Optical Detection of Long Electron Spin Transport Lengths in a Monolayer Semiconductor.

Using a spatially resolved optical pump-probe experiment, we measure the lateral transport of spin-valley polarized electrons over very long distances (tens of micrometers) in a single WSe_{2} monolayer. By locally pumping the Fermi sea of 2D electrons to a high degree of spin-valley polarization (up to 75%) using circularly polarized light, the lateral diffusion of the electron polarization can be mapped out via the photoluminescence induced by a spatially separated and linearly polarized probe laser. Up to 25% spin-valley polarization is observed at pump-probe separations up to 20 µm. Characteristic spin-valley diffusion lengths of 18±3 µm are revealed at low temperatures. The dependence on temperature, pump helicity, pump intensity, and electron density highlight the key roles played by spin relaxation time and pumping efficiency on polarized electron transport in monolayer semiconductors possessing spin-valley locking.

Spontaneous Valley Polarization of Interacting Carriers in a Monolayer Semiconductor.

We report magnetoabsorption spectroscopy of gated WSe_{2} monolayers in high magnetic fields up to 60 T. When doped with a 2D Fermi sea of mobile holes, well-resolved sequences of optical transitions are observed in both σ^{±} circular polarizations, which unambiguously and separately indicate the number of filled Landau levels (LLs) in both K and K^{'} valleys. This reveals the interaction-enhanced valley Zeeman energy, which is found to be highly tunable with hole density p. We exploit this tunability to align the LLs in K and K^{'}, and find that the 2D hole gas becomes unstable against small changes in LL filling and can spontaneously valley polarize. These results cannot be understood within a single-particle picture, highlighting the importance of exchange interactions in determining the ground state of 2D carriers in monolayer semiconductors.

Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields.

In semiconductor physics, many essential optoelectronic material parameters can be experimentally revealed via optical spectroscopy in sufficiently large magnetic fields. For monolayer transition-metal dichalcogenide semiconductors, this field scale is substantial-tens of teslas or more-due to heavy carrier masses and huge exciton binding energies. Here we report absorption spectroscopy of monolayer [Formula: see text], and [Formula: see text] in very high magnetic fields to 91 T. We follow the diamagnetic shifts and valley Zeeman splittings of not only the exciton's [Formula: see text] ground state but also its excited [Formula: see text] Rydberg states. This provides a direct experimental measure of the effective (reduced) exciton masses and dielectric properties. Exciton binding energies, exciton radii, and free-particle bandgaps are also determined. The measured exciton masses are heavier than theoretically predicted, especially for Mo-based monolayers. These results provide essential and quantitative parameters for the rational design of opto-electronic van der Waals heterostructures incorporating 2D semiconductors.

Detection of thermodynamic "valley noise" in monolayer semiconductors: Access to intrinsic valley relaxation time scales.

Together with charge and spin, many novel two-dimensional materials also permit information to be encoded in an electron's valley degree of freedom-that is, in particular momentum states in the material's Brillouin zone. With a view toward valley-based (opto)electronic technologies, the intrinsic time scales of valley scattering are therefore of fundamental interest. Here, we demonstrate an entirely noise-based approach for exploring valley dynamics in monolayer transition-metal dichalcogenide semiconductors. Exploiting their valley-specific optical selection rules, we use optical Faraday rotation to passively detect the thermodynamic fluctuations of valley polarization in a Fermi sea of resident carriers. This spontaneous "valley noise" reveals narrow Lorentzian line shapes and, therefore, long exponentially-decaying intrinsic valley relaxation. Moreover, the noise signatures validate both the relaxation times and the spectral dependence of conventional (perturbative) pump-probe measurements. These results provide a viable route toward quantitative measurements of intrinsic valley dynamics, free from any external perturbation, pumping, or excitation.

Scaling law for excitons in 2D perovskite quantum wells.

Ruddlesden-Popper halide perovskites are 2D solution-processed quantum wells with a general formula A2A'n-1M n X3n+1, where optoelectronic properties can be tuned by varying the perovskite layer thickness (n-value), and have recently emerged as efficient semiconductors with technologically relevant stability. However, fundamental questions concerning the nature of optical resonances (excitons or free carriers) and the exciton reduced mass, and their scaling with quantum well thickness, which are critical for designing efficient optoelectronic devices, remain unresolved. Here, using optical spectroscopy and 60-Tesla magneto-absorption supported by modeling, we unambiguously demonstrate that the optical resonances arise from tightly bound excitons with both exciton reduced masses and binding energies decreasing, respectively, from 0.221 m0 to 0.186 m0 and from 470 meV to 125 meV with increasing thickness from n equals 1 to 5. Based on this study we propose a general scaling law to determine the binding energy of excitons in perovskite quantum wells of any layer thickness.

Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor.

We report 65 T magnetoabsorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor WSe_{2}. The strongly field-dependent and distinct energy shifts of the 2s, 3s, and 4s excited neutral excitons permits their unambiguous identification and allows for quantitative comparison with leading theoretical models. Both the sizes (via low-field diamagnetic shifts) and the energies of the ns exciton states agree remarkably well with detailed numerical simulations using the nonhydrogenic screened Keldysh potential for 2D semiconductors. Moreover, at the highest magnetic fields, the nearly linear diamagnetic shifts of the weakly bound 3s and 4s excitons provide a direct experimental measure of the exciton's reduced mass m_{r}=0.20±0.01m_{0}.

Broadband spectroscopy of thermodynamic magnetization fluctuations through a ferromagnetic spin-reorientation transition.

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar+ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, S(ν), exhibits a remarkably robust ν -3/2 power law over frequencies ν from 1 kHz to 1 MHz. As the SRT region is traversed, however, S(ν) spectra develop a steadily-increasing critical frequency, ν 0, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.

Direct Measurements of Magnetic Polarons in Cd1-xMnxSe Nanocrystals from Resonant Photoluminescence.

In semiconductors, quantum confinement can greatly enhance the interaction between band carriers (electrons and holes) and dopant atoms. One manifestation of this enhancement is the increased stability of exciton magnetic polarons in magnetically doped nanostructures. In the limit of very strong 0D confinement that is realized in colloidal semiconductor nanocrystals, a single exciton can exert an effective exchange field Bex on the embedded magnetic dopants that exceeds several tesla. Here we use the very sensitive method of resonant photoluminescence (PL) to directly measure the presence and properties of exciton magnetic polarons in colloidal Cd1-xMnxSe nanocrystals. Despite small Mn2+ concentrations (x = 0.4-1.6%), large polaron binding energies up to ∼26 meV are observed at low temperatures via the substantial Stokes shift between the pump laser and the resonant PL maximum, indicating nearly complete alignment of all Mn2+ spins by Bex. Temperature and magnetic field-dependent studies reveal that Bex ≈ 10 T in these nanocrystals, in good agreement with theoretical estimates. Further, the emission line widths provide direct insight into the statistical fluctuations of the Mn2+ spins. These resonant PL studies provide detailed insight into collective magnetic phenomena, especially in lightly doped nanocrystals where conventional techniques such as nonresonant PL or time-resolved PL provide ambiguous results.

Gate-Controlled Spin-Valley Locking of Resident Carriers in WSe_{2} Monolayers.

Using time-resolved Kerr rotation, we measure the spin-valley dynamics of resident electrons and holes in single charge-tunable monolayers of the archetypal transition-metal dichalcogenide (TMD) semiconductor WSe_{2}. In the n-type regime, we observe long (∼130 ns) polarization relaxation of electrons that is sensitive to in-plane magnetic fields B_{y}, indicating spin relaxation. In marked contrast, extraordinarily long (∼2 µs) polarization relaxation of holes is revealed in the p-type regime, which is unaffected by B_{y}, directly confirming long-standing expectations of strong spin-valley locking of holes in the valence band of monolayer TMDs. Supported by continuous-wave Kerr spectroscopy and Hanle measurements, these studies provide a unified picture of carrier polarization dynamics in monolayer TMDs, which can guide design principles for future valleytronic devices.

Spin noise spectroscopy beyond thermal equilibrium and linear response.

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of (41)K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.

Two-colour spin noise spectroscopy and fluctuation correlations reveal homogeneous linewidths within quantum-dot ensembles.

'Spin noise spectroscopy' is an optical technique for probing electron and hole spin dynamics that is based on detecting their intrinsic fluctuations while in thermal equilibrium. Here we show that fluctuation correlations can be further exploited in multi-probe noise studies to reveal information that in general cannot be accessed by conventional linear optical spectroscopy, such as the underlying homogeneous linewidths of individual constituents within inhomogeneously broadened systems. This is demonstrated in singly charged (In,Ga)As quantum-dot ensembles using two weak probe lasers: When the lasers have similar wavelengths, they probe the same quantum dots in the ensemble and show correlated spin fluctuations. In contrast, mutually detuned probe lasers measure different subsets of quantum dots, giving uncorrelated fluctuations. The noise correlation versus laser detuning directly reveals the quantum dot homogeneous linewidth even in the presence of a strong inhomogeneous broadening. Such noise-based correlation techniques are not limited to semiconductor spin systems, but are applicable to any system with measurable intrinsic fluctuations.

Persistent optically induced magnetism in oxygen-deficient strontium titanate.

Strontium titanate (SrTiO3) is a foundational material in the emerging field of complex oxide electronics. Although its bulk electronic and optical properties are rich and have been studied for decades, SrTiO3 has recently become a renewed focus of materials research catalysed in part by the discovery of superconductivity and magnetism at interfaces between SrTiO3 and other non-magnetic oxides. Here we illustrate a new aspect to the phenomenology of magnetism in SrTiO3 by reporting the observation of an optically induced and persistent magnetization in slightly oxygen-deficient bulk SrTiO3-δ crystals using magnetic circular dichroism (MCD) spectroscopy and SQUID magnetometry. This zero-field magnetization appears below ~18 K, persists for hours below 10 K, and is tunable by means of the polarization and wavelength of sub-bandgap (400-500 nm) light. These effects occur only in crystals containing oxygen vacancies, revealing a detailed interplay between magnetism, lattice defects, and light in an archetypal complex oxide material.

Optical spectroscopy of spin noise.

Spontaneous fluctuations of the magnetization of a spin system in thermodynamic equilibrium (spin noise) manifest themselves as noise in the Faraday rotation of probe light. We show that the correlation properties of this noise over the optical spectrum can provide clear information about the composition of the spin system that is largely inaccessible for conventional linear optics. Such optical spectroscopy of spin noise, e.g., allows us to clearly distinguish between optical transitions associated with different spin subsystems, to resolve optical transitions that are unresolvable in the usual optical spectra, to unambiguously distinguish between homogeneously and inhomogeneously broadened optical bands, and to evaluate the degree of inhomogeneous broadening. These new possibilities are illustrated by theoretical calculations and by experiments on paramagnets with different degrees of inhomogeneous broadening of optical transitions [atomic vapors of 41K and singly charged (In,Ga)As quantum dots].

Magnetic-field-induced delocalized to localized transformation in GaAs:N.

The use of a high magnetic field (57 T) to study the formation and evolution of nitrogen (N) cluster and supercluster states in GaAs:N is demonstrated. A magnetic field is used to lift the conduction band edge and expose resonant N cluster states so that they can be directly experimentally investigated. The reduction of the exciton Bohr radius also results in the fragmentation of N supercluster states, enabling a magnetic field induced delocalized to localized transition. The application of very high magnetic fields thus presents a powerful way to probe percolation phenomena in semiconductors with bound and resonant isoelectronic cluster states.

Long-lived photoinduced magnetization in copper-doped ZnSe-CdSe core-shell nanocrystals.

Nanoscale materials have been investigated extensively for applications in memory and data storage. Recent advances include memories based on metal nanoparticles, nanoscale phase-change materials and molecular switches. Traditionally, magnetic storage materials make use of magnetic fields to address individual storage elements. However, new materials with magnetic properties addressable via alternative means (for example, electrical or optical) may lead to improved flexibility and storage density and are therefore very desirable. Here, we demonstrate that copper-doped chalcogenide nanocrystals exhibit not only the classic signatures of diluted magnetic semiconductors--namely, a strong spin-exchange interaction between paramagnetic Cu(2+) dopants and the conduction/valence bands of the host semiconductor--but also show a pronounced and long-lived photoinduced enhancement of their paramagnetic response. Magnetic circular dichroism studies reveal that paramagnetism in these nanocrystals can be controlled and increased by up to 100% when illuminated with above-gap (blue/ultraviolet) light. These materials retain a memory of the photomagnetization for hour-long timescales in the dark, with effects persisting up to ∼80 K.

Role of nuclear quadrupole coupling on decoherence and relaxation of central spins in quantum dots.

Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling on the spin correlators of electron and hole "central" spins localized in such dots. We show that when the quadrupolar coupling strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential. We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots.

Cascade of magnetic field induced spin transitions in LaCoO3.

We present magnetization and magnetostriction studies of LaCoO3 in magnetic fields approaching 100 T. In contrast with expectations from single-ion models, the data reveal two distinct first-order transitions and well-defined magnetization plateaus. The magnetization at the higher plateau is only about half the saturation value expected for spin-1 Co3+ ions. These findings strongly suggest collective behavior induced by interactions between different electronic configurations of Co3+ ions. We propose a model that predicts crystalline spin textures and a cascade of four magnetic phase transitions at high fields, of which the first two account for the experimental data.

Intrinsic spin fluctuations reveal the dynamical response function of holes coupled to nuclear spin baths in (In,Ga)As quantum dots.

The problem of how single central spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to the many-body couplings involved. Different models yield widely varying time scales and dynamical responses (exponential, power-law, gaussian, etc.). Here we detect the small random fluctuations of central spins in thermal equilibrium [holes in singly charged (In,Ga)As quantum dots] to reveal the time scales and functional form of bath-induced spin relaxation. This spin noise indicates long (400 ns) spin correlation times at a zero magnetic field that increase to ∼5 µs as dominant hole-nuclear relaxation channels are suppressed with small (100 G) applied fields. Concomitantly, the noise line shape evolves from Lorentzian to power law, indicating a crossover from exponential to slow [∼1/log(t)] dynamics.

Nano-engineered electron-hole exchange interaction controls exciton dynamics in core-shell semiconductor nanocrystals.

A strong electron-hole exchange interaction (EI) in semiconductor nanocrystals (NCs) gives rise to a large (up to tens of meV) splitting between optically active ('bright') and optically passive ('dark') excitons. This dark-bright splitting has a significant effect on the optical properties of band-edge excitons and leads to a pronounced temperature and magnetic field dependence of radiative decay. Here we demonstrate a nanoengineering-based approach that provides control over EI while maintaining nearly constant emission energy. We show that the dark-bright splitting can be widely tuned by controlling the electron-hole spatial overlap in core-shell CdSe/CdS NCs with a variable shell width. In thick-shell samples, the EI energy reduces to <250 µeV, which yields a material that emits with a nearly constant rate over temperatures from 1.5 to 300 K and magnetic fields up to 7 T. The EI-manipulation strategies demonstrated here are general and can be applied to other nanostructures with variable electron-hole overlap.

Revealing the exciton fine structure of PbSe nanocrystal quantum dots using optical spectroscopy in high magnetic fields.

We measure the photoluminescence lifetime τ of excitons in colloidal PbSe nanocrystals (NCs) at low temperatures to 270 mK and in high magnetic fields to 15 T. For all NCs, τ increases sharply below 10 K but saturates by 500 mK. In contrast to the usual picture of well-separated "bright" and "dark" exciton states (found, e.g., in CdSe NCs), these dynamics fit remarkably well to a system having two exciton states with comparable--but small--oscillator strengths that are separated by only 300-900 µeV depending on NC size. Importantly, magnetic fields reduce τ below 10 K, consistent with field-induced mixing between the two states. Magnetic-circular dichroism studies reveal exciton g factors from 2-5, and magnetophotoluminescence shows >10% circularly polarized emission.