PhRvL.109p6602M
2642:2009PhRvB..79q4436M
2582:2007PhRvL..99r7202G
2538:2006PhRvB..73n0408B
2481:2014NatCo...5.4547S
2422:2005JPCM...17L.407B
2325:2008ApPhL..93h2508I
2270:2004NatMa...3..862P
2219:2004NatMa...3..868Y
2171:2001ApPhL..79.1655B
2129:2001PhRvB..63v0403M
2091:2001PhRvB..63e4416B
2041:1995PhRvL..74.3273M
2006:1995JMMM..139L.231M
1963:1975PhLA...54..225J
1727:
1709:
814:body-centered cubic
216:non-volatile memory
2926:Scientific Reports
2490:10.1038/ncomms5547
2363:2011-04-27 at the
1859:
1839:
1809:
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1460:
1391:
1285:
1255:
1231:
1143:
1020:
981:
935:
707:
600:
429:
401:spin polarizations
386:
357:
322:
248:
94:sputter deposition
79:quantum mechanical
36:
3086:Magnetoresistance
2946:10.1038/srep45594
2877:Physical Review B
2854:10.1063/1.2976435
2754:Physical Review B
2630:Physical Review B
2526:Physical Review B
2385:Crocus Technology
2333:10.1063/1.2976435
2179:10.1063/1.1404125
1920:Magnetoresistance
1915:Quantum tunneling
1728:
1559:
1189:
1173:
1135:
1116:
1101:
1085:
1073:
1050:
1017:
964:
915:
902:
705:
598:
413:density of states
320:
173:Jagadeesh Moodera
162:Tohoku University
49:that occurs in a
16:(Redirected from
3093:
3061:
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3018:
3017:
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2974:
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2307:
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2278:10.1038/nmat1256
2253:
2247:
2246:
2227:10.1038/nmat1257
2202:
2193:
2192:
2190:
2159:Appl. Phys. Lett
2156:
2147:
2141:
2140:
2112:
2103:
2102:
2070:
2061:
2060:
2024:
2018:
2017:
1981:
1975:
1974:
1946:
1890:grain boundaries
1878:Zeeman splitting
1874:Green's function
1868:
1866:
1865:
1860:
1848:
1846:
1845:
1840:
1838:
1837:
1822:Therefore, only
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331:
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321:
319:
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304:
291:
290:
289:
275:
270:
214:, a new type of
208:hard disk drives
110:photolithography
21:
3101:
3100:
3096:
3095:
3094:
3092:
3091:
3090:
3066:
3065:
3064:
3029:Acta Materialia
3026:
3025:
3021:
2981:
2976:
2975:
2971:
2919:
2918:
2914:
2874:
2873:
2869:
2830:
2829:
2825:
2747:
2746:
2742:
2731:, Nature Phys.
2722:
2718:
2665:Phys. Rev. Lett
2662:
2661:
2657:
2626:
2625:
2621:
2566:
2565:
2561:
2519:
2518:
2514:
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2407:
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2389:
2387:
2380:
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2375:
2371:
2365:Wayback Machine
2356:Barry Hoberman
2355:
2348:
2309:
2308:
2301:
2255:
2254:
2250:
2213:(12): 868–871.
2204:
2203:
2196:
2154:
2149:
2148:
2144:
2114:
2113:
2106:
2072:
2071:
2064:
2029:Phys. Rev. Lett
2026:
2025:
2021:
1992:/Fe junction".
1991:
1987:
1983:
1982:
1978:
1948:
1947:
1943:
1939:
1911:
1886:
1851:
1850:
1829:
1824:
1823:
1793:
1788:
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1762:
1749:
1744:
1743:
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1674:
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1244:
1179:
1159:
1158:
1107:
1103:
1077:
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1034:
1033:
1001:
1000:
995:nonequilibrium
993:gauge-invariant
954:
949:
948:
905:
867:
866:
858:hard disk drive
845:
834:
810:magnesium oxide
806:
792:
788:
784:
780:
772:
762:
755:
741:antiferromagnet
694:
684:
677:
666:
656:
652:
631:
630:
625:
618:
582:
565:
547:
530:
529:
513:
496:
478:
461:
460:
447:
446:
417:
416:
374:
369:
368:
342:
337:
336:
308:
295:
277:
276:
255:
254:
240:
200:
183:magnesium oxide
171:insulator and
142:
118:
28:
23:
22:
15:
12:
11:
5:
3099:
3097:
3089:
3088:
3083:
3078:
3068:
3067:
3063:
3062:
3019:
2992:(12): 125002.
2969:
2912:
2867:
2823:
2740:
2735:, 898 (2009).
2716:
2655:
2636:(17): 174436.
2619:
2576:(18): 187202.
2559:
2532:(14): 140408.
2512:
2451:
2416:(41): L407–9.
2397:
2369:
2346:
2299:
2248:
2194:
2142:
2123:(22): 220403.
2104:
2062:
2035:(16): 3273–6.
2019:
1989:
1985:
1976:
1940:
1938:
1935:
1934:
1933:
1928:
1922:
1917:
1910:
1907:
1885:
1882:
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1805:
1800:
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1769:
1765:
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1012:
997:density matrix
977:
974:
971:
963:
960:
934:
928:
925:
922:
914:
911:
901:
897:
890:
886:
883:
879:
875:
847:The effect of
844:
841:
832:
805:
802:
790:
786:
782:
778:
775:Heusler alloys
770:
760:
753:
701:
697:
691:
687:
683:
680:
673:
669:
663:
659:
655:
649:
645:
642:
639:
623:
616:
596:
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585:
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570:
564:
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541:
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521:
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332:
316:
311:
303:
298:
294:
288:
285:
280:
273:
269:
266:
263:
239:
236:
199:
196:
169:aluminum oxide
141:
138:
126:magnetic field
122:magnetizations
117:
114:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3098:
3087:
3084:
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3046:
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2835:
2827:
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2807:
2802:
2797:
2793:
2789:
2785:
2781:
2777:
2773:
2768:
2763:
2760:(4): 041401.
2759:
2755:
2751:
2744:
2741:
2738:
2734:
2730:
2726:
2720:
2717:
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2692:
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2659:
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2647:
2643:
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2607:
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2579:
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2486:
2482:
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2474:
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2452:
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2439:
2435:
2431:
2427:
2423:
2419:
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2386:
2379:
2373:
2370:
2366:
2362:
2359:
2353:
2351:
2347:
2342:
2338:
2334:
2330:
2326:
2322:
2319:(8): 082508.
2318:
2314:
2306:
2304:
2300:
2295:
2291:
2287:
2283:
2279:
2275:
2271:
2267:
2264:(12): 862–7.
2263:
2259:
2252:
2249:
2244:
2240:
2236:
2232:
2228:
2224:
2220:
2216:
2212:
2208:
2201:
2199:
2195:
2189:
2184:
2180:
2176:
2172:
2168:
2164:
2160:
2153:
2146:
2143:
2138:
2134:
2130:
2126:
2122:
2118:
2111:
2109:
2105:
2100:
2096:
2092:
2088:
2085:(5): 054416.
2084:
2080:
2076:
2069:
2067:
2063:
2058:
2054:
2050:
2046:
2042:
2038:
2034:
2030:
2023:
2020:
2015:
2011:
2007:
2003:
2000:(3): L231–4.
1999:
1995:
1980:
1977:
1972:
1968:
1964:
1960:
1956:
1952:
1945:
1942:
1936:
1932:
1929:
1926:
1923:
1921:
1918:
1916:
1913:
1912:
1908:
1906:
1902:
1900:
1896:
1891:
1883:
1881:
1879:
1875:
1870:
1856:
1834:
1830:
1820:
1806:
1803:
1798:
1794:
1785:
1782:
1767:
1763:
1759:
1754:
1750:
1740:
1723:
1718:
1714:
1710:
1705:
1700:
1696:
1690:
1685:
1681:
1671:
1668:
1649:
1645:
1641:
1636:
1632:
1628:
1623:
1619:
1612:
1582:
1539:
1521:
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1491:
1470:
1452:
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1441:
1433:
1417:
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1383:
1372:
1361:
1358:
1350:
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1331:
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1277:
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1193:
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1129:
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1104:
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1090:
1087:
1081:
1078:
1059:
1053:
1031:
998:
994:
958:
945:
909:
877:
864:
861:
860:application.
859:
855:
850:
842:
840:
836:
830:
829:half-metallic
827:
823:
818:
815:
811:
803:
801:
799:
794:
776:
768:
763:
756:
748:
746:
745:exchange bias
742:
738:
733:
730:
726:
722:
717:
699:
695:
689:
685:
681:
678:
671:
667:
661:
657:
653:
647:
628:
626:
619:
610:
583:
562:
548:
514:
493:
479:
455:
452:
444:
442:
414:
410:
406:
402:
397:
375:
343:
309:
296:
292:
278:
271:
253:
252:
251:
244:
237:
235:
233:
227:
225:
221:
217:
213:
209:
205:
197:
195:
192:
188:
184:
181:
176:
174:
170:
167:
163:
159:
155:
151:
147:
139:
137:
135:
131:
127:
123:
115:
113:
111:
107:
103:
99:
95:
91:
86:
84:
80:
76:
72:
68:
64:
60:
56:
52:
48:
44:
40:
32:
19:
3032:
3028:
3022:
2989:
2985:
2972:
2929:
2925:
2915:
2880:
2876:
2870:
2840:(8): 39–42.
2837:
2833:
2826:
2757:
2753:
2743:
2732:
2728:
2724:
2719:
2668:
2664:
2658:
2633:
2629:
2622:
2573:
2569:
2562:
2529:
2525:
2515:
2472:
2468:
2413:
2409:
2388:. Retrieved
2384:
2372:
2316:
2312:
2261:
2257:
2251:
2210:
2206:
2165:(11): 1655.
2162:
2158:
2145:
2120:
2117:Phys. Rev. B
2116:
2082:
2079:Phys. Rev. B
2078:
2032:
2028:
2022:
1997:
1993:
1979:
1957:(3): 225–6.
1954:
1950:
1944:
1903:
1887:
1871:
1821:
1786:
1783:
1741:
1672:
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