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Ultrafast Magnetization Dynamics. T. Ostler 1 Dept . of Physics, The University of York, York, United Kingdom . December 2013. Increasing demand. 100TB storage. 25TB daily log. A few GB to TB’s. 2.5PB. 24PB daily. 330 EB demand in 2011. Estimated size of the internet 4ZB.

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## Ultrafast Magnetization Dynamics

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**Ultrafast Magnetization Dynamics**T. Ostler1 Dept. of Physics, The University of York, York, United Kingdom. December 2013**Increasing demand**100TB storage 25TB daily log A few GB to TB’s 2.5PB 24PB daily 330 EB demand in 2011 Estimated size of the internet 4ZB**Increasing demand**Now at 175million Users [millions] Months • If all storage demand was met by SSD’s/flash etc, $250 billion in plant construction is required. • Faster data access/writing is desirable.**Write speed challenge**• In 1953 IBM launched first commercial HHD with average data access times of just under 1 second! Me IBM 350 • A 50KB pdf would take a few days to copy. • How have data rates improved?**Speed limits in magnetism**• Huge increase in speeds since the 80’s. • Rate has been slowing in last 10 years.**Write times**Enterprise drive CD @ 1x How fast can we go? Faster write times Pulsed fields**Towards femtosecond processes**• Magnetic field processes. • Atomistic spin dynamics model for magnetization dynamics. • LLG • How we construct such a model • Including laser heating + parameterization • Limitations of the model • Finally femtosecond lasers processes. • Conclusion: reversal in hundreds of fs using laser without applied field. • Mechanism for switching without a field.**Precession and damping**• NB, if under- damped, many precesssion cycles may be necessary in order to reach equilibrium. • Current HDD has write pole around 1-2T. • Switching around 1ns. Landau-Lifshitz-Gilbert (LLG) equation Precession Damping**Ultrafast field switching in 200ps**• GaAsphotoswitches excited by fs laser pulse creates initial field. • Permally thin film, in-plane. • High field and low damping causes ringing oscillations in magnetization. Figures from :Nature, 418, 509-512 (2002). • GaAsphotoswitches excited by fs laser pulse creates initial field. • Second pulses (at a very specific delay time) can stop magnetization. • Reversal complete in 200 picoseconds.**Can we go faster?**• Control of magnetization dynamics in applied field limited by precession time. • There are a number of other ways to control magnetization: • Spin transfer torque • Heat assisted magnetic recording • The exchange interaction gives rise to magnetic order. • The strongest force in magnetism. Can we excite processes on this timescale? Timescale: 10’s -> 100’s fs**Femtosecond laser heating and measurement**E E • Rotation (θf) of polarization plane. • χ: susceptibility tensor • k: wave-vector • n: refractive index θF~MZ M Faradayeffect Fast demagnetization of Ni • MOKE in transmission. • Using femtosecond laser pulses Beaurepaire showed fs demagnetization. • Demagnetization in around 1ps. Remagnetization in a few ps. • Can we model this? Beaurepaireet al. PRL, 76, 4250 (1996).**Time-scale/Length-scale**Length 10-10 m (Å) 10-9 m (nm) 10-6 m (μm) 10-3 m (mm) TDFT/ab-initio spin dynamics 10-16 s (<fs) 10-15 s (fs) Superdiffusive spin transport 10-12 s (ps) Langevin Dynamics on atomiclevel Micromagnetics/LLB Time 10-9 s (ns) 10-6 s (µs) Kinetic Monte Carlo 10-3 s (ms) 10-0 s (s)+ http://www.psi.ch/swissfel/ultrafast-manipulation-of-the-magnetization http://www.castep.org/**The spin dynamics model**• Assume fixed atomic positions • Processes such as e-e, e-p and p-p scattering are treated phenomenologically(λ). • At each timestep we calculate a field acting on each spin and solve using numerical integration. • To calculate the fields we consider a Hamiltonian (below). Extended Heisenberg Hamiltonian Exchange Anisotropy Zeeman Dipole-Dipole**How do we find J/D/μ?**• Anisotropy can also be calculated from first principles. • Possible to have other anisotropy terms: • Surface • Cubic • Etc. • Jij can be found from DFT. Adiabatic approximation assuming electron motion much faster than spinwaves. • Assume frozen magnon picture • Spin spiral for particular q vector. • Integration in q-space gives exchange energy. • Can also assume nearest neighbour interaction and use experimental TC to determine Jij sc bcc fcc**Magnetization dynamics**Static properties: M(T), hysteresis What can we calculate? Distribution of spinwave energies Spinwave dispersion**The spin dynamics model**Heat bath • Damping is phenomenological. • Energy exchange is to/from bath and magnon-magnon interactions. Spinwaves**Modelling temperature effects**Damping Precession Noise**Laser heating**Chen et al. Int. Journ. Heat and Mass Transfer.49, 307-316 (2006)**How can the electron temperature be determined?**Usually known from literature Fitting initial decay to an exponential Final temperature determines Figure from Atxitiaet al. Phys. Rev. B. 81, 174401 (2010).**Laser heating**Experiment Theory • What governs the time-scale for demagnetization? • Can we control it? • What happens if we have multiple species?**Two sublattices**Jij>0 Jij<0 Model calculations Two sublattice ferromagnet Two sublattice ferrimagnet • Strongly exchange coupled. • But decoupled dynamics. • Fine in theory, what do we see experimentally? Radu, Ostler et al. submitted.**X-ray Magnetic Circular Dichroism (XMCD)**• XMCD used to measure individual magnetic elements. • Excite core electrons from spin-split valance bands. • Circularly polarized photons (+ħ,-ħ) give rise to different absorptions. Radu, Ostler et al. Nature, 472, 205-208 (2011).**Two sublattices**• Experiments of dynamics (via XMCD) shows qualitatively similar results. • What determines the rate of demagnetization? Radu, Ostler et al. submitted.**Time-scales of elements in different materials**• Measured demagnetization time to 50% demagnetization by tuning pump fluence. • Plot the above data against the magnetic moment. • Seems to scale with the magnetic moment. • Deviation due to exchange. Radu, Ostler et al. submitted. More details arXiv:1308.0993**Can we actually do something useful?**• Controlling demagnetization is interesting but can we actually do something with it? Element-resolved dynamics. • Switching in a magnetic field • Some interesting behaviour Experiment Model results Transient ferromagnetic-like state Reversal of the sublattices Different demagnetization times Initial State Raduet al. Nature, 472, 205-208 (2011).**Switching without a field**• What role is the magnetic field playing? • Model calculations show field playing almost no role! Sequence of pulses without a field Do we see the same experimentally? Ostler et al. Nat. Commun. 3, 666 (2012).**Experimental Verification: GdFeCo Microstructures**Initial state - two microstructures with opposite magnetisation - Seperated by distance larger than radius (no coupling) 2mm XMCD Experimental observation of magnetisation after each pulse. Ostler et al. Nat. Commun. 3, 666 (2012).**Beyond magnetization**How can we explain the observed effects in GdFeCo? Suggests something is occurring on microscopic level • No symmetry breaking external source.**Intermediate structure factor (ISF)**• To obtain information on the distribution of modes in the Brillouin zone we calculate the intermediate structure factor: 3D FFT 1.0 • For each time-step we obtain S(q). • We then apply Gaussian smoothing. 0.8 0.6 Normalized Amplitude 0.4 0.2 0.0 Χ Γ Μ**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, 3, 3262 (2013).**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). • J. Barker, T. Ostler et al. Nature Scientific Reports, 3, 3262 (2013).**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. • J. Barker, T. Ostler et al. Nature Scientific Reports, 3, 3262 (2013).**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. • J. Barker, T. Ostler et al. Nature Scientific Reports, 3, 3262 (2013).**Summary**• Field limit of magnetization switching. • The atomistic spin dynamics model of ultrafast magnetization dynamics. • How we model femtosecond laser heating. • Demagnetization and switching experiments and theory. • How we switch without a field. Slides available at: http://tomostler.co.uk/list-of-publications/conference-presentations/

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