Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal

HGST, San Jose, August 2012

Theoretical/Modelling Contributions

T. Ostler, J. Barker, R. F. L. Evans and R. W. ChantrellDept. of Physics, The University of York, York, United Kingdom.

U. Atxitia and O. Chubykalo-FesenkoInstituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, Madrid, Spain.

D. Afansiev and B. A. IvanovInstitute of Magnetism, NASU Kiev, Ukraine.

Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal

HGST, San Jose, August 2012

Experimental Contributions

S. El Moussaoui, L. Le Guyader, E. Mengotti, L. J. Heyderman and F. NoltingPaul Scherrer Institut, Villigen, Switzerland

A. Tsukamoto and A. ItohCollege of Science and Technology, Nihon University, Funabashi, Chiba, Japan.

A. M. Kalashnikova , K. Vahaplar, J. Mentink, A. Kirilyuk, Th. Rasing and A. V. KimelRadboud University Nijmegen, Institute for Molecules and Materials, Nijmegen, The

Netherlands.

Ostler et al., Nature Communications, 3, 666 (2012).

Outline

• Model outline: atomistic LLG of GdFeCo and laser heating

• Static properties of GdFeCo and comparison to experiment

• Transient dynamics under laser heating

• Deterministic switching using heat and experimental verification

• Mechanism of reversal

Background

• Inverse Faraday[1,2] effect relates E-field of light to generation of magnetization.

• Can be treated as an effective field with the chirality determining the sign of the field.

[1] Hertel, JMMM, 303, L1-L4 (2006).[2] Van der Ziel et al., Phys Rev Lett 15, 5 (1965).[3] Stanciu et al. PRL, 99, 047601 (2007).

σ-

σ+

Inverse Faraday effect

M(0)

• Control of magnetization of ferrimagnetic GdFeCo[3]

• High powered laser systems generate a lot of heat.

• What is the role of the heat and the effective field from the IFE?

Recall for circularly polarised light, magnetization induced is given by:

For linearly polarized light cross product is zero. Energy transferred as heat.

Two-temperature[1] model defines an electron and phonon temperature (Te and Tl) as a function of time.

Heat capacity of electrons is smaller than phonons so see rapid increase in electron temperature (ultrafast heating).

A model of laser heating

Electrons

e-

e-

e-

Lattice

e-

Gel

Laser inputP(t)

Two temperature model[1] Chen et al. International Journal of Heat and Mass Transfer. 49, 307-316 (2006)

Model: Atomistic LLG

For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011)

We use a model based on the Landau-Lifshitz-Gilbert (LLG) equation for atomistic spins.

Time evolution of each spin described by a coupled LLG equation for spin i.

Hamiltonian contains only exchange and anisotropy.

Field then given by:

is a (stochastic) thermal term allowing temperature to be incorporated into the model.

Sub-lattice magnetization

Fe

Gd

Atomic Level

Model: Exchange interactions/Structure

For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011)

Fe-Fe and Gd-Gd interactions are ferromagnetic (J>0)

Fe-Gd interactions are anti-ferromagnetic (J<0)

GdFeCo is an amorphous ferrimagnet. Assume regular lattice (fcc). In the model we allocate Gd and FeCo spins randomly.

Bulk Properties

Exchange values (J’s) based on experimental observations of sublattice magnetizations as a function of temperature.

Compensation point and TC determined by element resolved XMCD.

Variation of J’s to get correct temperature dependence.

Validation of model by reproducing experimental observations.

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

compensation point

Bulk Properties

Experimental hysteresis loops (measured for both Fe and Gd species) show out-of-plane magnetisation (see reference below for sample loops).

Experiments of various compositions of GdFeCo (with different compensation points) show diverging coercive field at compensation point.

Qualitative agreement with atomistic model.

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

Summary so far

A way of describing heating

effect of fs laser

Atomic level model of a ferrimagnet

with time

We investigate dynamics of GdFeCo and show differential sublattice dynamics and a transient ferromagnetic state.

Then demonstrate heat driven reversal via the transient ferromagnetic state.

Outline explanation is given for reversal mechanism.

Transient Dynamics in GdFeCo by XMCD & Model

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

Experiment Model results

Femtosecond heating in a magnetic field.

Gd and Fe sublattices exhibit different dynamics.

Even though they are strongly exchange coupled.

(an aside) Demagnetisation in ferromagnetic Ni50Fe50

Experiments performed by I. Radu

Model results

Femtosecond heating shows decoupled behaviour in NiFe. Sublattice magnetizations are measured by element specific XMCD. Each sublattice demagnetises on a different timescale.

Experiment

Demagnetisation in ferrimagnetic GdFeCo

Experiments performed by I. Radu

Model results

High fluence completely demagnetises GdFeCo as temperature quickly increases over the Curie temperature.

Again, dispite strong antiferromagnetic exchange coupling the two sublattices demagnetise at different rates.

Experiment

Characteristic demagnetisation time can be estimated as[1]:

GdFeCo has 2 sublattices with different moment (µ).

Even though they are strongly exchange coupled the sublattices demagnetise at different rates (with µ).

Timescale of Demagnetisation

Figures from Radu et al. Nature 472, 205-208 (2011).[1] Kazantseva et al. EPL, 81, 27004 (2008).

Experiment

Model results

Transient Ferromagnetic-like State

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

Laser heating in applied magnetic field of 0.5 T

• System gets into a transient ferromagnetic state at around 400 fs.

• Transient state exists for around 1 ps.

• As part of a systematic investigation we found that reversal occured in the absence of an applied field.

Numerical Results of Switching Without a Field

Very unexpected result that the field plays no role.

Is this determinisitic?

GdFeCo

No magnetic field

Sequence of pulses

Do we see the same effect experimentally?

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)

Experimental Verification: GdFeCo Thin Films

Initially film magnetised “up”

Gd

Fe

MOKE

Similar results for film initially magnetised in “down” state.

Beyond regime of all-optical reversal, i.e. cannot be controlled by laser polarisation. Therefore it must be a heat effect.

After action of each pulse the magnetization switches, independently of initial state.

What about the Inverse Faraday Effect?

Stanciu et al. PRL, 99, 047601 (2007)

• Orientation of magnetization governed by light polarisation.

Does not depend on chirality (high fluence)

Depends on chirality (lower fluence)

What about the Inverse Faraday Effect?

The Effect of Compensation Previous studies have tried to switch using the changing dynamics at the compensation point[ref].

Simulations show starting temperature not important.

Supported by experiments on different compositions of GdFeCo support the numerical observation.

Effect of a stabilising field• What happens now if we apply a field to oppose the formation of the transient

ferromagnetic state?

• Is this a fragile effect?

10 T

40 T

50 T

• Suggests probable exchange origin of effect (more later).

GdFeCo

Bz=10,40,50 T

Mechanism of Reversal

After heat pulse TM moments more disordered than RE (different demagnetisation rates).

On small (local) length scale TM and RE random angles between them.

The effect is averaged out over the system.

FMR Exchange

Exchange mode is excited when sublattices are not exactly anti-parallel.

Mechanism of Reversal

If we decrease the system size then we still see reversal via transient state.

For small systems a lot of precession is induced.

Frequency of precession associated with exchange mode.

For systems larger than 20nm3 there is no obvious precession induced (averaged out over system).

Further evidence of exchange driven effect.

TM sublattice

TM

RE

TM

end of pulse

end of pulse

μTM=μRE

Importance of Moments

As previously stated, the short time-scale demagnetisation time is governed by the magnitude of the correlator.

If we artificially make the local magnetic moments equal, the correlators are equal and no switching occurs.

Summary

Demonstrated numerically switching can occur using only a heat pulse without the need for magnetic field.

Switching is deterministic.

Verified the mechanism experimentally in microstructures (and thin films, see paper). Shown that stray fields play no role.

The magnetic moments are important for switching.

Demonstrated a possible explanation via a local excitation of exchange mode by decreasing system size and observing induced precession.

Acknowledgements Experiments performed at the SIM beamline of the Swiss Light Source, PSI.

Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), de Stichting voor Fundamenteel Onderzoek der Materie (FOM).

The Russian Foundation for Basic Research (RFBR).

European Community’s Seventh Framework Programme (FP7/2007-2013) Grants No. NMP3-SL-2008-214469 (UltraMagnetron) and No. 214810 (FANTOMAS),

Spanish MICINN project FIS2010-20979-C02-02

European Research Council under the European Union’s Seventh Framework Programme (FP7/2007- 2013)/ ERC Grant agreement No 257280 (Femtomagnetism).

NASU grant numbers 228-11 and 227-11.

Thank you for listening.

Mechanism of Reversal

After heat pulse TM moments more disordered than RE (different demagnetisation rates).

On small (local) length scale TM and RE random angles between them.

The effect is averaged out over the system.

FMR Exchange

Exchange mode is excited when sublattices are not exactly anti-parallel.

Numerical Model• Energetics of system described by Hamiltonian:

Dynamics of each spin given by Landau-Lifshitz-Gilbert Langevin equation.

Moments defined through the fluctuation dissipation theorem as:

Effective field given by:

Landau-Lifshitz-Bloch equation of motion So far we have used a model for each

atomic magnetic moment. A macro-spin approach should show the

same behaviour. We write a Landau-Lifshitz-Bloch (LLB)

equation for the TM and RE sublattices.

Usual precession and damping term

Longitudinal relaxation of magnetisation

(submitted) Full details of model from Atxitia el al. Arxiv 1206.6672

Relaxation Rates Temperature dependent relaxation rates are

important for ultrafast switching. Sign in highlighted area below changes sign.

(submitted) Full details of model from Atxitia el al. Arxiv 1206.6672

However, this change in sign alone cannot result in switching! Different longitudinal relaxation is very important but does not

produce switching.

Experimental Prediction Could we see reversal via this dynamical path experimentally? Effect is averaged out over large systems.

LLG

Linearising the LLB Equation From the atomistic simulations, after the pulse is turned off we assume that.

Linearise

Note: to simplify the analysis we have assumed a square pulse from 0K->1500K->0K

Perpendicular Component LLB analysis shows that we require a perpendicular component to induce

switching.

In LLG simulations, high thermal fluctuations give rise to local perpendicular component.

Note: high frequency of oscillations associated with exchange mode.

no transverse component, no switching (dashed)

small transverse component leads to switching (solid)

LLB simulation

System Close to Reversal Analysis shows that when the temperature is lowered there is a transfer of

angular momentum from the (unstable) linear (mz) component to transverse (ρ). Requires a small initial transverse component.

LLB LLG

T

t

Different pulse heights lead to different state before pulse turned off.

Transient Ferromagnetic-like State

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

Laser heating in applied magnetic field of 0.5 T

• For short time sublattices align against TM-RE exchange interaction

• “State” exists for around 1ps

Importance of moments

μTM=μRE

Linear Reversal Usual reversal mechanism (in a field) below TC via precessional switching

At high temperatures, magnetisation responds quickly without perpendicular component (linear route[1]). Laser heating results in linear demagnetisation[2].

The Effect of Heat

E

M+ M- M+ M-

50% 50%

E

M+ M-

System demagnetised

Heat (slowly) through TC Cool below TC

Equal chance of M+/M-

Heat

Cool

• Ordered ferromagnet• Uniaxial anisotropy

E

θ

Inverse Faraday Effect

http://en.wikipedia.org/wiki/Circular_polarization

Magnetization direction governed by E-field of polarized light.

Opposite helicities lead to induced magnetization in opposite direction.

Acts as “effective field” depending on helicity (±).

σ+

σ-

z

z

Hertel, JMMM, 303, L1-L4 (2006)

Outlook

Currently developing a macro-spin model based on the Landau-Lifshitz-Bloch (LLB) formalism to further support reversal mechanism.

How can our mechanism be observed experimentally? Time/space/element resolved magnetisation observation → spin-spin correlation function/structure factor.

Once we understand more about the mechanism, can we find other materials that show the same effect?

Differential Demagnetization Atomistic model agrees qualitatively with experiments Fe and Gd demagnetise in thermal field (scales with μ via correlator)

Fe fast, loses magnetisation in around 300fs

Gd slow, ~1ps

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

Kazantseva et al. EPL, 81, 27004 (2008).

What’s going on?

0 ps

time

- Ground state

0.5 ps

1.2 ps

-T>TC Fe disorders more quickly (μ)

10’s ps

-T<TC precessional switching (on atomic level)-Exchange mode between TM and RE- Transient state

Trivial solution in which transverse component is zero is unstable in regime of reversal.

Perturbations from zero lead to generation of perpendicular component in TM. This triggers the same motion of RE via angular momentum transfer.

Reversal

This process occurs on small length scales so effect can be averaged out in atomistic model.

By decreasing system size we see this effect.

LLB

LLG

Differential demagnetization times

How Can Magnetization Be Reversed?

Magnetic Field Circularly Polarised Spin Injection

E BzE Bz

M+ M- M+ M-

The Effect of HeatE

50% 50%

E E

?

E

M+ M- M+ M-

M+ M- M+ M- M+ M-

Macrospin

Fe

Gd

Atomic Level

Atomic Level Model of GdFeCo

For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011)

Each spins “motion” is described by a Landau-Lifshitz-Gilbert equation

Effective field in LLG augmented by thermal term at each time-step (temperature effects, more later):

TM-TM and RE-RE interactions are ferromagnetic

TM-RE interactions are anti-ferromagnetic

Hamiltonian includes only exchange and anisotropy

Femtosecond laser induced magnetisation dynamics

~100 fs

Femtosecond stimulation of magnetic materials

Atomistic modelling of non-equilibrium dynamic response

Two sub-lattice ferrimagnetic material GdFeCo

Exchange interaction

1500

1000

500

0 1 2 3

Te

Tl

Time [ps]

Tem

p [K

]

θ

θ

MTM

MRE

MRE

θTM

θRE

MTM

MRE

Fe disorders faster than Gd.

Once temperature is below TC, we have a distribution of angles between TM and RE spins.

Locally mode associated with AFM exchange (optical).

Fe

Gd

Bz

Laser heating

Magnetic field

Applied to system to prevent reversal of Fe