Optical manifestation of magnetic polarons bound to excitons and resident holes in a (Cd,Mn)Te quantum well

N. V. Kozyrev, R. R. Akhmadullin, B. R. Namozov, Yu. G. Kusrayev, G. Karczewski, and T. Wojtowicz

Phys. Rev. B 104, 045307 – Published 19 July 2021

Abstract

Photoluminescence and multiple ${Mn}^{2 +}$ spin-flip Raman scattering (SFRS) are studied in the (Cd,Mn)Te/(Cd,Mg)Te quantum well with excess resident hole concentration under resonance continuous-wave photoexcitation in the localized states of excitons and trions at $T = 1.5$ K. A magnetic polaron shift of both exciton and trion photoluminescence is observed to be increasing with an increase in the magnetic field up to 6 T applied perpendicularly to the sample growth axis (Voigt geometry). Exciton magnetic polaron shift in magnetic field is attributed to the adiabatic energy transfer from the exchange reservoir to the Zeeman reservoir during the precession of the ${Mn}^{2 +}$ ions in the summary field of external magnetic and exchange hole fields. A mechanism of the magnetic polaron shift of trion photoluminescence is suggested. It is related to direct photoexcitation of the triplet trion state, which is stable in the conditions which are provided by the resident hole magnetic polarons. In these conditions, the ${Mn}^{2 +}$ magnetic moment experiences additional magnetization in the double exchange field provided by two holes in the triplet trion state. It is observed that the maximum efficiency of multiple ${Mn}^{2 +}$ spin-flip Raman scattering falls into the energy range corresponding to the states of localized excitons where the exciton magnetic polaron shift is observed. From this we conclude that the magnetic polaron state could be an intermediate state of the multiple ${Mn}^{2 +}$ SFRS process.

Received 25 May 2021
Accepted 7 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.045307

Physics Subject Headings (PhySH)

Exchange interaction Excitons Trions

II-VI semiconductors Magnetic semiconductors Quantum wells

Spin

Photoluminescence Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

N. V. Kozyrev ^*, R. R. Akhmadullin , B. R. Namozov, and Yu. G. Kusrayev

Ioffe Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia

G. Karczewski

Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland

T. Wojtowicz

International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland

^*kozyrev.nikolay@bk.ru

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Vol. 104, Iss. 4 — 15 July 2021

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Images

Figure 1
(a) Colored curves represent resonant PL spectra under different photoexcitation energies in $B = 0$ . Black circles represent the trion PLE spectrum registered at 1.701 eV (T PLE). Letters “T” and “X” denote the position of the trion and exciton PL, respectively. (b) Normalized PL spectra are presented at different magnetic fields in the Faraday geometry under photoexcitation with energy that is higher than the PL maxima by 10–15 meV. $T = 1.5$ K.
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Figure 2
(a) Black curves represent PL spectra registered under photoexcitation with the energies that are higher than trion PL maxima by 10–15 meV in different magnetic fields in the Voigt geometry. Black triangles and green pluses represent trion and exciton PLE spectra, respectively, and orange circles represent manganese SFRS resonance contours in different magnetic fields in the Voigt geometry. All spectra are obtained at the $z (π σ) \bar{z}$ configuration, normalized and shifted vertically for clarity; horizontal dashed lines correspond to the zero intensity for each magnetic field. Letters “T” and “X” denote trion and exciton PL, respectively. (b) Magnetic field dependencies of the spectral positions of trion PL (red “T”) in the Faraday geometry (red circles) and of the exciton (black “X”) and the trion (black “T”) in the Voigt geometry (black circles); green circles represent the magnetic field dependence of the spectral position of the exciton PLE spectra maximum (PLE X), and orange circles represent the spectral position of the SFRS resonance contour maximum. The red dashed curve is the calculation of the giant Zeeman effect with the formula (1). (c) SFRS spectrum in $B = 6$ T in Voigt geometry with an energy of excitation photons of 1.7055 eV. All data are presented for $T = 1.5$ K.
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Figure 3
(a) Secondary radiation spectra under resonant photoexcitation (energy of the laser decreases from the upper spectrum to the lower one) in $B = 5.5$ T (Voigt) at $T = 1.5$ K registered in the $z (π σ) \bar{z}$ configuration. Spectra are normalized and shifted vertically for clarity. (b) Stokes shift of the exciton (X) and trion (T) PL over photoexcitation energy. $Δ E$ is a value of the constant Stokes shift in the magnetic field (clarification in text). (c) Magnetic field dependence of $Δ E$ for trion and exciton in Voigt geometry. (d) $B = 5.5$ T, $T = 1.5$ K. Orange and purple curves represent PLE spectra of the trion and exciton, respectively (right axis, log scale). Orange circles and purple crosses represent the spectral positions of the trion and exciton PL lines, respectively, for different photoexcitation energies (left axis). The red curve represents the normalized resonance contour of the manganese SFRS, and black curves represent PL spectra at the excitation with $E = 1.7055$ eV corresponding to the exciton state and with $E = 1.698$ eV, which is in the trion localized state's spectral range. The latter curves are on a linear scale and are not linked to any ordinate axis.
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Figure 4
Black circles represent the transverse magnetic field dependence of the EMP shift $Δ E$ . Black curves represent the calculation according to the model suggested in Ref. [11] with parameters $x_{Mn} = 0.018, T_{eff} = 3.5$ K, and $B_{ex} = 0.8$ T and different values of the $Δ_{lh - hh}$ parameter (the curve with $Δ_{lh - hh} = \infty$ corresponds to $φ \equiv 0$ in all $B$ ).
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Figure 5
Value $Δ E$ for trions (black circles) and the calculation of the model of the additional magnetization of manganese ions when the triplet trion state is excited (red dashed curve). On scheme $M^{(i, f)} = M (B_{total}^{(i, f)}, T_{eff})$ .
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