Intermag Vancouver May 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: 259986
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Slide1
Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal
Intermag, Vancouver, May 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
Intermag, Vancouver, May 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
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.Slide11
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.Slide12
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 resultsSlide13
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.Slide14
Numerical Results of Switching Without a Field
Very unexpected result that the field plays no role.Is this determinisitic?
GdFeCoNo magnetic fieldSlide15
Sequence of pulses
Do we see the same effect experimentally?Slide16
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)Slide17
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 TSlide18
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. Slide19
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 pulseSlide20
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.Slide21
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.Slide22
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:Slide23
The Effect of Compensation Point
Previous studies have tried to switch using the changing dynamics at the compensation point.
Simulations show starting temperature not important (not important if we cross compensation point or not). Supported by experiments on different compositions of GdFeCo support the numerical observation.Slide24
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 (
σ
+) the magnetization switches, independently of initial state.Slide25
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)Slide26
Importance of moments
μ
TM=μRE If moments are equal the no reversal occursSlide27
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].Slide28
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
anisotropySlide29
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)Slide30
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?Slide31
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).Slide32
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 stateSlide33Slide34
The Effect of Heat
E
50%
50%
E
E
?
E
M+
M-
M+
M-
M+
M-
M+
M-
M+
M-Slide35
Two Temperature Model
A semi-classical two-temperature model for ultrafast laser heating
Chen et al. International Journal of Heat and Mass Transfer 49, 307-316 (2006).Equations solved using numerical integration to give electron and phonon temperature as a function of time.Heat capacity of electrons is smaller than phonons so see rapid increase in electron temperature (ultrafast heating).Now we have changing temperature with time and we can incorporate this into our model.Example of solution of two temperature model equationsSlide36
Numerical Results of Switching
Without a Field
As a result of systematic investigation discovered that no field necessary. Applying a sequence of pulses, starting at room temperature (a). Reversal occurs each time pulse is applied (b).
Fe
Gd
Ground state
~1
ps
~2
ps
Ground stateSlide37
Mechanism of Reversal
Ferrimagnets have two eigenmodes for the motion of the sublattices; the usual FMR mode and an Exchange mode.
Exchange mode is high frequency associated with TM-RE exchange. We see this on a “local” level.FMRExchangeTM more disordered because of faster demagnetisation (smaller moment). Locally TM and RE are misaligned. Effect is averaged out because of random phase. Slide38
Experimental observations of femtosecond
heating in Nickel shows rapid demagnetisation.Chance of magnetization reversal by thermal activation (not deterministic) but generally magnetization recovers to initial direction.Our goal was to develop a model to provide more insight into such processes.
Femtosecond HeatingFigure from Beaurepaire et al. PRL 76, 4250 (1996).Experiments on NiSlide39
The stochastic process has the properties (via FDT):
Each time-step a Gaussian random number is generated (for x,y and z component of field) and multiplied by square root of variance.
Point to note: noise scales with T and µ. If T changes then so does size of noise.Model: Thermal Term More DetailsFor more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011)Image from thesis of U. Nowak.Example of a single spin in a field augmented by thermal term.