Angular dependence of giant Zeeman effect for semimagnetic cavity polaritons

R. Mirek, M. Król, K. Lekenta, J.-G. Rousset, M. Nawrocki, M. Kulczykowski, M. Matuszewski, J. Szczytko, W. Pacuski, and B. Piętka

Phys. Rev. B 95, 085429 – Published 21 February 2017

Abstract

The observation of spin-related phenomena of microcavity polaritons has been limited due to the weak Zeeman effect of nonmagnetic semiconductors. We demonstrate that the incorporation of magnetic ions into quantum wells placed in a nonmagnetic microcavity results in enhanced effects of magnetic field on exciton-polaritons. We show that in such a structure the Zeeman splitting of exciton-polaritons strongly depends on the photon-exciton detuning and polariton wave vector. Our experimental data are explained by a model where the impact of magnetic field on the lower polariton state is directly inherited from the excitonic component, and the coupling strength to the cavity photon is modified by an external magnetic field.

Received 29 August 2016
Revised 20 December 2016

DOI:https://doi.org/10.1103/PhysRevB.95.085429

Physics Subject Headings (PhySH)

Exciton polariton Magneto-optical effect

Photoluminescence

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

R. Mirek^1,*, M. Król¹, K. Lekenta¹, J.-G. Rousset¹, M. Nawrocki¹, M. Kulczykowski², M. Matuszewski², J. Szczytko¹, W. Pacuski¹, and B. Piętka^1,†

¹Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ulica Pasteura 5, PL-02-093 Warsaw, Poland
²Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02-668 Warsaw, Poland

^*rafal.mirek@student.uw.edu.pl
^†barbara.pietka@fuw.edu.pl

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Issue

Vol. 95, Iss. 8 — 15 February 2017

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Images

Figure 1
The structure of the microcavity sample: four 20-nm-wide QWs (red) containing ${Mn}^{2 +}$ ions sandwiched between 23 layers (bottom) and 20 layers (top) nonmagnetic distributed Bragg reflectors (alternating blue and white layers). Semimagnetic cavity polaritons result from the strong coupling of cavity photons with excitons confined in the semimagnetic QWs.
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Figure 2
Angle-resolved photoluminescence maps of semimagnetic exciton-polaritons for negative $(δ_{0 T} = - 6.0$ meV, top) and slightly positive $(δ_{0 T} = 0.2$ meV, bottom) photon-exciton detuning (determined at zero emission angle) at magnetic fields of 0, 1.7, 3.3, and 5.0 T. The giant Zeeman splitting is well resolved for positive detuning, but it is also observed for higher angles at negative detuning.
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Figure 3
Set of angle-resolved photoluminescence (top) and reflectivity (bottom) maps for different photon-exciton detuning (the detuning values are marked in the images for $σ^{+}$ and $σ^{-}$ polarization) in a magnetic field of 5 T. Grey dashed curves indicate the calculated energies of the uncoupled exciton and photon. The energies of polariton branches are marked by red $(σ^{-})$ and blue $(σ^{+})$ curves.
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Figure 4
(a) Energy change of heavy hole, $E_{hh}$ , light hole excitons, $E_{lh}$ , and a cavity photon induced by magnetic field. (b) Change of the Rabi energy in the magnetic field. The experimental results are obtained from the fitting of a solution of the Schrödinger equation with the Hamiltonian (1) to the data illustrated in the last panel of Fig. 3. The shading along the experimental curves represents the error margins of our fitting procedure. The dots illustrate the results of theoretical calculations based on a variational method applied to our structure.
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Figure 5
Map of the lower polariton Zeeman splitting in a magnetic field for the results in positive detuning, $δ_{0 T} = + 1.3$ meV. The right-hand panel gives cross sections of the map for different values of magnetic field. The bottom panel shows cross sections for different angles of emission. The map color code illustrates the value of the Zeeman splitting of the lower polariton in meV.
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Figure 6
(a) Evolution of the excitonic Hopfield coefficient, $χ^{2}$ , in a magnetic field for $σ^{+}$ and $σ^{-}$ polarized polaritons and for two different emission angles calculated for the detuning of $δ_{0 T} = + 1.3$ meV at 0 T. (b) Angular dependence of $χ^{2}$ for $σ^{+}$ and $σ^{-}$ polarized polaritons at magnetic fields of 2 T and 4 T.
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