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Atomistic Modelling of Ultrafast Magnetization Switching

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Atomistic Modelling of Ultrafast Magnetization Switching

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.

Ultrafast Conference on Magnetism

Overview

Deterministic all-thermal switching

Predicted using atomistic spin dynamics.

Single shot.

No applied field required.

Linear polarised light. No IFE.

Verified experimentally.

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

Important features of thedynamics

Element-resolved dynamics.

Transient ferromagnetic-like state

Reversal of the sublattices

Different demagnetization times

Initial State

Raduet al. Nature, 472, 205-208 (2011).

What we know/unanswered questions

?

Transient ferromagnetic like state

I. Raduet al., Nature 472, 205 (2011)

Deterministic reversal without field

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

Different demagnetisation times

I. Raduet al., Nature 472, 205 (2011)U. Atxitiaet al, arXiv:1308.0993.

?

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

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

The atomistic modelof GdFeCo

Random lattice model

Amorphous nature

Exchange Interactions: Heisenberg Hamiltonian

Dynamics

T. Ostleret 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?

Suggests something is occurring on microscopic level

Large demagnetization.

Deterministic switching.

Intermediate structure factor (ISF)

ISF distribution of modes even out of equilibrium.

975K

Above switching threshold

Below switching threshold

X/2

FeCo

1090K

Gd

M/2

X/2

M/2

No significant change in the ISF

Excited region during switching

2 bands excited

- J. Barker, T. Ostler et al. Nature Scientific Reports, in press. arXiv:1308.1314

Dynamic structure factor (DSF)

To calculate the spinwave dispersion from the atomistic model we calculate the DSF.

Relative Band Amplitude

FeCo

1090K

Gd

X/2

M/2

The point (in k-space) at which both bands are excited corresponds to the spinwave excitation (ISF).

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.

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

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.

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.

Predicting the switching window

VCA

LSWT

MFA

Clustering

By combining the analytic treatments:

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

Theoretical Prediction

Simulation Result

Laser Fluence

High

Switching

Low

No Switching

Can we now explain the observed effects?

Transient ferromagnetic like state

I. Raduet al., Nature 472, 205 (2011)

Deterministic reversal without field

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

Different demagnetisation times

I. Raduet al., Nature 472, 205 (2011)U. Atxitiaet al, arXiv:1308.0993.

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

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

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.

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

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

Acknowledgements/references

Thank you for your attention

Hoshen-Kopelmanmethod to calculate typical correlation length for a given Gd concentration.

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.

Virtual Crystal Approximation

Bogolioubov Transform

Virtual Crystal Approximation

Bogolioubov Transform

Predicting switching

VCA

LSWT

MFA

Percolation

Prediction

Switching observed in simulations

Laser Fluence

High

Switching

Low

No Switching

The transfer of energy between sublattices

Only a single band in the excited region.

Non-linear energy transfer between bands.

Large band gap precludes efficient energy transfer.

Important features of thedynamics

Element-resolved dynamics.

Transient ferromagnetic-like state

Reversal of the sublattices

Different demagnetization times

Initial State

Raduet al. Nature, 472, 205-208 (2011).