T Ostler 1 Dept of Physics The University of York York United Kingdom December 2013 Increasing demand A few GB to TBs 25TB daily log 100TB storage 25PB 24PB daily 330 EB demand in 2011 ID: 356114
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Slide1
Ultrafast Magnetization Dynamics
T. Ostler1Dept. of Physics, The University of York, York, United Kingdom.December 2013Slide2
Increasing demand
A few GB to TB’s
25TB daily log
100TB storage
2.5PB
24PB daily
330 EB demand in 2011
Estimated size of the internet 4ZBSlide3
Increasing demand
If all storage demand was met by SSD’s/flash etc, $250 billion in plant construction is required.Faster data access/writing is desirable.
Users [millions]
Months
Now at 175millionSlide4
Write speed challenge
In 1953 IBM launched first commercial HHD with average data access times of just under 1 second!MeIBM 350
A 50KB pdf would take a few days to copy.
How have data rates improved?Slide5
Speed limits in magnetism
Huge increase in speeds since the 80’s.
Rate has been slowing in last 10 years.Slide6
Write times
CD @ 1xEnterprise drivePulsed fields
Faster write times
How fast can we go?Slide7
Magnetic field processes.Atomistic spin dynamics model for magnetization dynamics.
LLGHow we construct such a modelIncluding laser heating + parameterizationLimitations of the modelFinally femtosecond lasers processes.Conclusion: reversal in hundreds of fs using laser without applied field.Mechanism for switching without a field.
Towards femtosecond
processesSlide8
Precession and damping
Landau-
Lifshitz
-Gilbert (LLG) equation
Precession
Damping
NB, if under- damped, many
precesssion
cycles may be necessary in order to reach
equilibrium.
Current HDD has write pole around 1-2T.
Switching around 1ns.Slide9
Ultrafast field switching in 200ps
GaAs photoswitches excited by fs laser pulse creates initial field.Permally thin film, in-plane.High field and low damping causes ringing oscillations in magnetization.
GaAs photoswitches excited by fs laser pulse creates initial field.
Second pulses (at a very specific delay time) can stop magnetization.
Reversal complete in 200 picoseconds.
Figures from :Nature
, 418, 509-512 (2002).Slide10
Control of magnetization dynamics in applied field limited by precession time.
There are a number of other ways to control magnetization:Spin transfer torqueHeat assisted magnetic recordingThe exchange interaction gives rise to magnetic order.The strongest force in magnetism. Can we excite processes on this timescale?
Can we go faster?
Timescale:
10’s -> 100’s
fsSlide11
Femtosecond
laser heating and measurementFast demagnetization of Ni
Beaurepaire et al. PRL, 76, 4250 (1996).
MOKE in transmission.
Using femtosecond laser pulses Beaurepaire
showed fs demagnetization.
Demagnetization in around 1ps. Remagnetization in a few ps.
Can we model this?
E
E
M
θ
F
~M
Z
Faraday
effect
Rotation (
θ
f
) of polarization plane.
χ
: susceptibility tensor
k: wave-vector
n: refractive indexSlide12
Time-scale/Length-scale
10-15 s (fs)10-12 s (ps)10-9 s (ns)
10-6 s (µs)
10
-3 s (ms)
Langevin Dynamics on atomic
level
Kinetic Monte Carlo
10
-0
s (s)+
10
-16
s (<
fs
)
TDFT/
ab
-initio spin dynamics
Time
10
-9
m (nm)
10
-6
m (
μm
)
10
-3
m (mm)
10
-10
m (Å)
Length
Micromagnetics
/LLB
http://www.psi.ch/swissfel/ultrafast-manipulation-of-the-magnetization
http://www.castep.org/
Superdiffusive
spin transportSlide13
The spin
dynamics modelAssume fixed atomic positionsProcesses such as e-e, e-p and p-p scattering are treated phenomenologically (λ).
At each timestep we calculate a field acting on each spin and solve using numerical integration.
To calculate the fields we consider a Hamiltonian (below).
Extended Heisenberg Hamiltonian
Exchange
Anisotropy
Zeeman
Dipole-DipoleSlide14
How do we find J/D/μ?
Jij can be found from DFT. Adiabatic approximation assuming electron motion much faster than spinwaves.Assume frozen magnon pictureSpin spiral for particular q vector.
Integration in q-space gives exchange energy.
Can also assume nearest neighbour interaction and use experimental TC
to determine Jij
Anisotropy can also be calculated from first principles.
Possible to have other anisotropy terms:
Surface
Cubic
Etc.
sc
bcc
fccSlide15
What can we calculate?
Distribution of spinwave energiesMagnetization dynamics
Static properties: M(T), hysteresis
Spinwave dispersionSlide16
The spin
dynamics model
Spinwaves
Heat bath
Damping is phenomenological.
Energy exchange is to/from bath and
magnon-magnon
interactions.Slide17
Modelling temperature effects
Precession
Damping
NoiseSlide18
Laser heating
Chen
et al
.
Int.
Journ
. Heat and Mass Transfer.
49
, 307-316 (2006)Slide19
How can the electron temperature be determined?
Figure from
Atxitia
et al. Phys. Rev. B.
81
, 174401 (2010).
Usually known from literature
Fitting initial decay to an exponential
Final temperature determinesSlide20
Laser heating
Theory
Experiment
What governs the time-scale for demagnetization?
Can we control it?
What happens if we have multiple species?Slide21
Two
sublattices
Model calculations
J
ij
>0
J
ij
<
0
Two sublattice
f
erromagnet
Two sublattice
f
errimagnet
Strongly exchange coupled.
But
decoupled dynamics.
Fine in theory, what do we see experimentally?
Radu
, Ostler
et al.
submitted.Slide22
X-ray Magnetic Circular
Dichroism
(XMCD)
XMCD used to measure individual magnetic elements.
Excite core electrons from spin-split valance bands.
Circularly polarized photons (+
ħ
,
-
ħ
) give rise to different absorptions.
Radu
, Ostler
et al. Nature
,
472
, 205-208 (2011).Slide23
Two
sublattices
Experiments of dynamics (via XMCD) shows qualitatively similar results.
What determines the rate of demagnetization?
Radu
, Ostler
et al.
submitted.Slide24
Time-scales of elements in different materials
Radu
, Ostler
et al.
submitted.
More details
arXiv
:1308.0993
Measured demagnetization time to 50% demagnetization by tuning pump
fluence
.
Plot the above data against the magnetic moment.
Seems to scale with the magnetic moment.
Deviation due to exchange. Slide25
Can we actually do something useful?
Controlling demagnetization is interesting but can we actually do something with it?
Element-resolved dynamics.
Initial State
Different demagnetization times
Transient ferromagnetic-like state
Reversal of the
sublattices
Radu
et al. Nature
,
472
, 205-208 (2011).
Switching in a magnetic field
Some interesting
behaviour
Experiment
Model resultsSlide26
Switching without a field
What role is the magnetic field playing?
Model calculations show field playing almost no role!
Sequence of pulses without a field
Do we see the same experimentally?
Ostler
et al. Nat.
Commun
.
3
, 666 (2012).Slide27
Experimental Verification: GdFeCo Microstructures
XMCD
2
m
m
Experimental observation of magnetisation after each pulse.
Initial state
- two microstructures with opposite magnetisation
-
Seperated
by distance larger than radius (no coupling)
Ostler
et al. Nat.
Commun
.
3
, 666 (2012).Slide28
Beyond magnetization
How can we explain the observed effects in GdFeCo?
Suggests something is occurring on microscopic level
No symmetry breaking external source.Slide29
To obtain information on the distribution of modes in the Brillouin zone we calculate the intermediate structure factor:
For each time-step we obtain S(q). We then apply Gaussian smoothing.0.00.2
0.40.6
0.8
1.0
Γ
Χ
Μ
3D FFT
Intermediate structure factor (ISF)
Normalized AmplitudeSlide30
Below switching threshold
No significant change in the ISFAbove switching thresholdExcited region during switching2 bands excited
975K
M/2
X
/2
1090K
FeCo
Gd
M/2
X
/2
Intermediate structure factor (ISF)
ISF
distribution of modes even out of equilibrium.
J. Barker, T. Ostler
et al. Nature Scientific Reports,
3
,
3262 (2013).Slide31
Relative Band Amplitude
Dynamic structure factor (DSF)
To calculate the spinwave dispersion from the atomistic model we calculate the DSF.
The point (in k-space) at which both bands are excited corresponds to the spinwave excitation (ISF).
1090K
FeCo
Gd
M/2
X
/2
J. Barker, T. Ostler
et al. Nature Scientific Reports,
3
,
3262 (2013).Slide32
Frequency gap
By knowing at which point in k-space the excitation occurs, we can determine a frequency (energy) gap.
This can help us understand why we do not get switching at certain concentrations of Gd.
Overlapping bands allows for efficient transfer of energy.
Large band gap precludes efficient energy transfer.
J. Barker, T. Ostler
et al. Nature Scientific Reports,
3
,
3262 (2013).Slide33
What is the significance of the excitation of both bands?
Excitation of only one band leads to demagnetization.Excitation of both bands simultaneously leads to the transient ferromagnetic-like state.
J. Barker, T. Ostler
et al. Nature Scientific Reports,
3
,
3262 (2013).Slide34
Summary
Slides available at:http://tomostler.co.uk/list-of-publications/conference-presentations/
Field limit of magnetization switching.
The atomistic spin dynamics model of ultrafast magnetization dynamics.
How we model femtosecond laser heating.
Demagnetization and switching experiments and theory.
How we switch without a field.