Ultrafast tutorial in Ultrafast Magnetism Richard F L Evans - - PowerPoint PPT Presentation

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Ultrafast tutorial in Ultrafast Magnetism Richard F L Evans - - PowerPoint PPT Presentation

Jun 29, 2023 102 likes •466 views

Ultrafast tutorial in Ultrafast Magnetism Richard F L Evans richard.evans@york.ac.uk www-users.york.ac.uk/~rfle500/ Overview Running VAMPIRE Pulse power = 0.8 2.2 1.2 2.6 1.0 Normalized magnetization 1.6 0.8 Demagnetization dynamics in

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Ultrafast tutorial in Ultrafast Magnetism

Richard F L Evans

richard.evans@york.ac.uk www-users.york.ac.uk/~rfle500/

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Overview

Running VAMPIRE Demagnetization dynamics in Ni Ultrafast thermally induced magnetic switching

0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 Normalized magnetization Time (ps) Pulse power = 0.8 1.2 1.6 2.2 2.6
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Spin Hamiltonian

Describes the energetics of a complete system

H = Hexc + Hani + Happ

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SLIDE 4

Spin dynamics

Si H Si x [Si x H] Si x H

∂Si ∂t = − γ (1 + λ2)[Si × Hi

eff + λSi × (Si × Hi eff)]

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SLIDE 5

Stochastic Landau-Lifshitz-Gilbert

Hi

eff = − 1

µs ∂H ∂Si + Hi,δ

th .

Hi

th = Γ(t)

s 2λkBT γµs∆t

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SLIDE 6

Open source and free C++

V A M P I R E

Simple text file interface Visualization Cross platform

vampire.york.ac.uk

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SLIDE 7

Tutorial resources

www-users.york.ac.uk/~rfle500/teaching/ultrafast-magnetism/

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SLIDE 8

Setting up a simulation in Vampire

input file (program control) material file (material properties)

#------------------------------------------ # Creation attributes: #------------------------------------------ create:crystal-structure=fcc create:periodic-boundaries-x create:periodic-boundaries-y create:periodic-boundaries-z #------------------------------------------ # System Dimensions: #------------------------------------------ dimensions:unit-cell-size = 3.524 !A dimensions:system-size-x = 4.0 !nm dimensions:system-size-y = 4.0 !nm dimensions:system-size-z = 4.0 !nm … #--------------------------------------------------- # Number of Materials #--------------------------------------------------- material:num-materials=1 #--------------------------------------------------- # Material 1 Nickel Generic #--------------------------------------------------- material[1]:material-name=Ni material[1]:damping-constant=0.01 material[1]:exchange-matrix[1]=2.757e-21 material[1]:atomic-spin-moment=0.606 !muB material[1]:uniaxial-anisotropy-constant=0.0 material[1]:material-element=Ni

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SLIDE 9

Spin Hamiltonian for Ni

H ¼ X

i<j

JijSi Sj X

i

kuS2

i;z;

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SLIDE 10

Ni.mat

#--------------------------------------------------- # Number of Materials #--------------------------------------------------- material:num-materials=1 #--------------------------------------------------- # Material 1 Nickel Generic #--------------------------------------------------- material[1]:material-name=Ni material[1]:damping-constant=0.01 material[1]:exchange-matrix[1]=2.757e-21 material[1]:atomic-spin-moment=0.606 !muB material[1]:uniaxial-anisotropy-constant=5.47e-26 material[1]:material-element=Ni

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input

#------------------------------------------ # Creation attributes: #------------------------------------------ create:crystal-structure=fcc create:periodic-boundaries-x create:periodic-boundaries-y create:periodic-boundaries-z #------------------------------------------ # System Dimensions: #------------------------------------------ dimensions:unit-cell-size = 3.524 !A dimensions:system-size-x = 4.0 !nm dimensions:system-size-y = 4.0 !nm dimensions:system-size-z = 4.0 !nm #------------------------------------------ # Material Files: #------------------------------------------ material:file=Ni.mat #------------------------------------------ # Simulation attributes: #------------------------------------------ sim:temperature=300 sim:minimum-temperature=0 sim:maximum-temperature=800 sim:temperature-increment=25 sim:time-steps-increment=1 sim:equilibration-time-steps=1000 sim:loop-time-steps=1000 #------------------------------------------ # Program and integrator details #------------------------------------------ sim:program=curie-temperature sim:integrator=monte-carlo #------------------------------------------ # Data output #------------------------------------------

  • utput:real-time
  • utput:temperature
  • utput:magnetisation
  • utput:magnetisation-length
  • utput:mean-magnetisation-length
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SLIDE 12

Getting and compiling vampire

  • Need to get code from source repository
  • This creates a directory ‘vampire
  • Checkout release version of the code
  • Compile

git clone https://github.com/richard-evans/vampire.git git checkout release make serial cd vampire

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Running vampire

  • Each simulation should be in a separate directory
  • Copy in the input files and executable
  • Now run the executable

cd .. mkdir Co cd Co ./vampire-serial cp ../vampire/Co.mat . cp ../vampire/input . cp ../vampire/vampire-serial .

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Curie temperature calculation

Calculate phase transition in Ni Essential temperature dependent property of a magnetic material

0.0 0.2 0.4 0.6 0.8 1.0 100 200 300 400 500 600 700 800 Normalized magnetization Temperature (K)

Jij = 3kBTc γz H = −∑

i<j

JijSi ·Sj

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SLIDE 15

input

#------------------------------------------ # Creation attributes: #------------------------------------------ create:crystal-structure=fcc create:periodic-boundaries-x create:periodic-boundaries-y create:periodic-boundaries-z #------------------------------------------ # System Dimensions: #------------------------------------------ dimensions:unit-cell-size = 3.524 !A dimensions:system-size-x = 4.0 !nm dimensions:system-size-y = 4.0 !nm dimensions:system-size-z = 4.0 !nm #------------------------------------------ # Material Files: #------------------------------------------ material:file=Ni.mat #------------------------------------------ # Simulation attributes: #------------------------------------------ sim:temperature=300 sim:minimum-temperature=0 sim:maximum-temperature=800 sim:temperature-increment=25 sim:time-steps-increment=1 sim:equilibration-time-steps=1000 sim:loop-time-steps=1000 #------------------------------------------ # Program and integrator details #------------------------------------------ sim:program=curie-temperature sim:integrator=monte-carlo #------------------------------------------ # Data output #------------------------------------------

  • utput:real-time
  • utput:temperature
  • utput:magnetisation
  • utput:magnetisation-length
  • utput:mean-magnetisation-length
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SLIDE 16

Curie temperature calculation

0.6 0.7 0.8 0.9 1.0 2000 4000 6000 8000 10000 Normalized magnetization Time steps

equilibration-time-steps loop-time-steps

<|m|>

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SLIDE 17

0.0 0.2 0.4 0.6 0.8 1.0 100 200 300 400 500 600 700 800 Normalized magnetization Temperature (K)

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Curie temperature calculation

0.0 0.2 0.4 0.6 0.8 1.0 100 200 300 400 500 600 700 800 Normalized magnetization Temperature (K)

m(T) =  1 − ✓ T Tc ◆ ◆αβ

Tc ~ 640 K

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SLIDE 19

Gnuplot for plotting data and curve fitting

p “output” u 2:7 w lp

plot file name using columns 2 and 7 with lines and points Start the gnuplot interactive plotting program on the command line:

gnuplot

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Gnuplot for plotting data and curve fitting

m(x) = (1-x/Tc)**beta Tc = 500.0 beta = 0.4 fit [0:Tc] m(x) “output” u 2:7 via Tc, beta p “output” u 2:7 w p ti “data”, m(x) w l

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SLIDE 21

Ultrafast demagnetization in Ni

  • E. Beaurepaire et al, Phys. Rev. Lett. 76 4250 (1996)
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Two temperature model

Free electron approximation Ce ∝ Te

400 600 800 1000 1200 1400 1600 0.5 1 1.5 2 Temperature (K) Time (ps) Tp Te

Ce ∂Te ∂t = −G(Te − Tl) + S(t) Cl ∂Tl ∂t = −G(Tl − Te)

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Input file for simulated laser pulse

sim:equilibration-time-steps=10000 sim:total-time-steps=50000 sim:laser-pulse-power=5.0 sim:laser-pulse-temporal-profile=two-temperature sim:program=laser-pulse sim:integrator=llg-heun sim:time-step=1.0e-16

  • utput:real-time
  • utput:electron-temperature
  • utput:phonon-temperature
  • utput:magnetisation-length
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SLIDE 24

Effect of pulse power in Ni

Stronger laser pulses show more demagnetization and slower recovery

0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 Normalized magnetization Time (ps) Pulse power = 0.8 1.2 1.6 2.2 2.6

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SLIDE 25

Plot |m| vs time with gnuplot

p “output” u 1:4 w l

plot file name using columns 1 and 4 with lines

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SLIDE 26

Thermally induced magnetic switching

  • T. Ostler et al, Nat. Commun.(2012)
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SLIDE 27

Sublattice magnetization dynamics

  • I. Radu et al, Nature (2011)
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GdFe ferrimagnet Gd Fe

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GdFe.mat

#--------------------------------------------------- # Number of Materials #--------------------------------------------------- material:num-materials=2 #--------------------------------------------------- # Material 1 Fe (TM) #--------------------------------------------------- material[1]:material-name=TM material[1]:damping-constant=0.02 material[1]:exchange-matrix[1]=2.835e-21 material[1]:exchange-matrix[2]=-1.09e-21 material[1]:atomic-spin-moment=1.92 !muB material[1]:uniaxial-anisotropy-constant=8.07246e-24 material[1]:material-element=Fe material[1]:minimum-height=0.0 material[1]:maximum-height=1.0 material[1]:alloy-host material[1]:alloy-fraction[2]=0.25 material[1]:initial-spin-direction=0,0,1 #--------------------------------------------------- # Material 2 Gd (RE) #--------------------------------------------------- material[2]:material-name=RE material[2]:damping-constant=0.02 material[2]:exchange-matrix[1]=-1.09e-21 material[2]:exchange-matrix[2]=1.26e-21 material[2]:atomic-spin-moment=7.63 !muB material[2]:uniaxial-anisotropy-constant=8.07246e-24 material[2]:material-element=Ag material[2]:minimum-height=0.0 material[2]:maximum-height=0.0 material[2]:initial-spin-direction=0,0,-1

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SLIDE 30

input file

sim:equilibration-time-steps=20000 sim:total-time-steps=50000 sim:temperature = 300.0 sim:equilibration-temperature = 300.0 sim:temperature-increment=25 sim:time-steps-increment=10 sim:preconditioning-steps = 200 sim:equilibration-time-steps=1000 sim:total-time-steps=50000 sim:two-temperature-electron-heat-capacity=2.25e2 sim:two-temperature-phonon-heat-capacity=3.1e6 sim:two-temperature-electron-phonon-coupling=2.5e17 sim:laser-pulse-temporal-profile = two-temperature sim:laser-pulse-time = 50 !fs sim:laser-pulse-power = 16.70

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input file (pt2)

sim:integrator=llg-heun sim:time-step=1.0e-16

  • utput:real-time
  • utput:electron-temperature
  • utput:phonon-temperature
  • utput:material-magnetisation
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SLIDE 32
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.2 0.4 0.6 0.8 1 2 3 4 5 Normalized magnetization Time (ps) Fe Gd

Calculated magnetization dynamics

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SLIDE 33

Dynamics for 7nm3 GdFe

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.2 0.4 0.6 0.8 1 2 3 4 5 Normalized magnetization Time (ps) Fe Gd

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Summary

Simulated Curie temperature and demagnetization dynamics in Ni Simulated TIMS in GdFe Many different types of simulations possible (materials, alloys, multilayers…)

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VA M PIRE

vampire.york.ac.uk