Two interacting electrons confined to a disk on a semiconductor surface are considered in a perpendicular magnetic field. As it is appropriate for experimental realizations, we use a two-dimensional harmonic-oscillator well to confine the electrons in the plane of the disk. We predict oscillations between spin-singlet and spin-triplet ground states as a function of the magnetic field strength. Phase diagrams describing this peculiar manifestation of the electron-electron interaction in a quantum dot are calculated for GaAs and experiments to verify them are proposed. Nanostructuretechnologies allow the lateral confinement of two-dimensional electron gases in heterojunctions or metal-oxide-semiconductor structures to widths comparable to the effective Bohr radius a* of the host semiconductor. ' In this case we have electron systems with discrete energy spectra that are commonly called zero-dimensional systems or quantum dots. Since their widths in the x-y plane are much larger than their extent in the z direction, which is the growth direction of the underlying semiconductor structure, quantum dots may be regarded as artificial atoms with disklike shapes. Electron numbers as low as one or two per dot have already been realized. ' So far, quantum dots have been investigated experimentally by capacitance-voltage spectroscopy and transport measurements, as well as by far-infrared spectroscopy.Capacitance-voltage and transport measurements are not favorable for the study of isolated dots since they require coupling to external contacts. Particularly for small dots their interpretation is additionally hampered by Coulomb blockade. Despite these difficulties, much information on the single electron ene-rgy spectra could be deduced from transport data. In many cases the value of far-infrared spectroscopy is limited as a consequence of the approximately harmonic shapes of the confining potentials and the associated validity of the generalized Kohn theorem. ' " This theorem states that, for strictly harmonic potentials, dipole radiation can only probe the center-of-mass motion of all electrons but is inadequate to see any effect due to the electron electron interaction.Here, we predict spin oscillations of the ground state of two electrons in a harmonic quantum dot as a function of the magnetic field strength, which are a peculiar consequence of the electron-electron interaction and the Pauli exclusion principle. Hence, they are a direct manifestation of the t~o-electron states in the quantum dot. The oscillations should be accessible to a different type of experiment, namely spin susceptibility ' and magnetization measurements ' that previously have been successfully applied to study electronic properties of two-dimensional electron gases in GaAs/Ga~-, AI"As and related heterostructures.In experimentally realized dots, the motion in the z direction is always frozen out into the lowest electric subband F;-0. Since the corresponding extent of the wave function is much less than the one in the x-y plane, we can treat the do...

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In experiments the distinction between spin-torque and Oersted-field driven magnetization dynamics is still an open problem. Here, the gyroscopic motion of current-and field-driven magnetic vortices in small thinfilm elements is investigated by analytical calculations and by numerical simulations. It is found that for small harmonic excitations the vortex core performs an elliptical rotation around its equilibrium position. The global phase of the rotation and the ratio between the semi-axes are determined by the frequency and the amplitude of the Oersted field and the spin torque. PACS numbers: 75.60.Ch, 72.25.Ba Recently it has been found that a spin-polarized current flowing through a magnetic sample interacts with the magnetization and exerts a torque on the local magnetization. 1,2 A promising system for the investigation of the spin-torque effect is a vortex in a micro-or nanostructured magnetic thinfilm element. Vortices are formed when the in-plane magnetization curls around a center region. In this few nanometer large center region 3 , called the vortex core, the magnetization turns out-of-plane to minimize the exchange energy. 4 It is known that these vortices precess around their equilibrium position when excited by magnetic field pulses 5,6 and it was predicted that spin-polarized electric currents can do the same. 7 The spacial restriction of the vortex core as well as its periodic motion around its ground state yield an especially accessible system for space-and time-resolved measurements with scanning probe and time-integrative techniques such as soft X-ray microscopy or X-ray photoemission electron microscopy. 5,6,8,9,10 Magnetic vortices also occur in vortex domain walls. The motion of such walls has recently been investigated intensively. 11,12 Understanding the dynamics of confined vortices can give deeper insight in the mechanism of vortex-wall motion. 13 An in-plane Oersted field accompanying the current flow also influences the motion of the vortex core. For the interpretation of experimental data it is crucial to distinguish between the influence of the spin torque and of the Oersted field. 14 (a) l X (b) FIG. 1: (a) Scheme of the magnetization in a square magnetic thinfilm element with a vortex that is deflected to the right. (b) Magnetization of a vortex in its static ground state. The height denotes the z-component while the gray scale corresponds to the direction of the in-plane magnetization.In this paper we investigate the current-and field-driven gyroscopic motion of magnetic vortices in square thin-film elements of size l and thickness t as shown in Fig. 1 and present a method to distinguish between spin torque and Oersted field driven magnetization dynamics. In the presence of a spinpolarized current the time evolution of the magnetization is given by the extended Landau-Lifshitz-Gilbert equationwith the coupling constant b j = P µ B /[eM s (1 + ξ 2 )] between the current and the magnetization where P is the spin polarization, M S the saturation magnetization, and ξ the degree o...

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Metal-oxide-semiconductor field-effect transistors (MOSFETs) on CdTe/HgTe/CdTe heterostructures are fabricated with silicon dioxide gate insulators. In these devices, the density of the quasi two-dimensional electron gas in the HgTe quantum well can be tuned in a wide range. In low magnetic fields we observe beating patterns in the Shubnikov-de Haas oscillations that render possible the determination of the coefficient α of the Rashba term in the Hamiltonian as a function of electron density. This coefficient consistently describes the splittings observed in cyclotron resonance in low magnetic fields.

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