Femtosecond Heating as a Sufficient Stimulus for Magnetization

Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal Theoretical/Modelling Contributions T. Ostler, J. Barker, R. F. L. Evans and R. W. Chantrell Dept. of Physics, The University of York, United Kingdom. U. Atxitia and O. Chubykalo-Fesenko Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, Madrid, Spain. D. Afansiev and B. A. Ivanov Institute of Magnetism, NASU Kiev, Ukraine. Intermag, Vancouver, May 2012

Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal Experimental Contributions S. El Moussaoui, L. Le Guyader, E. Mengotti, L. J. Heyderman and F. Nolting Paul Scherrer Institut, Villigen, Switzerland A. Tsukamoto and A. Itoh College 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. Intermag, Vancouver, May 2012

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

Outline • Model outline: atomistic LLG of Gd. Fe. Co and laser heating • Static properties of Gd. Fe. Co 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. σ+ σ- M(0) Inverse Faraday effect • Control of magnetization of ferrimagnetic Gd. Fe. Co[3] • High powered laser systems generate a lot of heat. • What is the role of the heat and the effective field from the IFE? [1] Hertel, JMMM, 303, L 1 -L 4 (2006). [2] Van der Ziel et al. , Phys Rev Lett 15, 5 (1965). [3] Stanciu et al. PRL, 99, 047601 (2007).

A model of laser heating § Recall for circularly polarised light, magnetization induced is given by: Laser input P(t) Electrons § 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). Two temperature model [1] Chen et al. International Journal of Heat and Mass Transfer. 49, 307 -316 (2006) Gel ee- e e- Lattice -

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

Model: Exchange interactions/Structure § Gd. Fe. Co is an amorphous ferrimagnet. § Assume regular lattice (fcc). § In the model we allocate Gd and Fe. Co spins randomly. Fe-Fe and Gd-Gd interactions are ferromagnetic (J>0) Fe-Gd interactions are anti-ferromagnetic (J<0) Fe Gd Atomic Level Sub-lattice magnetization For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011)

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. compensation point Figure from Ostler et al. Phys. Rev. B. 84, 024407

Summary so far Atomic level model of a ferrimagnet with time A way of describing heating effect of fs laser § We investigate dynamics of Gd. Fe. Co 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 Gd. Fe. Co by XMCD & Model § Femtosecond heating in a magnetic field. § Gd and Fe sublattices exhibit different dynamics. § Even though they are strongly exchange coupled. Experiment Model results Figures from Radu et al. Nature 472, 205 -208 (2011).

Timescale of Demagnetisation § Characteristic demagnetisation time can be estimated as[1]: § Gd. Fe. Co has 2 sublattices with different moment (µ). Experiment Model results § Even though they are strongly exchange coupled the sublattices demagnetise at different rates (with µ). [1] Kazantseva et al. EPL, 81, 27004 (2008). Figures from Radu et al. Nature 472, 205 -208 (2011).

Transient Ferromagnetic-like State 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. Figure from Radu et al. Nature 472, 205 -208 (2011). • 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 No magnetic field Gd. Fe. Co § § Very unexpected result that the field plays no role. Is this determinisitic?

Sequence of pulses § Do we see the same effect experimentally?

Experimental Verification: Gd. Fe. Co Microstructures Initial state - two microstructures with opposite magnetisation - Seperated by distance larger than radius (no coupling) 2 mm XMCD Experimental observation of magnetisation after each pulse.

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 Bz=10, 40, 50 T 40 T 50 T Gd. Fe. Co • Suggests probable exchange origin of effect (more later).

Mechanism of Reversal After heat pulse TM moments more disordered than RE (different demagnetisation rates). n On small (local) length scale TM and RE random angles between them. n The effect is averaged out over the system. n FMR Exchange mode is excited when sublattices are not exactly anti-parallel. n

Mechanism of Reversal end of pulse RE If we decrease the system size then we still see reversal via transient state. n For small systems a lot of precession is induced. n TM Frequency of precession associated with exchange mode. n For systems larger than 20 nm 3 there is no obvious precession induced (averaged out over system). n end of pulse Further evidence of exchange driven effect. n TM sublattice TM

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 n 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). n n The Russian Foundation for Basic Research (RFBR). European Community’s Seventh Framework Programme (FP 7/2007 -2013) Grants No. NMP 3 -SL-2008 -214469 (Ultra. Magnetron) and No. 214810 (FANTOMAS), n n Spanish MICINN project FIS 2010 -20979 -C 02 -02 European Research Council under the European Union’s Seventh Framework Programme (FP 7/2007 - 2013)/ ERC Grant agreement No 257280 (Femtomagnetism). n n NASU grant numbers 228 -11 and 227 -11. Thank you for listening.

Numerical Model • Energetics of system described by Hamiltonian: n Dynamics of each spin given by Landau-Lifshitz-Gilbert Langevin equation. n Effective field given by: n Moments defined through the fluctuation dissipation theorem as:

The Effect of Compensation Point Previous studies have tried to switch using the changing dynamics at the compensation point. n Simulations show starting temperature not important (not important if we cross compensation point or not). n Supported by experiments on different compositions of Gd. Fe. Co support the numerical observation. n

Experimental Verification: Gd. Fe. Co Thin Films n After action of each pulse (σ+) the magnetization switches, independently of initial state. Fe Initially film magnetised “up” Gd MOKE n n 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.

What about the Inverse Faraday Effect? • Orientation of magnetization governed by light polarisation. Stanciu et al. PRL, 99, 047601 (2007) Does not depend on chirality (high fluence) Depends on chirality (lower fluence)

Importance of moments n If moments are equal the no reversal occurs μTM=μRE

Linear Reversal Usual reversal mechanism (in a field) below TC via precessional switching n At high temperatures, magnetisation responds quickly without perpendicular component (linear route[1]). n Laser heating results in linear demagnetisation[2]. n

The Effect of Heat Ordered ferromagnet • Uniaxial anisotropy • Heat Cool below TC Heat (slowly) through TC E E 50% M+ M- System demagnetised M+ 50% M- Equal chance of M+/M-

Inverse Faraday Effect § Magnetization direction governed by E-field of polarized light. σ+ z § Opposite helicities lead to induced magnetization in opposite direction. § Acts as “effective field” depending on helicity (±). σ- z http: //en. wikipedia. org/wiki/Circular_polarization Hertel, JMMM, 303, L 1 -L 4 (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 n Fe and Gd demagnetise in thermal field (scales with μ via correlator) n Kazantseva et al. EPL, 81, 27004 (2008). Gd slow, ~1 ps Fe fast, loses magnetisation in around 300 fs Radu et al. Nature 472, 205 -208 (2011).

What’s going on? 0 ps - Ground state -T>TC Fe disorders more quickly (μ) 0. 5 ps 1. 2 ps 10’s ps e tim -T<TC precessional switching (on atomic level) -Exchange mode between TM and RE - Transient state

The Effect of Heat E E 50% M+ M- E ? M+ M-

Two Temperature Model § 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. A semi-classical two-temperature model for ultrafast laser heating Chen et al. International Journal of Heat and Mass Transfer 49, 307 -316 (2006). Example of solution of two temperature model equations

Numerical Results of Switching Without a Field As a result of systematic investigation discovered that no field necessary. n Applying a sequence of pulses, starting at room temperature (a). n Reversal occurs each time pulse is applied (b). n Fe Gd Ground state ~1 ps ~2 ps Ground state

Mechanism of Reversal FMR Ferrimagnets have two eigenmodes for the motion of the sublattices; the usual FMR mode and an Exchange mode. Exchange n Exchange mode is high frequency associated with TM-RE exchange. n n We see this on a “local” level. n. TM more disordered because of faster demagnetisation (smaller moment). n Locally TM and RE are misaligned. Effect is averaged out because of random phase. n

Femtosecond Heating § 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. Figure from Beaurepaire et al. PRL 76, 4250 (1996). Experiments on Ni

Model: Thermal Term More Details § The stochastic process has the properties (via FDT): Example of a single spin in a field augmented by thermal term. § 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. For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011) Image from thesis of U. Nowak.