Magneto-optical properties in IV-VI lead-salt semimagnetic nanocrystals
© Prado et al.; licensee Springer. 2012
Received: 2 February 2012
Accepted: 7 July 2012
Published: 7 July 2012
We present a systematic study of lead-salt nanocrystals (NCs) doped with Mn. We have developed a theoretical simulation of electronic and magneto-optical properties by using a multi-band calculation including intrinsic anisotropies and magnetic field effects in the diluted magnetic semiconductor regime. Theoretical findings regarding both broken symmetry and critical phenomena were studied by contrasting two different host materials (PbSe and PbTe) and changing the confinement geometry, dot size, and magnetic doping concentration. We also pointed out the relevance of optical absorption spectra modulated by the magnetic field that characterizes these NCs.
Recently, the successful fabrication of IV-VI nanocrystals doped with Mn has shown possible effective tuning of the emission energy from infrared (dot radius ≃ 200 Å) up to near-ultraviolet (dot radius ≃ 20 Å) regions. The IV-VI semiconductors, such as PbSe nanocrystals (NCs), provide access to the limit of strong quantum confinement where, besides the changes induced by very small dot size, the direct narrow band-gap that can also be engineered by the gradual addition of dilute amounts of magnetic Mn ions to the dot structure. The members of the lead-salt family, such as PbSe and PbTe, have rock-salt crystalline structure with a direct bandgap in the L-point and the energy branches are four-fold degenerate. The bottom of the conduction band has symmetry with the top of the valence band displaying symmetry of the double group D3. This corresponds to the opposite situation observed in III-V or II-VI zinc blend materials, since here the valence band-edge Bloch function displays s-like symmetry whereas the conduction band-edge Bloch function has p z -like symmetries, where z denotes the 〈111〉 direction of the cubic lattice.
where, with ∇2 as the 3D Laplacian operator, and are electron and hole effective mass terms while P t and P l are the anisotropic conduction-valence Kane-Dimmock coupling parameters for longitudinal and transverse directions; P z and P± = P x ± i P y are the momentum operators, whereas E g is the bandgap and m0 is the free electron mass. The relevant Kane-Dimmock parameters for the materials analyzed in this work can be found in[4, 5].
Also, H x = − x/2〈S z (B T)〉N0 · α(·β), where 〈S z (B T x)〉 is the mean field magnetization at temperature T, represented as a Brillouin function in dilute doped sample containing N0 unit cells and Mn content, x. Finally, α and β are the exchange constants for the semimagnetic materials, N0 · α = −0.08 eV and N0·β = 0.02 eV for PbMnSe, while N0·α = −0.45 eV and N0·β = 0.29 eV for PbMnTe.
For the spherical model, these states fulfill the boundary condition at the dot radius; thus, the function components have the form where An,L is a normalization constant, j L (x) is the spherical Bessel function, and are the spherical harmonics. The subspaces must be constructed with special combinations of even () or odd () with wave number, where is the n th zero of j L (x) = 0. For the semispherical structures, the states must also fulfill the boundary condition at the equator plane which restricts the set of quantum numbers L and M to the condition |L−M| = odd number. Hence, the parities of the spinor components differ from the full spherical case and the states for a semispherical confinement require the replacement 2L (2L + 1) in the second (third) line of Equation 2 by 2L + 1 (2L).
As noted in Figure3c,d, there are Mn concentration regions where the g factor becomes strictly positive or negative, independent of the confinement shape. For fixed dot radius, it is possible to predict the existence of a zero critical field value for a certain value x c for different dot and confinement geometries. For large dot sizes, a nonlinear increasing of B c is observed for low values of x and a quasi-linear behavior otherwise.
In order to discuss the optical absorption spectrum, the probability for dipole-allowed optical transitions between single electron and hole states has to be evaluated in detail. Within the electrical dipole approximation, the oscillator strength is a linear combination of the matrix elements of the optical transitions,. Here, is the light polarization vector, is the momentum operator, f j and u j are the envelope and periodic Bloch functions at the L point for each involved carrier j, respectively. The second term on the right-hand side is responsible for intraband optical transitions, since 〈u j |u j ′ 〉 = δ j j ′ . In this case the incident light couples, in the same band, state with different symmetries whenever the term for a given polarization. In our case the complete set of selection rules are obtained from the nonvanishing products of the matrix elements Ie,hδ L e , L h πα,α ′, where πα,α ′ is the matrix of the parity operator, and Ie,h = 〈fe,α|fh,α〉 is the overlap integral of the electron-hole envelope functions allowed by the interband transition. The allowed transitions between states belonging to the Hilbert subspaces described by spinors (2) are determined from the angular dependence of the wave functions.
In the case of semispherical geometry, the selection rules for the circular light polarization are the same as for the spherical case; meanwhile, for the linear light polarization, these allow transitions within the same subspace due to the parities of the components of the wave functions in the subspaces.
Summarizing, we have investigated the electronic and magneto-optical properties of P b1−xM n x Se and P b1−xM n x Te semimagnetic dots by taking advantage of their strong sensitivity to spatial confinement asymmetry and properties induced by the Mn doping. We have shown the appearance of the critical phenomena as the spin level crossing for certain concentration of Mn on the P b1−xM n x Te and the modulation of the optical absorption controlled by field B and confinement anisotropy. Subtle effects of Mn content variation were predicted for the energy spectra of the P b1−xM n x Se dots, whereas important consequences are expected for P b1−xM n x Te dots. We believe that these results may stimulate research groups working on these important materials to explore device applications working on the wide spectral range.
The authors acknowledge the financial support from the Brazilian agencies, FAPEMIG (SJP, LV-L), INCT-IQ (AMA) and FAPESP and CNPq (VL-R, GEM).
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