Optical-Frequency Magnetic Polarizability in a Layered Semiconductor

Ryan A. DeCrescent, Rhys M. Kennard, Michael L. Chabinyc, and Jon A. Schuller

Phys. Rev. Lett. 127, 173604 – Published 20 October 2021

Abstract

The optical response of crystals is most commonly attributed to electric dipole interactions between light and matter. Although metamaterials support “artificial” magnetic resonances supported by mesoscale structuring, there are no naturally occurring materials known to exhibit a nonzero optical-frequency magnetic polarizability. Here, we experimentally demonstrate and quantify a naturally occurring nonzero magnetic polarizability in a layered semiconductor system: two-dimensional (Ruddlesden-Popper phase) hybrid organic-inorganic perovskites. These results demonstrate the only known material with an optical-frequency permeability that differs appreciably from vacuum, informing future efforts to find, synthesize, or exploit atomic-scale optical magnetism for novel optical phenomena such as negative index of refraction and electromagnetic cloaking.

Received 15 June 2021
Accepted 28 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.173604

Physics Subject Headings (PhySH)

Electromagnetic interactions Magnetic susceptibility Metamaterials Spatial profiles of optical beams

Perovskites

Magnetic moment Polarizability

Optical absorption spectroscopy Optical spectroscopy Polarized optical microscopy

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Ryan A. DeCrescent ^1,2,*, Rhys M. Kennard³, Michael L. Chabinyc³, and Jon A. Schuller^2,†

¹Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
²Department of Electrical and Computer Engineering, University of California, Santa Barbara, California 93106, USA
³Materials Department, University of California Santa Barbara, Santa Barbara, California 93106, USA

^*Present address: National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
^†jonschuller@ece.ucsb.edu

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Issue

Vol. 127, Iss. 17 — 22 October 2021

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Images

Figure 1
(a) Schematic of normal-incidence focused $ϕ$ -polarized doughnut beam. (b) Calculated electric ( $| E |^{2}$ , blue solid line) and magnetic field intensities ( $| c B |^{2}$ , orange dot-dashed line) in the beam’s focal plane. (c) Optical and (d) atomic force microscope image of 2D HOIP exfoliated flakes. (e) Experimentally measured $ϕ$ -polarized $| E |^{2}$ profile of the excitation beam at the substrate surface. (f) PL intensity profile from a 2D HOIP exfoliated flake. Lower panels in (e) and (f) are false-color 2D images (horizontal dashed lines indicate line cuts shown in upper panels).
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Figure 2
(a) Comparison of PL from (green circles) ${BA}_{2} {PbI}_{4}$ and (orange squares) MEH-PPV under identical $ϕ$ -polarized excitation. Light (dark) blue region: electric field intensity profile with (without) Gaussian broadening. Right: magnified view of the beam center. (b) Black markers: difference between PL profiles from test and reference samples after proper electric field normalization (Fig. S5). Light (dark) gray region: calculated magnetic field intensity with (without) Gaussian broadening.
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Figure 3
(a) MR experiment schematic. WLS, white-light source; BFP, back focal plane; IP, real-space image plane; BS, beam splitter; LP, linear polarizer; IS, imaging spectrometer. Blue ellipses represent external Bertrand lenses. Inset shows sample geometry with an $s$ -polarized incident beam. Diffusing film is placed in the BFP nearest the source to scatter light into the system uniformly over momentum space. (b) Calculated field intensities in a 10 nm thin film ( $ε_{‖} = 6.7 + i 0.3$ ) for (left) $p$ -polarized and (right) $s$ -polarized beams. (c) Single-wavelength (533 nm) $s$ -polarized MR data and fits from a 17 nm 2D HOIP film. (d),(e) Summary of MR results: (d) [(e)] shows the real (imaginary) parts of the complex quantities specified in the legend. (f) Magnified view of (e). Solid black curve, wavelength-dependent ratio $Im [μ_{⊥} (λ)] / Im [ε_{‖} (λ)]$ ; black open star marker, value from $ϕ$ -polarized PL excitation measurements. Filled regions correspond to standard deviations over all independent measurements.
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Figure 4
(a) $Re [μ_{⊥} (λ)]$ derived directly from unconstrained MR analysis (markers) and from KK analysis (solid line) of $Im [μ_{⊥}]$ . Filled color region: standard deviation over all measurements. (b) Comparison of ${BA}_{2} {PbI}_{4}$ PL under tightly focused (purple triangles) $r$ -polarized and (green circles) $ϕ$ -polarized excitation.
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