Current-driven ferromagnetic resonance, mechanical torques and rotary motion in magnetic nanostructures Alexey A. Kovalev Collaborators: errit E.W. Bauer Arne Brataas Jairo Sinova
In the first part of the talk: Scattering matrix approach for multilayers (spin valves). Magnetoelectronic circuit theory (Kirchhoff s rules). on-monotonic magnetoresistance and zerotorque points. Incomplete absorption of transverse spincurrent in thin ferromagnetic layers and consequences for torques.
Perpendicular spin-valves:. Can contain layers as small as 30x90x5.5 nm. Usually contain one hard and one soft (excited) layer 3. Can be realized as free standing nano-pillars Cu Cu Py Cu i8e9 J. C. Sankey, P. M. Braganca, A... arcia, I.. Krivorotov,. A. Buhrman, and D. C. alph, Phys. ev. Lett. 96, 760 (006).
Magnetoelectronic circuit theory (Kirchhoff s rules) In the nodes, spin and charge currents are conserved!
We use reflection and transmission matrices between nodes. rˆ nm rnm = 0 r 0 nm ; tˆ nm t nm = 0 n, m numbers of transverse channels 0 t nm f ˆ Iˆ = ˆ f = (ˆ I 0 0 ˆ µ µ 0 σˆ σˆ I s = ˆ σˆ f ) / s µ S M µ S µ S
Collinear spin-transport. = mn r ( δ ( ) mn ) mn two-resistor model µ S M I I I
Transverse to the magnetization spin-transport. = µ S M µ S t = = mn mn ( * δ r ( r ) ) t mn mn ( t mn mn ) * mn
M µ S t S t S S S ) Im ( ) e ( ) Im ( ) e ( m m m m m m µ µ µ µ µ S [ ] = = S S S I µ µ m m I m ) ( µ ) ( ) ( µ ) ( 0 0 0 The magnetoelectronic circuit theory (generalized Kirchhoff s rules). Collinear part Transverse part When size sd << l
Physical meaning of the new conductances Leaking of spin accumulation into ferromagnet (e part of mixing conductance) µ S M ield effect on spin accumulation (Im part of mixing conductance) µ S M Penetration of transverse spin current through a ferromagnet (e, Im part of mixing transmission). µ S M
Penetration of transverse spin-current through a ferromagnet. M µ? S M E 4s ϕ = ( k k ) L 3d ferromagnet λ c = π /( k k )
Transverse spin-current is absorbed almost at the interface leading to torques I ixed layer ree layer
Mixing conductance and transmission for metallic layers Band structure calculations for perfect interfaces M. Zwierzycki et al., Phys. ev. B 7, 06440 (005)
Magnetoresistance in multilayers = ;, 4 4 () () = = () () ( θ ) = ( () () ( α ; () () )( - are the mixing conductances, () -conductances for the left (right) ferromagnet including normal metal. ) ( α )( α = cosθ ) α ) ( θ ) = 4 cos( θ ) / ; χ = χ( cos( θ ))
Magnetization torque ) )( ( ) ( s α α η [ ] ) ( ) ( m m m m m τ = f s ST e I η η h 0 η f
ood agreement with experiment on.0 multilayered structures. am (θ) 0.5 0.0-0.5 0.0 0.5.0.5 θ/π b( 50) Cu(0) emn(8) Py(6) Cu(0) Py(.5 ) Cu(0) b(50) cond-mat/040344, S. Urazhdin,. Loloee, W.P. Pratt Jr.
Zero-torque point 0.6 τ /τ 0 0.3 Im#0 Im=0 0.0 0.0 0.5.0 θ/π Ih τ ST = s f e [ η m ( m m ) η ( m m )] Can influence the steady precessional states!
Effect of mixing transmission on torque τ o = h I 0 e Simple explanation: t e > 0 t e < 0 µ S M µ S M Should be observable in the magnetization reversal experiments!
Important notes: or tunnel junctions, the imaginary part of the mixing conductance can be of the order of the spin-up and -down conductances. In weak ferromagnets like Pdi Cui, the coherence length is much larger and the mixing transmission can be of the order of the mixing conductance.
In the second part Mechanical torques due to spin transfer to the lattice Electrical detection of the ferromagnetic resonance Electrical detection of the spin-transfer mechanical torques via the resonant magnetovibrational coupling Spin-transfer mechanical torques and spin-transfer nanomotor
. Magnetic resonance force microscopy. Magneto-motive transducers in the range of Hz Some relevant examples of EMS J.A. Sidles et al. ev. Mod. Phys. 67, 49 (995). X. M. H. Huang et al., ature. 4, 496 (003).
Spin transfer due to spin-flip x j, j s s x j0 x j s = 0 = Ν( ε ) µ /τ 0 charge and spin current densities; µ spin accumulation; Ν ( ε ) density of states; τ spin-flip time. P. Mohanty,. Zolfagharkhani, S. Kettemann sf s sf and P. ulde, Phys. ev. B 70, 9530 (004)
By solving diffusion equation we find τ T = PIh / e ST 0 8 m, I = ma l sd, l sd τ 0 = Ih / e spin diffusion length in the ferromagnetic and normal metal P polarization
Spin transfer to the lattice through the shape and crystal anisotropies ixed base T = PIh / e ST I M H M T θ max ST = DθM M V s s 0 6 m, angle of magnetization deflection
Electrical detection of the current-driven M V I M M AC current Analogy with semiconductor diode I I <0 >0 J. C. Sankey et al., Phys. ev. Lett. 96, 760 (006).
Spin pumping by moving magnetization E Is Y. Tserkovnyak, A. Brataas, and. E. W. Bauer, Phys. ev. Lett. 88, 760 (00) Extra ilbert damping - α sp
Asymmetry and spin pumping as a source of extra DC voltage V AC current Voltage due to spin pumping is significant for thin layers in which the damping due to pumping is large Spin pumping voltage ectified voltage α α bulk sp α sp
When mechanical motion is slow, the magnetization is always along the minimum energy direction. M M ϕ In resonant magnetomechanical coupling, the mechanical motion is as fast as the magnetization motion. T M Hdem Hcryst
ormal modes of coupled system - Magnetic subsystem -Mechanical subsystem
Magnetovibrational modes
Electrical detection of M and magnetovibrational modes.0 DC voltage U 0 /V 0 0.5 0.0 ω = ω 0.9.0. AC currentfrequency ω/ω m g g = ( D D )( V / V )( M / )( L / a) anisotropies x z m l s µ saturation magnetization Lame constant 0.00 largest and smallest sizes of rod
Spin-transfer nanomotor MWT Pt MWT I T ST = PIh / e 0 9 m. Metallic wires have recently been grown inside MWT.. Half metals have recently been contacted to MWT. 3. In MWT bearing, the friction force is practically absent.
Conclusions We demonstrate different mechanisms of spin transfer to the lattice. Spin-transfer mechanical torques are generally small and require special techniques for detection. We propose to detect spin-transfer mechanical torques electrically by employing magnetovibrational coupling. We propose spin-transfer nanomotor operating without external magnetic field.