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Fourth Basic Circuit Element
V i
q
Voltage, V Current, A
Charge, C Flux, Wb
Resistor:
Capacitor:
Inductor:
Memristor:
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Memristive systems
itiwMV ),,(=
),,( tiwfdt
dw
=
Current-controlled
Memristive system
w = a set of n-state
variables
VtVwGi ),,(=
),,( tVwfdtdw =
Voltage-controlled
Memristive system
itqMV ))((=Ideal memristor Chua, 71
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Properties
1. Passivity criterion: .0),,( tiwM
2. No energy discharge property: . 0)()()( = titVtp
3. Frequency behavior: - as a non-linear resistor at low frequencies;
- as a linear resistor at high frequencies.
4. Doubled-valued Lissajous figure property.
V
i
Pinched Hysteresis Loop
Memristor Fingerprint
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Realizations and Applications
Non-volatile memory Programmable logic
Signal Processing
Neural networks
Thermistors
Ion channelsResistive switching systems:
Binary oxides: TiO2, CuO, NiO, CoO, Fe2O3 Strukov et al.,
Nature 2008
Perovskite oxides: SrTiO3, Pr1-x CaxMnO3
Sulfides: Cu2S, Ag2S
Organics: CuTCNQ, MIM (with pentacene, TPD, AIDCN, )
Semiconductors: GaAs, ZnSe-Ge
Spintronics devices
App
lic
ati
ons
Rea
liza
tions
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Semiconductor spintronics systems
YVP and M. Di Ventra,Phys. Rev. B 78,113309 (2008)
Requirements to observe memristive effects in semiconductor spintronics:
Transport properties should depend on the level of electron-spin polarization in a
semiconductor
Spin polarization in semiconductor should be influenced by an external control
parameter (applied current or voltage).Spin injection Spin extraction
An example:
semiconductor/half-metal junctions
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+V
Semiconductor
with non-degenerate electron gas
Half-metal
Spin-down cloud
YVP and M. Di Ventra, Phys. Rev. B 75, 193301 (2007).
j
Spin blockade
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Critical current: drift-diffusion equations
SemiconductorHalf-metal j
( )( ) ( ) ( )( )
+=
nn
ej
t
ne
sf2div
( ) ( ) ( )+=neDEj x
( )nNe
Ex =0
div
relaxation
diffusion
drift
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SemiconductorHalf-metal j
From condition n(0)=0 we find:
Critical current:
Critical electric field:
For GaAs, jc=10-7
A/m2
,
Boundary conditions fordrift-diffusion model:
j(0)=0 j()=j/2
j(0)=j j()=j/2
0 1 2 3 4 5 6 7 80.00
0.25
0.50
0.75
1.00
n/N
0
x
nn
Critical current
V
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Possible application:
Current stabilization device
Current-voltage characteristics
SC
A
FMcontact
V=Vcont +VSC
j~n(0) Vcont
0 10 20 30 40 500.0
0.2
0.4
0.6
0.8
1.0
j/jc
V/(sL jc )
c
0/(
sL)=0.1
c
0/(
sL)=0.5
c0/(
sL)=1
c
0/(
sL)=5
c
0/(
sL)=10
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Spin memristive systems
Memristive systemw = a set of n-state
variables
ItIwMV ),,(=
),,( tIwf
dt
dw=
In
NLV cs )
)0(2( 00
+=
( )( ) ( ) ( )( )
+=
nn
ej
t
ne
sf2div
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Spin memristive systems
A
FM contact SC
j
YVP and M. Di Ventra, Phys. Rev. B 78, 113309 (2008).
very low frequencies: nonlinear resistor
very high frequencies: linear resistor
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0 2 4 6 8 100
3
6
9
0.0
0.5
1.0
1.5
V(V)
j/jc
Time (ns)
Transient response
Current spikes!
j~n(0) Vcont
Usual conductors:
Ohms law I=V/R
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Memristive spin Hall effect
YVP and M. Di Ventra, Phys. Rev. B 79, 153307 (2008).
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Outline
Memory effects in semiconductor
spintronics
Spin generation in closed geometries
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Spin Hall and stirring effects
Y. K. Kato et al., Science 306, 1910 (2004) M. Switkes et al., Science 283, 1905 (1999)
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Main idea
V1(t)
V2
(t)V3
(t)
V4(t)
I
YVP, N. A. Sinitsyn, A. Kogan, A. Saxena, D. L. Smith, Appl. Phys. Lett. 95, 022114
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Results: current and potential
-1.5
-1.0
-0.5
(V)
y
(m)
0
1
2
01
2x
(m)
GaAs,R=1m, n=1015 cm-3 ,E0=5kV/cm
Averaged current density Potential distribution
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Results: spin polarization
0 1 2 3 4 52
3
4
5
6
7
8
9
0.2 0.4 0.6 0.8 1.00.01
0.1
1
10
pz
(10-4)
p
z(10
-4)
T(ns)
n (1016
cm-3)
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Different number of electrodes
= 3/2= 2/=
-6.000E-4
-3.500E-4
-1.000E-4
1.500E-4
4.000E-4
6.500E-4
9.000E-4
0.001150
0.001400
0.001600
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Screening effects
0 1 2 3 4 52
3
4
5
6
7
8
9
0.2 0.4 0.6 0.8 1.00.01
0.1
1
10
pz
(10
-4)
p
z(10-4)
T(ns)
n (1016cm-3)
-8.000E-5
-6.750E-5
-5.500E-5
-4.250E-5
-3.000E-5
-1.750E-5
-5.000E-6
7.500E-6
2.000E-5
-3.500E-4
-2.000E-4
-5.000E-5
1.000E-4
2.500E-4
4.000E-4
5.500E-4
7.000E-4
8.000E-4
n=1015
cm-3
n=1016
cm-3
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Conclusions
Short time memory effects are intrinsic in many
semiconductor spintronics devices
Transient response of semiconductor spintronics
devices may limit their operational frequency
All-electrical spin polarization generation scheme is
suggested based on a combination of Spin Hall
effect and stirring effect Such a scheme can be used, e.g., to control
magnetization of nano-magnets