Light-induced static magnetization: Nonlinear Edelstein effect

Haowei Xu, Jian Zhou, Hua Wang, and Ju Li

Phys. Rev. B 103, 205417 – Published 13 May 2021

Abstract

Light can interact with magnetism in materials. Motivated by the Edelstein effect, whereby a static electric field can generate magnetization in metals, in this work we theoretically and computationally demonstrate that static magnetization can also be generated through light in semiconductors. Such an effect is essentially a second-order nonlinear response and can be considered as a generalization of the Edelstein effect. This nonlinear Edelstein effect (NLEE) applies to semiconductors under both linearly and circularly polarized light, and there are no constraints from either spatial inversion or time-reversal symmetry. With ab initio calculations, we reveal several prominent features of NLEE. We find that the light-induced orbital magnetizations can be significantly greater than the spin magnetizations, in contrast to standard intrinsic magnetism where the orbital magnetic moment is strongly quenched under crystal field. We show that in multilayer (multisublattice) materials, different ferromagnetic and ferrimagnetic structures can be realized under photon pumping, depending on the interlayer (intersublattice) symmetry. It is also possible to switch the magnetic ordering in antiferromagnetic materials. The relationship between NLEE and other magneto-optic effects, including the inverse Faraday effect and inverse Cotton-Mouton effect, is also discussed.

Received 19 October 2020
Revised 17 April 2021
Accepted 19 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.205417

Physics Subject Headings (PhySH)

Magnetic order Magneto-optical effect Nonlinear optics

2-dimensional systems

Density functional theory First-principles calculations Wannier function methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Haowei Xu¹, Jian Zhou ¹, Hua Wang¹, and Ju Li ^1,2,*

¹Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*Corresponding author: liju@mit.edu

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Issue

Vol. 103, Iss. 20 — 15 May 2021

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Images

Figure 1
Simplified physical pictures of (a) linear Edelstein effect and (b) nonlinear Edelstein effect. The blue shading indicates electron occupation. For linear Edelstein effect, the static electric field modifies electron distribution in a single band (intraband process). For nonlinear Edelstein effect, light excites interband transitions between different bands (labeled with $l, m, n$ ). The three-band process in Eq. (2) is illustrated by the dashed arrows on the left side of (b), while the two-band process in Eq. (4) is illustrated by the solid arrow on the right side. (c) Local vortices of the photocurrent (blue curved arrows) and the associated orbital magnetization (blue straight arrows) under light (red wavy arrow) illumination.
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Figure 2
(a), (b) Top and side view of monolayer $Mo {Te}_{2}$ . The mirror symmetries are indicated by the dashed line. The red arrows in (b) denote the magnetization under CPL. (c) Orbital (blue) and spin (red) contributions to the total nonlinear Edelstein effect under circularly polarized light. The dash red curve is $ξ_{x y}^{z, S}$ amplified by 25 times for $ω < 2.2 eV$ . The magnetization is shown for a primitive cell. (d) Schematic spin and orbital projected band structure of $Mo {Te}_{2}$ near the K point. Blue (red) indicates spin up (down) states, while the valence and conduction bands have a major contribution from $d_{- 2}$ and $d_{0}$ orbitals, respectively. I–IV denote four possible interband transitions.
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Figure 3
The nonlinear Edelstein effect under linearly polarized light of bilayer $Mo {Te}_{2}$ with AA (left), ${AA}^{'}$ (middle), and AB (right column) stacking patterns. (a), (d), (e) are schematic plots of the stacking pattern. (b), (e), (h) show the magnetic order under linearly polarized light with the green arrows indicate the magnetization from the nonlinear Edelstein effect. Pink: Mo; cyan: Te. (c), (f), (i) show the response function $η_{x x}^{x, T} = - η_{y y}^{x, T}$ for the upper layer and the lower layer.
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Figure 4
(a) Reciprocal space local spin/orbital texture $P_{l} β_{m m}^{x} (k) P_{l}$ for the highest valence band on the upper and lower layer of bilayer $Mo {Te}_{2}$ . The left (right) column is the spin (orbital) texture. (b) Real-space magnetization texture on a moiré pattern. The blue and pink arrows indicate magnetization on the upper and lower layers, respectively.
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Figure 5
Nonlinear Edelstein effect of antiferromagnetic ${CrI}_{3}$ with magnetization along the $z$ axis. Under (a) linearly and (b) circularly polarized light, the light-induced magnetizations are antiparallel and parallel on the two layers, respectively. Inset of (a): atomic strcuture of bilayer ${CrI}_{3}$ . The green arrows indicate the equilibrium magnetization.
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