Optical Control of Magnetization and Modeling Dynamics Tom Ostler Dept. of Physics, The University of York, York, United Kingdom.

Magneto-Optics/Opto-magnetism E E M θ F ~M Z Faraday effect σ-σ- σ+σ+ M(0) Inverse Faraday effect  Rotation (θ f ) of polarization plane.  χ: susceptibility tensor  k: wave-vector  n: refractive index  Electric field of laser radiation, E, of light induces magnetisation along k.  σ+ and σ- induce magnetisation in opposite direction Hertel, JMMM, 303, L1-L4 (2006) *Van der Ziel et al., Phys Rev Lett 15, 5 (1965)

Inverse Faraday Effect  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+ σ-σ- z z Hertel, JMMM, 303, L1-L4 (2006)

Example: Optically Induced Precession Kimel et al. Nature 435, 655 (2005).  Light of different helicities applied to DyFeO 3.  Induces spin precession with opposite phase.

Example: Optically Induced Switching Stanciu et al.Phys Rev Lett, 99, (2007). *Hertel JMMM 303, L1-L4 (2006).  Light of different helicities applied to ferrimagnetic GdFeCo.  Recall effective field opposite for σ+ and σ-. Initial state final state

 Effective field from IFE  For σ-  For linear light (π) no effective field  What is the effect of heat and what is the role of the IFE? Linearly Polarised Light Hertel, JMMM, 303, L1-L4 (2006)

Choice of Model  Any model should be chosen carefully to include the physics important to the experiment.  Should also be appropriate to time-scale, length-scale and material.  An important aspect of femtosecond laser induced processes is including temperature into any model s (fs) s (ps) s (ns) s (µs) s (ms) e-s relaxation Magnetization precession Hysteresis All-optical/laser experiments Fast- Kerr/XMCD etc Conventional magnetometers Langevin Dynamics on atomistic level Kinetic Monte Carlo s (s)+ Micromagnetics /LLB s (<fs) TDFT/ab-initio spin dynamics Time

Timescale/Lengthscale s (fs) s (ps) s (ns) s (µs) s (ms) Langevin Dynamics on atomic level Kinetic Monte Carlo s (s) s (<fs) TDFT/ab-initio spin dynamics Time m (nm)10 -6 m (μm)10 -3 m (mm) m (Å) Length Micromagnetics /LLB

Atomistic LLG & LLB for fs laser induced dynamics Langevin Dynamics on atomistic level Landau-Lifshitz- Bloch (macrospin)  For each spin we solve a (coupled) LLG equation.  Different terms (zeeman, anisotropy, exchange) come in via effective field.  Includes temperature. Limited by system size.  Macrospin equation  Additional term for longitudinal relaxation unlike μmag.  Again includes temperature. Large systems.  No atomic resolution of processes. Handbook of Magnetism and Advanced Magnetic Materials (2007). Garanin Phys Rev B, 55, 5 (1997)

Laser Heating  Two temperature model defines a temperature for conduction electrons and phonons/lattice.  Thermal term added into effective field (stochastic process).  Assume Gaussian heat pulse for laser heat.  Laser interacts directly with electronic system which has a much smaller heat capacity than phonons.  Cooling down to room temperature governed by phonon relaxation on longer time-scale. Electrons e-e- e-e- e-e- energy flows Lattice e-e- G el Laser input P(t) TeTe TlTl *Chen et al. Journal of Heat and Mass Transfer 108, (2012) TeTe TlTl Time [ps] Temp [K]

IFE: Effective Field & Macrospin example  Can add in effective field from IFE to H eff that depends on chirality.  Add Zeeman term to fields in model.  σ+ and σ- assumed to give field with opposite direction (+H OM and -H OM ). Vahaplar et al. Phys Rev B 85, (2012).  LLB (macrospin) model used to describe optical reversal in GdFeCo.  Reversal of magnetization governed by orientation of field.  Needs heat and field.

LLG Example: Switching with Linearly Polarized Light Radu et al. Nature 472, (2011).  Atomistic LLG allows us to describe magnetization dynamics of individual moments.  Switching in applied field.  Linearly polarised light → heat only. Experiment Theory (atomistic LLG)  X-ray Magnetic Circular Dichroism technique.  Element specific time-resolved dynamics.  Good agreement between theory and experiment.

Overview  Control of magnetization by circularly polarised light.  Generates an effective field dependent on chirality of light.  Have to consider transfer of heat and IFE.  When developing a model need to consider time-scale/length-scale/material.  For femtosecond laser processes macrospin (LLB) or atomistic LLG equation appropriate.  Models capable of reproducing experiment to which further analysis can be easily applied.

Controlling Transitions De Jong et al. Phys Rev Lett 108, (2012).  (SmPr)FeO 3 undergoes a gradual reorientation transtion as temperature is increased. 98 K 103 K  Above T=103 K having magnetization along ±z is energetically equivalent.  Can use polarised light to govern final state.

Spin momentPhotons Spins

Choice of Model

Opto-magnetism  Light can induce a magnetization change  Change (±) depends on helicity of light  The polarised light can act as an effective field* Hertel, JMMM, 303, L1-L4 (2006) *Van der Ziel et al., Phys Rev Lett 15, 5 (1965)

Optical Reversal: modeling Vahaplar et al. Phys Rev B 85, (2012). Laser input and effective field (IFE)

Optical Reversal: experiments and modeling  Optical stimulation of GdFeCo with σ+ and σ- measured by time-resolved Faraday effect measurements.  LLB model used to describe optical reversal in GdFeCo.  Good agreement between experiment (top) and macro-spin LLB (bottom) model. Vahaplar et al. Phys Rev B 85, (2012).