1. 1. Magnetoresistncia Gigante: Precursor da Spintrnica R. B. Muniz Universidade Federal Fluminense Colaboradores: D. M. Edwards J. Mathon ! Filipe S. M. Guimares
2. 2. Uma parcela significativa de toda informao existente hoje (textos, imagens, sons e dados em geral) est armazenada em meios magnticos. Isto se deve ao aumento incrvel da capacidade de memria dos dispositivos de armazenagem de dados. Armazenagem de informao 3 TB
3. 3. Em 1980 o computador central da Universidade de Londres tinha apenas 200Kb de memria. Hoje os telefones celulares tem, em mdia, ~ 256 MB de memria. Um carto de memria de 64GB hoje custa ~R$200 Armazenagem de informao Um lanamento recente de pendrive: 7,12,62,1cm
4. 4. Particularmente, ao controle na produo de novos materiais, tais como Filmes ultrafinos Multicamadas Nanofios Aglomerados com dimenses nanoscpicas: 1nm = 10-9m Nanocincia e nanotecnologia Este progresso deve-se aos avanos na nanocincia e nanotecnologia.
5. 5. Fe/MgO/Fe Cu Co Multicamadas de Co/Cu(001) Nanoestruturas metlicas: alguns exemplos
6. 6. Nanoestruturas metlicas: alguns exemplos Nanofios de Au sobre NiAl As propriedades fsicas desses sistemas so muito diferentes das dos seus constituintes
7. 7. Nanoestruturas metlicas: alguns exemplos SCIENCE 305 23 JULY 2004 Au/NaCl Nanoestruturas magnticas so usadas em dispositivos de armazenagem e manipulao de informao.
8. 8. Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange G. Binasch et al., Physical Review B, Vol. 39, No. 7 (1989) Acoplamento magntico em multicamadas
9. 9. Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices M.N. Baibich et al., Physical Review Letters Vol. 61, No. 21 (1988) Magnetoresistncia gigante Mario Baibich
10. 10. Co Co Cu Cu Cu Stuart Parkin Magnetoresistncia gigante: acoplamento magntico oscilatrio em multicamadas Oscillatory magnetic exchange coupling through thin copper layers S. S. P. Parkin et al., Phys. Rev. Lett. 66, 21522155 (1991)
11. 11. Estas descobertas causaram um grande impacto na indstria magntica Sensores magnticos de alta sensibilidade
12. 12. Digitalizao Informao codificada em bits: contrao inglesa de binary digits (0,1) - 1 Byte = 8 bits 28 = 256 possibilidades - 1 palavra (word) = 4 Bytes = 32 bits = 232 = 4.294.967.296 possibilidades 0 0 1 1 1 0 0 1 Dois bits: 4 possibilidadesUm bit: 2 possibilidades 0 1 0 0 0 0 0 0 0 0
13. 13. Armazenagem de informao Em meios magnticos, os bits so unidades magnetizadas em uma direo ou outra 0 1
14. 14. Armazenagem de informao Para aumentar a capacidade de armazenamento precisamos reduzir o tamanho da unidade magntica que armazena os bits
15. 15. Corrente eltrica gera campo magntico Importncia tecnolgica: sensores magnticos de alta sensibilidade
16. 16. Sensores indutivos Lei de Faraday Campo magntico pode gerar corrente eltrica Importncia tecnolgica: sensores magnticos de alta sensibilidade
17. 17. Os primeiros discos rgidos comerciais utilizavam sensores indutivos para escrita e leitura
18. 18. Magnetic Recording Fundamentals 3 Consider the familiar audio cassette tape recorder in Figure 0-2. The recording/playback head is made of easily magnetised ferrite material and has a small air-gap at the point where it comes into contact with the recording tape, = 0. When energised, the coil winding on the structure is used to create a strong and concentrated magnetic field on the recording media as it moves along with a velocity v. During the playback mode, this coil detects the induced voltages. iw n s n sn sv recording media magnetic dipoles magnetic flux gap head distancemedia velocity fringing field substrate Figure 0-2 Basic Ring read/write head. The recording media in this case is a length of MYLAR (plastic) tape coated with a powdered ferric oxide compound which is magnetisable and has high remanence. This layer of magnetic material in the unmagnetised state may be conceived as made up of dipoles, tiny Cabeotes indutivos
19. 19. A corrente induzida depende da taxa de variao do uxo do campo magntico atravs da espira v iind A corrente induzida depende: tamanho da unidade magntica distncia da espira unidade magntica da velocidade com que a unidade magntica se move
20. 20. A corrente induzida depende da taxa de variao do uxo do campo magntico atravs da espira v iind
21. 21. Esta tecnologia tem limitaes A densidade de gravao no disco no uniformeA velocidade linear da periferia maior do que no centro ( )v = r ! 7200 rpm ! d d 3 nm
22. 22. Sensor magnetoresistivo V Magnetoresistncia gigante
23. 23. Impacto na Capacidade de Armazenamento
24. 24. Explicao para o efeito GMR
25. 25. Resistncia eltrica Nos metais os portadores de corrente eltrica so os eltrons de conduo. Os eltrons tm carga eltrica negativa (-e) e quando sujeitos um campo eltrico sofrem uma fora Resistncia eltrica ocorre devido a espalhamentos eletrnicos com impurezas e/ou heterogeneidades no material; quanto mais so espalhados maior a resistncia E F = eE E F
26. 26. Resistncia eltrica Quanto maior for a densidade de centros espalhadores, maior ser a resistncia do material, pois a probabilidade de colises aumenta. Entretanto, o espalhamento depende do nmero de estados disponveis para os quais eles podem ser espalhados. Se no houver estados disponveis, as colises so ineficientes.
27. 27. Estados eletrnicos Bandas de energia 3s 3s 3p tomo isolado 5 tomos prximos 3p Muitos tomos prximos 3s 3p
28. 28. Esquematicamente: Estados eletrnicos (E)
29. 29. Densidade de estados eletrnicos Um conceito til para analisar as propriedades eletrnicas em slidos em geral o da densidade de estados eletrnicos (E) = X n (E En) En ( ) E { Z (E)dE = 0 En ( ) E Z (E)dE = 1 Z (E)dE = # de estados no intervalo de energiafunciona com um contador de estados(E)
30. 30. Densidade de estados eletrnicos A densidade de estados representa o nmero de estados eletrnicos por unidade de energia. EF E E Metal Isolante kBT kBT Semicondutor (E) (E) (E) EF representa o nvel de Fermi (energia do ltimo estado ocupado) banda de valncia banda de conduo
31. 31. Propriedades eletrnicas
32. 32. Eltrons possuem massa 9.109382 91 -31 e-
33. 33. Eltrons possuem carga e- ~F --- +
34. 34. ? E o spin? e-
35. 35. O experimento de Stern-Gerlach mostrou que partculas possuem um momento angular intrnseco
36. 36. 9.109382 91 -31 Spin uma propriedade intrnseca do eltron ~F +e-
37. 37. e- Ao medir os spins, obtemos valores discretos e- ~B(~r)
38. 38. Eletrnica convencional
39. 39. Em um metal, os eltrons de conduo so livres para se movimentar e- e- e-e-
40. 40. Dispositivos eletrnicos convencionais no levam em conta o spin eletrnico e-
41. 41. Sensores magnetoresistivos
42. 42. Spin eletrnico: Stern-Gerlach Alm de possuirem massa e carga eltrica, os eltrons tambm possuem um momento angular intrnseco denominado spin. O spin eletrnico s pode ter 2 valores ou , dependendo da sua orientao em relao ao campo magntico externo.
43. 43. Metais magnticos Nos materiais magnticos, os estados eletrnicos para eltrons com spin so deslocados em energia em relao aos dos eltrons com spin (E) EF sp d E metal no-magntico metal magntico (E) EF sp d E
44. 44. Modelo de duas correntes A conduo feita pelos eltrons sp - os eltrons d tambm participam, porm, esto maispresosaos ncleos. A concentrao de impurezas/irregularidades a mesma para eltrons com spin e Espalhamentos que provocam mudana no spin eletrnico so desprezveis, eltrons com spin e trafegam em canais independentes; a resistncia do sistema dada por R = R R R + R Sir Nevil Mott
45. 45. Modelo No material no magntico No material magntico - Pelas Figs. (E) EF sp d E (E) EF sp d E metal NM R = R metal M RM = RM RM < RM R = R RM
46. 46. Modelo Cu: Co: - Pelas Figs. (E) EF sp d E (E) EF sp d E RCo " 6= RCo # RCo " < RCo # RCo # RCu " = RCu # RCu " = RCu #
47. 47. Resistores Co/Cu FMAF Co CoCu Cu Cu H Qual das duas configuraes possui menor resistncia? ferromagnetischen natrlich! (E) E (E) E Cu Co
48. 48. Manejo do fluxo de carga regulado pelo spin eletrnico Controle da corrente
49. 49. Spintrnica Essa corrente de spins pode ser usada para excitar outras unidades magnticas Bombeamento de spins rection cannot he (transverse) j, which is de- ave vectors k";# F metals [9]. A rromagnet can he neighboring . Each magnet e the transverse s the adiabatic oelectronic cir- ugh to suppress etostatic (Neel- hin lms with a lm thickness and, therefore, s2 s1 stationary (see the left drawing in Fig. 2) the d the other lm, Fi, is governed by the LLG equa damping parameter i 0 i 0 i enhanced spect to the intrinsic value 0 i by 0 i hg where i is the total magnetic moment of Fi FIG. 2 (color online). A cartoon of the dynam phenomenon. In the left drawing, layer F1 is at a re its precessing magnetic moment pumps spin curr spacer, while F2 is detuned from its FMR. In the rig both lms resonate at the same external eld, in B. Heinrich et al. PRL 90, 187601 (2003) Transporte de spins sem o transporte de cargas Transmisso de informao por correntes puras de spin
50. 50. A interao spin-rbita pode afetar substancialmente as propriedades magnticas de nano-estruturas
51. 51. O acoplamento spin-rbita pode favorecer a ocorrncia de ordenamento magntico no colinear M. Bode et al Nature 447, 05802 (2007); Ferriani et al PRL 101, 027201 (2008) tance of 0.47 6 0.03 nm matching the surface lattice constant along the [1110] direction. In an earlier publication13 this magnetic modu- lation was interpreted in terms of an in-plane AFM ground state of Mn/W(110). The line section in the lower panel of Fig. 2b reveals, however, that the magnetic amplitude is not constant but modulated with a period of about 6 nm. Further, the magnetic corrugation is not simply a symmetric modulation superimposed on a constant offset I0 of equation (5) (see Methods). Instead, we find an additional long- wave modulation of I0 (blue line), which we ascribe to spinorbit coupling induced variations of the spin-averaged electronic struc- ture14 . When using in-plane sensitive tips, the minima of the mag- netic corrugation are found to coincide with the minima of the long-wave modulation of the spin-averaged local density of states. Within the field of view (Fig. 2b), three antinodes of the magnetic contrast is always achieved at lateral positions where the magnetic moments are largest, independent of mT, in case (2) a rotation of mT can shift the position of maximum spin contrast. Such a rotation of mT can be achieved by subjecting an in-plane sensitive Fe-coated tip to an appropriate external magnetic field16,17 (see sketches in Fig. 3). For samples without a net magnetic moment, it is expected that the sample magnetization remains unaffected. The SP-STM images and line sections of Fig. 3 show data taken at a perpendicular field of m0H 5 0 T (Fig. 3a), 1 T (Fig. 3b) and 2 T (Fig. 3c). Using the encircled adsorbate as a marker, we observe maximum magnetic contrast at this lateral position in zero field, indicating large in-plane components of the sample magnetization here. This is also corroborated by the line section, whichin agree- ment with the in-plane sensitive measurements of Fig. 2bshows W W ca b W Mn Mn Mn [001] [001] [001] [110] 10 nm 2 nm [110] 0 0 4 8 5 Lateral displacement (nm) Corrugation(pm) 10 15 SDW h-SS c-SS [110] Figure 2 | SP-STM of the Mn monolayer on W(110) and potential spin structures. a, Topography of 0.77 atomic layers of Mn on W(110), b, high- resolution constant-current image (upper panel) of the Mn monolayer taken with a Cr-coated tip (tunnelling parameters: I 5 15 nA, U 5 13 mV). The stripes along the [001] direction are caused by spin-polarized tunnelling between the magnetic tip and the sample. The averaged line section (lower panel) reveals a magnetic corrugation with a nominal periodicity of 0.448 nm and a long-wavelength modulation. Comparison with a sine wave (red), expected for perfect AFM order, reveals a phase shift of p between adjacent antinodes. In addition, there is an offset modulation (blue line), which we attribute to a varying electronic structure owing to spinorbit coupling. c, Artists view of the considered spin structures: a spin-density wave (SDW), a helical spin spiral (h-SS) and a left-handed cycloidal spin spiral (c-SS). Mn/W(110) Spin spiral propagating along 110 crystallographic direction
52. 52. O acoplamento spin-rbita pode favorecer a ocorrncia de ordenamento magntico no colinear 0 2 4 6 8 10 12 lateral displacement (nm) 2 2.2 2.4 2.6 )(tnemecalpsidz +2T 0T -2T 0 T (c) +2 T (b) d /dI ULO HI external magnetic field Cr/W-tip +2 T -2 T (a) FIG. 2 (color). SPSTM measurements of Fe chains on Ir(001). (a) and (b) Typical sample area of 30 30 nm2 measured with an Fe- coated W tip without and with an applied external magnetic eld of B 2 T perpendicular to the sample surface, respectively, (constant current images colorized with simultaneously acquired dI=dU maps, measurement parameters: U 500 mV, I 5 nA, T 8 K). (c) Topographic line proles of the same Fe chain at B 0 T and B 2 T measured with a Cr-coated tip. The insets show schematically the tip magnetization and how a 120 spin spiral, which is inverting in opposite elds, could explain the experimental results. PRL 108, 197204 (2012) P H Y S I C A L R E V I E W L E T T E R S week ending 11 MAY 2012 Fe/Ir(001) Matthias Menzel, et al PRL 108, 197204 (2012) Bi-atomic Fe chains on Ir (001) surface
53. 53. O acoplamento spin-rbita pode favorecer a ocorrncia de ordenamento magntico no colinear M. M. Bezerra-Neto, et al, Sci. Rep. 3, 3054 (2013) Fe/Pt(111)
54. 54. A interao spin-rbita promove a inter-relao entre carga, spin e momento angular orbital em sistemas nano-estruturados.
55. 55. Isto amplia signicativamente as perspectivas na rea de spintrnica.
56. 56. A interao spin-rbita causa o efeito Hall de spin (SHE)
57. 57. Spin-Hall effect 7/8/12 Figure1 : Magnetism: A flood of spin current : Nature Materials NatureMaterials ISSN14761122 EISSN14764660 Figure1Interactingchargeandspincurrents. Fromthefollowingarticle Magnetism:Afloodofspincurrent SadamichiMaekawa NatureMaterials8,777778(2009) doi:10.1038/nmat2539 a,b,SpinHalleffect(a)andtheinversespinHalleffect(b),wherethelongitudinal chargecurrentisconvertedintothetransversespincurrentandviceversa. Uma corrente eltrica uindo em um material no magntico com SOC gera uma corrente transversa pura de spin M. I. Dyakonov and V. I. Perel, JETP Lett. 13, 467 (1971) J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999) Y. K. Kato et al., Science 306, 1910 (2004) Charge current hS+ i i(t) taken at position x 0 35 mm; the blue curve is taken at x 0 35 mm, corresponding to the two edges of the channel. These curves can be understood as the projection of the spin polarization along the z axis, which dimin- ishes with an applied transverse magnetic field because of spin precession; this is known as the Hanle effect (8, 20). The data are well fit to a Lorentzian function A0/ [(wLts)2 1], where A0 is the peak KR, wL 0 gmBBext/I is the electron Larmor precession frequency, ts is the electron spin lifetime, g is the electron g factor (21), mB is the Bohr magneton, and I is the Planck constant. is estimated to be less than 10 , which is below our detection capability. An interesting observation is that the width of the Lorentzian becomes narrower as the distance from the edge increases, correspond- ing to an apparent increase in the spin lifetime (Fig. 1E). It is possible that the finite time required for the spins to diffuse from the edge to the measurement position changes the lineshape of Bext scans. Another conceivable explanation is the actual change in ts for spins that have diffused away from the edge. Be- cause these spins have scattered predomi- nantly toward the center of the channel, spin relaxation due to the Dyakonov-Perel mecha- nism (20) may be affected. In Fig. 1G, Bext scans at x 0 35 mm for a range of E are shown. Increasing E leads to larger spin accu- mulation (Fig. 1H), but the polarization satu- rates because of shorter ts for larger E (Fig. 1I). The suppression of ts with increasing E is consistent with previous observations (22). The homogeneity of the effect is ad- dressed by taking a two-dimensional image GaAs (23) may give rise to Hall effect, this is unlikely ble spin splitting has be unstrained n-GaAs (24). Me also performed on anothe channel parallel to [110], a same behavior was reprodu Effects of strain. The stra ple, in contrast, offers the pos ing the intrinsic spin Hall effec extrinsic effect. The lattice strain in the InGaAs layer (25 relaxation causes the in-plane tropic (26). Using reciprocal s x-ray diffraction at room tem mined the in-plane strain alon to be 0.24% and 0.60%, re strain along [001] to be 0.13 layers show electron spin p applied magnetic field when electron spins are dragged wi field (24), which is due to an magnetic field Bint perpendi growth direction and the elect A possible explanation for s be strain-induced k-linear sp in the Hamiltonian, which is rise to the intrinsic spin Ha The strained InGaAs sam into a channel oriented alon 33 mm, l 0 300 mm, and h 0 wavelength of 873 nm and of 130 mW were used for t and typical results are show prisingly, the spin polarizatio Bext 0 0 mT, and we observe from Bext 0 0 mT. We attrib to the presence of Bint. Beca respond to the sum of Bext polarization is maximum at Bext cancels out Bint. The square-wave voltage causes from both positive and nega directions, resulting in a doub Although the spin polarizati Position (m) 0 20 40-20-40 Position (m) 0 20 40-20-40 (noitisoP)m 0 50 100 150 -50 -100 -150 ns (a.u.) Reflectivity (a.u.) 0 21-1-2 1 2 3 4 5 A B Fig. 2. (A and B) Two-dimensional images of spin density ns and reflectivity R, respectively, for the unstrained GaAs sample measured at T 0 30 K and E 0 10 mV mm1. 40 0 -40 Btxe)Tm(A0()dar 2 0 1 -1 -2 0 1-1 2-2 Position (m) Position (m) 0 40-20 E // [110] E // [110] A B C D 20-400 40-20 20-40 -20 20 Kerr rotation (rad) Fig. 3. Crystal orientation dependence of the spin Hall effect in the unstrained GaAs sample with w 0 77 mm. (A and B) KR as a function of x and Bext for E // [110] and E // [110], respectively, with E 0 10 mV mm1. A linear background has been subtracted from each Bext scan. (C and D) Spatial profile of A0 for E // [110] and E // [110], respectively. www.sciencemag.org SCIENCE VOL 306 10 DECEMBER 2004 ~Js = H ~Jc
58. 58. A interao spin-rbita d origem ao efeito Hall de spin inverso (ISHE)
59. 59. Uma corrente pura de spin uindo em um material no magntico com SOC gera uma corrente eltrica transversa/8/12 Figure1 : Magnetism: A flood of spin current : Nature Materials AboutNPG ContactNPG Accessibilitystatement Help Privacypolicy Useofcookies Legalnotice Terms Naturejobs NatureAsia NatureEducation RSSwebfeeds NatureMaterials ISSN14761122 EISSN14764660 Figure1Interactingchargeandspincurrents. Fromthefollowingarticle Magnetism:Afloodofspincurrent SadamichiMaekawa NatureMaterials8,777778(2009) doi:10.1038/nmat2539 a,b,SpinHalleffect(a)andtheinversespinHalleffect(b),wherethelongitudinal chargecurrentisconvertedintothetransversespincurrentandviceversa. Inverse spin-Hall effect ~Jc = D ~Js
60. 60. O ISHE usado para detectar o bombeamento de spin 2 3 (mV) (a) (b) (c) (d) dI/dH(arb.units) 15 20 25 FMR ) H (mT) 50 100 8 GHz ISHE: Powe signal generator 1 2 3 A in-pla x y z D. Wei et al, Nature Commu. | 5:3768 | DOI: 10.1038/ncomms4768 One of the main experimental diculties is to isolate it from the FMR signal which has the same frequency. Y. Tserkovnyak et al, PRL 88, 117601 (2002). DC and AC-ISHE
61. 61. ac-ISHE foi observado recentemente ac-ISHE is 12x larger than the dc-ISHE D. Wei et al, Nature Communications 5, 3768 (2014) Ni80Fe20/Pt Discussion The measured a.c. signals may also be generated by par mechanisms instead of ISHE. These are (i) inductive couplin the magnetization with the conducting wire loop used signal detection and (ii) anisotropic magnetoresistance (AM The magnitude of both of these effects will be addressed in following. The exclusion of an inductive signal component in presumed ISHE signal cannot be based on angular or rf-p dependency since the amount of out-of-plane magnetic generated by the in-plane component of the magnetization the same angular and power dependence as the ISHE signal2 illustrated in Supplementary Fig. 4. For this reason, we u series of different conducting materials with different spin angles to quantify the importance of inductive coupling in experiments. In Fig. 4b,c we show the a.c. voltage si generated at 8 GHz by Pt/Ni80Fe20, Au/Ni80Fe20, Cu/Ni80Fe20 Al/Ni80Fe20 bilayers with identical thicknesses (only the NM layer has a thickness of 20 nm). The experiments are perfor for both in-plane and out-of-plane congurations (cf. Fig. The scale bar for the out-of-plane data in Fig. 4c was chosen that the signal amplitude for the Pt/Ni80Fe20 measureme equal to the in-plane case. From the fact that the signa Au/Ni80Fe20 (90 mV) is about 10% of the Pt/Ni80Fe20 s (648 mV) it becomes clear that the inductive contribu must be less than 10% for the Pt/Ni80Fe20. For further d 30 40 50 60 0 50 100 d.c.-ISHE a.c.-ISHE 6 GHz 0H (mT) 150 200 2 Uac(mV) Cu 20 nm Al 10 nm Au 10 nm Uac (V) 200 400 In-plane Out-of-plane3 Cu 20 nm Al 10 nm Au 10 nm Uac(V) NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4768 ARTIC T f p d g t i s a e g A l f T t e A ( m w F v T e i t a a g F s S i c t c 30 40 50 60 0 50 100 d.c.-ISHE 0H (mT) 60 60 8080 0 1 2 Uac(mV) 100 Cu 20 nm Al 10 nm Au 10 nm Pt 10 nm 0 Uac (V) 100 200 400 In-plane Out-of-plane3 Cu 20 nm Al 10 nm Au 10 nm Pt 10 nm 0H (mT) 0H (mT) Uac(V) Figure 4 | Comparison of the a.c.- and d.c.-ISHE amplitude and material dependence. (a) Comparison of the a.c.- and d.c.-ISHE voltages for the same device measured at 6 GHz in the out-of-plane excitation conguration. The a.c.-ISHE voltage is B12 times larger than the d.c. one. (b,c) Comparison of the a.c.-ISHE signals for Pt/Ni80Fe20, Au/Ni80Fe20, Cu/Ni80Fe20 and Al/Ni80Fe20 measured at 8 GHz. (b) Shows data for samples with in-plane excitation while (c) shows the corresponding measurements with out-of-plane excitation. All NM and FM layers have a thickness of 10 nm. Only for NM Cu the NM layer is 20 nm.
62. 62. V h(t) H0 M Bombeamento de spins por FMR A. Azevedo e S. Rezende, UFPe
63. 63. Dependendo da combinao filme-substrato e da espessura do filme a direo de equilbrio da magnetizao pode ser ou ao filme. Anisotropia magntica perpendicular ? k Fe/Au t2ML Co/Au t14 Co/Pt t4.5
64. 64. Uma maneira de aumentar a densidade de gravao atravs do armazenamento perpendicular possvel aumentar em at 10 vezes a densidade de gravao Atualmente vrias empresas utilizam esta tcnica na fabricao de HDs Gravao perpendicular
65. 65. Conjunto de estados discretos com energia Perpendicular recording http://www.youtube.com/watch?v=pE-RqAVT2g0 http://www.youtube.com/watch?v=xb_PyKuI7II Gravao perpendicular
66. 66. Gravao perpendicular
67. 67. Magnetoresistncia Tnel Fe/MgO/Fe TMR ~600% a T=300K, e 1100% a T=4.2 K Appl. Phys. Lett. 93: 082508 (2009). PL = L L L + L PR = R R R + R I L R + L R I L R + L R M. Julliere Phys. Lett. 54A, 225 (1975) Modelo: TMR = I I I = 2PL PR 1 PLPR (E) EF E (E) E (E) EF E (E) E