Optical Control of Magnetization and Modeling Dynamics

Tom OstlerDept. of Physics, The University of York, York, United Kingdom.

Magneto-Optics/Opto-magnetismE E

M

θF~MZ

Faraday effect

σ-

σ+

M(0)

Inverse Faraday effect

Rotation (θf) 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

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-

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 DyFeO3.

Induces spin precession with opposite phase.

Example: Optically Induced Switching

Stanciu et al.Phys Rev Lett, 99, 047601 (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

http://en.wikipedia.org/wiki/Circular_polarizationHertel, 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.

10-15 s (fs)10-12 s (ps)10-9 s (ns)10-6 s (µs)10-3 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 Carlo10-0 s (s)+

Micromagnetics/LLB

10-16 s (<fs)TDFT/ab-initio spin dynamics

Tim

e

Timescale/Lengthscale

10-15 s (fs)10-12 s (ps)10-9 s (ns)10-6 s (µs)10-3 s (ms)

Langevin Dynamics on atomiclevel

Kinetic Monte Carlo10-0 s (s)+

10-16 s (<fs)TDFT/ab-initio spin dynamics

Tim

e

10-9 m (nm) 10-6 m (μm) 10-3 m (mm)10-10 m (Å)

Length

Micromagnetics/LLB

http://www.psi.ch/swissfel/ultrafast-manipulation-of-the-magnetizationhttp://www.castep.org/

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-

energy flows

Lattice

e-

Gel

Laser inputP(t)

Te Tl

*Chen et al. Journal of Heat and Mass Transfer 108, 157601 (2012).

1500

1000

500

0 1 2 3

Te

Tl

Time [ps]

Tem

p [K

]

IFE: Effective Field & Macrospin example

Can add in effective field from IFE to Heff that depends on chirality.

Add Zeeman term to fields in model.

σ+ and σ- assumed to give field with opposite direction (+HOM and -HOM).

Vahaplar et al. Phys Rev B 85, 104402 (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, 205-208 (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, 157601 (2012).

(SmPr)FeO3 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 moment Photons

Photons Spins

Choice of Model

http://www.psi.ch/swissfel/ultrafast-manipulation-of-the-magnetizationhttp://www.castep.org/

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, 104402 (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, 104402 (2012).