Atomistic Model of Ferrimagnetic GdFeCo Thomas Ostler, Richard Evans and Roy Chantrell October 2, 2009 Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
OUTLINE Motivation for developing the model Benefits of atomistic modelling Magneto-Optical Reversal Model details Mean Field results L=1 Static properties of ℏω 2 ℏω 2 Ferrimagnetic materials ℏ ( ω 1 − Ω m ) ℏω 1 Dynamic properties ℏ Ω m L=0 Summary and conclusion Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
OUTLINE 6 32% 36% H c [T] (Sweep Rate=10 8 T/s ) Motivation for 5 4 developing the model 3 2 Benefits of atomistic 1 modelling 0 0 100 200 300 400 500 600 T [K] Model details Efficient calculation of static Mean Field results magnetic properties Static properties of Ferrimagnetic 2.5 0% RE 12% RE 18% RE 2.0 24% RE materials 30% RE M s [ μ B /atom] 36% RE 1.5 Dynamic properties 1.0 Summary and 0.5 0.0 conclusion 0 200 400 600 800 1000 1200 T [K] Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
OUTLINE Motivation for developing the model Benefits of atomistic modelling Model details Mean Field results Atomistic level magnetisation dynamics Static properties of Ferrimagnetic 1.20 790K 910K 1.00 970K 1030K materials 0.80 1090K 1210K 1270K 0.60 M z /M 0 Dynamic properties 0.40 0.20 0.00 Summary and -0.20 -0.40 conclusion -1.0 0.0 10.0 20.0 30.0 40.0 50.0 Time [ps] Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
OUTLINE H Motivation for S x S x H developing the model S x H Benefits of atomistic S modelling Model details LLG, Hamiltonian, lattice structures.... Mean Field results Static properties of Ferrimagnetic materials Dynamic properties Summary and conclusion Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
OUTLINE Motivation for 2.0 1.5 M s (LLG) [ μ b per atom] developing the model 1.0 0% 1% 0.5 2% Benefits of atomistic 3% 0.0 2.0 modelling 1.5 0% 1.0 1% Model details 2% 0.5 3% 0.0 0 1050 Mean Field results T[K] M(T), χ � , χ ⊥ Static properties of Ferrimagnetic 0.2 χ � 0.18 χ ⊥ materials χ � , ⊥ /μ b [1/T Per Atom] 0.16 0.14 0.12 Dynamic properties 0.1 0.08 0.06 Summary and 0.04 0.02 0 conclusion 0 100 200 300 400 500 600 Time [s] Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
OUTLINE 2.0 Ferrimagnet Ferromagnet Motivation for 1.5 developing the model α eƒƒ 1.0 Benefits of atomistic 0.5 modelling 0.0 0 100 200 300 400 500 600 T [K] Model details M(T), H c (T), τ � , τ ⊥ and α eff Mean Field results Static properties of Ferrimagnetic 2.5 0% RE 12% RE 18% RE 2.0 24% RE materials 30% RE M s [ μ B /atom] 36% RE 1.5 Dynamic properties 1.0 Summary and 0.5 0.0 conclusion 0 200 400 600 800 1000 1200 T [K] Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
MOTIVATION Potential new mechanism for HDD writing of magnetic bits Magneto-Optical reversal seen in Amorphous GdFeCo Quantum or Thermodynamic process? Or both? Quantum: Stimulated Raman emission Thermodynamics: Combination of heat and Inverse Faraday Effect (IFE) Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
Motivation Potential new mechanism for HDD writing of magnetic bits Magneto-Optical reversal seen in Amorphous GdFeCo Quantum or Thermodynamic process? Or both? Quantum: Stimulated Raman emission Thermodynamics: Combination of heat and Inverse Faraday Effect (IFE) L=1 ℏω 2 ℏω 2 ℏ ( ω 1 − Ω m ) ℏω 1 L=0 ℏ Ω m Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
Motivation Potential new mechanism for HDD writing of magnetic bits Magneto-Optical reversal seen in Amorphous GdFeCo Quantum or Thermodynamic process? Or both? Quantum: Stimulated Raman emission Thermodynamics: Combination of heat and Inverse Faraday Effect (IFE) 1000 20 T e T B 800 16 T e/ [K] 600 12 B [T] 400 8 200 4 0 0 0.0 0.5 1.0 1.5 2.0 Time [ps] Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
STORY SO FAR 40fs laser pulses cause reversal depending on chirality of light Induced IFE leads to effective field ( ∝ E × E ∗ ) Raman type scattering effect causes mixing of L=1 wavefunction with L=0, causing ultrafast reversal with energy of a magnon Insufficient numbers of photons at frequencies ω 1 and ω 2 L=1 ℏω 2 ℏω 2 ℏ ( ω 1 − Ω m ) ℏω 1 L=0 ℏ Ω m Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
STORY SO FAR 40fs laser pulses cause reversal depending on chirality of light Induced IFE leads to effective field ( ∝ E × E ∗ ) Raman type scattering effect causes mixing of L=1 wavefunction with L=0, causing ultrafast reversal with energy of a magnon Insufficient numbers of photons at frequencies ω 1 and ω 2 L=1 ℏω 2 ℏω 2 ℏ ( ω 1 − Ω m ) ℏω 1 L=0 ℏ Ω m Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
BENEFITS OF ATOMISTIC MODELLING With the use of the Landau-Lifshitz-Gilbert equation we have the benefit of time resolved magnetisation dynamics on the very short time scale d S i γ i λ i γ i [ S i ( t ) × H i ( t )] − { S i ( t ) × [ S i ( t ) × H i ( t )] } = − dt ( 1 + λ 2 ( 1 + λ 2 i ) µ s i i ) µ s i On-site damping, gyromagnetic ratio and magnetic moment is very important for Ferrimagnets Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
BENEFITS OF ATOMISTIC MODELLING In theory any lattice namely the structure is possible Landau-Lifshitz-Bloch (LLB) equation Fitting of Hamiltonian to ab-initio data is possible to provide accurate physics for atomistic model Atomistic calculations can be parameterized for use with a macro-spin model Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
BENEFITS OF ATOMISTIC MODELLING In theory any lattice namely the structure is possible Landau-Lifshitz-Bloch (LLB) equation Fitting of Hamiltonian to ab-initio data is possible to provide accurate physics for atomistic model Atomistic calculations can be parameterized for use with a macro-spin model Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
BENEFITS OF ATOMISTIC MODELLING In theory any lattice namely the structure is possible Landau-Lifshitz-Bloch (LLB) equation Fitting of Hamiltonian to ab-initio data is possible to provide accurate physics for atomistic model Atomistic calculations can be parameterized for use with a macro-spin model Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
OUTLINE H Motivation for S x S x H developing the model S x H Benefits of atomistic S modelling Model details LLG, Hamiltonian, lattice structures.... Mean Field results Static properties of Ferrimagnetic materials Dynamic properties Summary and conclusion Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
HAMILTONIAN Ab-initio level work is underway to fit a Hamiltonian to magneto-optically active GdFeCo composition Currently use a generic Hamiltonian Uni-axial anisotropy, nearest neighbour Heisenberg exchange and Zeeman term Exchange: TM-TM = FM, RE-RE = FM, TM-RE = AFM N N N N H = − 1 D ( S i · n i ) 2 − J ij S i · S j − µ i B · S i � � � � 2 i = 1 j = 1 i = 1 i = 1 Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
HAMILTONIAN Ab-initio level work is underway to fit a Hamiltonian to magneto-optically active GdFeCo composition Currently use a generic Hamiltonian Uni-axial anisotropy, nearest neighbour Heisenberg exchange and Zeeman term Exchange: TM-TM = FM, RE-RE = FM, TM-RE = AFM N N N N H = − 1 J ij S i · S j − D ( S i · n i ) 2 − µ i B · S i � � � � 2 i = 1 j = 1 i = 1 i = 1 Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
HAMILTONIAN Ab-initio level work is underway to fit a Hamiltonian to magneto-optically active GdFeCo composition Currently use a generic Hamiltonian Uni-axial anisotropy, nearest neighbour Heisenberg exchange and Zeeman term Exchange: TM-TM = FM, RE-RE = FM, TM-RE = AFM N N N N H = − 1 D ( S i · n i ) 2 − J ij S i · S j − µ i B · S i � � � � (1) 2 i = 1 j = 1 i = 1 i = 1 Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
INTRODUCING THERMAL NOISE We use a stochastic thermal noise term which obeys the conditions j ( t ′ ) � = 2 δ ij δ ab δ ( t − t ′ ) λ i k B T � ζ a i ( t ) ζ b � ζ i ( t ) = 0 � ; µ i γ i White noise term presumes phonon and electron system act on timescale much faster than spins Question: Is this assumption valid for ultra-fast laser experiments? Thomas Ostler, Richard Evans and Roy Chantrell Atomistic Model of Ferrimagnetic GdFeCo
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