Ultrafast laser-driven spin dynamics in antiferromagnetic and ferromagnetic solids: Ab-initio studies with real-time TDDFT

Transcription

1 Ultrafast laser-driven spin dynamics in antiferromagnetic and ferromagnetic solids: Ab-initio studies with real-time TDDFT E.K.U. Gross Max-Planck Institute of Microstructure Physics Halle (Saale)

2 First experiment on ultrafast laser induced demagnetization Beaurepaire et al, PRL 76, 4250 (1996)

3 Possible mechanisms for demagnetisation Direct interaction of spins with the magnetic component of the laser Zhang, 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, (2005) Super-diffusive spin transport Battiato, Carva, Oppeneer, PRL 105, (2010) Our proposal for the first 50 fs: Laser-induced charge excitation followed by spin-orbit-driven demagnetization of the remaining d-electrons

4 Time-dependent density-functional theory (E. Runge, E.K.U.G., PRL 52, 997 (1984)) Basic 1-1 correspondence: 1-1 ( ) ¾ r ( rt) vrt KS theorem: The time-dependent density determines uniquely the time-dependent external potential and hence all physical observables for fixed initial state. The time-dependent density of the interacting system of interest can be calculated as density of an auxiliary non-interacting (KS) system with the local potential N ( ) ( ) 2 ρ rt = å j j j = 1 3 vs r't' rt v rt d r' rt 2 2 æ h Ñ ö ih j j rt = ç - + vs r rt jj rt t è 2m ø ( ) [ ]( ) ( ) ( r't) r éër ( ) ùû( ) = ( ) + ò + vxc ér r't' ù rt r- r' ë û ( ) ( )

5 Basic 1-1 correspondence: 1-1 ( ) ¾ r ( rt) vrt KS theorem: Time-dependent density-functional theory The time-dependent density determines uniquely the time-dependent external potential and hence all physical observables for fixed initial state. The time-dependent density of the interacting system of interest can be calculated as density of an auxiliary non-interacting (KS) system with the local potential (E. Runge, E.K.U.G., PRL 52, 997 (1984)) Genuine ab-initio approach, in principle exact N ( ) ( ) 2 ρ rt = å j j j = 1 3 vs r't' rt v rt d r' rt 2 2 æ h Ñ ö ih j j rt = ç - + vs r rt jj rt t è 2m ø ( ) [ ]( ) ( ) ( r't) r éër ( ) ùû( ) = ( ) + ò + vxc ér r't' ù rt r- r' ë û ( ) ( )

6 Generalization: Non-collinear-Spin-TDDFT with SOC é 1 i jk ( r, t) = -iñ- Alaser ( t) + vs r, r, t - µ Bs BS r, r, t t ê ë 2 ( ) 2 [ m]( ) [ m]( ) µ B ù + s Ñ S[ r m]( ) - Ñ j k 2c úû ( v, r, t ) ( i ) ( r, t) r ( r, t) [ ]( ) ( ) 3 vs r, m r, t = vlattice r + ò d r + vxc, r, t r- r [ r, m](, ) = (, ) + [ r, m](, ) B r t B r t B r t S external xc [ r m]( ) where j (, ) k rt are Pauli spinors

7 Generalization: Non-collinear-Spin-TDDFT with SOC é 1 i jk ( r, t) = -iñ- Alaser ( t) + vs r, r, t - µ Bs BS r, r, t t ê ë 2 ( ) 2 [ m]( ) [ m]( ) µ B ù + s Ñ S[ r m]( ) - Ñ j k 2c úû ( v, r, t ) ( i ) ( r, t) r ( r, t) [ ]( ) ( ) 3 vs r, m r, t = vlattice r + ò d r + vxc, r, t r- r [ r, m](, ) = (, ) + [ r, m](, ) B r t B r t B r t S external xc [ r m]( ) Universal functionals of r and m where j (, ) k rt are Pauli spinors

8 Quantity of prime interest: vector field of spin magnetization

9 Quantity of prime interest: vector field of spin magnetization Cr monolayer in ground state

10 K. Krieger, K. Dewhurst, P. Elliott, S. Sharma, E.K.U.G., JCTC 11, 4870 (2015)

11 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) (

12 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) ( ELK = Electrons in K-Space or Electrons in Kay's Space Kay Dewhurst Sangeeta Sharma

13 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) (

14 Analysis of the results

15 Calculation without spin-orbit coupling components of spin moment

16 Exact equation of motion M ( t) = i éh ˆ, s t h ë ˆ z KS z ù û { } = - ò 3 dr M x(r,t)b KS,y(rt) M y(r,t)b KS,x(rt) 1 + ò - 2c ëñ û ëñ t j(r, t) = sä ˆ pˆ spin current tensor { ˆ é ( ) ( ) ù ˆ ( ) ( ) } s y é s z ù 3 dr x v r,t j r,t y v r,t j r,t 2 û B KS(rt) = B ext (rt) + B XC(rt)

17 Exact equation of motion M ( t) = i éh ˆ, s t h ë ˆ z KS z ù û { } = - ò 3 dr M x(r,t)b KS,y(rt) M y(r,t)b KS,x(rt) 1 + ò - 2c ëñ û ëñ t j(r, t) = sä ˆ pˆ spin current tensor Global torque exerted by B KS { ˆ é ( ) ( ) ù ˆ ( ) ( ) } s y é s z ù 3 dr x v r,t j r,t y v r,t j r,t 2 û B KS(rt) = B ext (rt) + B XC(rt)

18 Exact equation of motion M ( t) = i éh ˆ, s t h ë ˆ z KS z ù û { } = - ò 3 dr M x(r,t)b KS,y(rt) M y(r,t)b KS,x(rt) 1 + ò - 2c ëñ û ëñ t j(r, t) = sä ˆ pˆ spin current tensor Global torque exerted by B KS { ˆ é ( ) ( ) ù ˆ ( ) ( ) } s y é s z ù 3 dr x v r,t j r,t y v r,t j r,t 2 û B KS(rt) = B ext (rt) + B XC(rt) Global torque = 0, if B ext = 0 (due to zero-torque theorem for B xc )

19 Note: Ground state of bulk Fe, Co, Ni is collinear

20

21 Demagnetization occurs in two steps: - Initial excitation by laser moves magnetization from atomic region into interstitial region. Total Moment is basically conserved during this phase. - Spin-Orbit term drives demagnetization of the more localized electrons until stabilization at lower moment is achieved

22 Beyond 3D bulk

23 Cr monolayer

24

25 (fs)

26 Streamlines for J x, 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).

27 (fs)

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29 Effect of spin transport across interfaces:

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31 Heusler compounds

32 Ni 2 MnGa Ga 0.02 µb Mn µb Ni µb

33 Ni 2 MnGa Laser parameters: ω=2.72ev Ipeak= 1x1015 W/cm2 J = 935 mj/cm2 FWHM = 2.42 fs See loss in global moment

34 Ni 2 MnGa Also change in local moments Transfer of moment from Mn to Ni (does not require SOC) Followed by spin-orbit mediated demagnetization on Ni

35 P. Elliott, T. Mueller, K. Dewhurst, S. Sharma, E.K.U.G., arxiv

36 M(t) (µ B ) Time(fs) Sb

37 NiMnSb

38 DOS (states/ev) M(t) (µ B ) Time(fs) Energy (ev)

39 Mn 3 Ga Ga Mn

40 Mn 3 Ga Laser parameters: ω=2.72ev Ipeak= 1x1015 W/cm2 J = 935 mj/cm2 FWHM = 2.42 fs Global moment M(t) preserved Local moments around each atom change P. Elliott, T. Mueller, K. Dewhurst, S. Sharma, E.K.U.G., arxiv

41 DOS (states/ev) Energy (ev)

42

43 Summary Demagnetization in first 50 fs is a universal two-step process: 1. Initial excitation of electrons into highly excited delocalised states (without much of a change in the total magnetization) 2. Spin-orbit coupling drives demagnetization of the more localized electrons No significant change in M x and M y in bulk Fe, Co, Ni Interfaces show spin currents as important as spin-orbit coupling Ultrafast (3-5 fs) transfer of spin moment between sublattices of Heusler compounds by purely optical excitation: Easily understood on the basis of the ground-state DOS

44 Kevin Krieger Sangeeta Sharma Florian Eich Kay Dewhurst Peter Elliott

45 Future: Include relaxation processes due to el-el scattering - in principle contained in TDDFT, - but not with adiabatic xc functionals - need xc functional approximations with memory vxc éër r't' ùû rt Include relaxation processes due to el-phonon scattering Include relaxation due to radiative effects simultaneous propagation of TDKS and Maxwell equations Include dipole-dipole interaction to describe motion of domains construct approximate xc functionals which refer to the dipole int Optimal-control theory to find optimized laser pulses to selectively demagnetize/remagnetize, i.e. to switch, the magnetic moment Create Skyrmions with suitably shaped laser pulses ( ) ( )