Zeeman Splitting Of Levels Research Articles

Interplay of vibration and Coulomb effects in transport of spin-polarized electrons in a single-molecule transistor

Tunnel transport of interacting spin-polarized electrons through a single-level vibrating quantum dot in external magnetic field is studied. By using density matrix method, the current-voltage characteristics and the dependence of conductance on temperature of a single-electron transistor were calculated. We found that a lifting of Coulomb blockade in external magnetic field happens in stages. The Franck-Condon steps associated with inelastic electron tunneling in our case are doubled due to contribution of two Zeeman-split levels in electron transport. The doubling of steps can be also observed in the presence of Coulomb interaction. For strong electron-vibron interaction the temperature dependence of conductance is shown to be non-monotonic and anomalous growth of conductance maximum weakly depends both on the Coulomb strength and the external magnetic field.

Spin-coherent dynamics and carrier lifetime in strained Ge1−xSnx semiconductors on silicon

We demonstrate an effective epitaxial route for the manipulation and further enrichment of the intriguing spin-dependent phenomena boasted by germanium. We show optical initialization and readout of spins in Ge-rich germanium-tin alloys and report on spin quantum beats between Zeeman-split levels under an external magnetic field. While heavy Sn atoms can be readily utilized to strengthen the spin-orbit coupling, our experiments reveal robust spin orientation in a wide temperature range and a persistent spin lifetime that noticeably approaches the nanosecond regime at room temperature. In addition, time decay photoluminescence experiments evidence a temperature-induced monotonic decrease of the carrier lifetime, eventually providing crucial insights also into nonradiative recombination mechanisms.

Axion dark matter detection by laser induced fluorescence in rare-earth doped materials

We present a detection scheme to search for QCD axion dark matter, that is based on a direct interaction between axions and electrons explicitly predicted by DFSZ axion models. The local axion dark matter field shall drive transitions between Zeeman-split atomic levels separated by the axion rest mass energy mac2. Axion-related excitations are then detected with an upconversion scheme involving a pump laser that converts the absorbed axion energy (~hundreds of μeV) to visible or infrared photons, where single photon detection is an established technique. The proposed scheme involves rare-earth ions doped into solid-state crystalline materials, and the optical transitions take place between energy levels of 4fN electron configuration. Beyond discussing theoretical aspects and requirements to achieve a cosmologically relevant sensitivity, especially in terms of spectroscopic material properties, we experimentally investigate backgrounds due to the pump laser at temperatures in the range 1.9 − 4.2 K. Our results rule out excitation of the upper Zeeman component of the ground state by laser-related heating effects, and are of some help in optimizing activated material parameters to suppress the multiphonon-assisted Stokes fluorescence.

Magnetic-field-induced mixed-level Kondo effect in two-level systems

We consider a two-orbital impurity system with intra and inter-level Coulomb repulsion that is coupled to a single conduction channel. This situation can generically occur in multilevel quantum dots or in systems of coupled quantum dots. For finite energy-spacing between spin-degenerate orbitals, an in-plane magnetic field drives the system from a local singlet ground state to a "mixed-level" Kondo regime, where the Zeeman-split levels are degenerate for opposite spin states. We use the numerical renormalization group approach to fully characterize this mixed level Kondo state and discuss its properties in terms of the applied Zeeman field, temperature and system parameters. Under suitable conditions, the total spectral function is shown to develop a Fermi level resonance, so that the linear conductance of the system peaks at a finite Zeeman field while it decreases as function of temperature. These features, as well as the local moment and entropy contribution of the impurity system are commensurate with Kondo physics, which can be studied in suitably tuned quantum dot systems.

Shaped electric fields for fast optimal manipulation of electron spin and position in a double quantum dot

We use quantum optimal control theory algorithms to design external electric fields that drive the coupled spin and orbital dynamics of an electron in a double quantum dot, subject to the spin-orbit interaction and Zeeman magnetic fields. We obtain time-profiles of multi-frequency electric pulses which increase the rate of spin-flip transitions by several orders of magnitude in comparison with monochromatic fields, where the spin Rabi oscillations were predicted to be very slow. This precise, with the accuracy higher than $10^{-4}$, and fast, at the timescale of the order of 0.1 ns, simultaneous control of the electron spin orientation and position is achieved while keeping the electron in the four lowest tunneling- and Zeeman-split levels through the duration of the pulse, facilitating high fidelity and suggesting useful applications in spintronics and quantum information devices.

Temperature-dependent magnetic properties of ferrimagneticDyCo3alloy films

Synchrotron soft x-ray magnetic circular and linear dichroism (XMCD and XMLD) spectroscopies at the Dy ${M}_{4,5}$ and Co ${L}_{2,3}$ edges are reported to investigate the temperature-dependent magnetic properties of rare earth--transition metal ${\mathrm{DyCo}}_{3}$ alloy films. In a temperature region between 4.4 K and 300 K, the two sites of Co and Dy are ferrimagnetic alloy coupled, with the Dy magnetization aligned to the applied field as the dominant site. The combined method of XMCD and XMLD and the application of the sum rules allows one to monitor the detailed changes in the magnetic contribution from both sites separately. It reveals that Dy possesses a very large moment of $8.2\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$/atom at low temperatures. At higher temperatures, the reduction of the total magnetic moment is dominated by the behavior of the Dy magnetic moments which exhibit a steeper decrease, especially in the temperature regime between 150 K and 200 K. The reoccupation of the Zeeman split levels of the $4f$ sites of Dy indicates that thermal fluctuations are the driving force.

Determination of Exciton Reduced Mass and Gyromagnetic Factor of Wurtzite (InGa)As Nanowires by Photoluminescence Spectroscopy under High Magnetic Fields

Semiconductor nanowires (NWs) have the prospect of being employed as basic units for nanoscale devices and circuits. However, the impact of their one-dimensional geometry and peculiar crystal phase on transport and spin characteristics remains largely unknown. We determine the exciton reduced mass and gyromagnetic factor of (InGa)As NWs in the wurtzite phase by photoluminescence (PL) spectroscopy under very high magnetic fields. For B perpendicular to the NW ĉ axis, the exciton reduced mass is 10% greater than that expected for the zincblende phase and no field-induced circular polarization of PL is observed. For B parallel to ĉ, an exciton reduced mass 35% greater than that of the zincblende phase is derived. Moreover, a circular dichroism of 70% is found at 28 T. Finally, an analysis of the PL line shape points at two Zeeman split levels, whose separation corresponds to an exciton gyromagnetic factor |g(e) - g(h,∥)| = 5.8. These results provide a quantitative estimate of the basic electronic and spin properties of NWs and may guide a theoretical analysis of the band structure of these fascinating nanostructures.

Determination of gyromagnetic ratios from the Zeeman splitting of levels of the 3p5f configuration of the silicon atom

We have studied the Zeeman structure of the 3p5f configuration of SiI and revealed its particular features in the range of variation of the magnetic field from 0 to 60 kOe. In this range, we have found 71 crossings of Zeeman sublevels with ΔM = ±1 and ±2 (M is the magnetic quantum number) and 4 anticrossings of lower F levels with j1 = 1/2 (j1 is the total angular momentum of the p electron). From splittings of levels in the assured linear range up to 40 Oe, we have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field.

Spin pumping and spin filtering in double quantum dots with time-dependent spin-orbit interactions

We propose a scheme of realizing both spin pumping and spin filtering in a double quantum dot with homogeneous Zeeman splittings in the presence of oscillating spin-orbit interactions. We find that a spin-polarized pumping current can be achieved by tuning the relative energies of the Zeeman-split levels of the dots. It is also found that a pure spin current can be generated at zero detuning, whose magnitude can be modulated by the external fields. At a certain constellation of system parameters, the pumping current can become almost fully spin-polarized. Therefore, it is possible to select a particular spin component of the current to be pumped from the left to the right lead. We finally give some discussions on the realization of the spin pumping and spin filtering effects.

SPIN-DEPENDENT BEATS CREATED BY IRRADIATION OF MICROWAVE FIELD THROUGH A QUANTUM DOT

We study spin-dependent transport through a quantum dot with Zeeman split levels coupled to ferromagnetic leads and under influence of microwave irradiation. Current polarization, spin current, spin accumulation and tunneling magnetoresistance are analyzed using nonequilibrium Green's function formalism and rate equations. Spin-dependent beats in spin resolved currents are observed. The effects of magnetic field, temperature and Coulomb interaction on these beats are studied.

Spin-polarized currents in double and triple quantum dots driven by ac magnetic fields

We analyze transport through both a double quantum dot and a triple quantum dot with inhomogeneous Zeeman splittings in the presence of crossed dc and ac magnetic fields. We find that strongly spin-polarized current can be achieved by tuning the relative energies of the Zeeman-split levels of the dots, by means of electric gate voltages: depending on the energy level detuning, the double quantum dot works either as spin-up or spin-down filter. We show that a triple quantum dot in series under crossed dc and ac magnetic fields can act not only as spin-filter but also as spin-inverter.

Characteristics of coherent population trapping in multilevel systems for magnetometry in plasma research

An analysis is presented of the feasibility of measurements of local poloidal magnetic fields in toroidal magnetic fusion devices using coherent population trapping (CPT) in hydrogen-like probing atoms. A measurement scheme is examined in which CPT suppresses the resonance fluorescence from a probing beam of light neutrals with Zeeman-split levels. Feasibility requirements for CPT in three- and five-level systems are discussed. As a result, a theory of CPT-based magnetometry is developed for a system significantly more complex than the conventional three-level Λ system. A theoretical analysis shows that this technique can be used to measure a local safety factor in a toroidal device to an accuracy of a few percent.

Detection of spin polarization in a quantum wire

We demonstrate detection of spin polarization in a quantum wire utilizing a side coupled quantum dot. By applying in-plane magnetic fields, spin split conducting channels are formed and produce spin polarization in the wire. The magnetic fields also create Zeeman split spin levels in the dot and these states are used as a spin polarization detector. Such kind of spin polarization detection with a side coupled quantum dot will operate even in the zero magnetic field by using two-electron singlet and triplet levels.

High-field Zeeman and Paschen-Back effects at high pressure in oriented ruby

High-field Zeeman and Paschen-Back effects have been observed in single crystals of ruby submitted to hydrostatic pressure up to 10 GPa. A specific setup with a miniature diamond-anvil cell has been developed to combine high pressure and pulsed magnetic fields and to perform magnetophotoluminescence measurements. Careful analysis of low-temperature (4.2 and 77 K) photoluminescence spectra with a 56 T magnetic field applied along the $c$ axis allows for the rectification of the assignment of observed emission lines to corresponding Zeeman-split levels. Besides, the intrinsic Zeeman-splitting factors of excited states reveal a linear pressure-induced increase. This enhancement is a signature of an increase in trigonal distortion induced by hydrostatic pressure. Moreover, spectra with magnetic field perpendicular to crystallographic $c$ axis exhibit a Paschen-Back effect reflecting the progressive alignment of ${\text{Cr}}^{3+}$ ions spin along the applied field. However, no pressure modification is observed in this compound, contrarily to the Heisenberg-to-Ising spin character pressure-induced transition observed in alexandrite.

Spin-dependent ringing and beats in a quantum dot system

We report spin-dependent quantum coherent oscillations (ringing) and beats of the total and the spin currents flowing through a quantum dot with Zeeman split levels. The spin-dependent transport is calculated via nonequilibrium Green function in the transient after a bias voltage is turned on at $t=0$. The dot is coupled to two electrodes that can be ferromagnetic or nonmagnetic. In the ferromagnetic case both parallel and antiparallel alignments are considered. The coherent oscillation and beat frequencies are controlled via the Zeeman energy ${E}_{Z}$. In particular, for ${E}_{Z}=0$ no beats are observed and the spin current is zero for nonmagnetic leads. In the ferromagnetic case a finite spin current is found for ${E}_{Z}=0$. The effects of temperature are also analyzed. We observe that with increasing temperature the ringing response and the beats tend to disappear. Additionally, the spin current goes to zero for nonmagnetic leads, remaining finite in the ferromagnetic case. The tunnel magnetoresistance also reveals quantum coherent oscillations and beats, and it attains negative values for small enough temperatures and short times.

Publisher's Note: Coherent effects in magnetotransport through Zeeman-split levels [Phys. Rev. B72, 205341 (2005)

Received 2 December 2005DOI:https://doi.org/10.1103/PhysRevB.72.249902©2005 American Physical Society

Coherent effects in magnetotransport through Zeeman-split levels

We study non-equilibrium electronic transport through a quantum dot or impurity weakly coupled to ferromagnetic leads. Based on the rate equation formalism we derive noise spectra for the transport current. We show that due to quantum interference between different spin components of the current the spectrum develops a peak or a dip at the frequency corresponding to Zeeman splitting in the quantum dot. The detailed analysis of the spectral structure of the current is carried out for noninteracting electrons as well as in the regime of Coulomb blockade.

Hysteresis Loops and Adiabatic Landau-Zener-Stückelberg Transitions in the Magnetic Molecule{V6}

We have observed hysteresis loops and abrupt magnetization steps in the magnetic molecule {V(6)}, where each molecule comprises a pair of identical spin triangles, in the temperature range 1-5 K for external magnetic fields B with sweep rates of several Tesla per millisecond executing a variety of closed cycles. The hysteresis loops are accurately reproduced using a generalization of the Bloch equation based on direct one-phonon transitions between the instantaneous Zeeman-split levels of the ground state (an S=1/2 doublet) of each spin triangle. The magnetization steps occur for B approximately 0, and they are explained in terms of adiabatic Landau-Zener-Stückelberg transitions between the lowest magnetic energy levels as modified by an intertriangle anisotropic exchange of order 0.4 K.

0.7 Structure in quantum wires observed at crossings of spin-polarised 1D subbands

Low-density ballistic 1D wires defined in GaAs/AlGaAs heterostructures show a spontaneous spin-splitting at crossings of Zeeman-split levels induced by an in-plane magnetic field, giving rise to additional unexpected conductance features. From measurements of magnetic field and temperature dependences, we suggest that the mechanism associated with the new features is similar to that of the 0.7 structure observed at zero magnetic field.

Effects of low magnetic fields in transient spectral hole-burning of the R 1-line in emerald, Be 3Al 2Si 6O 18:Cr(III)

Polarized transient spectral hole-burning in the R 1-line ( 2 A ̄ ( 2E) ← 4A 2) of Chatham lab grown emerald is reported as a function of low magnetic fields B∥ c and B⊥ c (<16 mT) and temperature. The experiments yield g-factors g ⊥( 4A 2)=1.96 ± 0.02, g ∥( 4A 2)=1.97 ± 0.02 and g ∥[ 2 A ̄ ( 2E)]=1.02 ± 0.03. The hole patterns indicate that spin-lattice relaxation between the Zeeman split spin levels of the ground and excited state is slow at 2.5 K. Spin-lattice relaxation by an Orbach process appears to become efficient for the 2 A ̄ ( 2E) levels at temperatures >8 K on the 2.5 ms experimental timescale but thermalization between the ±3/2 4A 2 levels stays relatively slow up to 25 K. The potential of transient hole-burning experiments is manifested by the present experiments: g-factors and spin-lattice relaxation times can be measured simultaneously for the ground and the excited state.