Enhanced Faraday rotation in CdMnTe quantum wells embedded in an optical cavity

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Abstract

We demonstrate an enhancement of Faraday rotation in reflection geometry (polar Kerr effect) for semimagnetic quantum wells embedded in a semiconductor–metal optical cavity. The theory of light reflection and Faraday rotation in multi-quantum well heterostructures is developed and applied to fit the experimental results. The large Faraday rotation (54.4° T−1) makes this structure suitable for use as magneto-optic layers in the Faraday microscopy of the magnetic flux pattern at the surface of superconducting films.

Introduction

Faraday rotation in II–VI diluted magnetic semiconductors (DMS) has proved to be quite large due to the giant Zeeman splitting of the exciton levels [1]. This effect arises from the sp–d exchange interaction between the magnetic ions and the carriers. In heterostructures containing CdMnTe quantum wells (QW) Faraday rotation may be further enhanced mainly due to the large excitonic oscillator strength and possibly the difference of oscillator strength for σ+ and σ circular polarizations [2]. When a CdMnTe QW is inserted in an optical microcavity a very large Faraday rotation can be achieved: a Faraday angle up to 140° in an applied magnetic field of 0.4 T was measured [3]. These results open the way for using CdMnTe heterostructures as magneto-optic layers (MOL) for high resolution Faraday microscopy at low temperature. In order to make a cartography of the magnetic field at the surface of a superconducting film for instance, a MOL is necessary [4]. The MOL is deposited on a metallic layer (the superconductor itself or an intermediate thin Al layer for high reflection). The sample is illuminated through the MOL by linearly polarized light. The plane of polarization of light is rotated in the areas that carry magnetic flux. After passing through a crossed (or slightly uncrossed) analyzer the reflected light is focused on a detector. The amplitude of the magnetic field is transformed into light intensity levels. In order to increase the Faraday angle, multiple reflections inside the MOL are needed which means that the MOL should be an almost anti-reflecting layer [5]. Since the magnetic field lines diverge out of the surface plane of the superconducting film, the active medium in the MOL must be as close as possible to the superconducting film to achieve a good spatial resolution. This precludes the use of a microcavity since Bragg mirrors are too thick. Instead, we plan to use an optical cavity made of the superconductor film as back mirror and DMS QWs in a semiconductor barrier as active layers. The absence of ferromagnetic domains in DMS as compared to the commonly used MOL (Eu-compounds or iron garnets) would be a valuable improvement. The present work is the first step in realizing the proposed goal. In Section 2 we introduce a model that allows theoretical estimations of the Faraday rotation angle, while the experimental results are presented and discussed in Section 3. The forthcoming steps towards the improvement of the structure are detailed in the conclusion.

Section snippets

Optical cavity with a single QW

We consider the structure containing from the left to the right a semiinfinite metal layer, an inner semiconductor barrier, a quantum well and a top barrier layer (Fig. 1).

Assuming an electromagnetic plane light wave of frequency ω is incident normally on the top barrier layer from the vacuum, we calculate the reflectivity of the structure Rs(ω)=|rs(ω)|2, where rs is the amplitude reflection coefficient. The frequency region of interest lies in the vicinity of the e1-hh1(1s) exciton resonance

Results and discussion

The sample was grown by molecular beam epitaxy. On the GaAs substrate a Cd0.85Mg0.15Te layer about 6 μm thick was grown. An intentional thickness gradient was made across the wafer by stopping the rotation of the sample in the course of the growth of the Cd0.85Mg0.15Te layer. Then three 100 Å-thick Cd0.94Mn0.06Te QWs separated by 558 Å CdMgTe barriers were grown and finally a 617 Å Cd0.85Mg0.15Te cap layer. A 10 μm thick indium layer was evaporated on top of the cap layer. Indium was chosen because

Conclusion

In conclusion, our experimental results demonstrate the potentialities of available CdMnTe/CdMgTe heterostructures as MOL for Faraday microscopy. The structures still need further optimization. Thickness inhomogeneities, most probably due to the interruption of the substrate rotation during the growth, have to be reduced which can help to achieve agreement with the theory as well in the minimum-to-maximum ratio of the rotation angle. The Mg concentration in the barrier should be larger in order

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