Ultrafast laser-induced demagnetization of solids...
Transcript of Ultrafast laser-induced demagnetization of solids...
Ultrafast laser-induced demagnetization of solids: Understanding the mechanism with real-time TDDFT simulations
Max-Planck Institute ofMicrostructure Physics
Halle (Saale)
E.K.U. Gross
Beaurepaire et al, PRL 76, 4250 (1996)
First experiment on ultrafast laser induced demagnetization
Possible mechanisms for demagnetization
Possible mechanisms for demagnetisation
• Direct interaction of spins with the magnetic component of the laserZhang, Huebner, PRL 85, 3025 (2000)
Possible mechanisms for demagnetisation
• Direct interaction of spins with the magnetic component of the laserZhang, Huebner, PRL 85, 3025 (2000)
• Spin-flip electron-phonon scattering(ultimately leading to transfer of spin angular momentum to the lattice)Koopmans et al, PRL 95, 267207 (2005)
Possible mechanisms for demagnetisation
• Direct interaction of spins with the magnetic component of the laserZhang, Huebner, PRL 85, 3025 (2000)
• Spin-flip electron-phonon scattering(ultimately leading to transfer of spin angular momentum to the lattice)Koopmans et al, PRL 95, 267207 (2005)
• Super-diffusive spin transportBattiato, Carva, Oppeneer, PRL 105, 027203 (2010)
Possible mechanisms for demagnetisation
• Direct interaction of spins with the magnetic component of the laserZhang, Huebner, PRL 85, 3025 (2000)
• Spin-flip electron-phonon scattering(ultimately leading to transfer of spin angular momentum to the lattice)Koopmans et al, PRL 95, 267207 (2005)
• Super-diffusive spin transportBattiato, Carva, Oppeneer, PRL 105, 027203 (2010)
• Our proposal for the first 50 fs: Laser-induced charge excitation followed by spin-orbit-driven demagnetization of the remaining d-electrons
Quantity of prime interest: vector field of spin magnetization
Quantity of prime interest: vector field of spin magnetization
Cr monolayer in ground state
Basic 1-1 correspondence:The time-dependent density determines uniquelythe time-dependent external potential and hence allphysical observables for fixed initial state.
( ) ( )v rt rt1-1←→ ρ
Time-dependent density-functional theory
KS theorem:The time-dependent density of the interacting system of interest canbe calculated as density
of an auxiliary non-interacting (KS) system
with the local potential
( ) ( )2N
j = 1 ρ rt = rtjϕ∑
( ) ( ) ( ) ( )3S
r ' tv r ' t ' rt v rt d r '
r r 'ρ
ρ = + + −∫
( ) [ ]( ) ( )2 2
j S ji rt v rt rtt 2m
∂ ∇ϕ = − + ρ ϕ ∂
( ) ( )xcv r ' t ' rt ρ
(E. Runge, E.K.U.G., PRL 52, 997 (1984))
Theoretical approach:
( ) ( )( ) [ ]( ) [ ]( )
[ ]( )( ) ( ) ( )
21, , , , ,2
, , ,2
k laser S B S
BS k
i r t i A t v r t B r tt
v r t i r tc
ϕ ρ µ σ ρ
µ σ ρ ϕ
∂ = − ∇− + − ⋅∂ + ⋅ ∇ × − ∇
m m
m
Generalization: Real-time TDDFT with SOC
[ ]( ) ( ) ( ) [ ]( )3,, , , ,S lattice xc
r tv r t v r d r v r t
r rρ
ρ ρ′
′= + +′−∫m m
[ ]( ) ( ) [ ]( ), , , , ,S external xcB r t B r t B r tρ ρ= +m m
( ),k r tϕwhere are Pauli spinors
K. Krieger, K. Dewhurst, P. Elliott, S. Sharma, E.K.U.G., JCTC 11, 4870 (2015)
• Wave length of laser in the visible regime(very large compared to unit cell)
Dipole approximation is made(i.e. electric field of laser is assumed to be spatially constant)
Laser can be described by a purely time-dependent vector potential
• Periodicity of the TDKS Hamiltonian is preserved!
• Implementation in ELK code (FLAPW) (http://elk.sourceforge.net/)
Aspects of the implementation
• Wave length of laser in the visible regime(very large compared to unit cell)
Dipole approximation is made(i.e. electric field of laser is assumed to be spatially constant)
Laser can be described by a purely time-dependent vector potential
• Periodicity of the TDKS Hamiltonian is preserved!
• Implementation in ELK code (FLAPW) (http://elk.sourceforge.net/)
Aspects of the implementation
ELK = Electrons in K-SpaceorElectrons in Kay's Space
Kay Dewhurst Sangeeta Sharma
• Wave length of laser in the visible regime(very large compared to unit cell)
Dipole approximation is made(i.e. electric field of laser is assumed to be spatially constant)
Laser can be described by a purely time-dependent vector potential
• Periodicity of the TDKS Hamiltonian is preserved!
• Implementation in ELK code (FLAPW) (http://elk.sourceforge.net/)
Aspects of the implementation
( ) ( ) ( )j ij ii1. Set , t c tψ = χ∑r r
( ) ( )2. Compute , t and , tρ r m r
( ) ( ) ( ) ( )s s s KSˆ3. Compute v , t , , t , , t to give H tr B r A r
( )ij i KS jˆ4. Compute H H t≡ χ χ
ik kj j ij5. Solve H d d for d and =∈ ∈
( ) ( )ki t*ij jk lk ilkl
6. Compute c t t d d e c t− ∈ ∆+ ∆ =∑7. Goto 1
Algorithm for time propagation
K. Krieger, K. Dewhurst, P. Elliott, S. Sharma, E.K.U.G., JCTC 11, 4870 (2015)
Analysis of the results
components of spin moment
Calculation without spin-orbit coupling
( )z KS zi ˆ ˆM t H ,
t∂ = σ ∂
{ }( ) ( ) ( ) ( ){ }
3x KS,y y KS,x
3s y s z2
d r M (r, t)B (rt) M (r, t)B (rt)
1 ˆ ˆd r x v r, t j r, t y v r, t j r, t2c
= −
+ ⋅ × − ⋅ ×
∫
∫ ∇ ∇
KS ext XCB (rt) B (rt) B (rt)= +
ˆˆj(r, t) p= σ⊗
spin current tensor
Exact equation of motion
( )z KS zi ˆ ˆM t H ,
t∂ = σ ∂
{ }( ) ( ) ( ) ( ){ }
3x KS,y y KS,x
3s y s z2
d r M (r, t)B (rt) M (r, t)B (rt)
1 ˆ ˆd r x v r, t j r, t y v r, t j r, t2c
= −
+ ⋅ × − ⋅ ×
∫
∫ ∇ ∇
KS ext XCB (rt) B (rt) B (rt)= +
ˆˆj(r, t) p= σ⊗
Global torqueexerted by BKS
spin current tensor
Exact equation of motion
( )z KS zi ˆ ˆM t H ,
t∂ = σ ∂
{ }( ) ( ) ( ) ( ){ }
3x KS,y y KS,x
3s y s z2
d r M (r, t)B (rt) M (r, t)B (rt)
1 ˆ ˆd r x v r, t j r, t y v r, t j r, t2c
= −
+ ⋅ × − ⋅ ×
∫
∫ ∇ ∇
KS ext XCB (rt) B (rt) B (rt)= +
ˆˆj(r, t) p= σ⊗
Global torqueexerted by BKS
Global torque = 0, if Bext = 0 (due to zero-torque theorem for Bxc )
spin current tensor
Exact equation of motion
Note: Ground state of bulk Fe, Co, Ni is collinear
Demagnetization occurs in two steps:
- Initial excitation by laser moves magnetization from atomic regioninto interstitial region. Total Moment is basically conservedduring this phase.
- Spin-Orbit term drives demagnetization of the more localized electrons until stabilization at lower moment is achieved
Playing with laser parameters
Influence of approximation for xc functional
The four steps of any functional theory
Step 1: Basic Theorems (Hohenberg-Kohn-Sham/ Runge-Gross)
Step 2: Find approximate functionals for
Step 3: Write code that solves the KS equations efficiently
Step 4: Run code for interesting systems/questions
( ) ( )xcv r ' t ' rt ρ
Problem: In all standard approximations of Exc (LSDA, GGAs)m(r) and Bxc(r) are locally parallel
S. Sharma, J.K. Dewhurst, C. Ambrosch-Draxl, S. Kurth, N. Helbig, S. Pittalis, S. Shallcross, L. Nordstroem E.K.U.G., Phys. Rev. Lett. 98, 196405 (2007)
Why is that important?
Ab-initio description of spin dynamics:
microscopic equation of motion (following from TDSDFT)
XC Sm(r, t) m(r, t) B (r, t) J (r, t) SOC= × − ∇⋅ +
in absence of external magnetic field
Consequence of local collinearity: m×Bxc = 0: → possibly wrong spin dynamics→ how important is this term in real-time dynamics?
Construction of a novel GGA-type functional
Traditional LSDA: Start from uniform electron gas in collinear magnetic state. Determine from QMC or MBPT and parametrize touse in LSDA.
New non-collinear functional: Start from spin-spiralphase of e-gas. Determine from MBPT andparametrize to use as non-collinear GGA.
XCe [n,m]
XCe [n,m]
XCe [n, m]XCe [n, m]
F.G. Eich and E.K.U. Gross, Phys. Rev. Lett. 111, 156401 (2013)
( )( )( )
2
scosm m ssin
1 s
⋅
= ⋅ −
q rr q r
Magnetisation of a spin-spiral state in the uniform electron gas
SSW SSWxc xc (n,m,q,s)ε = ε
Illustration of spin spiral waves along one spatial coordinate for two different choices of wavevectorq=k1/2.
( ) ( )( ) ( ) ( )
2T2
2 4T T
Ds
D m d=
+r
rr r r ( ) ( ) ( ) ( )
( ) ( )
2 4T T2
4T
D m dq
m D+
=r r r
rr r
[ ] ( ) ( ) ( ) ( ) ( )( )GGA 3 SSWxc xcE n,m d r n n ,m ,q ,s= ε∫ r r r r r
( ) ( ) ( )( ) 22Td m m= × ∇r r r ( ) ( ) ( )( ) 2
TD m m= × ∇⊗r r r
F.G. Eich and E.K.U. Gross, Phys. Rev. Lett. 111, 156401 (2013)
Beyond 3D bulk
Cr monolayer
0 50 100 150 200 (fs)
Streamlines for Jx, the spin-current vector field of the x component of spin, around a Ni atom in bulk (left) and for the outermost Ni atom in the slab (right).
0 50 100 150 200 (fs)
Heusler compounds
GaMn
Mn3Ga
Laser parameters: ω=2.72eV Ipeak= 1x1015 W/cm2 J = 935 mJ/cm2 FWHM = 2.42 fs
Global moment |M(t)| preservedLocal moments around each atom change
Mn3Ga
P. Elliott, T. Mueller, K. Dewhurst, S. Sharma, E.K.U.G., arXiv 1603.05603
Ga 0.02 μBMn -3.14 μBNi -0.37 μB
Ni2MnGa
See loss in global moment
Laser parameters: ω=2.72eV Ipeak= 1x1015 W/cm2 J = 935 mJ/cm2 FWHM = 2.42 fs
Ni2MnGa
Also change in local momentsTransfer of moment from Mn to Ni (does not require SOC)Followed by spin-orbit mediated demagnetization on Ni
Ni2MnGa
P. Elliott, T. Mueller, K. Dewhurst, S. Sharma, E.K.U.G., arXiv 1603.05603
Summary
• No demagnetization without Spin-Orbit coupling
• Demagnetization in first fs is a two-step process:1. Initial excitation of electrons into highly excited states
(without much of a change in the total magnetization)2. Spin-orbit coupling drives demagnetization of localized
electrons (mainly d electrons)
• No significant change in Mx and My
• New xc functional derived from spin-spiral phase of uniform e-gasyields results very similar to non-collinear LSDA
• Ultrafast transfer of spin moment between sublattices of Heuslercompounds: Easily understood on the basis of the ground-state DOS
Florian Eich
Kay Dewhurst
Sangeeta SharmaKevin Krieger
Peter Elliott