HGST San Jose August 2012 TheoreticalModelling Contributions T Ostler J Barker R F L Evans and R W Chantrell Dept of Physics The University of York York United Kingdom U ID: 259991
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Slide1
Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal
HGST, San Jose, August 2012
Theoretical/Modelling ContributionsT. 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.Slide2
Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal
HGST, San Jose, August 2012
Experimental ContributionsS. El Moussaoui, L. Le Guyader, E. Mengotti, L. J. Heyderman and F. NoltingPaul Scherrer Institut, Villigen, SwitzerlandA. 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. Kimel
Radboud University Nijmegen, Institute for Molecules and Materials, Nijmegen, The Netherlands.Slide3
Ostler
et al., Nature Communications, 3, 666 (2012).Slide4
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 reversalSlide5
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?Slide6
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
-
two temperature model energy transfers
Lattice
e
-
G
el
Laser input
P
(t)
Two temperature model
[1] Chen
et
al
.
International Journal of Heat and Mass Transfer.
49
, 307-316
(
2006)Slide7
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.Slide8
Sub-lattice magnetization
Fe
GdAtomic LevelModel: Exchange interactions/StructureFor 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.Slide9
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 pointSlide10
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)Slide11
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.Slide12
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.Slide13
(an aside) Demagnetisation in ferromagnetic Ni
50Fe50
Experiments performed by I. RaduModel resultsFemtosecond heating shows decoupled behaviour in NiFe.Sublattice magnetizations are measured by element specific XMCD.Each sublattice demagnetises on a different timescale.ExperimentSlide14
Demagnetisation in ferrimagnetic GdFeCo
Experiments performed by I. RaduModel 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. ExperimentSlide15
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 DemagnetisationFigures from Radu et al. Nature 472, 205-208 (2011).[1] Kazantseva et al. EPL, 81, 27004 (2008).
Experiment
Model resultsSlide16
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.Slide17
Numerical Results of Switching Without a Field
Very unexpected result that the field plays no role.Is this determinisitic?
GdFeCoNo magnetic fieldSlide18
Sequence of pulses
Do we see the same effect experimentally?Slide19
Experimental Verification: GdFeCo Microstructures
XMCD
2
m
m
Experimental observation of magnetisation after each pulse.
Initial state
- two microstructures with opposite magnetisation
-
Seperated
by distance larger than radius (no coupling)Slide20
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.Slide21
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)Slide22
What about the Inverse Faraday Effect?Slide23
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.Slide24
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
B
z
=10,40,50 TSlide25
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.FMRExchange Exchange mode is excited when sublattices are not exactly anti-parallel. Slide26
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 sublatticeTMRE
TM
end of pulse
end of pulseSlide27
μ
TM
=μREImportance of MomentsAs 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.Slide28
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.Slide29
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.Slide30
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.FMRExchange Exchange mode is excited when sublattices are not exactly anti-parallel. Slide31
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:Slide32
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 termLongitudinal relaxation of magnetisation
(submitted) Full details of model from
Atxitia
el al.
Arxiv
1206.6672Slide33
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 1206.6672However, this change in sign alone cannot result in switching!
Different longitudinal relaxation is very important but does not produce switching.Slide34
Experimental Prediction
Could we see reversal via this dynamical path experimentally?
Effect is averaged out over large systems.LLGSlide35
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->0KSlide36
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 simulationSlide37
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.Slide38
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 1psSlide39
Importance of moments
μ
TM=μRESlide40
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].Slide41
The Effect of Heat
E
M+M-
M+
M-
50%
50%
E
M+
M-
System demagnetised
Heat (slowly) through T
C
Cool below T
C
Equal chance of M+/M-
Heat
Cool
Ordered
ferromagnet
Uniaxial
anisotropy
E
θSlide42
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-zz
Hertel
, JMMM, 303
, L1-L4 (2006)Slide43
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?Slide44
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 300fsGd slow, ~1psRadu et al. Nature 472, 205-208 (2011).
Kazantseva
et al. EPL, 81, 27004 (2008).Slide45
What’s going on?
0 ps time
- Ground state
0.5
ps
1.2
ps
-T>T
C
Fe disorders more quickly (
μ
)
10’s
ps
-T<T
C
precessional
switching (on atomic level)
-Exchange mode between TM and RE
- Transient stateSlide46
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
Thi
s process occurs on small length scales so effect can be averaged out in atomistic model.
By decreasing system size we see this effect.
LLB
LLGSlide47Slide48
Differential demagnetization timesSlide49
How Can Magnetization Be Reversed?
Magnetic Field
Circularly PolarisedSpin InjectionEB
z
E
B
z
M+
M-
M+
M-Slide50
The Effect of Heat
E
50%
50%
E
E
?
E
M+
M-
M+
M-
M+
M-
M+
M-
M+
M-Slide51
Macrospin
Fe
GdAtomic LevelAtomic Level Model of GdFeCoFor 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
anisotropySlide52
Femtosecond laser induced magnetisation dynamics
~100
fsFemtosecond stimulation of magnetic materialsAtomistic modelling of non-equilibrium dynamic response
Two sub-lattice
ferrimagnetic
material
GdFeCo
Exchange interactionSlide53
1500
1000
5000123TeTlTime [ps]Temp [K]
θ
θ
M
TM
M
RE
M
RE
θ
TM
θ
RE
M
TM
M
RE
Fe disorders faster than Gd.
Once temperature is below T
C
, we have a distribution of angles between TM and RE spins.
Locally mode associated with AFM exchange (optical).
Fe
Gd
B
z
Laser heating
Magnetic field
Applied to system to prevent reversal of Fe