Ultrafast spin, charge and nuclear dynamics
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Ultrafast spin, charge and
nuclear dynamics
Sangeeta Sharma
Max-Born institute for non-linear optics, Berlin, Germany
Ultrafast spin, charge and nuclear dynamics Theory collaborators: J.K. Dewhurst, E. K. U. Gross, K. Krieger, T. Müller, C. Wang, Q. Lee, P. Scheid, N. Singh, J. Krishna, P. Elliott, S. Shallcross. Experimental collaborators: M. Schultze, M. Münzenberg, S. Mathias, M. Aeschlimann, J. Chen, D. Steil, U. Bovensiepen, A. Eschenlohr, C. Von-Korff Schmising, S. Eisebitt, W. Kuch, J. Biegert, I. Radu, D. Schick Funding: DFG TRR227 and SPP-QUTIF
Evolution of multi-core processors
Femto-magnetism
Ultrafast manipulation of
spins with light
I Efficient devices based in
spin currents
I Fast (femtoseconds)
operational times
Laser-induced demagnetization
Expt: Beaurepair et al. PRL 76 4250 (1996)
Leading order terms in expansion of QED H
X 1 X e2 1X e
H= p2i − eVext (ri ) + + pi · Aext (ri )
i
2m r
i
Models to explain this demagnetisation 1. Elliott-Yafet mechanism: electron-phonon or electron-impurity mediated spin-flip causing a global demagnetization B. Koopmans, Nature Mater. 6, 715 (2007) 2. Spin-lattice relaxation causing global demagnetization W. Hübner and K. H. Bennemann, PRB 53, 3422 (1996) 3. Super-diffusive model: Electron and spin current flows causing a local demagnetization M. Battiato, K. Carva, and P. M. Oppeneer, PRL. 105, 027203 (2010) 4. Electron -electron and -phonon scattering causing global demagnetization B. Y. Mueller et al., PRL 111, 167204 (2013)
Method: Ab-initio theory Our aim is to make quantitative predictions with a computer code knowing only the atomic species and crystal structure No adjustable parameters
Theory: fully ab-initio approach
∂ψj (r, t) 1 1
i = i∇ + Aext (t) 2 + vs (r, t) (1)
∂t 2 c
1→− 1 −
+ σ · Bs (r, t) + 2 →σ · (∇vs (r, t) × i∇) ψj (r, t)
2c 4cTheory: fully ab-initio approach
∂ψj (r, t) 1 1
i = i∇ + Aext (t) 2 + vs (r, t) (1)
∂t 2 c
1→− 1 −
+ σ · Bs (r, t) + 2 →σ · (∇vs (r, t) × i∇) ψj (r, t)
2c 4c
Effective potentials:
Bs [ρ, m] = Bext + Bxc [ρ, m], vs [ρ, m] = vcl + vxc [ρ, m] (2)Theory: fully ab-initio approach
∂ψj (r, t) 1 1
i = i∇ + Aext (t) 2 + vs (r, t) (1)
∂t 2 c
1→− 1 −
+ σ · Bs (r, t) + 2 →σ · (∇vs (r, t) × i∇) ψj (r, t)
2c 4c
Effective potentials:
Bs [ρ, m] = Bext + Bxc [ρ, m], vs [ρ, m] = vcl + vxc [ρ, m] (2)
Density:
X
ρ(r, t) = ψj∗ (r, t)ψj (r, t) (3)
j
Magnetization density(unconstrained vector field):
ψj∗ (r, t)→
−
X
m(r, t) = σ ψj∗ (r, t) (4)
j
E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984)Demagnetisation in supercell of fcc Ni
A field I Inter-site non-collinearity
and magnons do not
0
mx my contribute in early times
m(t)-m(t=0)
-0,1
-0,2
-0,3
4x4 super-cell of Ni I 4c12 →
−
σ · (∇vs (r, t) × i∇)
mz
-0,4
-0,5
I The physics is dominated
0,6
Total
bulk Ni by spin-orbit induced
m(t) (µΒ)
0,4
spin-flips
0,2
Excited localized
0
0 2 4 6 8 10 12 14 16 18 20
Time(fs)
Krieger et al. JCTC 11, 4870 (2015),
Elliott et al. New J. Phys. 18, 013014 (2016),
Dewhurst et al. Computer Phys. Comm. 209, 92 (2016)How fast?–exchange and spin-orbit times in femto-seconds
Metal Exchange Spin-orbit
Fe 52 50
Co 80 52
Ni 380 48
Table: Exchange time is Heisenberg exchange parameter converted to
time. SO time is the time at which SO coupling causes spin flips in
Fe/Mn, Co/Mn and Ni/Mn interfaces.Faster than spin-orbit
1. A new ultrafast phenomena called OISTR.
1.1 Spin manipulation faster than spin-orbit.
1.2 Spin manipulation at sub-exchange time scales.
1.3 Sub-exchange, sub-spin-orbit switching the magnetic order.
1.4 Spin manipulation times coherently controlled by laser
pulse.
2. Experimental demonstration of OISTR
3. What is missing and how we can try to change thatFerri-magnetic layers: Mn2/Co4/Cu(001)
Magnetization dynamics in Mn2/Co4/Cu(001)
2
FWHM=25fs, E=16mJ/cm
A(t)3
2
M(t) [µΒ]
1
Co4
0 Co3
Co2
-1 Co1
Mn2
Mn1
-2
0 10 20 30 40 50 60
Time(fs)
I Ground-state is Ferri-magnetic
I ∼ 29fs one of the Mn layers switches the direction of spin
I Stays in transient FM state at least till 150fs
Dewhurst, Elliott, Shallcross, Gross and Sharma, Nano Lett. 18, 1842, (2018)Spin-flips, spin current, charge current
1 1 1−
Ĥs = i∇ + Aext (t) 2 + vs (r, t) + → σ · Bxc (r, t) (5)
2 c 2c
1 →−
+ σ (∇vs (r, t) × i∇)
4c2
∂
m(r, t) = ih[Ĥs , σ̂n̂(r, t)]i (6)
∂t
∂ ←→ 1
m(r, t) = − ∇ · J (r, t) + [Bxc (r, t) × m(r, t)]
∂t c
1
+ [∇n(r, t) × ∇vs (r, t)]
4c2
1 ← → ←→
+ [ J T (r, t) − T r{ J (r, t)}] · ∇vs (r, t) (7)
2c2
Krieger et al. JPCM 29 , 224001 (2017),
Dewhurst et al. Computer Phys. Comm. 209, 92 (2016)Magnetization dynamics in Mn2/Co4/Cu(001) without SO
3
with SO
2
without SO
Moment(µΒ)
1
0
-1
-2
0 10 20 30 40 50 60 70
Time (fs)
I Spin flips play no role in switching of magnetic order.
Dewhurst et al. Nano Lett. 18, 1842, (2018)Optical inter-site spin transfer (OISTR)
m = nup − ndnTransient state density
∞ Z
X
DOS(ω, t) = δ(ω − εik )gik (t), (8)
i=1 BZ
with
X 2
k
gik (t) = njk Oij (t) , (9)
j
where njk is the occupation number of the j th time-evolving
orbital and
Z
Oij (t) = d3 rφ∗ik (r)ψjk (r, t).
k
(10)
Here φi are the ground-state Kohn-Sham orbitals. In absence of
any time-dependent perturbation ψjk (r, t = 0) = φ∗jk (r)
Elliott et al. Sci. Rep. 6, 38911 (2016)Transient occupied states
2
Mn1
1
Tr-DOS
0
-1
-2
2
Mn2
1
Tr-DOS
0
-1
-2
-6 -4 -2 0 2 4 6
Energy (eV)
M = nup − ndn
I Optical inter-site spin transfer (OISTR) is responsible for
switching
I Availability of states enforces OISTROutlook for OISTR: Ultrafast GMR
Laser induced transient OCMR device
J
Resistance change of 385% in CuCoMn multilayers from
Boltzmann simulations (Ingrid Mertig)Experimental confirmation of OISTR
Quantitative but indirect agreement with experiemnts
Expt-Ni
1,2 Expt-Fe
Theory-Fe
Theory-Ni
1
M(t)/M(0)
0,8
0,6
0,4
-50 0 50 100 150 200 250 300 350 400
Time (fs)
Laser-induced local increase in
moment
Hofherr et al. Science Advs. 6, eaay8717
Attosecond dynamics via OISTR
(2019)
Siegrist et al. Nature 571, 240 (2019)Linear response TDDFT
Interacting response function:
ε−1 (q, ω) = 1 + χ0 (q, ω) [1 − (vcl + fxc (q, ω))χ0 (q, ω)] −1 (11)
Non-interacting response function:
X φ∗ (r)φ∗mk (r0 )φlk (r0 )φmk (r)
χ0 (r, r0 , ω) = (nlk − nmk ) lk (12)
ω − lk + mk + iη
lmkLinear response TDDFT
ε−1 (q, ω) = 1 + χ0 (q, ω) [1 − (vcl + fxc (q, ω))χ0 (q, ω)] −1 (13)
All quantities are treated as matrices in reciprocal space vectors
G,G’ to account for LFE.
Local field effects(LFE)– charge density rearrangement caused
by the external perturbation leads to creation of local
microscopic fields.
Light of the form ei(G+q).r produces a response also of the form
0
ei(G +q).r
Simplest approximations:
fxc = 0 (RPA, i.e. no excitons) and G=G’=0 (no LFE)CoPt: experimental response vs theoretical disaster
0.02
Expt.
0
Theory
-0.02
∆β(ω)
-0.04
-0.06
-0.08
-0.1
45 50 55 60 65 70
Energy (eV)
Disagreemet believed to be due to
(a) Missing many-body corrections and
(b) missing excitonic physics (i.e. fxc 6= 0).Theory guiding experiments
Co@CoPt Pt@CoPt
(a) (b) Agreement requires:
0,005 0,005
Expt. Expt. I Many-body correction
0 0 via GW
∆β(ω)
-0,005
Co Pt
-0,005 I Excitonic physics
included via bootstrap
-0,01 -0,01
Total Total approximation
-0,015
45 50 55 60 65 70 75 45 50 55 60 65 70
-0,015
75 I Local field effects by
Energy (eV) Energy (eV)
solving matrix equation.
Dewhurst et al. Phys. Rev. Lett. 124,
077203, (2020),
Willems et al. Phys. Rev. Lett. 122,
217202, (2019),
Willems et al. Nat. Comm. 11, 1-7, (2020)Transient response function in CoPt
-3
x10
4
2 Pt N7-edge
0
Pt O3-edge 57.2 eV
∆β(ω,t)
-2
Co M23-edge
-4
Pt O3 -edge
54.1 eV
-6
-8
-50 0 50 100 150 200 250
time (fs)
Dewhurst et al. Phys. Rev. Lett. 124, 077203, (2020)Where does the angular momentum go?
L+S+N is conserved
(a) (b)
Ni Co L(t)/L(0) -1
0.2 S(t)/S(0) -1 0.1
ex. charge
0
0
-0.1
-0.2
-0.2
-0.3
-0.4 -0.4
-0.5
0 5 10 15 20 0 5 10 15 20 25 30
time(fs) time(fs)What is missing from the theory?
Even the exact functional will
not yield full predictiveness!Relativistic interaction terms
Leading order terms in expansion of QED H
X 1 X e2 1X e
H= p2i − eVext (ri ) + + pi · Aext (ri )
i
2m r
iRelativistic
interaction
terms
Exchange-correlation
functional
developmentDFT of magnetic dipolar interactions
" #
1 e2 X 3(ri − rj )(ri − rj ) 1
Hdip =− 2 2 si · 5 − 3 · sj
c m rij rij
iRelativistic
interaction
terms
Exchange-correlation
functional
development
Radiation
via
Maxwell's equationsRelativistic
interaction
terms
Exchange-correlation Extending
functional space-time
development boundaries
(ultra long-range
TDDFT)
Radiation
via
Maxwell's equationsLong length scale physics
Spin-spiral ansatz
!
u↑nk (r) ei(q/2)·(r)
Φkn (r) = eik·r (14)
u↓nk (r) ei(-q/2)·(r)
Ultra long-range anstaz
!
X u↑nk (r) i(k+κ)·(r+R)
Φkα (r + R) = cαnk+κ e (15)
nκ
u↓nk (r)Self-consistent density for a 3456 atom cell of LiF Müller, Sharma, Gross and Dewhurst, Phys. Rev. Lett. 125, 256402 (2020)
Skyrmion in iron on iridium substrate Plot of the surface magnetization density averaged in each unit cell in the Fe plane. Each triangle represents a unit cell and the ultracell vectors were scaled by 0.8, 0.9, 1.0 and 1.1.
Relativistic
interaction
terms
Exchange-correlation Extending
functional space-time
development boundaries
(ultra long-range
TDDFT)
Radiation
via
Maxwell's equationsRelativistic
interaction
terms
Exchange-correlation Extending
functional space-time
development boundaries
(ultra long-range
TDDFT)
Nuclear degrees Radiation
of freedom via
(quantum or classical) Maxwell's equationsNuclear degrees of freedom Treat nuclei as classical point particles: Ehrenfest dynamics Quantum nuclei required for superconductivity!
Coupled spin nuclear dynamics in FePt
With nuclear dynamics
Without nuclear dynamics
2.5
Fe@FePt M(t) [µΒ]
2
1.5
0 5 10 15 20 25 30 35 40
time(fs)1.4
LDA
LDA+electron-phonon
DOS (states/eV/unit cell)
1.2 mean field theory
1
0.8
0.6
0.4
0.2
0
-10 -8 -6 -4 -2 0 2 4 6 8 10
Energy (eV)
Change in the band gap
This work -365 meV
S. Poncé et al.,
Comp. Mat. Sci. 83, 341 (2014) -409 meV1
SCDFT
LDA+Electron-phonon
0.8 mean field theory
FACE / DOS
0.6
0.4
0.2
0
-100 -80 -60 -40 -20 0 20 40 60 80 100
Energy (meV)
Superconducting gap in niobium
This work ≈ 3.1 meV
Bonnet et al.,
Phys. Lett. A 25, 452 (1967) 2.32 meVRelativistic
interaction
terms
Exchange-correlation Extending
functional space-time
development boundaries
(ultra long-range
TDDFT)
Nuclear degrees Radiation
of freedom via
(quantum or classical) Maxwell's equationsVarious combinations yield new predictiveness
(
light propagation
long-range + Maxwell’s equations + TDDFT =⇒
density wave propagationVarious combinations yield new predictiveness
(
light propagation
long-range + Maxwell’s equations + TDDFT =⇒
density wave propagation
long-range + spin-orbit + spin-TDDFT =⇒ skyrmion dynamicsVarious combinations yield new predictiveness
(
light propagation
long-range + Maxwell’s equations + TDDFT =⇒
density wave propagation
long-range + spin-orbit + spin-TDDFT =⇒ skyrmion dynamics
long-range + dipole-dipole interaction + spin-DFT =⇒ magnetic domainsVarious combinations yield new predictiveness
(
light propagation
long-range + Maxwell’s equations + TDDFT =⇒
density wave propagation
long-range + spin-orbit + spin-TDDFT =⇒ skyrmion dynamics
long-range + dipole-dipole interaction + spin-DFT =⇒ magnetic domains
1 e
P
long-range + superconductivity + c i m pi · Aext (ri ) =⇒ Abrikosov vortices
New physics can be found at competing energy scales!Elk code: full potential LAPW method
Science 351, 6280 (2016) Gold standard for electronic structure
of solids. Features include:
I Ground state
I Most single particle observables
I Structural optimization
I Many-body methods: GW and
beyond, RDMFT, BSE ...
I Response functions: magnons,
phonons, plasmons, excitons ...
I Wannier90 interface
I Tensor moments
I Non-equilibrium spin dynamics
I Superconductivity: calculation of Tc,
Eliashberg
J. K. Dewhurst, S. Sharma, L. Nordström and E. K. U. Gross .......
http://elk.sourceforge.net/You can also read
