Atomistic Modelling of Ultrafast Magnetization Switching

Ultrafast Conference on Magnetism

J. Barker1, T. Ostler1, O. Hovorka1, U. Atxitia1,2, O. Chubykalo-Fesenko2 and R. W. Chantrell1

1Dept. of Physics, The University of York, York, United Kingdom.2Instituto de Ciencia de Materiales de Madrid, CSIC, Madrid, Spain.

Overview

Thermal switching observed

• No good explanation.

Can we develop a theory/framework?

• Can we predict something?

• Better/new materials.

Is it predictive?

• Can it explain all observed behaviour?

• Verification.

Deterministic all-thermal switching

Predicted using atomistic spin dynamics.

No applied field required.

Verified experimentally.

Ostler et al. Nat. Commun., 3, 666 (2012).

Single shot.

Linear polarised light. No IFE.

Element-resolved dynamics.

Initial State

Different demagnetization

times

Transient ferromagnetic-like

state

Reversal of the sublattices

Important features of the dynamics

Radu et al. Nature, 472, 205-208 (2011).

Different demagnetisation timesI. Radu et al., Nature 472, 205 (2011)

U. Atxitia et al, arXiv:1308.0993.

Transient ferromagnetic like stateI. Radu et al., Nature 472, 205 (2011)

Deterministic reversal without fieldT.A. Ostler et al., Nat. Commun. 3, 666 (2012)

Difference in magnetic moment (mostly, see talk by O. Chubykalo-Fesenko)

?

?

What we know/unanswered questions

Understanding the mechanism driving this process is crucial for finding new materials.

The atomistic model of GdFeCo

Amorphous nature

Random lattice model

Exchange Interactions: Heisenberg Hamiltonian

Dynamics

T. Ostler et al., Phys. Rev. B 84, 024407 (2011)

Femtosecond heating

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

Beyond magnetization

How can we explain the observed effects in GdFeCo?

Large demagnetization.

Deterministic switching.

Suggests something is occurring on microscopic

level

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, in press. arXiv:1308.1314

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

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.

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.

Can we predict where in k-space both bands will be excited?

Effects of clustering

Randomly populating lattice

Recall overlap in spectrum.

Length-scale corresponds to physical clusters.

The point at which we have band overlap in the spinwave spectrum and the cluster size are correlated.

Clustering

Linear Spin Wave Theory

Virtual Crystal Approximation

Bogolioubov Transform

Spinwave dispersion

From linear spinwave theory (LSWT) we can derive the magnon dispersion relation.

Use cluster analysis to determine which part of spectrum to consider gap.

No Switching

Switc

hing

Laser Fluence

High

Low

By combining the analytic treatments:

Predicting the switching window

We can predict the energy gap required to excite modes in both bands at significant |k|.

Theoretical Prediction Simulation Result

VCA ClusteringMFALSWT

Different demagnetisation timesI. Radu et al., Nature 472, 205 (2011)

U. Atxitia et al, arXiv:1308.0993.

Transient ferromagnetic like

stateI. Radu et al., Nature

472, 205 (2011)

Deterministic reversal without field

T.A. Ostler et al., Nat. Commun. 3, 666 (2012)

Difference in magnetic moment (mostly, see talk by O. Chubykalo-

Fesenko)

Can we now explain the observed effects?

• transient state arising from two magnon excitation • cooling ~ps means excitation decays

Summary

Our aim was to explain observed dynamics.

Distribution of modes showed excitation at finite k-vector.

Transient state arises from two-magnon excitation.

Energy of two-magnon excitation predicts composition dependent switching.

Conclusions/outlook

Understanding this mechanism we can engineer other anti-ferromagnetically coupled materials/structures[1].

Key ingredients

Two bands arising from two (or more) species

AFM coupled

Stimulus with sufficient energy

to excite both bands

Stimulus must be faster than the

timescale of the decay of the

modes

The species that reverses first

must form stable sublattice

[1] R. Evans et al., arXiv: (2013)

Acknowledgements/references

References

Demagnetization times: Atxitia et al. arXiv:1308.0993 (2013).

Transient ferromagnetic-like state: Radu et al. Nature 472, 205-208 (2011).

Atomistic model of GdFeCo: T. Ostler et al., Phys. Rev. B 84, 024407 (2011).

Thermally induced switching: Nat. Commun. 3, 666 (2012).

Switching in heterostructures: R. Evans et al. arXiv:1308.1314 (2013).

Switching mechanism: J. Barker et al. Nat. Sci. Rep. (in press) arXiv:1308.1314.

Thank you for your attention

Only A is fitted to account for finite size lattice, pc and ν are

universal exponents.

The spin wave spectrum and physical clustering are correlated.

Hoshen-Kopelman method to calculate typical correlation

length for a given Gd concentration.

Clustering effects

Linear Spin Wave Theory

Virtual Crystal Approximation

Bogolioubov Transform

Linear Spin Wave TheoryVirtual Crystal Approximation

Bogolioubov Transform

Prediction Switching observed in simulations

VCA PercolationMFALSWT

No Switching

Switc

hing

Laser Fluence

High

Low

Predicting switching

Non-linear energy transfer between

bands.

Only a single band in the excited region.

Large band gap precludes efficient

energy transfer.

The transfer of energy between sublattices

Element-resolved dynamics.

Initial State

Different demagnetization

times

Transient ferromagnetic-like

state

Reversal of the sublattices

Important features of the dynamics

Radu et al. Nature, 472, 205-208 (2011).