DMIによる反転電流低減のシミュレーション解析

1731096 DMI

STT-MRAM

STT-MRAM

DMI

DMI

STT-MRAM

ECC

1ns

10ns

33%

10%

ECC

ECC

DMI

3

~4

ECC

1ns

10ns

DMI

72 %

80 %

DMI

ECC

STT-MRAM

DMI

31 3 10

3 STT-MRAM STT-MRAM DMI DMI STT-MRAM ECC DMI DMI α DMI 1ns 33% 10ns 10% α Ku α DMI θ0 ECC DMI ECC DMI 3 4 ECC D = 0.0 erg/cm2 tp=1ns 72 tp=10ns 80

5 1 7 1.1 . . . 7 1.1.1 . . . 7 1.1.2 . . . 7 1.1.3 MRAM( ) . . . 7

1.1.4 STT-MRAM(Spin Transfer Torque - Magnetoresistive Random Access Memory) . . . 7

1.1.5 Dzyaloshinskii - Moriya interaction(DMI) . . . 8

1.1.6 Exchange Coupled Composite(ECC) . . . 9

1.2 . . . 9 1.3 . . . 9 2 11 2.1 . . . 11 2.2 LLG . . . 11 2.3 . . . 12 2.3.1 . . . 12 2.3.2 . . . 12 2.3.3 . . . 13 2.3.4 . . . 13 2.3.5 . . . 13 2.4 . . . 13 2.4.1 . . . 14 2.4.2 . . . 14 2.4.3 . . . 14

2.5 Dzyaloshinskii - Moriya interaction(DMI) . . . 14

2.6 Exchange - Coupled Composite (ECC) . . . 15

3 17 3.1 . . . 17 3.1.1 . . . 17 3.2 LLG . . . 18 3.2.1 LLG . . . 18 3.2.2 4 Runge-Kutta . . . 19 3.2.3 . . . 20 3.2.4 . . . 24 3.3 . . . 24 3.3.1 . . . 25 3.3.2 . . . 25 3.4 . . . 25

6 4 DMI 27 4.1 DMI . . . 27 4.2 Ku DMI . . . 28 4.3 DMI . . . 28 4.3.1 . . . 31 4.4 . . . 36 5 ECC DMI 37 5.1 Ku . . . 37 5.2 Ku . . . 41 5.3 Ainter . . . 45 5.4 Ainter . . . 46 5.5 . . . 56 6 59

7

1

1.1

1.1.1

CPU DRAM DRAM DRAM ( ) MRAM( )

1.1.2

(MRAM)

(ReRAM) (FeRAM) MRAM

1.1.3

MRAM(

)

(Magnetoresistive Random Access Memory)

1.1.4

STT-MRAM(Spin Transfer Torque - Magnetoresistive Random Access

Mem-ory)

MRAM

STT-MRAM STT-MRAM STT-RAM,SpinRAM

8 1 1.1: MRAM STT-MRAM [1] STT-MRAM 1.1 [2] Isw = 2eMsV µBgP ! αγHk+C1 tp " (1.1) C1 = = [ln (1− cos(θcrit))/(1 + cos(θcrit))− ln (1 − cos(θinit))/(1 + cos(θinit))] /2 (1.2)

1.1 1 2

1.2: [2]

1.1.5

Dzyaloshinskii - Moriya interaction(DMI)

Dzyaloshinskii - Moriya interaction( DMI)

1.2. 9

1.3: DMI [5]

1.1.6

Exchange Coupled Composite(ECC)

ECC

HDD STT-MRAM

[3]

1.2

STT-MRAM

STT-MRAM DMI STT-MRAM

STT-MRAM ECC

1.3

2 3 4 DMI DMI 5 ECC DMI ECC DMI 6

11

2

LLG LLG DMI ECC

2.1

(magnetic pole) + -2.1: 2.1 l +q -q |⃗m_{| = ql [emu]} (2.1) emu/cm3

2.2

LLG

Landau-Lifshitz-Gilbert ( LLG ) LLG 2.2 [7] ˙⃗ M =_−|γ|#M⃗ _{× ⃗}H$+ α M # ⃗ M_×M˙⃗$ (2.2) ⃗ M H⃗ γ α M (_{| ⃗}M_|)

12 2

2.3

LLG DMI

2.3.1

( ) 2.3 ϵK = Ku(1− m2z) (2.3) Ku emu/cm3 ⃗ HK = −δϵ K δ ⃗M = ₋ 1 Ms δϵK δ ⃗m (2.4) 2.4 x, y, z HxK = − 1 Ms ⎛ ⎝−_∂m∂ϵK x + ∂ ∂x ' ∂ϵK ∂(∂mx ∂x ) * + ∂ ∂y ⎛ ⎝ ∂ϵK ∂#∂mx ∂y $ ⎞ ⎠ + ∂ ∂z ' ∂ϵK ∂(∂mx ∂z ) *⎞ ⎠ (2.5) HyK = − 1 Ms ⎛ ⎝−_∂m∂ϵK y + ∂ ∂x ⎛ ⎝ ∂ϵK ∂#∂my ∂x $ ⎞ ⎠ + ∂ ∂y ⎛ ⎝ ∂ϵK ∂#∂my ∂y $ ⎞ ⎠ + ∂ ∂z ⎛ ⎝ ∂ϵK ∂#∂my ∂z $ ⎞ ⎠ ⎞ ⎠ (2.6) HzK = − 1 Ms ⎛ ⎝−_∂m∂ϵK z + ∂ ∂x ' ∂ϵK ∂(∂mz ∂x ) * + ∂ ∂y ⎛ ⎝ ∂ϵK ∂#∂mz ∂y $ ⎞ ⎠ + ∂ ∂z ' ∂ϵK ∂(∂mz ∂z ) *⎞ ⎠ (2.7) 2.5,2.6,2.7 2.3 2.8,2.9,2.10 HxK = 0 (2.8) HyK = 0 (2.9) HzK = 2Ku M mz (2.10) 2.8,2.9,2.10 2.11 ⃗ HK= ⎡ ⎢ ⎣ 0 0 2Ku M mz ⎤ ⎥ ⎦ (2.11)

2.3.2

2.12 ϵA = A(_∇⃗m)2= A 3! ∂mx ∂x "2 + ! ∂my ∂y "2 + ! ∂mz ∂z "24 (2.12)

2.4. 13 A erg/cm ⃗ HA = ₋δϵ A δ ⃗M = −_M1 s δϵA δ ⃗m (2.13) 2.13 x, y, z HxA = − 1 Ms ⎛ ⎝−_∂m∂ϵA x + ∂ ∂x ' ∂ϵA ∂(∂mx ∂x ) * + ∂ ∂y ⎛ ⎝ ∂ϵA ∂#∂mx ∂y $ ⎞ ⎠ + ∂ ∂z ' ∂ϵA ∂(∂mx ∂z ) *⎞ ⎠ (2.14) HyA = − 1 Ms ⎛ ⎝−_∂m∂ϵA y + ∂ ∂x ⎛ ⎝ ∂ϵA ∂#∂my ∂x $ ⎞ ⎠ + ∂ ∂y ⎛ ⎝ ∂ϵA ∂#∂my ∂y $ ⎞ ⎠ + ∂ ∂z ⎛ ⎝ ∂ϵA ∂#∂my ∂z $ ⎞ ⎠ ⎞ ⎠ (2.15) HzA = − 1 Ms ⎛ ⎝−_∂m∂ϵA z + ∂ ∂x ' ∂ϵA ∂(∂mz ∂x ) * + ∂ ∂y ⎛ ⎝ ∂ϵA ∂#∂mz ∂y $ ⎞ ⎠ + ∂ ∂z ' ∂ϵA ∂(∂mz ∂z ) *⎞ ⎠ (2.16) 2.14,2.15,2.16 2.12 2.17,2.18,2.19 HxA = 2A Ms ∂2_m x ∂x2 + 2A Ms ∂2_m x ∂y2 + 2A Ms ∂2_m x ∂z2 (2.17) HA y = 2A Ms ∂2_m y ∂x2 + 2A Ms ∂2_m y ∂y2 + 2A Ms ∂2_m y ∂z2 (2.18) HzA = 2A Ms ∂2_m z ∂x2 + 2A Ms ∂2_m z ∂y2 + 2A Ms ∂2_m z ∂z2 (2.19)

2.3.3

2.3.4

2.3.5

d 2.20 [9] −τ−1η( ⃗m_{× (⃗}m_{× ⃗p))} (2.20) −τ−1= g|µB| · 4π · Ie 2Ms· 125.6637 · |e| ⃗

p g gyromagnetic splitting factor µB e η

Ie

14 2

2.4.1

2.2 ( ) ( ) 2.2:

2.4.2

MRAM

2.4.3

MRAM 60 10 [6]

2.5

Dzyaloshinskii - Moriya interaction(DMI)

Dzyaloshinskii - Moriya interaction( DMI) [11][12] DMI

DMI 2.21

EDM I =_−Dij· (Si× Sj) (2.21)

2.6. Exchange - Coupled Composite (ECC) 15

2.3: DMI

DMI DMI 2.21 DMI 2.22

ϵDM I =_−D 5! mx ∂mz ∂x − mz ∂mx ∂x " + ! my ∂mz ∂y − mz ∂my ∂y "6 (2.22) 2.22 DMI HDM I = ∂ϵ DM I ∂M (2.23) = 1 Ms ∂ϵDM I ∂m (2.24) 2.24 2.25 2.26 2.27 HDM I x = 1 Ms ⎡ ⎣∂ϵDM I ∂mx + ∂ ∂x 3 ∂ϵDM I ∂(∂mx ∂x ) 4 + ∂ ∂y ⎧ ⎨ ⎩ ∂ϵDM I ∂#∂mx ∂y $ ⎫ ⎬ ⎭+ ∂ ∂z 3 ∂ϵDM I ∂(∂mx ∂z ) 4⎤ ⎦ (2.25) HyDM I = 1 Ms ⎡ ⎣∂ϵDM I ∂my + ∂ ∂x ⎧ ⎨ ⎩ ∂ϵDM I ∂#∂my ∂x $ ⎫ ⎬ ⎭+ ∂ ∂y ⎧ ⎨ ⎩ ∂ϵDM I ∂#∂my ∂y $ ⎫ ⎬ ⎭+ ∂ ∂z ⎧ ⎨ ⎩ ∂ϵDM I ∂#∂my ∂z $ ⎫ ⎬ ⎭ ⎤ ⎦ (2.26) HzDM I = 1 Ms ⎡ ⎣∂ϵDM I ∂mz + ∂ ∂x 3 ∂ϵDM I ∂(∂mz ∂x ) 4 + ∂ ∂y ⎧ ⎨ ⎩ ∂ϵDM I ∂#∂mz ∂y $ ⎫ ⎬ ⎭+ ∂ ∂z 3 ∂ϵDM I ∂(∂mz ∂z ) 4⎤ ⎦ (2.27) 2.25 2.26 2.27 2.22 2.28 2.29 2.30 HxDM I = − 2D Ms ∂mz ∂x (2.28) HyDM I = − 2D Ms ∂mz ∂y (2.29) HzDM I = 2D Ms ! ∂mx ∂x + ∂my ∂y " (2.30)

2.6

Exchange - Coupled Composite (ECC)

ECC

STT-MRAM [4]

17

3

LLG LLG 4 Runge-Kutta LLG

3.1

3.1.1

3.1 3.1.1 ECC 3.1.1 (a) (b) ECC 3.1: 3.2 3.2 3.3

18 3 3.2: 3.3:

3.2

LLG

3.2.1

LLG

LLG LLG ( 2.2) ˙⃗ M =_−|γ|#M⃗ _{× ⃗}H$+ α M # ⃗ M_×M˙⃗$ (3.1) 3.1 (M )˙⃗ 2.2 m⃗ ˙⃗ M = _−|γ|#M⃗ _{× ⃗}H$+ α M # ⃗ M_×M˙⃗$ M ˙⃗m = −|γ|M#m⃗ × ⃗H$+ αM#m⃗ × ˙⃗m$ ˙⃗m = −|γ|#m⃗ _{× ⃗}H$+ α#m⃗ _{× ˙⃗}m$ (3.2) ⃗ m_{× ˙⃗}m = _−|γ|⃗m_×#m⃗ _{× ⃗}H$+ α ⃗m_×#m⃗ _{× ˙⃗}m$ = _−|γ|=#m⃗ _{· ⃗}H$m⃗>+ α=#m⃗ _{· ˙⃗}m$m⃗ _{− (⃗}m_{· ⃗}m) ˙⃗m> = ( ⃗m_{· ⃗}m)#_{|γ| ⃗}H_{− α ˙⃗}m$+=_−|γ|#m⃗ _{· ⃗}H$+ α#m⃗ _{· ˙⃗}m$>m⃗ = _|⃗m_|2_{|γ| ⃗}H_{− α|⃗}m_|2 ˙⃗m +=_−|γ|#m⃗ _{· ⃗}H$+ α#m⃗ _{· ˙⃗}m$>m⃗ = |γ| ⃗H− α ˙⃗m− |γ|#m⃗ · ⃗H$m⃗ (3.3) 3.2 3.3 3.4 ˙⃗m = −|γ|#m⃗ × ⃗H$+ α|γ| ⃗H− α2_{˙⃗m − α|γ|}#_m⃗ · ⃗H$m⃗ ˙⃗m = |γ| = α ⃗H_{− ⃗}m_{× ⃗}H_{− α}#m⃗ _{· ⃗}H$m⃗> α2_{+ 1} = −_α2|γ|_{+ 1} ? ⃗ m× ⃗H + α=#m⃗ · ⃗H$m⃗ − ⃗H>@ (3.4)

3.2. LLG 19 ⃗ m_{· ⃗}H m⃗ _{× ⃗}H 3.5 3.6 ⃗ m· ⃗H = mxHx+ myHy+ mzHz (3.5) ⃗ m× ⃗H = ⎛ ⎜ ⎝ myHz− mzHy mzHx− mxHz mxHy− myHx ⎞ ⎟ ⎠ (3.6) 3.6 3.4 3.7 3.8 3.9 ˙ mx = − |γ| α2_{+ 1} ? (myHz− mzHy) + α{(mxHx+ myHy+ mzHz) mx− Hx} @ (3.7) ˙ my = − |γ| α2_{+ 1} ? (mzHx− mxHz) + α{(mxHx+ myHy+ mzHz) my− Hy} @ (3.8) ˙ mz = − |γ| α2_{+ 1} ? (mxHy− myHx) + α{(mxHx+ myHy+ mzHz) mz− Hz} @ (3.9)

3.2.2

4

Runge-Kutta

LLG Euler 4 Runge-Kutta 3.2.2.1 Euler Euler 3.2.2.1 ⃗ m(t + ∆t) = ⃗m(t) + ∆t_{· ˙⃗}m(t) (3.10) ∆t 3.11 3.12 3.13 mx(t + ∆t) = mx(t) + ∆t ˙mx(t) (3.11) my(t + ∆t) = my(t) + ∆t ˙my(t) (3.12) mz(t + ∆t) = mz(t) + ∆t ˙mz(t) (3.13) 3.2.2.2 4 Runge-Kutta 4 Runge-Kutta f ( ⃗m(t)) = ˙⃗m(t) 3.14 ⃗ m(t + ∆t) = m(t) +⃗ 1 6 # ⃗ k1+ 2 ⃗k2+ 2 ⃗k3+ ⃗k4 $ (3.14) ⃗ k1 = ∆t· f(⃗m(t)) (3.15) ⃗ k2 = ∆t· f(⃗m(t + ∆t/2) + ⃗k1/2) (3.16) ⃗ k3 = ∆t· f(⃗m(t + ∆t/2) + ⃗k2/2) (3.17) ⃗ k4 = ∆t· f(⃗m(t + ∆t) ⃗k3) (3.18) k t_{→ ∆t}

20 3

3.2.3

LLG (2.2 ) ( ⃗H) DMI 2.2 3.19 ⃗ H = ⃗HK_{+ ⃗H}A_{+ ⃗H}D_{+ ⃗H}EXT _{+ ⃗H}S_{+ ⃗H}DM I _(3.19) 3.2.3.1 2.11 3.2.3.2 2.17,2.18,2.19 ∂2mx ∂x2 , ∂2my ∂y2 , ∂2_m z ∂z2 Taylor 3.20 3.28 ∂2_m x ∂x2 ≈ mxi+1,j,k− 2mxi,j,k+ mxi−1,j,k dx2 (3.20) ∂2_m x ∂y2 ≈

mxi,j+1,k− 2mxi,j,k+ mxi,j−1,k

dy2 (3.21)

∂2_m x

∂z2 ≈

mxi,j,k+1− 2mxi,j,k+ mxi,j,k−1

dz2 (3.22) ∂2_m y ∂x2 ≈ myi+1,j,k− 2myi,j,k+ myi−1,j,k dx2 (3.23) ∂2_m y ∂y2 ≈

myi,j+1,k− 2myi,j,k+ myi,j−1,k

dy2 (3.24)

∂2_m y

∂z2 ≈

myi,j,k+1− 2myi,j,k+ myi,j,k−1

dz2 (3.25)

∂2_m z

∂x2 ≈

mzi+1,j,k− 2mzi,j,k+ mzi−1,j,k

dx2 (3.26)

∂2_m z

∂y2 ≈

mzi,j+1,k− 2mzi,j,k+ mzi,j−1,k

dy2 (3.27)

∂2_m z

∂z2 ≈

mzi,j,k+1− 2mzi,j,k+ mzi,j,k+1

dz2 (3.28) 3.20 3.28 2.17,2.18,2.19 3.29 ⃗ HA = −δϵ A δ ⃗M ≈ _M2A sdx2 ⎡ ⎢ ⎣

mxi−1,j,k− 2mxi,j,k+ mxi+1,j,k myi−1,j,k− 2myi,j,k+ myi+1,j,k mzi−1,j,k− 2mzi,j,k+ mzi+1,j,k ⎤ ⎥ ⎦ + 2A Msdy2 ⎡ ⎢ ⎣

mxi,j−1,k − 2mxi,j,k+ mxi,j+1,k myi,j−1,k− 2myi,j,k+ myi,j+1,k mzi,j−1,k− 2mzi,j,k+ mzi,j+1,k

⎤ ⎥ ⎦ + 2A Msdz2 ⎡ ⎢ ⎣

mxi,j,k−1− 2mxi,j,k+ mxi,j,k+1 myi,j,k−1− 2myi,j,k+ myi,j,k+1 mzi,j,k−1− 2mzi,j,k+ mzi,j,k+1

⎤ ⎥

⎦ (3.29)

3.2.3.3

3.2. LLG 21 3.4: xy,yz,zx _±Mz ±Mx ±My xy xz yz yz (x1,y,z) 3.30 ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ∆Hx=−M_r2xx1_r ∆y∆z ∆Hy=−M_r2y y r∆y∆z ∆Hz=−Mr2z z r∆y∆z r =Dx12_{+ y}2_{+ z}2 (3.30) 3.31 Hx= E z0 z1 E y0 y1 ∆Hx, Hy = E z0 z1 E y0 y1 ∆Hy, Hz= E z0 z1 E y0 y1 ∆Hz, (3.31) yz xy xz 3.32 [13] ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ Hx= qxx· mx+ qxy· my+ qxz· mz Hy = qyx· mx+ qyy· my+ qyz· mz Hz= qzx· mx+ qzy· my+ qzz· mz (3.32) (i,j)

22 3 3.33 3.35 O(n2₎ Hx(i, j) = nx F i′=1 ny F j′=1 qxx(i′− i, j′− j) · mx(i′, j′) + qxy(i′− i, j′− j) · my(i′, j′) + qxz(i′− i, j′− j) · mz(i′, j′(3.33)) Hy(i, j) = nx F i′₌₁ ny F j′₌₁ qyx(i′− i, j′− j) · mx(i′, j′) + qyy(i′− i, j′− j) · my(i′, j′) + qyz(i′− i, j′− j) · mz(i′, j′(3.34)) Hz(i, j) = nx F i′=1 ny F j′=1 qzx(i′− i, j′− j) · mx(i′, j′) + qzy(i′− i, j′− j) · my(i′, j′) + qzz(i′− i, j′− j) · mz(i′, j′(3.35))

convolution O(n2_{) O(n)}

convolution A(i) = n F j=1 C(j_{− i) · B(j),} i = 1,_{· · · , n} (3.36) A,B n C 2n− 1 n 2

Convolution A(1),_{· · · , A(n)} O(n2₎

B C n C n

3.36

I. B C Br(B ) Bi(B ) Cr(C

) Ci(C )

II. Ar, Ai

Ar(i) = Br(i)· Cr(i) − Bi(i) · Ci(i), (3.37)

Ai(i) = Br(i)· Ci(i) + Bi(i) · Cr(i), i = 1,· · · , n (3.38)

III. Ar, Ai A I III n O(n log(n)) II n O(n log(n)) n B C 2n B′_{, C}′ B′ : B(1), B(2),_{· · · , B(n), 0, 0, · · · , 0} C′ : 0, C(_{−n + 1), C(−n + 2), · · · , C(0), C(1), · · · , C(n − 1)} B′ B 0 n C′ 0 Convolution 2n_{− 1} B′_{, C}′ A′ _A′_{(n + 1),· · · , A}′_(2n) 3.5 3.6

3.2. LLG 23 3.5: B’ 3.6: C’ n 2 n 2 n B 3.2.3.4 LLG 2.20 LLG (3.1 ) 3.39 ˙⃗m = −|γ|#m⃗ _{× ⃗}H$+ α#m⃗ _{× ˙⃗}m$_{− τ}−1η( ⃗m_{× (⃗}m_{× ⃗p))} (3.39) 3.7: 3.7 3.39 3.39 ˙⃗m = −|γ|Gm⃗ × 5 ⃗ H +τ −1_η |γ| ( ⃗m× ⃗p) 6H + α#m⃗ × ˙⃗m$ (3.40) 3.40 LLG 3.40 η = 1 3.2.3.5 DMI

2.28,2.29,2.30 _∂x∂ mx,_∂y∂ my,_∂x∂ mz,_∂y∂ mz Taylor 3.41 3.42 3.43 3.44

∂mx ∂x ≈ mxi+1,j,k− mxi−1,j,k 2dx (3.41) ∂my ∂y ≈ myi,j+1,k− myi,j−1,k 2dy (3.42) ∂mz ∂x ≈ mzi+1,j,k− mzi−1,j,k 2dx (3.43) ∂mz ∂y ≈ mzi,j+1,k − mzi,j−1,k 2dy (3.44)

24 3 3.41 3.42 3.43 3.44 2.28 2.29 2.30 DMI 3.45 3.46 3.47 HxDM I ≈ − 2D Ms mzi+1,j,k− mzi−1,j,k 2dx (3.45) HyDM I ≈ − 2D Ms mzi,j+1,k− mzi,j−1,k 2dy (3.46) HDM I z ≈ 2D Ms !_m xi+1,j,k− mxi−1,j,k 2dx + myi,j+1,k− myi,j−1,k 2dy " (3.47)

3.2.4

DMI DMI [14] DMI 3.48 ∂m ∂n = D 2A( ˆz× n) × m (3.48) 3.48 n x, ˆˆ y 3.49,3.50 ∂m ∂ ˆx = D 2A( ˆz× ˆx)× m = D 2A ⎡ ⎢ ⎣ mz 0 −mx ⎤ ⎥ ⎦ (3.49) ∂m ∂ ˆy = D 2A( ˆz× ˆy)× m = D 2A ⎡ ⎢ ⎣ 0 mz −my ⎤ ⎥ ⎦ (3.50) 3.49 x 1 3.51 3.50 y 1 3.52 0 n_{− 1} ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ m−1x = m0x− dx · m0z·2AD m−1 y = m0y m−1 z = m0z+ dx· m0x·2AD mn x = mnx−1+ dx· mnz−1· 2AD mn y = mny−1 mn z = mnz−1− dx · mnx−1· 2AD (3.51) ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ m−1 x = m0x m−1 y = m0y− dy · m0z·2AD m−1 z = m0z+ dy· m0x· 2AD mn x= mnx−1 mn y = mny−1+ dy· mnz−1·2AD mn z = mn−1z − dy · mn−1x ·2AD (3.52)

3.3

3.4. 25

3.3.1

DMI 3.57 ϵK = Ku(1− m2z) (3.53) ϵA _{= A(} ∇⃗m)2 _(3.54) ϵD = ₋1 2M ⃗m· ⃗H D _(3.55) ϵDM I = −D 5! mx∂mz ∂x − mz ∂mx ∂x " + ! my∂mz ∂y − mz ∂my ∂y "6 (3.56) E = (ϵK_{+ ϵ}A_{+ ϵ}D_{+ ϵ}DM I)_{V (3.57)} V = dx_{· dy · dz} (3.58) 3.59 EBarrier= EM ax− EM in (3.59)

3.3.2

(∆) 3.60 ∆ = ∆E kBT ! = KuV kBT " (3.60) ∆E kB T

3.4

3.61 ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ : Ms= 600.0 emu/cm3 : A = 1.0 µerg/cm : γ = 1.76_{× 10}7 _rad/(s · Oe) : ⃗p =_{{0.0, 0.0, 1.0}}

gyromagnetic splitting factor : g = 2.0_{× 1.001159657} : µB = 9.27408× 10−21 J/T : e = 1.602189_{× 10}−19 _C g : η = 1.0 : kB= 1.380658× 10−16 erg/K : T = 300 K (3.61) 3.62 ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ : dx = dy = 1.875 nm ( ) : dz = 2.0 nm (ECC ) : dz = 1.0 nm : nx = ny = 16 (3.62)

27

4

DMI

STT-MRAM DMI DMI DMI DMI Ku Ku D DMI

4.1

DMI

⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ α = 1.0 ⃗ m = (1.0, 0.0, 0.0) tp= 8.0 ns (4.1) tp ⎧ ⎨ ⎩ D = 0.0, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0 erg/cm2 Ku= 3.0 6.0 Merg/cm3 (4.2) 2.5 3 3.5 4 4.5 5 5.5 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 E (perg) _θ (rad) t (ns) Energy(DMI=0.0 erg/cm2) θ(DMI=0.0 erg/cm2) Energy(DMI=1.0 erg/cm2) θ(DMI=1.0 erg/cm2) 4.1: DMI 4.1 4.1 DMI

28 4 DMI

4.2

K

u

DMI

Ku D (∆≥60) 4.2 20 30 40 50 60 70 80 90 100 3.5 4 4.5 5 5.5 6 ∆ K_u (Merg/cm3) DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 4.2: DMI Ku ∆ 4.2 DMI ∆ 60 Ku 4.2 4.1: DMI ∆_{≥ 60} Ku D(erg/cm2_{) K} u(Merg/cm3) 0.0 3.44 0.1 3.62 0.2 3.72 0.4 3.97 0.6 4.29 0.8 4.68 1.0 5.15

4.3

DMI

Ku D x 1Oe ( ) θ0 θ′ = π− θ0 4.3

4.3. DMI 29 0 0.5 1 1.5 2 2.5 3 3.5 100 120 140 160 180 200 220 240 θ (rad) j (GA/m2) DMI=0.0(erg/cm2) DMI=0.2(erg/cm2) DMI=0.4(erg/cm2) DMI=0.6(erg/cm2) DMI=0.8(erg/cm2) DMI=1.0(erg/cm2) 4.3: (α = 0.001, tp= 1.0ns, HxEXT = 1.00Oe) 4.3 ⎧ ⎨ ⎩ α = 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1.0 tp= 1.0, 3.0, 10.0 ns (4.3) 4.4 35 36 37 38 39 40 41 42 43 44 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) 4.4: DM I jsw (α = 0.003, tp= 10.0 ns, HxEXT = 1.00 Oe) 4.4 x 0.95Oe 1.05Oe 11 ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ α = 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1.0 tp= 1.0, 3.0, 10.0 ns HxEXT = 0.95 1.05 Oe (4.4) 4.5,4.6

30 4 DMI 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 jswx / j sw0 D (erg/cm2) tp=1ns tp=3ns tp=10ns (a) α = 0.001 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 jswx / j sw0 D (erg/cm2) tp=1ns tp=3ns tp=10ns (b) α = 0.003 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 jswx / j sw0 D (erg/cm2) tp=1ns tp=3ns tp=10ns (c) α = 0.01 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 jswx / j sw0 D (erg/cm2) tp=1ns tp=3ns tp=10ns (d) α = 0.03 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 jswx / j sw0 D (erg/cm2) tp=1ns tp=3ns t_p=10ns (e) α = 0.1 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 jswx / j sw0 D (erg/cm2) tp=1ns tp=3ns t_p=10ns (f) α = 0.3 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 jswx / j sw0 D (erg/cm2) t_p=1ns tp=3ns t_p=10ns (g) α = 1 4.5: DMI α

4.3. DMI 31 10 100 1000 10000 0.0001 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0(erg/cm2) DMI=0.4(erg/cm2) DMI=1.0(erg/cm2) (a) tp= 1 ns 10 100 1000 10000 0.0001 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0(erg/cm2) DMI=0.1(erg/cm2) DMI=0.2(erg/cm2) DMI=0.4(erg/cm2) DMI=0.6(erg/cm2) DMI=0.8(erg/cm2) DMI=1.0(erg/cm2) (b) tp= 3 ns 10 100 1000 10000 0.0001 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0(erg/cm2) DMI=0.4(erg/cm2) DMI=1.0(erg/cm2) (c) tp= 10 ns 4.6: α DMI α DMI α DMI DMI α DMI 1ns 10ns 33% 10%

4.3.1

1.2 1.1

32 4 DMI 4.7: Isw = 2eMsV µBgP ! αγHk+C1 tp " = 2eMsV µBgP ! αγ2Ku Ms +C1 tp "

C1 = = [ln (1− cos(θcrit))/(1 + cos(θcrit))− ln (1 − cos(θinit))/(1 + cos(θinit))] /2

1.2 1.1 1 1.1 2 1.1 1 Ku 2 1.2 θ0 1 4.2 DMI Ku 1 2 DMI 4.8 4.8: DMI

4.3. DMI 33

4.8 DMI θinit 1.2 DMI

C1 DMI 2

DMI=0 DMI> 0 4.9

4.9: DMI

4.10,4.11

34 4 DMI 4.11: DMI ( ) DMI 4.10 4.11 DMI Keff u θ0 1 Hkeff= -Hkeff = Hkz− Hdz 2Keff u Ms = 2Ku Ms − Hdz Kueff = Ku− Ms 2 Hdz (4.5) Hdz DMI=0 DMI 4.5 4.12,4.13

4.3. DMI 35 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 H D (MOe) Ku eff (MOe) D (erg/cm2) HD K_ueff 4.12: DMI HD_{, K}eff u (α = 1.0) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 0 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 jswx / j sw0 Kux eff / K u0 eff D (erg/cm2) jsw(1ns) jsw(10ns) jsw(100ns) jsw(0.1ns) jsw(0.01ns) Kueff Ku 4.13: DMI Keff u (α = 1.0) 1ns 10ns DMI Ku Kueff θ0 1.2 C1 4.14

36 4 DMI 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jswx / j sw0 C1x / C 10 D (erg/cm2) jsw(1ns) jsw(10ns) jsw(100ns) jsw(0.1ns) jsw(0.01ns) C1 4.14: D C1 (α = 0.0001) 4.13 1 DMI=0 Kueff 4.14 2 0 DMI=0 C1 1.1 4.13,4.14 DMI 1 Keff u 2 C1

4.4

DMI α DMI DMI 1ns 33% 10ns 10%

37

5

ECC

DMI

ECC DMI DMI DMI DMI Ku Ku D Ainter DMI DMI

5.1

K

u ECC DMI 2 ECC DMI Ku D (∆_≥60) Ku D ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ α = 1.0 ⃗ m = (1.0, 0.0, 0.0) tp= 8.0 ns Ainter= 1.0 µerg/cm (5.1) ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ DM I = 0.0 1.0 erg/cm2 Khard u = 0.0 15.0 Merg/cm3 Ksoft u = 0.0 15.0 Merg/cm3 (5.2) 5.1,5.2

38 5 ECC DMI 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (a) DM I = 0.0 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (b) DM I = 0.1 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (c) DM I = 0.2 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (d) DM I = 0.4 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (e) DM I = 0.6 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (f) DM I = 0.8 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8 9 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (g) DM I = 1.0 erg/cm2 5.1: DMI Khard u Kusof t ∆ (DMI )

5.1. Ku 39 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (a) DM I = 0.0 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (b) DM I = 0.1 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (c) DM I = 0.2 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (d) DM I = 0.4 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (e) DM I = 0.6 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (f) DM I = 0.8 erg/cm2 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8 9 ∆ K_usoft (Merg/cm3) K_uhard =2 Merg/cm3 K_uhard =3 Merg/cm3 K_uhard =3.5 Merg/cm3 K_uhard =4 Merg/cm3 K_uhard =5 Merg/cm3 (g) DM I = 1.0 erg/cm2 5.2: DMI Khard u Kusof t ∆ (DMI )

40 5 ECC DMI 5.1,5.2 ∆ =60 Kuhard Kusoft D 5.3,5.4 0 2 4 6 8 10 0 2 4 6 8 10 Ku soft (Merg/cm 3 ) K_uhard (Merg/cm3) DMI=0.0 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 5.3: ∆ = 60 Ku (DMI ) 0 2 4 6 8 10 0 2 4 6 8 10 Ku soft (Merg/cm 3 ) K_uhard (Merg/cm3) DMI=0.0 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 5.4: ∆ = 60 Ku (DMI ) 5.3,5.4 DMI 5.3,5.4 5.3,5.4 DMI Khard u Kusoft 5.1

5.2. Ku 41

5.1: DMI ∆_{≥ 60} Ku(erg/cm2)

D(erg/cm2_{) DMI K}

u 3:1 DMI Ku 1:0 DMI Ku 3:1 DMI Ku 1:0

0.0 5.34,1.78 7.12,0.00 5.31,1.77 7.11,0.00 0.1 5.46,1.82 7.29,0.00 5.46,1.82 7.29,0.00 0.2 5.61,1.87 7.49,0.00 5.61,1.87 7.50,0.00 0.4 6.00,2.00 8.02,0.00 6.00,2.00 8.02,0.00 0.6 6.51,2.17 8.68,0.00 6.48,2.16 8.67,0.00 0.8 7.08,2.36 9.45,0.00 7.05,2.35 9.46,0.00 1.0 7.77,2.59 10.4,0.00 7.77,2.59 10.41,0.00

5.2

K

u Khard u Kusoft D ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ α = 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1.0 tp= 1.0, 3.0, 10.0 ns HxEXT = 0.95 1.05 Oe (5.3) 5.5,5.6,5.7,5.8

42 5 ECC DMI 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (a) α = 0.001 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (b) α = 0.003 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (c) α = 0.01 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (d) α = 0.03 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 tp=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (e) α = 0.1 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 tp=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (f) α = 0.3 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 tp=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (g) α = 1

5.2. Ku 43 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (a) α = 0.001 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (b) α = 0.003 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (c) α = 0.01 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 t_p=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (d) α = 0.03 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 tp=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (e) α = 0.1 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 tp=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (f) α = 0.3 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jsw x /jsw 0 D (erg/cm2) tp=1ns, Ku0:1 tp=1ns, Ku1:3 tp=10ns, Ku0:1 tp=10ns, Ku1:3 tp=1ns,SL tp=10ns,SL (g) α = 1

44 5 ECC DMI 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (a) tp= 1 ns, Ku 0:1 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (b) tp= 1 ns, Ku 1:3 10 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (c) tp= 10 ns, Ku 0:1 10 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (d) tp= 10 ns, Ku 1:3 5.7: α DMI Ku (DMI )

5.3. Ainter 45 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (a) tp= 1 ns, Ku 0:1 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (b) tp= 1 ns, Ku 1:3 10 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (c) tp= 10 ns, Ku 0:1 10 100 1000 10000 0.001 0.01 0.1 1 jsw (GA/m 2 ) α DMI=0.0 erg/cm2 DMI=0.1 erg/cm2 DMI=0.2 erg/cm2 DMI=0.4 erg/cm2 DMI=0.6 erg/cm2 DMI=0.8 erg/cm2 DMI=1.0 erg/cm2 DMI=0.0 erg/cm2,SL (d) tp= 10 ns, Ku 1:3 5.8: α DMI Ku (DMI ) 5.5,5.6,5.7,5.8 5.5,5.6,5.7,5.8 Ku 1:3 0:1 DMI α DMI α DMI DMI α DMI 1ns 10ns 40% 10% ECC 5.5,5.6 ECC DMI

5.3

A

inter 5.2 ECC ECC ECC Ainter

46 5 ECC DMI 0 2 4 6 8 10 12 0 2 4 6 8 10 12 K soft u (Merg/cm 3 ) Khard_u (Merg/cm3) DMI=0.0 DMI=0.1 DMI=0.2 DMI=0.4 DMI=0.6 DMI=0.8 DMI=1.0

(a) Ainter= 0.5 µerg/cm

0 2 4 6 8 10 12 0 2 4 6 8 10 12 K soft u (Merg/cm 3 ) Khard_u (Merg/cm3) DMI=0.0 DMI=0.1 DMI=0.2 DMI=0.4 DMI=0.6 DMI=0.8 DMI=1.0 (b) Ainter= 0.1 µerg/cm 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 K soft u (Merg/cm 3 ) Khard_u (Merg/cm3) DMI=0.0 DMI=0.1 DMI=0.2 DMI=0.4 DMI=0.6 DMI=0.8 DMI=1.0 (c) Ainter= 0.05 µerg/cm 5.9: ∆ = 60 Ku Ainter (DMI )

5.9 DMI Ainter = 1.0 µerg/cm

Ainter Ku Ku

5.4

A

inter Khard u Kusoft D ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ α = 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1.0 tp= 1.0, 10.0 ns Ainter = 1.0, 0.3, 0.1, 0.09, 0.08, 0.07, 0.06, 0.05, 0.04, 0.03, 0.02, 0.01 erg/cm HxEXT = 0.95 1.05 Oe (5.4) 5.10 5.17

5.4. Ainter 47 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.001,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.001,Ku 1:3 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.003,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.003,Ku 1:3 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 0.01,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 0.01,Ku 1:3 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (g) α = 0.03,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (h) α = 0.03,Ku 1:3

5.10: ECC DMI α Ku Ainter (DMI α =

48 5 ECC DMI 300 350 400 450 500 550 600 650 700 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.1,Ku 0:1 300 350 400 450 500 550 600 650 700 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.1,Ku 1:3 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.3,Ku 0:1 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.3,Ku 1:3 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 1.0,Ku 0:1 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 1.0,Ku 1:3

5.11: ECC DMI α Ku Ainter (DMI α =

5.4. Ainter 49 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.001,Ku 0:1 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.001,Ku 1:3 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.003,Ku 0:1 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.003,Ku 1:3 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 0.01,Ku 0:1 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 0.01,Ku 1:3 40 60 80 100 120 140 160 180 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (g) α = 0.03,Ku 0:1 40 60 80 100 120 140 160 180 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (h) α = 0.03,Ku 1:3

5.12: ECC DMI α Ku Ainter (DMI α =

50 5 ECC DMI 100 150 200 250 300 350 400 450 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.1,Ku 0:1 100 150 200 250 300 350 400 450 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.1,Ku 1:3 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.3,Ku 0:1 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.3,Ku 1:3 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 1.0,Ku 0:1 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 1.0,Ku 1:3

5.13: ECC DMI α Ku Ainter (DMI α =

5.4. Ainter 51 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.001,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.001,Ku 1:3 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.003,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.003,Ku 1:3 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 0.01,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 0.01,Ku 1:3 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (g) α = 0.03,Ku 0:1 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (h) α = 0.03,Ku 1:3

5.14: ECC DMI α Ku Ainter (DMI α =

52 5 ECC DMI 300 350 400 450 500 550 600 650 700 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.1,Ku 0:1 300 350 400 450 500 550 600 650 700 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.1,Ku 1:3 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.3,Ku 0:1 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.3,Ku 1:3 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 1.0,Ku 0:1 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 1.0,Ku 1:3

5.15: ECC DMI α Ku Ainter (DMI α =

5.4. Ainter 53 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.001,Ku 0:1 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.001,Ku 1:3 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.003,Ku 0:1 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.003,Ku 1:3 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 0.01,Ku 0:1 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 0.01,Ku 1:3 40 60 80 100 120 140 160 180 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (g) α = 0.03,Ku 0:1 40 60 80 100 120 140 160 180 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (h) α = 0.03,Ku 1:3

5.16: ECC DMI α Ku Ainter (DMI α =

54 5 ECC DMI 100 150 200 250 300 350 400 450 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (a) α = 0.1,Ku 0:1 100 150 200 250 300 350 400 450 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (b) α = 0.1,Ku 1:3 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (c) α = 0.3,Ku 0:1 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm A_inter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (d) α = 0.3,Ku 1:3 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (e) α = 1.0,Ku 0:1 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 jsw (GA/m 2 ) D (erg/cm2) Ainter=1.0µerg/cm Ainter=0.1µerg/cm Ainter=0.08µerg/cm Ainter=0.06µerg/cm Ainter=0.04µerg/cm Ainter=0.02µerg/cm SL (f) α = 1.0,Ku 1:3

5.17: ECC DMI α Ku Ainter (DMI α =

0.1 1.0, tp=10 ns)

5.10 5.17 5.2

Ainter= 1.0 µerg/cm Ainter Ainter

5.4. Ainter 55 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (a) Ku 0:1, tp=1 ns 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (b) Ku 1:3, tp=1 ns 1 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (c) Ku 0:1, tp=10 ns 1 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (d) Ku 1:3, tp=10 ns 5.18: α DMI Ku (DMI )

56 5 ECC DMI 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (a) Ku 0:1, tp=1 ns 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (b) Ku 1:3, tp=1 ns 1 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (c) Ku 0:1, tp=10 ns 1 10 100 1000 10000 0.001 0.01 0.1 1 0.01 0.1 1 jsw (GA/m 2 ) Ainter opt (erg/cm) α DMI=0.0erg/cm2 DMI=0.1erg/cm2 DMI=0.2erg/cm2 DMI=0.4erg/cm2 DMI=0.6erg/cm2 DMI=0.8erg/cm2 DMI=1.0erg/cm2 SL(DMI=0.0erg/cm2) (d) Ku 1:3, tp=10 ns 5.19: α DMI Ku (DMI ) 5.18,5.19 DMI Ainter Ku Ku 0:1 1:3 Ku 1:3 Ku 1 3 5.10 5.19 DMI ECC 3

ECC DMI D = 0.0 erg/cm2 _t

p=1ns 72 tp=10s 80

5.5

ECC α DMI ∆≥ 60 Ku 1ns 10ns 40% 10% Ku DMI Ainter DMI ECC 3 ECC DMI D = 0.0 erg/cm2 _{1ns 10ns} 72% 80% tp=1ns 72 tp=10s 80

5.5. 57 Ainter

59

6

STT-MRAM STT-MRAM DMI DMI STT-MRAM ECC DMI DMI α DMI 1ns 33% 10ns 10% α Ku α DMI θ0 ECC DMI DMI ECC 3 4

ECC DMI D = 0.0 erg/cm2

tp=1ns 72 tp=10ns 80

61

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1 31

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[6] STT-MRAM (5)

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[9] J.Miltat, et.al., Spin transfer into an inhomogeneous magnetization distribution , J.Appl. Phys. 89, 6982-6984(2001)

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