Download Current induced DW motion

Current induced domain wall motion
in Rashba quantum wires
Capri Spring School 2013
Martin Stier*, Reinhold Egger** and Michael Thorwart*
*
**
Universität Hamburg
Universität Düsseldorf
Outline
•
domain walls
1D wires (Luttinger liquid)
Spin-orbit (Rashba) interaction
•
numerical results
DW velocity
current pulses
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 2
11.04.2013
Domain walls
• application: racetrack
memory
• reliable and fast motion of
domain walls
• motion at low current
densities
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 3
11.04.2013
Current induced Domain Wall motion
spin polarized current
domain wall
interaction
spin torque on domain wall
additional effects may change s
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 4
11.04.2013
Our set-up
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Landau-Lifshitz-Gilbert equation describes DW dynamics
●
electronic sub-system includes Rashba term
●
describe electrons in 1D wire as Luttinger liquid
●
calculate s and with it T by an equation of motion technique
M Stier, R Egger, M Thorwart - arXiv:1301.0389, 2013
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 5
11.04.2013
Luttinger liquid
•
left and right movers
•
easy to define currents
•
1D system
•
excitations only around
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 6
11.04.2013
Solution
adiabatic
non-adiabatic
Rashba field
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 7
11.04.2013
Numerical calculations
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solve LLG explicitly
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choose Bloch(y) wall
●
Rashba field HR~ey can directly
accelerate / decelerate DW
R
standard parameters:
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 8
11.04.2013
Steady current
●
momentary motion determined by both: current and (Rashba) field
●
oscillation frequency dependent on Rashba coupling and current density
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 9
11.04.2013
Current pulse
DW still in motion after
current pulse ('drifting')
●
direction of velocity
dependent on amplitude
at the end of pulse
●
drifted distance can be
remarkably long
●
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 10
11.04.2013
Controlling effective velocity by pulses
●
contains traveled distance while and after current pulse
●
depending on pulse
length → resulting velocity
strongly increased or decreased
●
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 11
11.04.2013
Non-linear dependence on current density
oscillation period controlled
by current density
●
the stronger the current the
smaller the period
●
this determines if the pulse
end at positive or negative
amplitude
●
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 12
11.04.2013
Conclusions
•
derived current induced spin torque under influence of
Rashba interaction
•
Rashba field arises
•
oscillatory behavior of DW velocity
•
rich behavior for current pulses
strongly in-/decrease of effective velocity
possible negative velocities
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 13
11.04.2013
Thank you for your attention!
Support by
Current induced DW motion
in Rashba nanowires
is gratefully acknowledged
Martin Stier
[email protected]
Seite 14
11.04.2013
Hamiltonian
spin density of left or right
(p=L/R) moving particles
magnetization of domain wall
direction defined by
Rashba interaction
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 15
11.04.2013
Equation of motion
additional relaxation
gradient expansion in derivatives of n:
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 16
11.04.2013
Equation of motion
relaxation rate
extrinsic relaxation
stationary state
Current induced DW motion
in Rashba nanowires
Martin Stier
[email protected]
Seite 17
11.04.2013