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Optical control of spins in condensed matter systems such as semiconductor nanostructures requires precise knowledge of the polarization properties of the associated optical transitions subject to an external magnetic field. Here, we demonstrate that coherent optical spectroscopy in the form of photon echoes can be successfully used to evaluate the magnetic anisotropies of valence-band states. It manifests in drastic changes of the transient signals when the orientation of the magnetic field with respect to the crystallographic axes is varied. In particular, we use the two-pulse spin-dependent photon echo to study the in-plane hole spin anisotropy in a 20-nm-thick CdTe/Cd_{0.76}Mg_{0.24}Te single quantum well by exciting the donor-bound exciton resonance. We take advantage of the photon echo sensitivity to the relative phase of the electron and hole spin precession in the ground and excited states, respectively, and study various interactions contributing to the hole in-plane spin properties. The main contribution is found to arise from the crystal cubic symmetry described by the Luttinger parameter q=0.095±0.005, which is substantially larger than the one theoretically expected for CdTe or found in other quantum well structures. Another contribution is induced by the strain within the quantum well. These two contributions lead to different harmonics of the spin precession frequencies in the photon echo experiment, when the strength and orientation of the Voigt magnetic field are varied. The magnitude of the effective in-plane hole g factor is found to vary in the range |g_{h}[over ̃]|=0.125–0.160 in the well plane.

Multidimensional coherent optical spectroscopy is one of the most powerful tools for investigating complex quantum mechanical systems. While it was conceived decades ago in magnetic resonance spectroscopy using microwaves and radio waves, it has recently been extended into the visible and UV spectral range. However, resolving MHz energy splittings with ultrashort laser pulses still remains a challenge. Here, we analyze two-dimensional Fourier spectra for resonant optical excitation of resident electrons to localized trions or donor-bound excitons in semiconductor nanostructures subject to a transverse magnetic field. Particular attention is devoted to Raman coherence spectra, which allow one to accurately evaluate tiny splittings of the electron ground state and to determine the relaxation times in the electron spin ensemble. A stimulated steplike Raman process induced by a sequence of two laser pulses creates a coherent superposition of the ground-state doublet which can be retrieved only optically because of selective excitation of the same subensemble with a third pulse. This provides the unique opportunity to distinguish between different complexes that are closely spaced in energy in an ensemble. The related experimental demonstration is based on photon-echo measurements in an n-type CdTe/(Cd,Mg)Te quantum-well structure detected by a heterodyne technique. The difference in the sub-μeV range between the Zeeman splittings of donor-bound electrons and electrons localized at potential fluctuations can be resolved even though the homogeneous linewidth of the optical transitions is larger by 2 orders of magnitude.

In this work, we use electrostatic control of quantum Hall ferromagnetic transitions in CdMnTe quantum wells to study electron transport through individual domain walls (DWs) induced at a specific location. These DWs are formed due to the hybridization of two counterpropagating edge states with opposite spin polarization. Conduction through DWs is found to be symmetric under magnetic field direction reversal, consistent with the helical nature of these DWs. We observe that long domain walls are in the insulating regime with a localization length of 4-6  μm. In shorter DWs, the resistance saturates to a nonzero value at low temperatures. Mesoscopic resistance fluctuations in a magnetic field are investigated. The theoretical model of transport through impurity states within the gap induced by spin-orbit interactions agrees well with the experimental data. Helical DWs have the required symmetry for the formation of synthetic p-wave superconductors. The achieved electrostatic control of a single helical domain wall is a milestone on the path to their reconfigurable network and ultimately to a demonstration of the braiding of non-Abelian excitations.

We present a theoretical and experimental study of the interplay between spin-orbit coupling (SOC), Coulomb interaction, and motion of conduction electrons in a magnetized two-dimensional electron gas. Via a transformation of the many-body Hamiltonian we introduce the concept of spin-orbit twisted spin waves, whose energy dispersions and damping rates are obtained by a simple wave-vector shift of the spin waves without SOC. These theoretical predictions are validated by Raman scattering measurements. With optical gating of the density, we vary the strength of the SOC to alter the group velocity of the spin wave. The findings presented here differ from that of spin systems subject to the Dzyaloshinskii-Moriya interaction. Our results pave the way for novel applications in spin-wave routing devices and for the realization of lenses for spin waves.

The excitations of a two-dimensional electron gas in quantum wells with intermediate carrier density (ne∼1011  cm-2), i.e., between the exciton-trion and the Fermi-sea range, are so far poorly understood. We report on an approach to bridge this gap by a magnetophotoluminescence study of modulation-doped (Cd,Mn)Te quantum well structures. Employing their enhanced spin splitting, we analyzed the characteristic magnetic-field behavior of the individual photoluminescence features. Based on these results and earlier findings by other authors, we present a new approach for understanding the optical transitions at intermediate densities in terms of four-particle excitations, the Suris tetrons, which were up to now only predicted theoretically. All characteristic photoluminescence features are attributed to emission from these quasiparticles when attaining different final states.

We present zero-, one-, and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the coherent nonlinear optical response. Distinct peaks in the spectra are manifestations of exciton-exciton and exciton-trion coherent coupling. Excellent agreement using density matrix calculations highlights the essential role of many-body effects on the coupling. Strong exciton-trion coherent interactions open up the possibility for novel conditional control schemes in coherent optoelectronics.

By means of spin- and angle-resolved photoelectron spectroscopy we studied the spin structure of thin films of the topological insulator Bi2Se3 grown on InP(111). For thicknesses below six quintuple layers the spin-polarized metallic topological surface states interact with each other via quantum tunneling and a gap opens. Our measurements show that the resulting surface states can be described by massive Dirac cones which are split in a Rashba-like manner due to the substrate induced inversion asymmetry. The inner and the outer Rashba branches have distinct localization in the top and the bottom part of the film, whereas the band apices are delocalized throughout the entire film. Supported by calculations, our observations help in the understanding of the evolution of the surface states at the topological phase transition and provide the groundwork for the realization of two-dimensional spintronic devices based on topological semiconductors.

We report on magnetic field-induced oscillations of the photon echo signal from negatively charged excitons in a CdTe/(Cd,Mg)Te semiconductor quantum well. The oscillatory signal is due to Larmor precession of the electron spin about a transverse magnetic field and depends sensitively on the polarization configuration of the exciting and refocusing pulses. The echo amplitude can be fully tuned from the maximum down to zero depending on the time delay between the two pulses and the magnetic-field strength. The results are explained in terms of the optical Bloch equations accounting for the spin level structure of electrons and trions.

Two coupled CdTe quantum dots, selected from a self-assembled system, one of them containing a single Mn ion, were studied by continuous wave and modulated photoluminescence, photoluminescence excitation, and photon correlation experiments. Optical writing of information on the spin state of the Mn ion has been demonstrated, using the orientation of the Mn spin by spin-polarized carriers transferred from the neighboring quantum dot. Mn spin orientation time values from 20 to 100 ns were measured, depending on the excitation power. Storage time of the information on the Mn spin was found to be enhanced by application of a static magnetic field of 1 T, reaching hundreds of microseconds in the dark. Simple rate equation models were found to describe correctly the static and dynamical properties of the system.

We study zero-bias spin separation in (Cd,Mn)Te/(Cd,Mg)Te diluted magnetic semiconductor structures. The spin current generated by electron gas heating under terahertz radiation is converted into a net electric current by applying an external magnetic field. The experiments show that the spin polarization of the magnetic ion system enhances drastically the conversion process due to giant Zeeman splitting of the conduction band and spin-dependent electron scattering on localized Mn(2+) ions.

The evolution of the magnetization in (Cd,Mn)Te quantum wells after a short pulse of magnetic field was determined from the giant Zeeman shift of spectroscopic lines. The dynamics in the absence of a static magnetic field was found to be up to 3 orders of magnitude faster than that at 1 T. Hyperfine interaction and strain are mainly responsible for the fast decay. The influence of a hole gas is clearly visible: at zero field anisotropic holes stabilize the system of Mn ions, while in a magnetic field of 1 T they are known to speed up the decay by opening an additional relaxation channel.

The g-factor enhancement of the spin-polarized two-dimensional electron gas was measured directly over a wide range of spin polarizations, using spin flip resonant Raman scattering spectroscopy on two-dimensional electron gases embedded in Cd(1-x)Mn(x)Te semimagnetic quantum wells. At zero Raman transferred momentum, the single-particle spin flip excitation, energy Z*, coexists in the Raman spectrum with the spin flip wave of energy Z, the bare giant Zeeman splitting. We compare the measured g-factor enhancement with recent spin-susceptibility enhancement theories and deduce the spin-polarization dependence of the mass renormalization.

Field effect transistors with ferroelectric gates would make ideal rewritable nonvolatile memories were it not for the severe problems in integrating the ferroelectric oxide directly on the semiconductor channel. We propose a powerful way to avoid these problems using a gate material that is ferroelectric and semiconducting simultaneously. First, ferroelectricity in semiconductor (Cd,Zn)Te films is proven and studied using modified piezoforce scanning probe microscopy. Then, a rewritable field effect device is demonstrated by local poling of the (Cd,Zn)Te layer of a (Cd,Zn)Te/CdTe quantum well, provoking a reversible, nonvolatile change in the resistance of the 2D electron gas. The results point to a potential new family of nanoscale one-transistor memories.

Basically different mechanisms of optical second harmonic generation (SHG) in semiconductors, induced by an external magnetic field H, have been identified experimentally by studying the diluted magnetic semiconductor (Cd,Mn)Te. For paramagnetic (Cd,Mn)Te the SHG response is governed by spin quantization of electronic states, in contrast with diamagnetic CdTe with its dominating orbital quantization. The mechanisms can be identified by the distinct magnetic field dependence of the SHG intensity which scales with the spin splitting in the paramagnetic case as compared to the H2 dependence observed for the diamagnetic case.

Giant magnetic linear dichroism (MLD) is observed in the ferromagnetic semiconductor Ga(0.98)Mn(0.02)As. The contribution to this effect induced by the spontaneous magnetization can be clearly identified by azimuthal dependencies. The spectral dependence of the effect in the range from 1.4 to 2.4 eV shows that the MLD induced by the spontaneous magnetization is strongly enhanced for excitations from the electronic states that are responsible for the ferromagnetism in this material. This spectral sensitivity and the size of the effect makes MLD a powerful tool for the study of (III, Mn)V alloys and similar novel ferromagnetic semiconductors.

Static and time-resolved magneto-optical spectra of the ferromagnetic semiconductor (Ga,Mn)As show that a pulsed photoexcitation with a fluence of 10 microJ/cm(2) is equivalent to the application of an external magnetic field of about 1 mT, which relaxes with a decay time of 30 ps. This relaxation is attributed to the spin relaxation of electrons in the conduction band and is found to be not affected by interactions with Mn ions.

Collective and single-particle spin-flip excitations of a two-dimensional electron gas in a semimagnetic Cd(1-x)Mn(x)Te quantum well are observed by resonant Raman scattering. Application of a magnetic field splits the spin subbands and a spin polarization is induced in the electron gas. Above 1 T the collective modes, which disperse with the in-plane wave vector, dominate the spectra. The local spin-density approximation provides a good description of our results and enables us to confirm that the energy of the low wave vector collective mode is given by the bare Zeeman energy.

We have studied the low energy spin excitations in n-type CdMnTe based dilute magnetic semiconductor quantum wells. For magnetic fields for which the energies for the excitation of free carriers and Mn spins are almost identical, an anomalously large Knight shift is observed. Our findings suggest the existence of a magnetic-field-induced ferromagnetic order in these structures, which is in agreement with recent theoretical predictions [Phys. Rev. Lett. 91, 077202 (2003)]].

We report on the observation of the Ising quantum Hall ferromagnet with Curie temperature T(C) as high as 2 K in a modulation-doped (Cd,Mn)Te heterostructure. In this system field-induced crossing of Landau levels occurs due to the giant spin-splitting effect. Magnetoresistance data, collected over a wide range of temperatures, magnetic fields, tilt angles, and electron densities, are discussed taking into account both Coulomb electron-electron interactions and s-d coupling to Mn spin fluctuations. The critical behavior of the resistance "spikes" at T-->T(C) corroborates theoretical suggestions that the ferromagnet is destroyed by domain excitations.

Electrical transport measurements are reported on a 2DEG in a CdMnTe quantum well structure. The amplitude of the Shubnikov-de Haas oscillations show a distinct beating pattern with nodes corresponding to coincidences between the spin splitting and a half integer multiple of the cyclotron energy. The observed pattern of nodes is a direct consequence of the large Pauli paramagnetism induced by the s-d exchange interaction between the spins of electronic states and the localized magnetic moments.