Spin-torque nano-oscillators trends and challenging
Domain Microstructure and Dynamics in Magnetic ElementsHeraklion, Crete, April 8 – 11, 2013
Giovanni FinocchioDepartment of Electronic Engineering, Industrial Chemistry and Engineering
University of Messina
N S
extH�
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
Giant magneto-resistance Introduction (1/4)
Spin torque effect
Introduction (2/4)Giant MagnetoResistance
(GMR)
Electronic Transportaffected by
Magnetic State
Fert – Gruenberg (1988)
Spin-Transfer Torque(STT)
Magnetic Stateaffected by
Electronic Transport
Slonczewski – Berger (1996)two sides of the same coin
Introduction (3/4)
eff ext exch ani M TH= + + + +H H H H H H
( )0 3
2 ( , ) ( )B
EffS s
Jd d
dt M dt d M e
µαγ χ = − × + × − × ×
M MM H M M P M M P
J. Slonczweski, J. Magn. Magn. Mat. 159, L1-L6 (1996).
Amp MC+ +H H
Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation
Equation of motion
Oersted Field
MagnetostaticCoupling
Exchange
iS�
jS�
External Field
N SextH
�
Anisotropy Magnetostatic
Contribution
+ + + +
+ +
- - - - -
- - -dH�
Thermal Field
Introduction (4/4)Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation
Semi-implicit algorithm based on the Adams-Bashforth algorithm as a predictor, and a second order Adams-Moulton procedure as a corrector in the Landau–Lifshitz–Gilbert-Slonczewski equation.
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
� Technological point of view
STO very interesting
After the first experimental observation of persistent magnetization dynamics reported by Tsoi and co-workers in point contact geometries with an out-of-plane bias field, there was a huge numbers of experimental and theoretical works.
, , , STO – An overview (1/2)
� Fundamental point of view Technological point of view
– nanoscale size
– broad working temperature
– low dissipation power
– large output power
– ultralow critical current
– microwave emission atzero field
– high oscillation frequency
– narrow linewidth
– …
Fundamental point of view
� compensation of the damping losses
� very rich dynamical behaviour
� smallest self-oscillator known in nature
� excitation of uniform and non-uniform modes
� …
, , , STO – An overview (2/2)
In-plane Out-of-plane
Classification
In-plane polarizer
Out-of-plane free layer
In-plane Out-of-plane
Two in-plane free layers
Two out-of-plane polarizers
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
, , , STO – Effect of the in-planefield
In-plane
� The linewidth is strongly dependent on the in plane field angles.� Non-uniform mode near easy axis – uniform mode near hard in-plane axis� Sub-critical vs Super-critical Hopf bifurcation � Sub-critical vs Super-critical Hopf bifurcation
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
, , , STO – Solitonmode
� Self-oscillation driven by injection of a non uniform current!� Excitation of a sub-GHz mode at zero field. Is a non-uniform mode?
solving the Poisson equation .
V. L. Pokrovskii, G. V. Uimin. Sov. Phys.
G. Finocchio, O. Ozatay, et al. Phys. Rev. B 78, 174408 (2008)
Details of device fabrication and measurement technique
O. Ozatay, et al. Appl. Phys. Lett.88, 202502 (2005).
V. L. Pokrovskii, G. V. Uimin. Sov. Phys. JETP Lett. 41, 128-132 (1985).
S. Komineas. Phys. Rev. Lett. 99, 117202 (2007).
, , , STO – Solitonmode
� Excitation of a Vortex-antivortex pair!
G. Finocchio, O. Ozatay, et al. Phys. Rev. B 78, 174408 (2008)
V. L. Pokrovskii, G. V. Uimin. Sov. Phys. JETP Lett. 41, 128-132 (1985).
S. Komineas. Phys. Rev. Lett. 99, 117202 (2007).
, , , STO – Solitonmode
� Excitation of a different soliton modes! A stable vortex quadripole!
G. Finocchio, S. Komineas, et al in preparation.
V. Puliafito, G. Finocchio, S. Komineas, et al, Poster Tuesday.
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– STOwith interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
STO - Two free layers
� Zero field, high frequency microwave emission!
STO - Two free layers
( ) ( , )
( ) ( , )
eff Gt
eff GP
d d
d dd d
d d
ατ τ
ατ τ
−
−
= − × + × − = − × + × −
t tt t t t b
b bb b b t b
m mm h m T m m
m mm h m T m m
2
( , )( ) ( )( , )
e
ptBg j
dM
ε εµγ ε ε
× × − × = − × × − ×
t t b t b t pb t
m m m m m m mT m m
m m m m m m m
eff ext exch ani M Oe th MC− − − − − − −= + + + + + +t t t t t t th h h h h h h h
eff ext exch ani M Oe th MC− − − − − − −= + + + + + +b b b b b b bh h h h h h h h
�Spin Torque Effect
�Magnetostatic Contribution
G. Finocchio,et al,Phys. Rev. B 76,174408 (2007).
( , ) ( , )ε ε=p f f pm m m m
COUPLING
20
( , ) e ( , )( ) ( )s pbdMγ ε ε
= − × × − ×
b tb b t b t b p
T m mm m m m m m m
Torque from perpendicular
Polarizers
STO - Two free layers( , )sinε θt bm m
20
21
Bth
s
K TD
V M t
αµ γα
= =′∆ ∆+
H ξ ξ
Thermal fluctuationsGaussian process
�Zero mean�Unit variance
( ) ( )13 3/ 2( , ) 4 1 3 4ε η η
− = − + + + • t b b tm m m m
( , ) 0.4ε =p fm m
( , ) 0.2ε =p fm m
( )zthythxthth HHH ,,, ,,=H
( ) 0=tH kth ,
( ) ( ) ( )ttDtHtH kllthkth ′−=′ δδ,,
W. F. Brown, Jr., Phys. Rev. 130, 1677, 1963.
STO - Two free layers� Phase locking between the dynamics in the two free layer! � Frequency doubling in the GMR signal!
� Excitation of a strong non uniform mode !
STO - Two free layers
� Phase locking between the dynamics in the two free layer!
� Systematic study
– Elliptical cross section (170nm x 130nm)
– Circular cross section (140nm)
– Symmetric polarizer (CoNi)
– Asymmetric polarizer (CoNi - CoPt)
� Injection locking at zero field!
STO - Two free layers
23
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
, , ,
Electrostatic interaction MgO/CoFeB� surface perpendicular anisotropy
STO - Interface perpendicular anisotropy
The easy axis depends on
thethickness of the CoFeB
A B C
, , ,
To reduce the out-of-plane demagnetizing field
STO - Interface perpendicular anisotropy
while maintaining the orientation of both the two magnetizations in the film plane
STO properties – demonstrated separately – frequency tunability (field and current)
– nanoscale size
– broad working temperature
– low dissipation power
– large output power
, , ,
Spin-torque compensates the damping losses.
STO - Interface perpendicular anisotropy
– large output power
– ultralow critical current
– microwave emission atzero field
– high oscillation frequency
– very interesting non-autonomous behavior
– narrow linewidth
– …
IDEAL� all-in-one STO
, , ,
Ultralow current density and bias-field-free spin-transfer nano-oscillator Z. M. Zeng, G. Finocchio, B. S. Zhang, J. A. Katine, I. Krivorotov, Y. Huai,
J. Langer, B. Azzerboni, P. Khalili Amiri, K. L. Wang, and H. W. JiangScientific Reports 3, 1426, (2013).
Out-of-plane free layer – in-plane polarizer
STO - Interface perpendicular anisotropy
, , ,
Ultralow current density and bias-field-free spin-transfer nano-oscillator Z. M. Zeng, G. Finocchio, B. S. Zhang, J. A. Katine, I. Krivorotov, Y. Huai,
J. Langer, B. Azzerboni, P. Khalili Amiri, K. L. Wang, and H. W. JiangScientific Reports 3, 1426, (2013).
STO properties– nanoscale size
– low dissipation power <60 µW
– large output power > 60nW
STO - Interface perpendicular anisotropy
– large output power > 60nW
– ultralow critical current <1×10 6 A/cm2
– microwave emission at zero field
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
• Pt/Co/AlO
– Out-of-plane easy axis
– Switchingdrivenby anin-planecurrent
Model (3)
– Switchingdrivenby anin-planecurrent
– Main source: Rashba Effect
• Pt/Co/AlO
– Out-of-plane easy axis
– Switching driven by an in-plane current
– Main source: Spin-Hall Effect (systematic experimentalstudy)
Self-oscillator based on Spin-Hall-Effect
Slonczewski-like torqueSlonczewski-like torque
Self-oscillator based on Spin-Hall-Effect
2 20
2 20 0
1
(1 ) (1 )
(1 ) (1 )
S
J J
S S
d
M dt
d d
M M
αγ α α
αα γ α γ
= − × − × ×+ +
− × × + ×+ +
EFF EFFm
m h m m h
m m σ m σ
σ
Spin-current direction in Pt B H
JS
jd
eM d
µ α=
Slonczewski-like torque
Self-oscillator based on Spin-Hall-Effect
• Ta/CoFeB/MgO
– In-plane easy axis
– Switching driven by an in-plane currentLiu et al, PRL 109, 186602 (2012)
�Dynamics (field applied along 30°with respect to the easy axis)
� Improvement of the output power!
Self-oscillator based on Spin-Hall-Effect
Excitation of a uniform mode
Slightly dependence of the oscillation frequency on current
Liu et al, PRL 109, 186602 (2012)
R. H. Liu, W. L. Lim, and S. Urazhdin, arXiv:1210.2758.
Outline
� Introduction
�Spin-Transfer-torque Oscillators (STO)– An overview
– Effect of the in-plane field angle
– Soliton mode
– Two free layers
– Interface perpendicular anisotropy
�Self-oscillator based on Spin-Hall-Effect
�Conclusions
Remain STO challenges � microwave emission atzero field
– large output power
synchronization of array of STOs
optimization of the geometrical and physical parameters
– ultralow critical current
voltageinduced magneto-crystalline anisotropy
, , , Conclusions
voltageinduced magneto-crystalline anisotropy
– high oscillation frequency
two free layer devices
– narrow linewidth
Synchronization
Injection locking
� microwave emission spin-orbit torque
� Spin-Hall
� Rashba
� Dzyaloshinskii-Moriya
Thank You for Your attention!Thank You for Your attention!
SHE effect
• Spin dependent scattering (Mott)