Ultrafast Magnetization Dynamics

T. Ostler1

Dept. of Physics, The University of York, York, United Kingdom.

December 2013

Increasing demand

KB

Megabyte (10002)

Gigabyte (GB 10003)

Terabyte (TB 10004)

Petabyte (PB 10005)

Exabyte (EB 10006)

Zetabyte (ZB 10007)

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 4ZB

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.

Use

rs [m

illio

ns]

Months

Now at 175million

Write speed challenge

• In 1953 IBM launched first commercial HHD with average data access times of just under 1 second!

Me IBM 350

• A 50KB pdf would take a few days to copy.

• How have data rates improved?

Speed limits in magnetism

• Huge increase in speeds since the 80’s.• Rate has been slowing in last 10 years.

Write times

CD @ 1xEnterprise drive

Pulsed fields

Faster write times

How fast can we go?

• 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.

Towards femtosecond processes

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.

• 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).

• 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.

• The strongest force in magnetism. Can we excite processes on this timescale?

Can we go faster?

Timescale:

10’s -> 100’s fs

Femtosecond laser heating and measurement

Fast 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

θF~MZ

Faraday effect

Rotation (θf) of polarization plane.

χ: susceptibility tensor k: wave-vector n: refractive index

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 atomiclevel

Kinetic Monte Carlo10-0 s (s)+

10-16 s (<fs)TDFT/ab-initio spin dynamics

Tim

e

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-magnetizationhttp://www.castep.org/

Superdiffusive spin transport

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

• Anisotropy can also be calculated from first principles.

• Possible to have other anisotropy terms:• Surface• Cubic• Etc.

scbccfcc

What can we calculate?

Distribution of spinwave energies

Magnetization dynamicsStatic properties: M(T), hysteresis

Spinwave dispersion

The spin dynamics model

p-p

e-p e-e

Spinwaves

Heat bath

• Damping is phenomenological.

• Energy exchange is to/from bath and magnon-magnon interactions.

Modelling temperature effects

PrecessionDamping

Noise

Laser heating

Chen et al. Int. Journ. Heat and Mass Transfer. 49, 307-316 (2006)

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 determines

Laser heating

TheoryExperiment

• What governs the time-scale for demagnetization?

• Can we control it?

• What happens if we have multiple species?

Two sublattices

Model calculationsJij>0 Jij<0

Two sublattice ferromagnet

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

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.

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 results

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

XMCD2mm

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).

Beyond magnetization

How can we explain the observed effects in GdFeCo?

Suggests something is occurring on microscopic

level

• No symmetry breaking external source.

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.

0.0

0.2

0.4

0.6

0.8

1.0

ΓΧ Μ

3D FFT

Intermediate structure factor (ISF)

Nor

mal

ized

Ampl

itude

Below switching threshold

No significant change in the ISF

Above switching threshold

Excited region during switching2 bands excited

975K

M/2

X/2

1090K FeCoGd

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).

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 FeCoGd

M/2

X/2

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.

• 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).

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).

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.