1. Magnetoresistncia Gigante: Precursor da Spintrnica R. B.
Muniz Universidade Federal Fluminense Colaboradores: D. M. Edwards
J. Mathon ! Filipe S. M. Guimares
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. 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. 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. Fe/MgO/Fe Cu Co Multicamadas de Co/Cu(001) Nanoestruturas
metlicas: alguns exemplos
6. Nanoestruturas metlicas: alguns exemplos Nanofios de Au
sobre NiAl As propriedades fsicas desses sistemas so muito
diferentes das dos seus constituintes
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. 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. 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. 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. Estas descobertas causaram um grande impacto na indstria
magntica Sensores magnticos de alta sensibilidade
13. Armazenagem de informao Em meios magnticos, os bits so
unidades magnetizadas em uma direo ou outra 0 1
14. Armazenagem de informao Para aumentar a capacidade de
armazenamento precisamos reduzir o tamanho da unidade magntica que
armazena os bits
15. Corrente eltrica gera campo magntico Importncia tecnolgica:
sensores magnticos de alta sensibilidade
16. Sensores indutivos Lei de Faraday Campo magntico pode gerar
corrente eltrica Importncia tecnolgica: sensores magnticos de alta
sensibilidade
17. Os primeiros discos rgidos comerciais utilizavam sensores
indutivos para escrita e leitura
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. 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. A corrente induzida depende da taxa de variao do uxo do
campo magntico atravs da espira v iind
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. Sensor magnetoresistivo V Magnetoresistncia gigante
23. Impacto na Capacidade de Armazenamento
24. Explicao para o efeito GMR
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. 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. Estados eletrnicos Bandas de energia 3s 3s 3p tomo isolado
5 tomos prximos 3p Muitos tomos prximos 3s 3p
28. Esquematicamente: Estados eletrnicos (E)
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. 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. Propriedades eletrnicas
32. Eltrons possuem massa 9.109382 91 -31 e-
33. Eltrons possuem carga e- ~F --- +
34. ? E o spin? e-
35. O experimento de Stern-Gerlach mostrou que partculas
possuem um momento angular intrnseco
36. 9.109382 91 -31 Spin uma propriedade intrnseca do eltron ~F
+e-
37. e- Ao medir os spins, obtemos valores discretos e-
~B(~r)
38. Eletrnica convencional
39. Em um metal, os eltrons de conduo so livres para se
movimentar e- e- e-e-
40. Dispositivos eletrnicos convencionais no levam em conta o
spin eletrnico e-
41. Sensores magnetoresistivos
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. 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. 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. 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. 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. 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. Manejo do fluxo de carga regulado pelo spin eletrnico
Controle da corrente
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. A interao spin-rbita pode afetar substancialmente as
propriedades magnticas de nano-estruturas
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. 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. 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. A interao spin-rbita promove a inter-relao entre carga,
spin e momento angular orbital em sistemas nano-estruturados.
55. Isto amplia signicativamente as perspectivas na rea de
spintrnica.
56. A interao spin-rbita causa o efeito Hall de spin (SHE)
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. A interao spin-rbita d origem ao efeito Hall de spin
inverso (ISHE)
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. 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. 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. V h(t) H0 M Bombeamento de spins por FMR A. Azevedo e S.
Rezende, UFPe
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. 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. 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. Gravao perpendicular
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