Chapter 11
Floquet Theory and Ultrafast Control of
Magnetism
Masahiro Sato
Abstract The development of laser science and technology has stimulated the study
of condensed matter physics, especially, dynamical or non-equilibrium nature in
solids. The laser technique in terahertz (THz) regime, whose photon energy is comparable to those of typical collective modes in solids such as magnetic excitations,
phonons, etc., has remarkably proceeded in the last decade. Theoretical tools for
non-equilibrium states have also progressed. Thanks to these backgrounds, magnetooptics, especially, the study of controlling magnetism with laser, now enters a new
stage. For such controls, Floquet engineering is a key concept, which means the
method of controlling static properties of targets with high-frequency external fields
like laser. I review the theoretical foundation of Floquet engineering and its application to magnetic insulators. Basic magnetic quantities such as magnetization, spin
chirality, and spin current are shown to be controlled with intense THz laser or wave.
11.1 Introduction
Laser science and technology have continuously developed in the last decades. The
application of laser to solids is being one of the hottest topics in condensed-matter
physics. If we apply intense laser to materials, their quantum states quickly change
into a non-equilibrium one and we can observe non-equilibrium or relaxation dynamics, nonlinear responses to the intense AC field, ultrafast change of physical quantities, etc. In recent years, the significant development of terahertz (THz) laser science
in the range of ∼0.1–10 THz [1–4] (THz = 10
12 Hz) has accelerated the study of
ultrafast control of magnetism with THz laser because its photon energy is comparable to the energy of magnetic excitations, especially, those of antiferromagnets [5].
The maximum intensity of currently available THz laser has attained the electricfield amplitude 1–10 [MV/cm] which corresponds to a few Tesla of the AC magnetic
field amplitude. In addition to THz laser science, the magnetic resonance study with
M. Sato (B)
Department of Physics, Ibaraki University, Mito, Ibaraki 310-8512, Japan
e-mail: masahiro.sato.phys@vc.ibaraki.ac.jp
© Springer Nature Switzerland AG 2021
E. Kamenetskii (ed.), Chirality, Magnetism and Magnetoelectricity,
Topics in Applied Physics 138,
https://doi.org/10.1007/978-3-030-62844-4_11
265
Floquet Theory and Ultrafast Control of
Magnetism
Masahiro Sato
Abstract The development of laser science and technology has stimulated the study
of condensed matter physics, especially, dynamical or non-equilibrium nature in
solids. The laser technique in terahertz (THz) regime, whose photon energy is comparable to those of typical collective modes in solids such as magnetic excitations,
phonons, etc., has remarkably proceeded in the last decade. Theoretical tools for
non-equilibrium states have also progressed. Thanks to these backgrounds, magnetooptics, especially, the study of controlling magnetism with laser, now enters a new
stage. For such controls, Floquet engineering is a key concept, which means the
method of controlling static properties of targets with high-frequency external fields
like laser. I review the theoretical foundation of Floquet engineering and its application to magnetic insulators. Basic magnetic quantities such as magnetization, spin
chirality, and spin current are shown to be controlled with intense THz laser or wave.
11.1 Introduction
Laser science and technology have continuously developed in the last decades. The
application of laser to solids is being one of the hottest topics in condensed-matter
physics. If we apply intense laser to materials, their quantum states quickly change
into a non-equilibrium one and we can observe non-equilibrium or relaxation dynamics, nonlinear responses to the intense AC field, ultrafast change of physical quantities, etc. In recent years, the significant development of terahertz (THz) laser science
in the range of ∼0.1–10 THz [1–4] (THz = 10
12 Hz) has accelerated the study of
ultrafast control of magnetism with THz laser because its photon energy is comparable to the energy of magnetic excitations, especially, those of antiferromagnets [5].
The maximum intensity of currently available THz laser has attained the electricfield amplitude 1–10 [MV/cm] which corresponds to a few Tesla of the AC magnetic
field amplitude. In addition to THz laser science, the magnetic resonance study with
M. Sato (B)
Department of Physics, Ibaraki University, Mito, Ibaraki 310-8512, Japan
e-mail: masahiro.sato.phys@vc.ibaraki.ac.jp
© Springer Nature Switzerland AG 2021
E. Kamenetskii (ed.), Chirality, Magnetism and Magnetoelectricity,
Topics in Applied Physics 138,
https://doi.org/10.1007/978-3-030-62844-4_11
265