Ultrafast Magnetization Dynamics
T. Ostler1
Dept. of Physics, The University of York, York, United Kingdom.
December 2013
Increasing demand
25TB daily log
100TB storage
KB
A few GB to TB’s
Megabyte
(10002)
Gigabyte (GB
10003)
Terabyte (TB 10004)
2.5PB
24PB daily
Petabyte (PB 10005)
Exabyte (EB 10006)
Zetabyte (ZB 10007)
330 EB demand in 2011
Estimated size of the internet 4ZB
Users [millions]
Increasing demand
Now at 175million
Months
• If all storage demand was met by
SSD’s/flash etc, $250 billion in plant
construction is required.
• Faster data access/writing is desirable.
Write speed challenge
• In 1953 IBM launched first commercial HHD with average data access
times of just under 1 second!
Me
• A 50KB pdf would take a few days to copy.
• How have data rates improved?
IBM 350
Speed limits in magnetism
• Huge increase in speeds since the 80’s.
• Rate has been slowing in last 10 years.
Write times
Enterprise
drive
How fast can
we go?
Faster write times
Pulsed fields
CD @ 1x
Towards femtosecond processes
• Magnetic field processes.
• Atomistic spin dynamics model for magnetization dynamics.
–
–
–
–
LLG
How we construct such a model
Including laser heating + parameterization
Limitations of the model
• Finally femtosecond lasers processes.
• Conclusion: reversal in hundreds of fs using laser without
applied field.
• Mechanism for switching without a field.
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.
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.
Figures from :Nature, 418, 509-512 (2002).
•
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.
Can we go faster?
•
Control of magnetization dynamics in applied field limited by precession time.
•
There are a number of other ways to control magnetization:
–
–
•
Spin transfer torque
Heat assisted magnetic recording
The exchange interaction gives rise to magnetic order.
Timescale:
10’s -> 100’s fs
•
The strongest force in magnetism. Can we excite processes on this timescale?
Femtosecond laser heating and measurement
E
E
θF~MZ
M
Faraday effect
•
MOKE in transmission.
•
Using femtosecond laser pulses Beaurepaire showed fs
demagnetization.
•
Demagnetization in around 1ps. Remagnetization in a few
ps.
•
Can we model this?
 Rotation (θf) of polarization
plane.
 χ: susceptibility tensor
 k: wave-vector
 n: refractive index
Fast demagnetization of Ni
Beaurepaire et al. PRL, 76, 4250 (1996).
Time-scale/Length-scale
Length
10-10 m (Å)
Time
10-16
s (<fs)
10-9 m (nm)
Superdiffusive
spin transport
10-12 s (ps)
Langevin
Dynamics on
atomic
level
s (ns)
10-3 m (mm)
TDFT/ab-initio
spin dynamics
10-15 s (fs)
10-9
10-6 m (μm)
Micromagnetics
/LLB
10-6 s (µs)
10-3 s (ms)
10-0
s (s)+
Kinetic Monte Carlo
http://www.psi.ch/swissfel/ultrafast-manipulation-of-the-magnetization
http://www.castep.org/
The spin dynamics model
•
Assume fixed atomic positions
•
Processes 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-Dipole
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 picture
•
Spin 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
sc
bcc
fcc
•
Anisotropy can also be calculated from
first principles.
•
Possible to have other anisotropy
terms:
• Surface
• Cubic
• Etc.
Static properties: M(T), hysteresis
Magnetization dynamics
What can we calculate?
Distribution of spinwave energies
Spinwave dispersion
The spin dynamics model
Heat bath
• Damping is phenomenological.
e-p
• Energy exchange is to/from bath
and magnon-magnon
interactions.
e-e
p-p
Spinwaves
Modelling temperature effects
Damping
Precession
Noise
Laser heating
Chen et al. Int. Journ. Heat and Mass Transfer. 49, 307-316 (2006)
How can the electron temperature be determined?
Usually known from literature
Fitting initial decay to an exponential
Final temperature determines
Figure from Atxitia et al. Phys. Rev. B. 81, 174401 (2010).
Laser heating
Experiment
Theory
• What governs the time-scale for demagnetization?
• Can we control it?
• What happens if we have multiple species?
Two sublattices
Jij>0
Two sublattice
ferromagnet
Jij<0
Model calculations
Two sublattice
ferrimagnet
• Strongly exchange coupled.
• But decoupled dynamics.
• Fine in theory, what do we see experimentally?
Radu, Ostler et al. submitted.
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).
Two sublattices
• Experiments of dynamics (via XMCD) shows qualitatively similar results.
• What determines the rate of demagnetization?
Radu, Ostler et al. submitted.
Time-scales of elements in different materials
• 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.
Radu, Ostler et al. submitted.
More details arXiv:1308.0993
Can we actually do something useful?
• Controlling demagnetization is interesting but can we actually do something with
it?
Element-resolved dynamics.
• Switching in a magnetic field
• Some interesting behaviour
Experiment
Initial State
Different
demagnetization times
Radu et al. Nature, 472, 205-208 (2011).
Model results
Transient
ferromagnetic-like
state
Reversal of the
sublattices
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).
Experimental Verification: GdFeCo Microstructures
Initial state
- two microstructures with
opposite magnetisation
- Seperated by distance larger
than radius (no coupling)
2mm
XMCD
Experimental observation of magnetisation after each pulse.
Ostler et al. Nat. Commun. 3, 666 (2012).
Beyond magnetization
How can we explain the observed effects in GdFeCo?
• No symmetry breaking external
source.
Suggests something is
occurring on microscopic
level
Intermediate structure factor (ISF)
 To obtain information on the distribution of modes in the Brillouin zone we calculate the
intermediate structure factor:
3D FFT
 For each time-step we obtain
S(q).
 We then apply Gaussian
smoothing.
Normalized Amplitude
1.0
0.8
0.6
0.4
0.2
0.0
Χ
Γ
Μ
Intermediate structure factor (ISF)
• ISF  distribution of modes even out of equilibrium.
Above switching threshold
Below switching threshold
1090K
975K
X/2
X/2
M/2
M/2
No significant change in the ISF
J. Barker, T. Ostler et al. Nature Scientific Reports, 3, 3262 (2013).
FeCo
Gd
Excited region during switching
2 bands excited
Dynamic structure factor (DSF)
• To calculate the spinwave dispersion from the atomistic model we calculate the
DSF.
1090K
Relative
BandFeCo
Amplitude
Gd
X/2
M/2
• The point (in k-space) at which both bands are excited corresponds to the
spinwave excitation (ISF).
J. Barker, T. Ostler et al. Nature Scientific Reports, 3, 3262 (2013).
Frequency gap
• By knowing at which point in k-space the excitation occurs, we can determine a
frequency (energy) gap.
Overlapping bands
allows for efficient
transfer of energy.
• This can help us understand why we do not get switching at certain concentrations
of Gd.
Large band gap
precludes efficient
energy transfer.
J. Barker, T. Ostler et al. Nature Scientific Reports, 3, 3262 (2013).
What is the significance of the excitation of both bands?
• Excitation of only one
band leads to
demagnetization.
•
J. Barker, T. Ostler et al. Nature Scientific Reports, 3, 3262 (2013).
Excitation of both
bands simultaneously
leads to the transient
ferromagnetic-like
state.
Summary
• 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.
Slides available at:
http://tomostler.co.uk/list-of-publications/conference-presentations/