Ritwik Mondal Department of Physics and Astronomy

Relativistic theory of magnetic inertia in

ultrafast spin dynamics

Ritwik Mondal, Marco Berritta, Ashis K. Nandy, Peter M. Oppeneer

Dresden, 2017, March 211

Ritwik Mondal Department of Physics and Astronomy

What is inertia?• Newton’s first law of motion: Concept of inertia • Newton’s 2nd law of motion • Larger mass, greater inertia • Concept of mass in EM theory? Everything

with energy density gravitates.

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Ritwik Mondal Department of Physics and Astronomy

Possible importance of inertia?

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pulse > 2 ps

ultrashort pulse

Ritwik Mondal Department of Physics and Astronomy

Inertia dynamics

• What are the fundamental mechanisms? • Can we derive such a dynamics within

Dirac-Kohn-Sham formalism? • What is the ab initio expression for the

inertia parameter?

• Is it a higher order relativistic effect? (Hint - It is expected in ultrashort timescales i.e., sub-ps)

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M

He↵

Precession

Nutation

Damping

M.-C. Ciornei et al. Phys. Rev. B 83, 020410 (2011)D. Böttcher et al. Phys. Rev. B 86, 020404(R) (2012)

Ritwik Mondal Department of Physics and Astronomy

Relativistic Hamiltonian• Dirac Hamiltonian, excited by an external source (light):

• Electrons can be described within extended Pauli theory.

• Foldy-Wouthuysen transformation up to an order

5Mondal et al. Phys. Rev. B 91, 174415 (2015)

Ritwik Mondal Department of Physics and Astronomy

Spin-orbit Coupling (SOC) Gilbert damping

• time-independent, responsible for relativistic precession.

• time-dependent, responsible for Gilbert damping.

• For an uniform magnetic field , the magnetisation dynamics for a harmonic field:

• The Gilbert damping parameter (tensor):

Mondal et al. Phys. Rev. B 94, 144419 (2016) 6

Ritwik Mondal Department of Physics and Astronomy

Higher-order SOC - Inertia dynamics

• Using a linear relationship, : for a general time-dependent field, the inertia magnetisation dynamics

• For a harmonic field: • Corresponding magnetisation dynamics

7Mondal, Berritta, Nandy, Oppeneer (submitted)

Ritwik Mondal Department of Physics and Astronomy

Comparison

• electronic and magnetic parts

• fast timescale (ns, ps) • imaginary part of

susceptibility • dimensionless

• magnetic part only, no electronic part

• ultrafast timescale (ps, fs) • real part of susceptibility +

unity (matrix) • dimension = time

8Mondal, Berritta, Nandy, Oppeneer (submitted)

Fähnle et al. PRB 84, 172403 (2011) Thonig et al. arxiv:1607.01307 (2016)

Mondal et al. Phys. Rev. B 94, 144419 (2016)

Ritwik Mondal Department of Physics and Astronomy

Conclusions

• Inertia magnetisation dynamics from Dirac-Kohn-Sham theory

• Relativistic Hamiltonian up to an order has been derived

• Derived magnetisation dynamics: Gilbert damping and magnetic inertia on the same footing

• Gilbert damping parameter depends on electronic and magnetic contributions, imaginary susceptibility

• Inertia damping parameter depends on only magnetic contributions, real susceptibility

• Inertia dynamics is expected in ultrafast timescales

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Ritwik Mondal Department of Physics and Astronomy

Acknowledgements• Danny Thonig • Pablo Maldonado • Alex Aperis

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Thank you for your attention!