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Damped expectations for the second generation:
controlling the chaos
Theorist
Theorist Experimentalist
or
Wow, you’re working on your report already? It’s not due until Thursday!
Yeah, I know … Mom says the pills I’m taking are starting to work.
I thought we could go outside and play … it’s snowing … Calvin?
What? Oh, sorry, I wasn’t listening.
I really have to finish this.
total magnetization
macroscopic picture microscopic picture
microscopic picture
total magnetization
macroscopic picture
Background Field driven magnetodynamics
G H
HMdtdM /mgddtdL /
M
LL ˆ
precession
damping MM ˆ
precession
damping
L
d
Background Equation of Motion (damped-driven oscillator)
MMHM-M ˆ
precession
damping
}
{
Background
H
V+ V- e-
50 mm
After current Before current
Current-driven magnetodynamics
Background Current driven magnetodynamics
Wide domain wall
Electron flow
If spins follow magnetization direction
Reaction torque on magnetization
Domain wall translates
s
Bs
eM
jPmv
Adiabatic spin-transfer torque
Background Equation of Motion
)M(vM)M(vMMHM-M ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Field (H) driven terms Current (vs) driven terms
Background
Background
Background Magnetic state affects current
Mfixed
Mfree q
2.04
2.00
R(W)
H (T) -0.2 0.2 0
Giant Magnetoresistance
Albert Fert Peter Grünberg
Cu
Co
Cu
Co
Cu
Background Magnetic state affects current
Mfixed
Mfree q
2.04
2.00
R(W)
H (T) -0.2 0.2 0
Giant Magnetoresistance
Nobel prize
2007 Albert Fert Peter Grünberg
Cu
Co
Cu
Co
Cu
Background Currents control magnetic state
Mfixed
Mfree q
2.04
2.00
R(W)
H (T) -0.2 0.2 0
Giant Magnetoresistance
J. Z. Sun et al. JAP (2003)
Spin-Transfer Torque
I (mA) -20 20 0
2.05
2.00
R(W) Antiparallel
Cu
Co
Cu
Co
Cu
Spin currents can switch magnetization!
Background Current-induced switching dynamics
Low current damped motion
High current switching
High current, high field stable precession
M
Heff Damping torque
Spin transfer torque
Better MRAM
Current-tunable microwave oscillators
Background Complex phase diagram
-0.5 1.5
J (108 A/cm2)
0.16
0 0.0
0.2
0.08
0.5
Parallel
Antiparallel
Precession
DR
(W
)
Fie
ld (
T)
Mfixed
Mfree q
Cu
Co
Cu
Co
Cu
Background Equation of Motion
)M(vM)M(vMMHM-M ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Field (H) driven terms Current (vs) driven terms
well understood, conservative
well understood, conservative
less well understood, dissipative
less well understood, dissipative
Background Equation of Motion
)M(vM)M(vMMHM-M ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
well understood, conservative
well understood, conservative
less well understood, dissipative
less well understood, dissipative
We want to understand the origin of these parameters
Background Equation of Motion
precession
damping
}
{
well understood, conservative
less well understood, dissipative
MMHM-M ˆ
Model Motivating data
Ni
Co Fe
Temperature (K)
Dam
pin
g,
Ferromagnetic resonance
measurements
MMH-MM ˆ
Coupling to the environment
uniform precession
magnons electronic excitations
phonons
eddy currents
electron-hole pairs
Stoner excitations
electron-lattice scattering
scattering to degenerate modes
magneto-striction
magnon-phonon scattering
Extrinsic effects
Intrinsic effects
Model Effective Field Model
eff
0
M
1H =
M
Em
nk nk
nk
E f
eff
0
M M
1H =
M
nk nknk nk
nk
ff
m
reversible
magnetocrystalline anisotropy
dM M
H0
conductivity-like
resistivity-like
Temp.
Dam
pin
g
irreversible
Fermi Surfaces
Real Fermi Surfaces Representative Fermi Surfaces
kx
ky kz
Up Spin Down Spin
Iro
n
Co
bal
t N
icke
l
Band Structure
H nk = nk nk
Breathing Fermi Surface : Hso(t) = -x l s(t)
kx
ky kz
kx
ky kz
kx
ky kz
t
t Energy pumped from Zeeman to spin-orbit type producing electron-hole pairs
Scattering of excited electrons into holes reestablishes equilibrium
kx
ky kz
t
t
Continued pumping and scattering damp the precession
M
M
M
M
dM
dM
.
Model State energies change with precession
F
k
M
Generation of electron-hole pairs due to energy
changes – breathing Fermi surface
ground state excited state
Spin-orbit energy depends on spin
direction (s)
nk
nknkso mH )ˆ(sx
M M M
Representative spin:
lattice scattering
time axis
nk
nknkf
M
0M
1
m eff
H
Model
Conductivity-like term decreases as scattering rate increases
F
k Total
~ s(T)
Temperature
Dam
pin
g lattice
scattering
lattice scattering
short lifetime small damping
F
k
long lifetime large damping
The breathing Fermi surface contribution
Bubbling Fermi Surface : V(t) = Hso(t) - Hso
kx
ky kz
The effective perturbation generates electronic excitations over the Fermi surface, reducing the Zeeman energy.
M
M dM
V(0) = 0
V(t) = Hso(t) – Hso(0)
Electron-electron and electron-lattice scattering restores equilibrium.
kx
ky kz
Model State populations change with precession
M
Generation of electron-hole pairs due to
population changes – bubbling Fermi surface
Eigenstates depend on spin direction (s)
)ˆ()ˆ( zHmHV sososo
M M M
Representative spin:
time axis
F
k
nk
nknkf
mM
0M
1effH
Model
Resistivity-like term increases as scattering rate increases
F
k
DOS
F
The bubbling Fermi surface contribution
~r(T)
Temp.
Dam
pin
g
Total
Model Qualitative prediction
eff
0
s M M
1H =
M
nk nknk nk
nk
ff
m
conductivity-like ‘breathing’ terms
Resistivity-like ‘bubbling’ terms
eff
0 (1)
s M
1H =
M
nknk
nk
f
m
eff
0 (2)
s M
1H =
M
nknk
nk
fm
total damping
conductivity-like
resistivity-like Dam
pin
g,
Scattering rate (temperature)
Qualitative predication
MMH-MM ˆ
Model Qualitative match with experiment
total damping
conductivity-like
resistivity-like Dam
pin
g,
Scattering rate (temperature)
Qualitative predication
Ni
Co Fe
Temperature (K)
Dam
pin
g,
Ferromagnetic resonance measurements
MMH-MM ˆ
Background
Current (vs) driven terms Field (H) driven terms
Equation of Motion
)M(vM)M(vMMHM-M ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Model Non-adiabatic STT as extension of damping
),,0(Im Eq
),,(Im 0Eq
)M(vM)M(vMMH-MM ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Conservative torques
Dissipative torques
Model Non-adiabatic STT as extension of damping
),,0(Im Eq
),,(Im 0Eq
)M(vM)M(vMMH-MM ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Conservative torques
Dissipative torques
precession on
current off
Rotation in time:
Model Non-adiabatic STT as extension of damping
),,0(Im Eq
),,(Im 0Eq : all Fermi level electrons contribute nk
nk
)M(vM)M(vMMH-MM ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Conservative torques
Dissipative torques
precession on
current off
Rotation in time:
Model Non-adiabatic STT as extension of damping
),,0(Im Eq
),,(Im 0Eq : all Fermi level electrons contribute nk
nk
)M(vM)M(vMMH-MM ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Conservative torques
Dissipative torques
precession off
current on
Rotation in space:
Model Non-adiabatic STT as extension of damping
),,0(Im Eq
),,(Im 0Eq : all Fermi level electrons contribute
: Fermi level electron contributions are weighted by their velocity
nk
nk
nk
nknk
sv
v
)M(vM)M(vMMH-MM ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Conservative torques
Dissipative torques
precession off
current on
Rotation in space:
Model Non-adiabatic STT as extension of damping
),,0(Im Eq
),,(Im 0Eq : all Fermi level electrons contribute
: Fermi level electron contributions are weighted by their velocity
nk
nk
nk
nknk
sv
v
)M(vM)M(vMMH-MM ss ˆˆ
precession
damping
}
{
adiabatic spin torque
non-adiabatic spin torque
{ }
Conservative torques
Dissipative torques
rr
s
t
s
dt
sd ˆˆˆ
Model Qualitative Summary
total dissipation
changes in energy
changes in populations
o
r
Scattering rate (temperature)
nk
nknk
sv
v
rr
s
t
s
dt
sd ˆˆˆ
Dissipation occurs through the spin-orbit interaction and electron-lattice scattering
nk
nknkf
mM
0M
1effH
conductivity-like breathing terms
resistivity-like bubbling terms
: precession dissipation parameter : spin-transfer torque dissipation parameter
Model
Model
Model
Newton’s apple tree England
Descendant of Newton’s apple tree
NIST, Maryland
HAPPY BIRTHDAY!
Thanks for the chaotic upbringing
END
Damped expectations for the second generation