Generalized Pitaevskii relation between rectifying and linear responses: Application to reciprocal magnetization induction

Hikaru Watanabe and Akito Daido

Phys. Rev. B 110, 014405 – Published 2 July 2024

Abstract

Nonlinear optics has regained attention in recent years, especially in the context of optospintronics and topological materials. Nonlinear responses involved in various degrees of freedom manifest their intricacy more pronounced than linear responses. However, for a certain class of nonlinear responses, a connection can be established with linear-response coefficients, enabling the exploration of diverse nonlinear-response functionality in terms of the linear-response counterpart. Our study quantum mechanically elucidates the relation between such nonlinear and linear responses we call the Pitaevskii relation and identifies the condition for the relation to hold. Following the obtained general formulation, we systematically identify the Pitaevskii relations such as the inverse magnetoelectric effect and inverse natural optical activity unique to systems manifesting the space-inversion-symmetry breaking. These results provide a systematic understanding of intricate nonlinear responses and may offer further implications to ultrafast spintronics.

Received 11 April 2024
Revised 18 June 2024
Accepted 24 June 2024

DOI:https://doi.org/10.1103/PhysRevB.110.014405

Physics Subject Headings (PhySH)

Faraday effect Light-induced magnetic effects Magneto-optics Nonlinear optics Optical activity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hikaru Watanabe ^1,* and Akito Daido ²

¹Research Center for Advanced Science and Technology, University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan
²Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

^*Contact author: hikaru-watanabe@g.ecc.u-tokyo.ac.jp

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Issue

Vol. 110, Iss. 1 — 1 July 2024

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Images

Figure 1
DC magnetization responses to (a) unpolarized or linearly polarized light and (b) circularly polarized light. Blue arrows are the induced magnetization and orange arrows are the propagating electromagnetic fields. The induced magnetization is not flipped and flipped under inversion of incident light for the $P$ -even and $P$ -odd rectification responses, respectively. In terms of reciprocity, panels are for (c) inverse Cotton-Mouton effect, (d) inverse magnetoelectric effect, (e) inverse Faraday effect, and (f) inverse natural optical activity.
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Figure 2
(a) Zigzag chain comprised of $A$ and $B$ sublattices. Dimerization is denoted by the thick lines. (b) $T$ -symmetric and $P$ -broken state resulting from the staggered onsite potential. (c) $PT$ -symmetric and $P$ -broken state due to the antiferromagnetic order. (d) Band structures of the parastate (dashed line), that in the case of (b) (red solid line), and that in the case of (c) (green solid line).
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Figure 3
Spectrum of the reciprocal magnetization induction $κ_{y y z}^{B B E} (ω)$ (RMI) and magnetoelectric susceptibility $\partial_{B_{y}} κ_{y z}^{B E} (ω)$ (ME) of the $T$ -symmetric model. The resonant particle-hole excitations are present in the shaded area. The chemical potential is $μ = 0$ corresponding to the insulator phase. Real (imaginary) parts of two response functions almost overlap with each other. (Inset) Spectrum of $Δ = \partial_{B_{y}} κ_{y z}^{B E} - κ_{y y z}^{B B E}$ . The deviation gets negligible well below the optical gap.
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Figure 4
Spectrum of the reciprocal magnetization induction $κ_{y x z}^{B B E} (ω)$ (RMI) and magnetoelectric susceptibility $\partial_{B_{y}} κ_{x z}^{B E} (ω)$ (ME) of the $PT$ -symmetric model. The resonant particle-hole excitations are present in the shaded area. The chemical potential is $μ = 0$ corresponding to the insulator phase. (Inset) Enlarged view of the spectrum in the in-gap regime. Note that no multiplication is applied to each response plotted in the inset, different from the main plot. The imaginary parts of two responses coincide with each other, whereas the real parts are vanishingly small.
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Figure 5
Same plots as those in Fig. 4, while the chemical potential is $μ = - 0.6$ corresponding to the metal phase. We note that the optical gap is shifted to $ω \sim 1.2$ , different from that of Fig. 4. (Inset) Enlarged view of the spectrum in the in-gap regime.
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Figure 6
Phenomenological-scattering-rate dependence of the reciprocal magnetization induction $κ_{y x z}^{B B E} (ω)$ (RMI) and magnetoelectric susceptibility $\partial_{B_{y}} κ_{x z}^{B E} (ω)$ (ME) of the $PT$ -symmetric model. The frequency of light is $ω_{0} = 0.5$ , and the chemical potential is $μ = - 0.6$ where the metallic conductivity is present.
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