Plasmon-induced carrier polarization in semiconductor nanocrystals

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coreshell nanocrystals20 have served as a guideline to predict the conditions for and the behaviour of plasmon–exciton interactions in semiconductor ...

Letters https://doi.org/10.1038/s41565-018-0096-0

Plasmon-induced carrier polarization in semiconductor nanocrystals Penghui Yin, Yi Tan, Hanbing Fang, Manu Hegde and Pavle V. Radovanovic* Spintronics1 and valleytronics2 are emerging quantum electronic technologies that rely on using electron spin and multiple extrema of the band structure (valleys), respectively, as additional degrees of freedom. There are also collective properties of electrons in semiconductor nanostructures that potentially could be exploited in multifunctional quantum devices. Specifically, plasmonic semiconductor nanocrystals3–10 offer an opportunity for interface-free coupling between a plasmon and an exciton. However, plasmon– exciton coupling in single-phase semiconductor nanocrystals remains challenging because confined plasmon oscillations are generally not resonant with excitonic transitions. Here, we demonstrate a robust electron polarization in degenerately doped In2O3 nanocrystals, enabled by non-resonant coupling of cyclotron magnetoplasmonic modes11 with the exciton at the Fermi level. Using magnetic circular dichroism spectroscopy, we show that intrinsic plasmon–exciton coupling allows for the indirect excitation of the magnetoplasmonic modes, and subsequent Zeeman splitting of the excitonic states. Splitting of the band states and selective carrier polarization can be manipulated further by spin–orbit coupling. Our results effectively open up the field of plasmontronics, which involves the phenomena that arise from intrinsic plasmon–exciton and plasmon–spin interactions. Furthermore, the dynamic control of carrier polarization is readily achieved at room temperature, which allows us to harness the magnetoplasmonic mode as a new degree of freedom in practical photonic, optoelectronic and quantum-information processing devices. Localized surface plasmon resonance (LSPR)12 renders metal nanoparticles particularly interesting for different technologies, which include photovoltaics13, chemical and biomolecular sensors14, and photothermal cancer therapy15. The possibility to control charge-carrier type and density by aliovalent doping3–6, photodoping7,8, charge transfer16 and native defect (vacancy) generation9,10 has led to the recent emergence of colloidal plasmonic semiconductor nanocrystals17. In contrast to metal nanostructures, these alternative plasmonic nanocrystals have LSPR frequencies tunable in the nearto mid-infrared region, which potentially expands the applications to terahertz imaging, heat-responsive devices and surface-enhanced infrared absorption spectroscopy18. The phenomena observed in semiconductor–metal nanocomposites19 and/or heterostructured core–shell nanocrystals20 have served as a guideline to predict the conditions for and the behaviour of plasmon–exciton interactions in semiconductor nanocrystals. At the heart of these phenomena is the resonant coupling between a plasmon and an exciton that results, for instance, in the enhancement of the excitonic absorption and emission, and the optical Stark effect. Recently, control of the carrier polarization in complex oxides using externally induced plasmon resonances has also been achieved. A notable example is

the generation of spin current in a Pt/BiY2Fe5O12 bilayer film with embedded gold nanoparticles under resonant conditions21. In the presence of an external electric and magnetic field, free electrons associated with LSPR experience Lorentz force (F), and their oscillation can be expressed according to the Drude model as: F = m(dv∕dt ) + γm v = −e E−e(v × B), where e, m and v are the charge, effective mass and velocity of the electron, respectively, γ is the damping factor and E and B are external electric and magnetic fields, respectively. When excited by circularly polarized light with opposite helicity, free electrons undergo cyclotron motion in opposite directions to give rise to two energetically degenerate plasmonic modes with the resonance frequency ω0. In the presence of an external magnetic field applied parallel to the light propagation direction, the two plasmonic modes split, which leads to a difference in the absorption of left circularly polarized (LCP (ρ​−)) and right circularly polarized (RCP (ρ​+)) beams, and results in a derivativeshaped magnetic circular dichroism (MCD) spectrum (Fig. 1a). The model11 developed from the Drude equation of motion allows for an accurate prediction of the shift of the magnetoplasmonic modes, Δω, for a given magnetic field (Δω = ∣ωB−ω0∣ = g (ω0 )B) , where ωB is the frequency of the magnetoplasmonic mode (ωB−, ωB+) and g (ω0 ) = −e ∕2m is the proportionality constant. The linear dependence of the MCD intensity on the magnetic field has also been observed for LSPRs of other plasmonic nanocrystals8,22. Normalized absorption spectra of Sn-doped In2O3 (indium tin oxide (ITO)) nanocrystals in the near-infrared region are presented in Fig. 1b (Supplementary Figs. 1 and 2 give the nanocrystal characterization). Broad bands, which shift to higher energy and increase in intensity with increasing doping level3, can be ascribed to LSPR generated by aliovalent substitutional doping of nanocrystals with Sn4+ (Methods). The blue shift of the LSPR with increasing doping concentration is accompanied by a blue shift of the band-edge absorption, as shown by extrapolation of the spectra in Fig. 1c (that is, Tauc plots). The shift of the band edge to higher energy is associated with the increased conduction-band (CB) occupancy, and is known as the Burstein–Moss effect. We used MCD spectroscopy in a Faraday configuration to examine the excitonic properties of ITO nanocrystals (Methods and Supplementary Fig. 3). Figure 2a (blue trace) shows the 300 K absorption spectrum of ITO nanocrystals that contain 10 mol% Sn4+ in the visible range. The MCD spectrum of In2O3 nanocrystals synthesized under similar conditions and collected at 300 K and 7 T (red trace) shows no measurable intensity. However, variablefield MCD spectra of ITO nanocrystals (black and dashed traces) are dominated by negative bands that coincide with the nanocrystal band-edge absorption. The intensity of the MCD band maximum at ~4.34 eV is plotted as a function of magnetic field in Fig. 2b (black squares). The bandgap MCD intensity is linearly dependent on the magnetic field, as is evident from the best linear fit to

Department of Chemistry, University of Waterloo, Waterloo, ON, Canada. *e-mail: [email protected] Nature Nanotechnology | www.nature.com/naturenanotechnology

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the experimental data (blue line), identical to the MCD intensity of LSPR. The Brillouin function fit to the same data for the spin state S =​ 1/2 and the electron-spin Landé g-factor, gS =​  2.002 (red dashed line), shows a significant deviation from the experimental data, which confirms that the observed field dependence is not associated with the Curie-type paramagnetism. Another unusual signature behaviour of the cyclotron magnetoplasmonic modes is the temperature independence of their MCD intensity—it has been found that the LSPR MCD intensity remains temperature independent at least up to 30 K (refs 8,22). Figure 2c shows the 7 T MCD spectra of ITO nanocrystals in the optical bandgap region collected at various temperatures from 5 to 300 K. All the spectra are essentially identical, which attests to the temperature independence of the excitonic MCD intensity. The field and temperature behaviours of the MCD signal are specific to the cyclotron motion of free electrons. Individual free or weakly bound carriers in an external magnetic field give rise to spin-split Landau levels, owing to their cyclotron oscillations. However, the absorption and MCD spectra that involve quantized Landau levels are generally observed at low temperatures and high magnetic fields, and, in contrast to our observations, have a specific oscillatory pattern (Supplementary Information). The results in Fig. 2 imply that the exciton MCD spectra of ITO nanocrystals are associated with the cyclotron magnetoplasmonic oscillations as a collective electronic property, and involve splitting of the electronic band state rather than intraband sublevels. This is a surprising result because plasmons and excitons are non-resonant, and LSPR is not directly excited in these measurements. Furthermore,

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Fig. 2 | Electron polarization by magnetoplasmonic modes in ITO nanocrystals. a, Absorption (solid blue line) and MCD (solid black and coloured dashed lines) spectra of ITO nanocrystals (that contain 10% Sn4+) collected at 300 K. MCD spectra were recorded at different external magnetic field strengths, as indicated. The 300 K MCD spectrum of In2O3 nanocrystals (collected at 7 T) is shown for comparison (solid red line). b, Magnetic field dependence of MCD intensity at 4.34 eV for ITO nanocrystals in a as a function of the magnetic field strength. c, The 7 T MCD spectra of nanocrystals in a collected at different temperatures. d, Schematic representation of the splitting of the conduction band (CB) states induced by angular momentum of the cyclotron magnetoplasmonic modes. On excitation with LCP and RCP light in a magnetic field, cyclotron magnetoplasmonic modes with helicities ρ​− (curved dashed blue line) and ρ​+ (curved dashed red line), respectively, are formed. These modes couple with the exciton and transfer angular momentum (blue and red curved arrows) to the CB excited states, which causes their splitting (MJ =​ ±​ 1) and the difference in absorption of LCP (vertical blue arrow) and RCP (vertical red arrow) light. Valence band (VB) states are not subject to splitting. a.u., arbitrary units.

unlike classically treated plasmon oscillations, the excitonic absorption involves transitions between discrete quantum levels, which suggests the magnetoplasmonic-mode-induced splitting of the nanocrystal band states. Variable-temperature MCD measurements are very helpful to address the nature of band splitting in semiconductor nanocrystals. Specifically, the temperature independence of MCD intensity, characteristic for the A term, is associated with the lack of ground-state splitting (Methods and Supplementary Fig. 4)23. Zeeman perturbation, represented as μB (L + 2Ŝ )B, where μB is the Bohr magneton, L and Ŝ are the orbital and spin angular momentum operators, respectively, leads to splitting of the lowest unoccupied CB states. In the absence of any source of paramagnetism, the total angular momentum is due to the orbital angular momentum (that is, J =​  L =​ 1), with the Zeeman energy of the split states given by E Zeeman = μB MJB, where MJ =​  ±​ 1. Taken together, the field- and temperature-dependent measurements suggest that the cyclotron Nature Nanotechnology | www.nature.com/naturenanotechnology

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Fig. 3 | Spin-induced manipulation of Zeeman splitting in plasmonic IMO nanocrystals. a, Typical scanning transmission electron microscopy image of IMO nanocrystals. Inset: lattice-resolved TEM image of a single nanocrystal. b, LSPR absorption spectra of IMO nanocrystals that have different doping concentrations. With increasing doping concentration the LSPR band shifts to higher energy and increases in intensity, as expected from the Drude–Lorentz model. c, Absorption (solid blue line) and MCD (solid black line and dashed coloured lines) spectra of 0.3% IMO nanocrystals collected at 5 K. External magnetic field strengths that correspond to different MCD spectra are indicated. d, Magnetic field and temperature dependence of MCD intensity recorded at 3.93 eV for IMO nanocrystals in c. The data for MCD intensity dependence on the magnetic field and temperature are fit to a linear function (solid line) and Curie’s law (dashed blue line), respectively. e, Schematic representation of the excitonic splitting for IMO nanocrystals due to the paramagnetism induced by the presence of the molybdenum dopant in the +​5 oxidation state. The presence of an unpaired electron on Mo5+ dopants (d1 transition metal ion) causes additional anomalous (spin-induced) Zeeman splitting of the VB and CB states. The structure and splitting of the VB is simplified for the purpose of conceptual representation and clarity. Blue and red vertical arrows indicate the absorption of LCP and RCP light, respectively.

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magnetoplasmonic modes impart significant orbital angular momentum to the nanocrystal excited state, which leads to the formation of oppositely polarized electronic states around the Fermi level (Fig. 2d). Importantly, the appearance of the MCD signal with a singular sign (in this case negative) indicates a complete polarization of the carriers by the magnetoplasmonic modes. To demonstrate the generality of the plasmon-induced electron polarization and the possibility of its manipulation, we synthesized Mo-doped In2O3 (IMO) nanocrystals. Most nanocrystals have a truncated tetragonal bipyramidal morphology (Fig. 3a) and the bixbyite crystal structure (Supplementary Fig. 5). The LSPR absorption spectra of IMO nanocrystals that have different doping levels are shown in Fig. 3b. An increase in the number density of free electrons is also accompanied by the blue shift of the onset of the band-edge absorption (Supplementary Fig. 6). The effect of molybdenum dopants on the electronic structure of In2O3 and the comparison between the electronic structure of ITO and IMO were explored in more detail using density functional calculations (Supplementary Fig. 7). MCD spectra of 0.3% IMO nanocrystals collected at different magnetic field strengths are shown in Fig. 3c (black and dashed traces). A robust derivative-shaped MCD signal with a negative maximum at ~3.93 eV coincides with the band-edge absorption (blue trace in Fig. 3c). The intensity of this peak also follows a linear dependence on the magnetic field (Fig. 3d, squares), which confirms that it originates from the Zeeman splitting of the band states due to their coupling with the magnetoplasmonic modes (Supplementary Fig. 8). However, unlike MCD spectra of ITO nanocrystals, the intensity of this band decreases rapidly on heating the sample and then levels off, with a drop of ~25% from 5 to 300 K (Fig. 3c, triangles). A temperature dependence of the MCD intensity typically indicates the presence of ground-state splitting, and is characteristic for the C term (Supplementary Fig. 4)23. At room temperature the MCD spectra have only A term intensity, owing to the balanced population of the two ground-state sublevels. However, at low temperatures the Boltzmann population of the higher energy sublevel is reduced, which results in a combination of the A and C terms. The C term is generally observed for the species with ground-state paramagnetism, and follows a Curie-type temperature dependence. Paramagnetism in IMO nanocrystals is due to the presence of Mo5+ (Supplementary Fig. 9), which is formed in situ by reduction of the Mo6+ precursor, similarly to MoO3–x nanocrystals23,24. Simulated MCD temperature dependence for a d1 transition metal ion (Mo5+) is shown by the dashed line in Fig. 3d. Though a decrease in the MCD intensity with temperature for IMO nanocrystals obeys Curie behaviour at low temperatures (dashed line in Fig. 3d and Supplementary Fig. 10), the majority of the intensity measured at 5 K persists up to room temperature, which indicates a dominant

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Fig. 4 | Control of the charge carrier polarization in IMO nanocrystals. a, Normalized A term MCD spectra (collected at 100 K) of IMO nanocrystals with different molybdenum doping concentrations in the fundamental bandgap region. b, Normalized C term MCD spectra of IMO nanocrystals in a. c, Exciton MCD spectra of 0.3% IMO nanocrystals recorded at 5 K for the opposite polarities of the external magnetic field of 7 T. Nature Nanotechnology | www.nature.com/naturenanotechnology

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A term intensity associated with plasmon–exciton coupling. These results indicate that the spin angular momentum is coupled with the orbital angular momentum to provide additional splitting in the ground and excited states (Fig. 3e). We also explored the possibility of controlling the magnitude and orientation of charge-carrier polarization using cyclotron magnetoplasmonic modes. Figure 4a compares A term MCD spectra of IMO nanocrystals with different doping concentrations, but the same bandgap absorbance. The C term intensity has exactly the opposite trend (Fig. 4b). As the strength of plasmon–exciton coupling decreases with decreasing doping concentration, the relative contribution of the C term increases. Furthermore, to demonstrate the full control over carrier polarization, we measured the MCD spectra of IMO nanocrystals for the opposite directions of the external magnetic field (Fig. 4c). The observed reversal of the sign of the exciton MCD signal demonstrates switching of the carrier polarization by controlling the direction of the cyclotron motion of free electrons. The mechanism of this plasmon-induced carrier polarization is an intriguing and challenging problem. We hypothesize that optical phonons play a particularly important role in this mechanism, because they couple with both excitons25 and plasmons26 in semiconductor nanocrystals. Importantly, the phonons can transfer angular momentum27, which allows for both the generation of the magnetoplasmonic modes and the splitting of the band states in an external magnetic field. Though more theoretical and experimental work is necessary for a quantitative understanding of the phenomena that involve quasiparticle interactions in correlated functional materials, it is particularly instructive to compare the properties of plasmonic semiconductor nanocrystals to those of diluted magnetic semiconductors in which polarized electron-spin states arise from sp–d exchange interactions28. These exchange interactions typically decrease rapidly with temperature following Curie’s law. The practical utilization of a diluted magnetic semiconductor requires a system that supports itinerant-carrier-mediated ferromagnetic ordering of dopant centres at or above room temperature, that is compatible with the current semiconductor technology and, ideally, transparent to visible light29. Additionally, the minimum device size is generally limited thermodynamically by the size of the ferromagnetic domains30. However, carrier polarization in plasmonic semiconductor nanocrystals is a universal phenomenon that persists above room temperature. Importantly, LSPR is inherently a single-nanocrystal effect31 that can be attained in particles several nanometers in size that contain only a few free carriers5,7,8. In analogy to the emerging electronic technologies that rely on different degrees of freedom to achieve the polarization of charge carriers, which include spintronics (electron spin) and valleytronics (discrete values of crystal momentum), we refer to harnessing the cyclotron plasmonic modes for information processing, transmittal and storage as plasmontronics. The dynamic control of the carrier polarization is enabled by intrinsic plasmon–exciton coupling, which is responsible for the excitation of the cyclotron magnetoplasmonic oscillations and subsequent Zeeman splitting of the band states. Cyclotron plasmonic modes might also be sensitive to nanocrystal size and shape6, as well as the resonant enhancement of the electron–phonon coupling26, potentially allowing for a variety of ways to further enhance carrier polarization in plasmonic semiconductor nanocrystals at room temperature. One dimensional semiconductors (nanowires) could be a particularly interesting nanodevice platform, because carrier polarization could be detected and exploited by magneto-electrical measurements. The ability to achieve complete polarization of carriers in individual single-phase nanocrystals at room temperature opens up the possibilities for fundamental investigations of plasmon–exciton and plasmon–spin interactions in reduced dimensions, and for technological applications in photonics, optoelectronics and quantum-information processing.

Methods

Methods, including statements of data availability and any associated accession codes and references, are available at https://doi. org/10.1038/s41565-018-0096-0. Received: 3 August 2017; Accepted: 14 February 2018; Published: xx xx xxxx

References

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Author contributions

P.Y. and P.V.R. designed the experiments. P.Y., Y.T. and H.F. prepared and characterized the samples. P.Y. and Y.T. conducted MCD measurements. P.Y. analysed the data. M.H. performed the DFT calculations and analysis. P.V.R. and P.Y. interpreted the results and wrote the manuscript with contributions from the other authors. P.V.R. conceived and supervised the project.

Competing interests

The authors declare no competing interests.

Additional information

Acknowledgements

We acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) (RGPIN-2015-67304032), Canada Foundation for Innovation (Project no. 204782) and the University of Waterloo (UW-Bordeaux Collaborative Research Grant). This research was undertaken thanks, in part, to funding from the Canada First Research Excellence Fund. P.V.R. acknowledges the support from the Canada Research Chairs Program (NSERC).

Supplementary information is available for this paper at https://doi.org/10.1038/ s41565-018-0096-0. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to P.V.R. Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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NaTUre NanOTecHnOlOgy

Methods

Materials. All reagents and solvents are commercially available and were used as received. Indium(iii) acetylacetonate (In(acac)3, 98%) and tin(iv) chloride pentahydrate (SnCl4·5H2O, 98%) were purchased from Strem Chemicals. Bis(acetylacetonato)dioxomolybdenum(vi) (MoO2(acac)2), oleylamine (70%) and oleic acid (90%) were purchased from Sigma-Aldrich. Synthesis of ITO and IMO nanocrystals. The synthesis of ITO and IMO nanocrystals was based on the experimental procedure reported previously3,32. In a 100 ml three-neck round-bottom flask, 0.9 g of In(acac)3, 7.2 g of oleylamine and different amounts of doping precursors, SnCl4·5H2O or MoO2(acac)2, were mixed together. The reaction mixture was heated to 250 °C within 1 h and then allowed to react for another 1 h in argon with continuous stirring. The reaction for In2O3 nanocrystals was performed under oxidizing conditions in air to minimize the concentration of oxygen vacancies33, which could also contribute to the carrier generation. The mixture was slowly cooled to room temperature and the precipitate was collected by centrifugation at 3,000 revolutions per minute (r.p.m.) for 10 min. After the precipitate was washed with ethanol three times, 1.5 ml oleic acid was added and the mixture was heated to 90 °C for 30 min. This procedure was performed to remove any surface-bound dopant ions and impurities34. The nanocrystal samples were subsequently precipitated again and washed with ethanol three times. The obtained nanocrystals were dispersed in a non-polar solvent, such as hexane or toluene. Characterization and measurements. Transmission electron microscopy (TEM) images were collected with a JEOL-2010F microscope operated at 200 kV. Copper grids with lacey Formvar/carbon support films purchased from Ted Pella, Inc., were used to prepare the specimen for TEM measurements. Powder X-ray diffraction patterns were obtained with an INEL diffractometer with a position-sensitive detector and monochromatic Cu Kα​radiation (λ =​ 1.5418 Å). X-ray photoelectron spectra were recorded with a VG Scientific ESCALAB 250 spectrometer using Al Kα​radiation (1,486.6 eV photon energy) as the excitation source. The ultraviolet–visible–near infrared absorption spectra were collected with a Varian Cary 5000 spectrophotometer. The measurements were performed on colloidal suspensions of nanocrystals or upon dropcasting the colloidal suspensions onto quartz substrates. Fourier transform infrared (FTIR) spectroscopy measurements were performed using a FTIR Bruker Tensor 37 spectrometer. FTIR spectra were collected using KBr pellets on which colloidal nanocrystals were dropcast. MCD measurements. MCD spectroscopic measurements were carried out in a Faraday configuration using a Jasco J-815 spectropolarimeter to generate circularly polarized light and signal detection (Supplementary Fig. 3). Samples were housed in an Oxford SM 4000 magneto-optical cryostat that allows for a variable temperature (1.5–300 K) and a variable field (0–7 T) operation. The nanocrystals were deposited on strain-free quartz substrates by dropcasting the colloidal suspensions in toluene. The MCD intensity (the difference in absorption of the LCP and RCP light) was expressed as ellipticity (θ, millidegree) of the transmitted light. The magnetic-field-dependent MCD measurements were made at 5 and 300 K under varied magnetic fields from 1 to 7 T with 1 T interval. The full-range spectra were collected from 200 to 800 nm with 1 nm data pitch, 1 nm bandwidth, 1 s response time and 1 accumulation. The MCD spectra in the bandgap region were collected in the range 250–400 nm using the same spectroscopic parameters but with a 2 s response time and 2 accumulations. The variable-temperature MCD spectra were collected at 7 T and different temperatures (5, 10, 20, 50, 100, 200 and 300 K). Plasmonic properties of ITO nanocrystals. The LSPR absorption band maximum intensities and energies as a function of the Sn4+ doping concentration follow 1 ∕2 the Drude–Lorentz model, with ωp ∝ n and αabs ∝ n, where ωp is the plasma frequency, αabs is the absorption coefficient and n is the number density of free electrons3. Specifically, the absorption coefficient for the LSPR is directly proportional to the charge carrier density, according to equation (1): αabs =

ne 2 m*ε0nRI cτω2

(1)

where e and m* are the charge and effective mass, respectively, of an electron, ε0 is the vacuum permittivity, τ is the mean time between two electron scattering events, nRI is the refractive index of undoped semiconductor, and c and ω are the speed and frequency of light, respectively. On the other hand, the plasma frequency has a square root dependence on the free electron concentration: ωp =

ne 2 m*εoptε0

(2)

where εopt = nRI2 is the dielectric constant measured in the transparent region of the spectrum of an undoped semiconductor. Agreement of the experimental data with the Drude–Lorentz model has been demonstrated previously 3.

MCD analysis. The circular polarization of light was defined according to the ‘optics’ convention (that is, referenced to the detector or looking towards the source). The corresponding MCD spectra were represented as outlined elsewhere23,35. The MCD intensity is defined as Δ​A =​  AL −​  AR, where AL and AR are the absorption of left (ρ​−) and right (ρ​+) circularly polarized light, and are represented as a degree of ellipticity (Supplementary Fig. 3). The MCD intensities were converted to Δ​A/A from ellipticity (θ) using the relationship: ΔA θ = A 32982 × A

(3)

where θ is in millidegrees and A is the bandgap absorbance determined from the absorption spectrum simultaneously collected by the circular dichroism detector. The magnetic field dependence of the exciton MCD intensity was obtained from the high-resolution MCD spectra collected at different fields from 1 to 7 T, after the baseline subtraction using the spectrum collected at 0 T. The corrected field-dependent intensities at the MCD band maximum were fitted to a linear function in B to compare with the field dependence of the MCD intensity for LSPR (Fig. 2b, black line). In addition, to distinguish it clearly from the Curie behaviour, the magnetic field dependence of the intensity of the MCD spectra at the bandedge energy was also fitted with the spin-only Brillouin function36,37:    g μ B  g μ B 1 MS = NgSμB (2S + 1)coth (2S + 1) S B  −coth  S B     2kBT    2 2 k T  B  

(4)

where S is the spin quantum number, gS is the corresponding Landé g-factor, B is the external magnetic field, kB is the Boltzmann constant and T is the temperature (Fig. 2b, dashed red line). For the fitting, considering the case of free electrons, we used the values gS =​  2.002 and S =​  1/2, whereas N was treated as the fitting parameter. For the temperature-dependent MCD intensity measurements, the spectra collected in the absence of a magnetic field were used as baselines to correct the MCD spectra measured at different temperatures from 5 to 300 K. The fitting of temperature-dependent MCD intensities for IMO nanocrystals involves the deconvolution of A and C terms from the overall MCD intensity (see below for a more detailed discussion of the A and C terms). The C term MCD intensity vanishes almost completely at high temperatures, and the MCD intensity measured at room temperature was taken as the A term contribution only. The maximum exciton MCD intensity at 300 K was subtracted from the maximum intensities measured at all other temperatures to obtain the temperature dependence of the C term, which was fitted with the Curie-type relationship: M=

N T

(5)

where T is the temperature, which ranges from 5 K to 300 K, and N is chosen as the fitting parameter. Adding the A term intensity (300 K) to the fitting curve for the C term intensity reproduces very well the temperature dependence of the overall MCD intensity (Fig. 3d, dashed blue line). The doping concentration dependence of the A term (Fig. 4a) and C term (Fig. 4b) intensities were obtained in a similar way. Correlation between excitonic splitting and MCD terms. The MCD intensity for a transition from the ground state |A>​to an excited state |J>​is defined as: 3 2   ∂f (E)    ΔA  2N0 π α Clloge   + B + C0  f (E) =   μBB A1 − 0       E kT   250hcnRI    ∂E   

(6)

where Δ​A is the differential absorption between the LCP and RCP light, E =​  hν​, α is the electric permeability, C is the concentration and l is the path length. A1, B0 and C0 are known as the MCD A, B and C terms, respectively, f(E) is the absorption spectrum band shape and ∂f (E)∕∂E is its first derivative. Under the external magnetic field along the light propagation direction (z), the ground and/or excited states are split due to a Zeeman perturbation of −μz B = μB(gLLz + gSŜz )B, where μz is the electron magnetic dipole moment, Lz and Ŝz are the orbital and spin angular momentum operators, respectively, and gL = 1 and gS =​ 2.002 are the corresponding gyromagnetic ratios. The overall electron angular momentum responsible for the electron polarization is J =​  L +​  S, with the MCD selection rule Δ​MJ =​  ±​1 (+​1 for LCP light and –1 for RCP light). One of the most reliable ways to differentiate experimentally between different terms is the temperature dependence of the MCD intensity. A term MCD occurs in the system that has degenerate excited states. Under a magnetic field, the excited states are split due to the Zeeman effect. As the Zeeman splitting is usually only a few wavenumbers, the two oppositely signed absorption bands will sum to a derivative-shape MCD signal, as shown in Supplementary Fig. 4a. On the contrary, C term MCD requires degenerate ground states that undergo Zeeman splitting in the external magnetic field. At low temperatures, kT is comparable to or smaller than the magnitude of the Zeeman splitting in the presence of a strong magnetic field, which causes the Boltzmann population of the lower ground-state sublevel Nature Nanotechnology | www.nature.com/naturenanotechnology

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Letters

NaTUre NanOTecHnOlOgy to be larger than that of the higher-energy sublevel. Hence, two oppositely signed absorption bands will have different intensities, which results in a band shape that has mostly absorption band shape, as shown in Supplementary Fig. 4b. C term MCD is generally associated with the Zeeman splitting due to ground-state paramagnetism, and therefore follows a temperature-dependence characteristic for the Curie law (Supplementary Fig. 4c). C term intensity is generally observed in the MCD spectra of diluted magnetic semiconductors36,37. Computational method. The density functional theory (DFT) calculations were performed using the plane-wave self-consistent field (SCF) approximation implemented in the Quantum Espresso code5. The Perdew–Burke–Ernzerhof exchange correlation functional was used within the generalized gradient approximation. For the ITO and IMO calculations, two In1 (8b) sites were replaced with Sn and Mo atoms, respectively, in the 80 atom conventional In2O3 cell to yield a doping concentration of 6.25%. For SCF calculations a 6 ×​  6  ×​  6 Monkhorst– Pack k-point grid was used. For non-self-consistent field (NCSF) calculations a denser Monkhorst–Pack grid of 9 ×​  9  ×​ 9 was used. We performed the geometry optimization such that all In2O3 lattice cells, doped and undoped, were relaxed until the total energy converged to 10−4 and the total force on each atom to 10−3 atomic Rydberg units. During the optimization process, atoms in the lattice were allowed to move freely along the x, y and z directions. The equilibrium lattice parameters obtained from the optimization procedure were used for further SCF and NSCF calculations.

Data availability. The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

32. Hutfluss, L. N. & Radovanovic, P. V. Controlling the mechanism of phase transformation of colloidal In2O3 nanocrystals. J. Am. Chem. Soc. 137, 1101–1108 (2015). 33. Wang, T. & Radovanovic, P. V. In-situ enhancement of the blue photoluminescence of colloidal Ga2O3 nanocrystals by promotion of defect formation in reducing conditions. Chem. Commun. 47, 7161–7163 (2011). 34. Dave, N., Pautler, B. G., Farvid, S. S. & Radovanovic, P. V. Synthesis and surface control of colloidal Cr3+-doped SnO2 transparent magnetic semiconductor nanocrystals. Nanotechnology 21, 134023 (2010). 35. Mason, W. R. A Practical Guide to Magnetic Circular Dichroism Spectroscopy (Wiley, Hoboken, 2007). 36. Ju, L. et al. Interplay between size, composition and phase transition of nanocrystalline Cr3+-doped BaTiO3 as a path to multiferroism in perovskitetype oxides. J. Am. Chem. Soc. 134, 1136–1146 (2012). 37. Farvid, S. S. et al. Evidence of charge-transfer ferromagnetism in transparent diluted magnetic oxide nanocrystals: switching the mechanism of magnetic interactions. J. Am. Chem. Soc. 136, 7669–7679 (2014).

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