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Estudo de propriedades estruturais e magnéticas de filmes epitaxiais de MnAs sobre GaAs (001)

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4 # $ % # D 3 3 G # D α # D β3 $ # 2 # % % $ 8 # # % ? & 3 C G @ 2 # 2 # $ 2 3 G # ' B B " \ = "8> D " . 1 3 % 3 2@ G B G @ $ 8 2 C 2 C # D % % =55M>$ 3 3 # % G $ G # G 2 $ # 2@ D $ 8 ! > # ? # 2 % % 2 # ] > ? N # % $ 2 3 2 2 # 2 # # # 2@ # # 2 # E D 3 G 2 3 # # 2@ # $ 3 G N # % # # D 3 D % 3 G N G G $ G 2 # # 2 #

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U 4$T! F 2 XKY$ + C# J5 -5 # D = G N # # 2 >3 G JL -L 2 ' $ " G G # D $ ' 2 # D 3 # 4$V3 . G ' 2 G # D 3 2 2 # $ 4$V! ' 2 # 2 # D XKY$ # =- > G =-5> # D $ " 3 A # 2@ 3 A =-5>$ " 3 # 3 3 # $ % # ' . D 2 G # 2 N 3 # C ' 2 $ # -J / D -' 2

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M6 D . > C =55M> % = C C > O$4 $ O$4! = > 2 2 DC % % 3 = > 2 # C C =55M>. % C =555M>. % $ D DC # O$4 @ G # $ ' @ # 2 # 3 + X45Y N !3 DC 3 2 X555MY3 ! 3 G A # 3 2 Y 5 4 MM X A # 2 XMM55Y3 # O$M$ 8

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MT 8 N =$> # # 2 N # 33 ' N XMUY3 G 2 O$M 2 ! $ = 5− =O$M> 0 G _M34 # O$43 2@ XMM5Y XMM5Y % $ N G 3 G $ ∼O5d $ "∼Sd$ # 455 P 3 # . # 2@ G # D @ N $ " 3 G # # 3 3 2@ # = MT5P 65P > # D # G 45 ' G $ 8 G @ # 2@ # A $ % G 2 X555MY % 3 # O$O Q X45Y # % * % # 2 G V =445> % . 6 =5554> % $ ' 6*V ' N O5d Td$ 8 . # 2 # C 3 G @ 6*V . @ D 4 % 3 ' V*U$ % # 2 # ' G 2 X555MY % D @ # 2@ # $

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MV % C @ 2 XMM45Y3 $"3 G D @ # B N # 2@ 2 # G @ 3 # O$6$ O$6! # % * % 2 XMM45Y3 % G # 2@ X45Y$ 2 # N DC N 2@ @ $ " 2 D 2@ # 3 @ $ 8 . 3 G 2 XMM45Y3 D # $ " . G # 2@ 3 G C C N $ # # 2 # D 2 # @ # $ Y 555M X Y 5 4 MM X

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MU O$T! = .#> # # # % * % X46Y$ = > C# # 2 2 B 4V3KP $ % # D # # D # 2 # # $ % 2 Y 55 M M X 3 G A # 3 # α [O G # β$ % # O$T # 2 # 3 ' G 2 # # $ " G ! M> " - f 64P 3 = > G # ' 2 # 2 # α= > 2 XMM45Y] 4> 2 3 # = > # 2 G # D 2 X555MY$ # 3 G # D # 2 3 = > = >$ O> % = > =#> G # α 2 $ = > " 2 =µ > % = >

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MK % # O$T C# # 2 2 B # O$T $ " . G 2 # D # E 3 λ# Mµ $ -G λ# 2 # X4TY # X4OY$ 8 G # O$T G D MTP 3 BC D @ # G # Q $ 2 2 G 3 BC # 3 N # # 2 % $ 3 N ! # 3 G C = G ? > ED 3 3 2 2 XKY$ 3 @ # . Q D 3 G 2 3 3 ' 3 G ? C $ G # G G # 2 3 2 Q 3 2 $ % 3 @ # . Q G # B # $ Z G G # % # 2 .D3 # 2 # D 3 # D $ D # 2 .D 6$

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45 2 $ % 2@ # % % =55M> %5 15G ! • % 2 - .%5! % 2 2@ C# # ! XM M 55Y % ** X55MY % ] Y 5 4 MM X % ** XMM5Y % ] X555MY % ** XM M 5Y % ] G ' 2 # 2 3 D,3 , =[T5 8 > 2 XMM45Y % G G 2@ , f M5 :8 $ " 3 D #C ' 2 C 2@ XMM45Y % $ • % 2 - .15! + 2 XM M 5MY % 3 2@ 2@ C# # % % ! XM M 5MY % ** X55MY % ] Y 5 4 MM X % ** XM M 5Y % ] XM M 54Y % ** XMM5Y % ] + 3 D, G D #C ' 2 2@ XMM45Y % $ J # . G D #C ' 2 D # % 2@ $ % %5 15 3 G D 2@ 2@ # O$V$ D G # 2 2 DC 53 M 4 b$

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4M O$V! F 2 2 DC 2 C # % $ . # %5 15 G D ! A 2 XMM5Y XM M 5Y % 3 3 D ! # $ 0 DC D ! # # N D O5P %M 1M3 D ! 2 G %5 15$ 0 DC O5P3 D ! # %4 14$ 0 D ! A # 3 N %b 1b$ C G ' 2@ # % % =55M> C 2 D X4SY$ 5!6! 8 # % % =55M> G # 3 5 )' )( $6 7 8 3 1 % 3 $ / ' e '$ ' B G # 3 D 3 O$M! 2

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46 - X4K3O5Y$ # # E G # # ! 4 O 4 M 9 9 7 9 ( = =6$4> 0 +M3 +4 +O & C # D ? 2@ 7 # C 3 G XMOY! : ; ; 7 = $ 8 # G 2@ C C B $ G & C G # 2 # D .D$ 6! !2 = .D = C > G # N α$ % ' r 3 C # r C r $ % # 6$M ! 6$M! .D$ % 2 ' # 2 A G 2 , ' XOMY 2 G 2

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4T # N 3 ! # , <α=0# = # > # , +<α=0# = > =6$O > =6$O > " 2@ α # N <α= +<α= ' # D XO4Y$ ^ # D .D # N G # D B # $ # Q # D D G # 2 .D G $ " .D3 # 2 XOOY! β δ β π λ 9⋅>⋅ + = − + − = M 4 M 4 =6$6> + G 2 3 9 3 > & Q _ "? " C β # 2 $ δ .D δ [ M5.T3 G # 2 G .D3 G M G M5.T$ # # Q # D D .D$ + 3 N # D .D # G N ? C N =α > $ 8 N ? . N G # 2 # D $ % # D D G _M3 N ! α α α α =6$T> " α 53MP MP XO6Y$ 3 # 2 .D G N ? # D XOOY!

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4V M> ^ α ff α . G +@ # 2 2 A # 3 # 6$4$ # 2 .D$ # 2 N # = $ >$ " . # 2@ G 3 3 2 @ # ] 6$4! # 2 .D$ 8 G # D # C A # $ + G N ? # D # $ 4> ^ α [ α # 2 3 & A & $$ $ % # 6$O ? $ + # 2 . G ! b % # # 2 ] b % G 2 # D G = > C # 2 3 # A 2 # +] b 0 α G α # # 2 # D N ? ] G " ' (

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4S 6$O! # 2 .D ? = >$ 8 # D .D ED N # D D 2 # 2 A # $ % ' 2 = >$ " . # 2 # G # # 2@ ? $ " # # . 3 # ' 2 3 # 2 2 # D ] 6! !5 7 K % 1 = G 2 6$M> N N # 2 G D N 4θ # D $ % 1 2 G # # 2 G # D 3 2 G ' $ - 2 # 2 # 3 G # $ % # 2 ? # 2@ G $ " # # # 2 G 9 - N # 2 .D G # 2 = G C 2 >$ G

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4U D # 2 G # # 2@ # $ F 2 9 # 2 $ % 2 9 G 2 1 C # G # # 9 XMOY$ % # 9 C $ % # 6$6 2 & =M55> 2 # 2 6$6 $ % # 6$6 M55 # 2 r r r − = 5 = θ.4θ> # 2 = : > = gGgL"π? g 3g_g g_"π?λ>$ 6$6! = > F 2 & $ = > F 2 =M55> 2 # 2 $ % D D 7 & B 7θ.4θ<! h &  J 2 2 # 2 $ + # 6$6 2 M55 # 2 $ D # N 1 θ1 # D # $ 8 # 2@ G $ = > = > O 4 M

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4K h θ.4θ  J r $ + # 6$6 M55 2 # 2 G N 1 $ D ' = N θ = N 4θ> # $ " Gi # 2@ < =$ % D # ' C $

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O5 % # # D .D3 ' 2 G ' RF 4 G C # 2@ $ % E 2 2 3 # ' C 2 E ' # D C # ' $ % # 3 &) & 3 $ 3 3 3 # # Q XOTY$ % # 6$T G '! 6$T! G ' RF 4 # 2 .D 2 $ 8 E .D3 # 6$V 3 G # 2 # ' # D .D # D Q BC D $ 8 3 # 6$V 3 0 =MMM> 3 # N 3 D 2 C # D 3 3 # 2 $ # Q

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OM = > = > 6$V! = > F .D = > 0 / ' RF 4 /+/0$ % ' # # ' $ ' # ' # D O5 M # D ' S$K6 C M35 DM35 4$ % # D 2 M5555$ % E # D B # C ' # D $ % # Q C # D .D 2 $ 8 G 3 # Q =, 1 F3 # 6$S> G C # 2@ # 3 G C ' 2 # D # $

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O4 6$S! # Q , 1 F$ + # # Q C G $ 8 # Q G $ - ? 2 ! θ3χ φ=# 6$U>3 G # D G N 4.θ$ 8 C # D # E G # Q θ.4θ 2 4.θ$ + # G ' # 2 # Q $ # G # Q C G $ 6$U # Q # 2 .D RF 4 /+/0 # # % $ θθθθ 2&θθθθ χχχχ N R c 1 2 4.θ D 2

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OO % 2 # # Q # D .D # ' $ 3 N θ3 χ j # D $ 0 G =0" > . # ' D # D 3 # ' G θG 4.θ # $

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+ 2 D D ' 2 2 2 # # % $ 8 B G # Q RF 4 # D@ D # # O$V$ 8 2 2 # α β. % $ 6!5! " 01 0: 8 2 2 # 3 # Q 2 ' ' D ! = 2 > 2 # D $ X55MY % # 2 3 # χ _ 5P 2 XM M 5Y % # 2 3 # j _ 5P$ $ + D # ' # D C SV55 J $ 2 # % 3 C 2@ # $ # 'C θ.4θ $ % 3 2 4θ ≅4K3OP3 # G # =M M 55> % G %5G

(42)

O6 15$ 2 # / 1 3 . N G # $ 8 D 2 4θ ≅ OO3UP3 . # 2 =M M 5M> % G χ φ 5P 1M$ % # 2 C 3 # ' φ_ K5P 2 XMM5Y % # # 2 $ 0 D ! 2 # D =φ_5P # % φ_K5P 1>3 χ # DC 3 B 3 V5P # 3 O5P # kM M 55l # kMM 4 5l$ " # 2@ D 3 # 6$M G 2 N θ3χ j G 2 # 2 # $ + # %b 1b$ E 2 # 2 3 =& A & $$ >3 G . # ' 2 1 A # 3 # 2 # 2 G A 2 # $ " 2 3 χ K5P # # 2 N 3 D φG # ' θ$ . χ θ# D 3 φ.4θ %b 1b 4θ_ 4K3OP3 =M M 55> X4SY$ ' 6$M # ? 3 # ' C # D@ G A 2 $ + T ' 2@ ' 2 $

(43)

OT

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(44)

OV 8 ' # 2 # D B # 2 θ.4θ F $ " D ' # # # D =MM 55> # D A 2 .%5$ % # T P TT P D T G ' # # 2 $ Z 2 # % D % Q $ # 2 $ % # 6$M5 # G ! 6$M5! # , 3 G RF 4 2 $ 8 RF 43 . # . # # G G

B .4VO P =[M5I> TT P =[O4UI>$ %

535M P $ # B 3 G G 2 # D .D$ % # # B D $ G 2 # # ' 2 D = > D 2 G # Q 3 3 # 0 # D .D % = B 1 >

(45)

OS " $ 0 ' G # Q 3 $ + ED 2@ D 2 # # % $ ' 2 # I .E # D = ? %> G # Q 3 G # 2 .D C $

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01

" 2 # # % % # ' D 2 B 2 # 2 2 # $ % G 3 C # C 2 8 $ $ $ . + % " 2@ D $ 6!6! K 01 F ' # 2 .D # 2 G 3 & # 3 $ 8 # D DC 3 2 XMM 4 5Y3 G D #C ' 2 3 ? A $ 8 # # # 5 8 O :8 $ % # B A 2 # Q RF 4 /+/03 . B G 2 3 G # $ % # 6$MM # 2 D 3 # Q $

(46)

OU 8 B D # 2 # 2 # D #C ' 2 $ 8 T$ 6$MM! D 2 D # Q RF 4 /+/0$ 6!6!2 O + & P " 2 # # # % 3 ' # I .E = 8I > # 2 .D # 2 $ % 8I 2 # .E A # D ' # ' G ' ' # # ' ' 2 XOVY$ 8 C A ' # D XOSY G G ' 2 # $ 0 # ' 2 3 # $ " 3 ' I 3 B ' # 3 ' 2

0

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(47)

OK # # # XOUY G $ + D # # G ' # # I 3 # 6$M4 XOSY$ 6$M4! G # I XOSY ' ' ' ' 2 = > # $ + # I 3 2 ' 2 3 G # I 3 # # # D '$ % 2 3 2 D #C ' 2 3 G D XMM 4 5Y3 D ! % $ " ' 8I N A # 2 .D3 I # Q ' RF 4 /+/03 # 6$MO$ = VOT > # G G 3 G ' D & # 3 G O :8 $ % ' # # $ 8 I # ) $ + # 6$MO # A '$ J & # # 3 G D #C ' 2 D $ " # 3 # .D ' $

(48)

65 6$MO! D # I .E # Q ' RF 4 /+/0$ 8 B ' # I N A # 2 .D3 # 3 2 # $

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(49)

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+ D G # 3 G B # 2 # # # % * % =55M>$ 2 # # 2 2 # C # 2 α. % # 2 0M3 04 0O$ 3 # C G 2 # 2 # 0M 0O$ J G D # I .E N A # 2 .D 0M$ % D # 2 .D 2 # 2 N # α β. % # 2 0M$ + # ? G ? 2 # D 2 # $

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" 2 # % * % # ' C # 2@ D 3 6$M$ # Q 2 6$O$M3 2 2@ D # G 2 # $ G % C 2 =55M>3 # D@ % ED $ =55M>. % XMOY3 # D =554>$ 8 C# # T$M T$M

(50)

64 θ.4θ 3 φ_χ_5P3 0M 0O D =554>. % 3 G SV55 J 4θ_ OO3TP$ T$M! " # # 2 θ.4θ = > 0M = > 0O$ % # # 2 # T$M T$M 3 # % 4θ_OO3TP3 4θ_4K3OP3 G 2 2@ %5 15 $ % # ' = > = > 4U 4K O5 OM O4 OO O6 OT M5.O M5.4 M5.M M55 M5M 7 G α α α α& 2 7 α α α α& 7L ( ! ! 2θθθθ 4U 4K O5 OM O4 OO O6 OT M55 M5M M54 M5O M56 M5T 2θθθθ ( ! ! 7L28 ββββ& 2 7 αααα&

(51)

6O # 3 4TP 0M M5P 0O3 G C# # T$M D G # D =M M 55>3 4θ_4K3OP3 # A # Q 3 4θ_4K3SP3 G # D =554>$ C# # T$M M5P 3 2 # α$ % C# 0O3 G D 4θ_OO3SP3 # C # D =M M 5M>3 G j_χ_5P 2 2@ 1M = 6$M>$ C# 0M$ " # D 2@ %5 153 0M G 0O3 # ' θ.4θ3 3 # 2@ ! _ 5P3 _ O5P 4θ _ T4P # 2 %5 _ 5P3 _ O5P 4θ _ OO3UP # D ? 15$ % # T$4 0O! = > = > TM$5 TM$T T4$5 T4$T TO$5 M .T M .6 M .O 5$5M 5$M M β α -_45 P λ_M3V4K66a ( ! ! 2θθθθ T$4! C# 0O # D ! = > =4 4M5>3 G # %5 = > =MM5M>3 G # 15$ % 2 # 2 # T$43 D ? 2@ %5 15$ ' # T$M # # D 3 G 15 4d # $ 0 D ? 2@ %

OO$T O6$5 O6$T M5.4 -_MK λ_M3VOMOSa α 2θθθθ ( ! !

(52)

66 G 13 # ' j.4θ # 2@ 2@ # T$O ! T$O! " # # 2 j.4θ 0O3 =MM55>3 # 2 2 1b$ 8 # 2 # 2 =MM55> # α β$ " 3 # 2 2 1b3 2 6$O$M$ " G 0O 3 2@ ! %53 153 1M3 1b$ # % % $ % 0M3 04 06 # $ " 0M 06 # # D@ # A 2@ %5 = C# # T$4n>$ C 043 # 2@ ! j_5P3χ_O5P 4θ_4K3OP # M M 553 G 2 %M 1M] 2 j_K5P3 χ_.O5P 4θ_4K3OP 3 # =M M 55>3 G G # 2 %M$ % # T$6 C# θ.4θ 04 45P !

4U$T 4K$5 4K$T O5$5 O5$T OM$5

M5.V MDM5.T MDM5.6 β α λ_M3VOMOSa -_OT ( ! ! 2θθθθ

(53)

6T

4U$T 4K$5 4K$T O5$5 O5$T

5$555 5$55T 5$5M5 5$5MT 5$545 5$54T β α - _ 45P λ_ M3VOMOSa

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!

!

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θθθθ T$6! " # # 2 θ.4θ =j_K5P3χ_.O5P> 04$ + C# 3 # α β. % D ? # $ 8 # # 2 2 # . =M M 55> # 2@ %M3 6$M = 6>$ - 2 5 C X4S3 D Y$

8!2 ?

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' G 2 # % 3 C # 2 $ 8 B # 2@ 2 # α. % β. % $ + O BC # G 2 # # # % $ + # 2 3

(54)

6V G D ? # D Q G OTP $ G 3 G # $3 # T$T # 2 .D3 = # D _SV55 J> # %5 0O3 $ " G # 3 2 =M M 55> # α. % =554> # β. % $ 4K$5 4K$4 4K$6 4K$V 4K$U O5$5 5 MDM5T 4DM5T ODM5T β. % 8 Q α. % , D - P ( ! ! 2θθθθ MT 45 46 4K OV 6M 6T TM T$T! # 2 .D 0O3 %53 # D =MM55> # α =554> # β # G $ B # # G # # D@ $ 2 # # % C # 2 .D3 G # G # $ 8 # # 2 # α. % D 3 2 # α β. % $ G C D $

(55)

6S 8 C B . # 2 / ' G C 3 G 2 =T$M>! 4 4 4 4 4 4 4 M M M 5 M M              − + +               − + + = D ! ! D ! ! =T$M> 0 3 ! 2 D # α = _M> β= _4>$ % 2 N D3 # 2 α. % 2 =T$4>$ 4 4 4 4 4 M M M 4 M M M * * * 7 D 7 D 7 D 7 + = α =T$4> 0 73 # # D@ # $ 3 D ' 2 # # 2 # α. % D 3 G # $ 8 $ 8 C# # T$V 2 %5 0O$ # # 2 =M M 55> # $

(56)

6U 5 M5 45 O5 65 T5 V5 S5 - %5 0 -' 01 αααα & 7 C T$V! 2 G α. % # 2 2 %5 0O$ + # % # 3 G # G G 3 ' 2 G # Q 2 $ G 3 2 # D 2 $ + 2 # # $ ^ # 2 # ' 3 # 2 3 2 # G C # G C $ 3 G 2 # # G # $ % # T$S C# 0M3 04 0O$ 8 B # 2@ $ " 3 0M # A

(57)

6K 2 %53 04 2 %M 0O3 2@ %53 1M 1b$ M5 45 O5 65 T5 V5 5$5 5$4 5$6 5$V 5$U M$5 0O! % 5 0O! 1b 0O! 1M 0M! % 5 04! % M

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(58)

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(59)

TM 5 M5 45 O5 65 T5 V5 5$5 5$4 5$6 5$V 5$U M$5

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(60)

T4 8!5!2 O + & P " 2 # 3 ' N # 2 .D # I . E = 8I >3 BC 63 # # Q RF 4 /+/03 G # I $ 8 # # " 3 ' G # 3 # 2 .D $ D 0M3 C =M M 55> # T$M5 # I OUP 3 46P M5P $ .4 .M 5 M 4 .M$5 .5$T 5$5 5$T M$5 E P ! ! ? P -_OUP -_46P -_M5P T$M5! , 0M 8I OUP 3 46P M5P $ " C# # T$M5 $ 8 I D 3 A ' 2 C =6 4> C ' A TP 3 BC $ 8 I A G

(61)

TO 2 = D #C ' 2 >$ ^ G # α =M5P 3 D >3 I # G G 3 G 2 # 3 # α # β =O6P 3 D > I G # $ 3 ' 0 I # 2 # 2 α. % # 2 .D$ 8 # T$MM # 2 α. % # 2 $ T$MM! F # 2 α. % # 2 .D # I N ' RF 4 /+/0$ % # T$MM # 2 α. % # 2 .D ' 2 ' # I # 2 0M$ " 3 D ? # D O5P 3 N G 2@ # $ + # D 45P O5P G G ' 2 5 M5 45 O5 65 T5 V5 S5 5$5 5$4 5$6 5$V 5$U M$5

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(62)

T6 G 2 # 2 α$ # I ' 2 ' ' 2 # X65Y$ 2 # % * % # ? 65. 6O$

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(63)

TT " C 2 N # 2 # '. ' C # 2 N 2 N % = >3 ' 2 =T$6>! $ − = ∆ =T$6> + D # ' # =# 6$MM> # 2 RF 4 /+/0$ 8 B # D =554> # # G G B # D@ =455> =545> # $ % ' 2 G # 2 .D ? # D@ $ % C # 2 3 N # 2 3 4θ3 ' 1 = G 2 6$M> N # D 3 $ 8 ' D # λ_ M3K5Sa G # A 2 I =VTOK J>$ 8 # 2 # D@ =455>3 =545> =554>3 C 3 # T$MO$ 8 C# # # # G ' 2 2 3 # # 2@ $ % 2 # 2 N # α β # 2 $ D N 3 B 3 2 % # # D $ " 3 G 2 T$T! =-> _ 3=-5>×=M`αo =-.-5>> =T$T> + G 2 3 N - -53αo # D % % $ " % # # N $

(64)

TV % D αo C XS3M53M6Y! • %  αo _ V×M5.VI.M • % 3 N  αo_ U×M5.TI.M • % 3 N # α  αo_ .M×M5.6I.M3 -5_ 45P ] • % 3 N # β  αo_ U×M5.TI.M3 -5_ 65P ] T$MO! F 2 @ # 2 # D@ > =455>3 > =545> > =554> C 0M$ 8 # 2 # D =455>3 # T$MO 3 G D 2 2 # 2 $ C 2@ 3 X545Y X554Y D ? # 2 # VM$5 VM$T V4$5 V4$T VO$5 VO$T ' ββββ ' αααα M5P TP 5P 6TP 65P OSP OTP O4P O5P 4SP 4TP 45P MTP T5P -_TTP ( ! ! 2θ θ θ θ

OU$5 OU$T OK$5 OK$T

' ααααL ' ββββ TP M5P MTP 45P 4TP 4SP O5P O4P OTP OSP 65P 6TP -_T5P ( ! ! 2θθθθ VM$5 VM$T V4$5 V4$T VO$5 VO$T ' ββββ ' αααα M5P TP 5P 6TP 65P OSP OTP O4P O5P 4SP 4TP 45P MTP T5P -_TTP ( ! ! 2θ θ θ θ = > = > = >

(65)

TS D 45P $ " # D =545>3 ' 2 3 G G =554>3 # 2 # 2 $ ' # 2 .D # T$MO >3 > >3 2 # D@ =455>3 =545> =554> # 2 N Q # α β # % $ 8 C# # T$M6 T$MT $ .M5 5 M5 45 O5 65 T5 T$S5 T$SM T$S4 T$STV T$SV5 T$SV6 T$SVU O R 7 C 0 $ $ J 2 - $ % % T$M6! " N # 2 0M$ 8 D # = > = >$ % B 2 % 2 2 # # D % $ 8 D # T$M63 G % G # % * % =55M> N G Md % $ " . G N = D !> 2 2 # MP $ % 2 # C 2 G # A 2 3 ED D =

(66)

TU # > G 2 # # D % $ # G N N ) 2 $ T$MT! " N = > = > 3 # 2 0M$ 8 D # α # # β N # $ % B 2 % 2 2 # # D % $ 5 M5 45 O5 65 T5 V5 O$V6 O$VV O$VU O$S5 O$S4 O$S6 J 2 - $ % % O R 7 C α. % 3 $ α. % 3 $ β. % 3 $ β. % 3 $ 5 M5 45 O5 65 T5 V5 V$O6 V$OV V$OU V$65 V$64 V$66 V$6V O R 7 C α. % 3 $ α. % 3 $ β. % 3 $ β. % 3 $ % = > = >

(67)

TK 8 N # N % 3 D # αG # β N % :3 G # ? D . != > $ " D % 2@ Q G D % =55M>$ + # T$MT C N ) $) 3 # α 2 % :$ C # β G # D 2@ 2 = N # >3 # ' G N B 2 2@ $ 8 C G N 2 $ 3 # 3 G ? G N ) 3 3 2 $ N # T$M63 BC # $ N 3 # T$MT 3 D # α G β3 B B 2 % % $ % # 2 # β N 3 2 % 3 .Md `536d$ % 2 # 2 3 N 5P 3 G D # α TTP G D E # β3 G N 2 = # T$MT >3 3 E # 3 E C 2 $ D # 2 2@ 2 X545Y X45Y$ ED - 2@ # C 2 N 2 $ % 2 # 2 .D # 2 =G G >3 # 2 2 N C $ . G G # α

(68)

V5 =-pO5P >3 # α B G # β . G # β . $ =554>3 =545> # 2 # β G # α$ % A 2 2@ G # β. % N G # α$ & C C # C# # T$MV 2 Q % # 2 # α β$ 5 M5 45 O5 65 T5 MO6 MOT MOV MOS MOU K R 5 7 C α. % 3 $ α. % 3 $ β. % 3 $ β. % 3 $ T$MV! J 2 Q # % * % =55M> # 2 0M$ 8 G # α A 2 N C N = > = G >$ 8 # β # # $ % # β G # α # = N > # T$MT $ ' 2 @ 3 N

(69)

VM N 3 G 2 G DC = >$ " 2 D 3 G # % % =55M>$ + 2 N # 2 3 3 C # 2 # 2 % # # 2 # % $ = C A 2 % " ( / 3 D $>

8!8

Q

αααα ββββ

3

+ O # G 2 # # % D ? # α β$ J # O$T .# G D ? # # D = > 2 X555MY % $ + # O$T G λ$ # # α =λα3 # D > A # # β=λβ3 # D >$ E & X4T3 66Y # ' @ E λ$3 G 2 # $ 5 X46Y3 # # =# O$T> G λ$ $ + B 2 G 3 # 2 .D3 2@ N # 2 =# T$MT >3 # G # D $ J G 2 λα λβ3 A 2 # 2 .D 2 # D 3 G # λ#$ % # T$MS G C # % 2 # 3 # 2 # D α β$

(70)

V4 T$MS! F 2 G C # D 2 X555MY G D # $ C C # D .D G 3 G # D $ / 2 @ # D G # =554>3 λ_M3K5S6Ta3 N 1 θ_MS34TP3 # D M × O36 $ 0M MO5 3

# D J-≅M b O36 b MO5 _ 636bM5.MO O$ 8

C 5P3 B 3 E # α = B C# T$MV> J _ MOS3TbM5.O5 O $ & C + G # D .D G 2 T$V! MT - O34bM5 J J + = = C =T$V> " G C 2 = 5P >3 2 N 3 ! + _O36 *T3SVa_T3UbM5V 2 D + _ M35 *O3VKa_43SbM5V 2 D + _ MO5µ *V36Ta_454 2 D =T$S > =T$S > =T$S > " G # D # D .D3 G # D $ " 3 D EF X4OY3 # MO5 3 # D λ#_S45

ββββ&

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(71)

VO $ % 3 & # D 3 +λ3 # D 2 S45 3 2 T$U! +λ_ M * S45 _ MOUK =T$U> ? 2@ ! M> % # # ] 4> 8 & C 2@ D 2 # 3 C # D = >$ " & C 2 G G C # α # β] O> 8 # # 2 ] ? 2@ 3 A C G # A # D =554>3 $ " # D 3 # XMOY α_4T36 β_ 6M36$ G # D # D α β ! λ#_λα`λβ =T$K> # D ' N # 2 G C # D 3 G # D . D3 2 T$M5! λ _ =->b + * +λ3 _α3β =T$M5> % # # G 2 T$MM3 ! =-> _ +- =-> b 43 _α3β =T$MM> 0 +- # & C G # 2 3 2 T$M4! +- _ + b + b + 3 _α3β =T$M4>

(72)

V6 ' 2@ =T$S > =T$S > ! +- _ M34bM5Kb + 3 _α3β =T$MO> 0 =T$MO> 2 =T$MM> C 2 D G 2 =T$M6>! + 4 K b M5 b 4 3 M > -= = 3 _α3β =T$M6> 0 G 2 =T$M6> G 2 =T$M5> # D =-> D 2 N % b9 = _ α3β> B / ' G = G 2 T$M> # 2 $ % 3 C# C # 2 3 # 2 # D =554> 0M3 3 # T$MU$ % # α β $ T$MU! # 2 # 2 =554> 0M3 $ % D # α3 G G # β. % N $ % # $ 5 M5 45 O5 65 T5 5$55 5$56 5$5U 5$M4 5$MV ( ! 7 C α β 0 α` β

(73)

VT 8 C# 2 # D =554> 0M # 2 3 G 3 G C ED ' 3 E D # α3 # 3 # β G # α $ " G 3 OTP 3 G # βBC 3 G G # C # β G G # C # α$ " ' 3 C # ' ' 2 3 D C $ % A # α = _5$5UT $ $ -_5P 3 # T$MU > & C # D 3 2 =T$V>$ A # β = _5$M64 $ $ -_T5P 3 # T$MU N > $ # 2 2 C & C # $ % ' 2 # # ! +α- _ 4 4 M3ObM5 6 6 3 4T 5UT $ 5 = = α α 7 ( O34bM5MT3 # α +β- _ 4 4 U3ObM5 T 6 3 6M M64 $ 5 = = β β 7 ( O34bM5MT3 # β # α =β> O34bM5MT

M3OMbM5.6 =U3O5bM5.T>$ 8 & C +- # 2

. # ' # $ ' G 2 =T$M6> & C 2 D G 2 =T$M5> # D # # λα λβ λ#$ % # T$MK 3 C # # D #

(74)

VV # 2 # 0M$ Z # 3 G G # D $ 5 M5 45 O5 65 T5 5 4555 6555 V555 U555 M R 7 C λ α λ β λ #_λα`λβ T$MK! / # D # α β # # 2 $ % # α 3 G # β N # C $ 8 # T$MK G # D α β G D 3 A G 2 # G # $ 8 # D # # α β. % E 2 N # 2 $ N G N C 2 X545Y. % = XMM 4 5Y 2 D > A # D # 3 $ 8 C ED λ#_S45 3 # $ Z G # # 2 .D G λα λβ $ G C E X4T366Y$

(75)

VS % G # T$MT T$MK G 2 # 3 # # % * % =55M> 2@ N . G 2 3 G E 3 # A # $ 2 # 3 2 # 3 λ#= > # T$MK$

(76)

VU

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+ ' . C # # % 5P TTP G D ? # α β$ % D ? # # D # 2 # D 2 D . D ' @ C G D # D N $ % ' # # 2 .D ' ' RF 4 /+/0$ 8 # 2 2@ D # ? 2 $ # % 2@ G D ! C 2 2 $ 2@ E $ " # ' C 2 ? N # α β 2 # $ + # . D 2 N N D ! # 2@ 2 $ G N # D $ # 2 2 # D α β # 2 .D G # $ % # G ' 2 2 N . G G ? G ' 2 # D 2 $

(77)

VK =0^ 8I >3 2 D 3 D G 2@ D $ % ' 2@ 2@ # 2 2 2@ 1M 2 5 C $ - ' 2 # ' 2 2 # 2 .D3 G O :8 # 2 # $ % ' # I N A G 2@ .D3 G G 2 # N 3 G B # $ # 455O F # G $ & & $ # 5 D $ # ' # % 2 D # # ? 2 2 $ % ? % $

(78)

S5 XMY ,$ %$ 3 0 35 3 MOOT =455O>]

X4Y 0$ %$ #3 $ $ %9 3 F$ %$ 1 3 $ $ 3 0$ C 3 $ /$ F : 3 %$ q$ : 3 $ $ - 3 0 32J63 M6UU =455M>] XOY $ 1 :3 $ J F (3 J$ ( 3 c$ / 3 I$ 3 $ 1 3 # 3 6 23 O =4554>] X6Y $ %$ " '3 " ( $ - (6;3 TU =MKKT>] XTY $ - : 3 $"$ , 3 % $ " ( $ / $983 MKV6 =MKK6>] XVY $ - : 3 $"$ , 3 $ % $ " ( $3B93 V4SU =MKK6>] XSY F$ ,$ 3 $ 0$ I 3 % ( $ B3 KT =MKV6>] XUY F$ $ $ : ##] 4 3 $ 63 4P $3 = ( r 0 3 $3 MKVU>] XKY $"$ 1 3 $0$ F 3 " ( $ F $3 293 M56 =MKV4>] XM5Y $ %$ 3 0 $ " ( $ 0 0 4O3 U6M =MKUM>]

XMMY $-$F 3 ,$ 0 3 & 3 $ M3 $ 63 MUK =% " 3 MKVO>]

XM4Y $ I 3 ( 4 4 5 3 VP $3 $ MT = ( r 0 3 MKUV>] XMOY 1$ $ (3 # $ H) ' $$ 3 4P $=% . (3 MKSU>] XM6Y 1$ -$ $ 3 ,$ "$ F : (3 " $ " ( $ 0 $ / 1VS3 4K5 =MKT6>] XMTY $ +$ 0 3 % ! < #= # ! 7 ! I J 3 - 3 ) + % " =MKK5>] XMVY $%$ , 3 ,$ 0 3 1 D(3 J S3 $ M3 MP $ =0 J 3 MKUK>] XMSY $ - : 3 $ "$ , 3 -$ 0 3 -$ /$ : 3 J$ $ I 3 $ $ F 3 $ J $ 0 $ - $3G 2 2 3 M5KM =MKK6>]

(79)

SM XMKY $ 0 3 %$ - 3 /$ e '3 I$ ,$ " 3 $ J $ 0 $ - $3 G B 6 3 MSMV =MKKK>] X45Y %$ - 3 $ 0 3 /$ e9 '3 I$ ,$ " 3 % $ " ( $ / $B;3 46VM =455M>] X4MY %$ I 3 $ " 3 %$ + (3 -$ , B 3 /$ e9 '3 F$ I 3 I$ ,$ " 3 " ( $ F $ / $J 3 5US45O =455O>] X44Y $ (3 -$ , B 3 %$ + (3 q$ - : : 3 F$ I 3 /$ e9 '3 I$ ,$ " 3 % $ " ( $ / 3;53 4U4K =455O>] X4OY $ Ie 3 $ , 3 /$ e9 '3 I$ ,$ " 3 $ % $ " ( $3 J23 TSMM =4554>] X46Y -$ " : 3 $ F 3 J$ $ I 3 1$ 3 $ Ie 3 /$ e9 '3 I$ ,$ " 3 % $ " ( $ / $; 3 4T4O =4554>] X4TY J$ $ I 3 1$ 3 $ 0 3 $ 1 3 /$ e9 '3 I$ ,$ " 3 " ( $ F $ 13993 56O5T =4554>] X4VY /$ e9 '3 $ Ie 3 -$ , B 3 -$ " : 3 1$ 3 I$ ,$ " 3 $ ( 9 328 3 4KS =455O>] X4SY $ : 9 3 $ $ 0$ "$ 1 3 8$ $ $ 3 $ % 3 $ 3 /$ e '3 % $ " ( $ / $ 5VM6OV =4556>] X4UY $ - : 3 $"$ , 3 $ $ " :3 $ $ F 3 $ ( 9 3 8 3 MMO4 =MKKT>] X4KY "$ $ 9 3 F $ " $ " ( $38J3 MOOK =MKKV>] XO5Y $ I$ F 3 4 $ & $ S # , : 0( F 3 = 0 " 3 MKKM>] XOMY $ $ : 3 # 3 OP 3 $ M63 = ( r 0 3 $3 MKKU>] XO4Y $ 1 3 $ #3 5 $ 3 ( " =MKKU>]

XOOY ,$ 3 " ( $ F $ 13583 4MOS =MKUS>]

XO6Y ,$ 3 5 4 $ ( $ K # H)

(80)

S4 XOVY 1$ $ (3 ( & 3 M $3 $ K =% . (3 MKS4>] XOSY 8 Q # I # # *0 3 ,$ 1$ 3 -3 . + % " =4554>] XOUY $ : 9 3 "$J$ 0 3 $ Ie 3 $ 0 3 /$ e9 '3 " ( $ F $ 1983 45TO4U =4554>] XOKY # ? " 1 D D " \ " 2 ^ N % *% % 3 "$ $ 3 - 3 . + % " =4556>] X65Y % % % % 3 8$ $ $ 3 - 3 . + % " =4556>] X6MY $ : 9 3 $ I 3 "$J$ 0 3 $ % 3 8$ $ $ 3 $ $ 0$ "$ 1 3 $ 3 F$ $ " 3 /$ e '3 $ $ $2B2&2B93 MMT6 =4556>] X64Y -$ " : 3 -$ , B 3 $ (3 $ Ie 3 /$ e9 '3 I$ ,$ " 3 % $ " ( $ / $;23 4O5U =455O>] X6OY $ : 9 3 $ I 3 "$J$ 0 3 $ % 3 8$ $ $ 3 $ $ 0$ "$ 1 3 $ 3 F$ $ " 3 /$ e '3 " ( $ F $ 13B 3 56TOMK =455T>] X66Y J$ $ I 3 1$ 3 $ 0 3 $ 1 3 /$ e9 '3 I$ ,$ " 3 " ( $ F $ / 3;83 O6M =4555>] X6TY D 2@ # 3 $ "$ $ (3 - 3 . + % " =4554>]

(81)

SO

S

1

" 2 # # % * % =55M> ' # 2 .D 2 $ " D # # Q ' RF 4$ " # ' D # : 9 = . + % ">3 # # 2 G # XOK36TY$ % # %$M # # = > # = >$ = > = > %$M! G # = > = > 2 D XOKY$ + 3 # 3 D ED A # CD $ 8 G # # 2 $ " # = D >3 . # G # 3 # # D Uµ $ # B A 2 # Q RF 4 /+/03 G # D .D = > G % 2 # % %

(82)

S6 %$4! 2 # Q ' RF 4 /+/0$ " # C ? # D B 3 # %$4 $ 8 C # G # ? G C $ # D C 3 G # G $ " 3 B # 2 O3 T S $ S + B # D # 2 # # 3 D 3 S # 2 D 534d$ % # %$O %$6 0M 06 G D $ 8 C# # 2 α. % @ 3 B # @ $

1

(83)

ST 2 α. % - =P > + _ T + _ S %O! 2 α. % # 2 # @ 0M$ α - =P > % 06 0 + _ O + _ T + _ S %6! 2 α. % # 2 # @ 06$

(84)

SV # @ 0M 06 $ " G 2 # 2 D $ # E 3 # O G # 2 # $ # B C E # # 2 # D $ 2 D # % * % =55M> 5 D C 3 D $

G

1M> F G $ & & ] L D & ! $ L$ $ : 9 3 $ I 3 "$ J$ 0 3 $ % 3 8$ $ $ 3 $ $ 0$ "$ 1 3 $ 3 F$ ." 3 /$ e9 '3 $ $ $ $ 2B2&2B93 MMT6.MMTV =4556>$ 14> F 5 C ] L#$$ $ ? $ ) L$ $ : 9 3 $ $ 0$ "$ 1 3 8$ $ $ 3 $ % 3 $ 3 /$ e9 '3 3 % $ " ( $ / $ ;83 44T5 =4556>$ 1O> F 5 D ] L & $ LM $ : 9 3 $ I 3 "$ J$ 0 3 $ % 3 8$ $ $ 3 $ $ 0$ "$ 1 3 $ 3 F$ ." 3 /$ e9 '3 " ( $ F $G B 3 56TOMK =4556>$ 1O> F 5 D C ] NC $$ & $ B$ $ : 9 3 $ $ 0$ "$ 1 3 $ % 3 8$ $ $ 3 $ 3 "$ J$ 0 3 /$ e9 '3 $ F 3 0$ 0 3 " ( $ F $ / $J83 5SS45O =445T>$

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