Abstract

Magnetic doping of semiconductor nanostructures is actively pursued for applications in magnetic memory and spin-based electronics^{1, 2}. Central to these efforts is a drive to control the interaction strength between carriers (electrons and holes) and the embedded magnetic atoms^{3, 4, 5}. In this respect, colloidal nanocrystal heterostructures provide great flexibility through growth-controlled 'engineering' of electron and hole wavefunctions in individual nanocrystals^{6, 7}. Here, we demonstrate a widely tunable magnetic sp–d exchange interaction between electron–hole excitations (excitons) and paramagnetic manganese ions using 'inverted' core–shell nanocrystals composed of Mn²⁺-doped ZnSe cores overcoated with undoped shells of narrower-gap CdSe. Magnetic circular dichroism studies reveal giant Zeeman spin splittings of the band-edge exciton that, surprisingly, are tunable in both magnitude and sign. Effective exciton g-factors are controllably tuned from -200 to +30 solely by increasing the CdSe shell thickness, demonstrating that strong quantum confinement and wavefunction engineering in heterostructured nanocrystal materials can be used to manipulate carrier–Mn²⁺ wavefunction overlap and the sp–d exchange parameters themselves.

Introduction

Traditionally, embedding paramagnetic atoms into low-dimensional semiconductor structures requires molecular-beam epitaxy or chemical vapour deposition techniques^{3, 4, 5}. There now exists a rich variety of 'diluted magnetic semiconductor' (DMS) quantum wells, superlattices and hetero-interfaces, with recent work demonstrating magnetic doping of epitaxially grown 'zero-dimensional' quantum dots^{8, 9, 10}. In parallel, advances in colloidal chemistry have recently enabled magnetic doping of semiconductor nanocrystals^{11, 12, 13, 14, 15, 16}, providing an alternative and potentially lower-cost route towards magnetically active quantum dots. With a view towards enhancing carrier/paramagnetic ion spin interactions, colloidal nanocrystals typically generate stronger spatial confinement of electronic wavefunctions compared with their epitaxial counterparts, which is thought to enhance sp–d exchange coupling even for a single magnetic dopant atom^{12, 17}.

Whereas magnetically doped monocomponent nanocrystals are well established¹⁶, wavefunction engineering using magnetic multicomponent colloidal heterostructures^{18, 19} has not been extensively explored. One new class of nanocrystal heterostructure that holds promise for tuning sp–d exchange interactions are 'inverted' core–shell designs, wherein wide-gap semiconductor cores are overcoated with narrower-gap shells. With increasing shell thickness, the electron and hole envelope wavefunctions, _e,h(r), migrate towards the nanocrystal periphery⁷ (albeit at different rates), thus tuning their overlap with magnetic atoms embedded, for example, in the core alone. Here, we investigate precisely this type of wavefunction engineering and exchange interaction control using 'inverted' ZnSe–CdSe core–shell nanocrystals in which the cores are doped with paramagnetic, spin-5/2Mn²⁺ ions (see Fig. 1). Magnetic circular dichroism (MCD) spectroscopy at the nanocrystal absorption edge reveals a giant sp–d exchange interaction that inverts sign with increasing shell thickness, suggesting a confinement-induced sign inversion of the electron–Mn²⁺ exchange constant, , accompanied by significant reduction of the hole–Mn²⁺ overlap due to wavefunction engineering.

Figure 1: An 'inverted core–shell' approach to tuning sp–d spin-exchange interactions in heterostructured colloidal nanocrystals.

a,b, Mn²⁺-doped cores of wide-bandgap ZnSe are overcoated with narrower-gap CdSe shells of increasing thickness h. The conduction and valence band diagrams show the notional electron and hole wavefunctions in these nanocrystals. Room-temperature photoluminescence (PL) and absorption spectra (OD: optical density) from representative solutions of Mn²⁺-doped ZnSe cores alone (a) and Mn²⁺-doped cores with thick (h8 Å) CdSe shells (b). With increasing h, the band-edge photoluminescence energy approaches and drops below the internal Mn^2+ 4T₁⁶A₁ emission at 2.15 eV. c, Dependence of the band-edge exciton photoluminescence energy on the 1S absorption peak energy. Red symbols show nanocrystals with Mn²⁺-doped cores, and blue symbols show nanocrystals with non-magnetic 'reference' cores. The Mn²⁺ emission at 2.15 eV is shown by black squares.

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Four series of ZnSe–CdSe nanocrystals were grown, each having ZnSe cores of radius . In each series the CdSe shell thickness, h, systematically increases from 0 to 8 Å. Two series used non-magnetic (undoped) 'reference' cores, and two used Mn²⁺-doped cores. Elemental analysis of pyridine-washed magnetic cores indicates 2 Mn²⁺ ions per core, on average. Paramagnetic resonance studies are consistent with the Mn²⁺ residing primarily in the ZnSe core, for all h (see Supplementary Information). Figure 1a shows absorption and photoluminescence spectra from the Mn²⁺-doped ZnSe cores alone (h=0). The absorption peak at 3.2 eV is due to the fundamental band-edge (1S) exciton transition. On the other hand, the photoluminescence is dominated by the 2.15 eV internal ⁴T₁⁶A₁ Mn²⁺ transition, which results from efficient energy transfer from band-edge excitons to the excited ⁴T₁ Mn²⁺ state¹¹. The photoluminescence also shows a small peak at 2.95 eV from direct recombination of band-edge excitons^{14, 19}.

To suppress energy transfer and realize strong exciton photoluminescence, the nanocrystal bandgap must be tuned below 2.15 eV, as recently demonstrated in Mn²⁺-doped CdSe nanocrystals (ref. 20). This regime is accessible here using sufficiently thick shells (see Fig. 1b). Increasing h shifts _e(r) and _h(r) towards the shell, reducing the bandgap and redshifting both the absorption and the photoluminescence. When , the exciton photoluminescence energy drops below 2.15 eV. The dependence of the exciton photoluminescence energy on the absorption energy is summarized in Fig. 1c, for both Mn²⁺-doped and non-magnetic nanocrystals.

The most compelling evidence for successful Mn²⁺incorporation is an enhanced exciton Zeeman splitting, E_Z, due to carrier–Mn²⁺ sp–d exchange. Low-temperature MCD spectroscopy provides a direct, quantitative measure of E_Z at the fundamental 1S absorption peak²¹. Figure 2 shows E_Z versus magnetic field H at different temperatures for four important cases: non-magnetic and Mn²⁺-doped ZnSe–CdSe nanocrystals, each having 'thin' and 'thick' shells. Non-magnetic nanocrystals with thin or thick shells show MCD signals that track the derivative of the absorption peak and increase linearly with field from 1–6 T (Fig. 2a,b, insets). The exciton Zeeman splittings, E_Z=g_exBH, where _B is the Bohr magneton, indicate small, temperature-independent, positive exciton g-factors of order unity (g_ex=+2.1 and +2.5, respectively), in approximate agreement with previous studies of non-magnetic monocomponent nanocrystals (refs 14,21). As expected, shell thickness does not strongly influence the small intrinsic electron and hole g-factors in these non-magnetic nanocrystals.

Figure 2: Magnetic-field- and temperature-dependent Zeeman spin splitting, E_Z, and MCD spectra from both magnetic and non-magnetic core–shell nanocrystals.

E_Z versus H at the fundamental 1S absorption peak from ZnSe–CdSe nanocrystals at T=3 K (circles), 10 K (squares), 20 K (triangles) and 50 K (diamonds). The insets show absorption and MCD spectra at T=3 K, for H=2, 4 and 6 T. a–d, Measurements on nanocrystals having undoped ZnSe cores and thin (h<1 Å) CdSe shells (a), undoped cores with thick (h7 Å) shells (b), Mn²⁺-doped cores with thin shells (c) and Mn²⁺-doped cores with thick shells (d). Note that the MCD and E_Z inverts sign in Mn²⁺-doped nanocrystals when shell thickness increases (c,d). The black dashed lines in c,d show modified Brillouin-function fits to E_Z at T=3 K, using effective temperatures T+T₀=4 and 9 K, respectively (see the Methods section).

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Magnetic nanocrystals having thin shells (Fig. 2c) exhibit much larger MCD of opposite sign. E_Z is negative, quite large, and tracks the temperature-dependent magnetization of the paramagnetic Mn²⁺ ions, which is described by a Brillouin function (dashed line). These data reveal a strong sp–d exchange interaction between the absorption-edge exciton and the Mn²⁺ in the ZnSe core, and are qualitatively similar to previous studies^{12, 14, 15} of monocomponent ZnSe or CdSe nanocrystals doped with Mn²⁺ or Co²⁺.

In surprising contrast, Fig. 2d reveals that in Mn²⁺-doped nanocrystals with thick CdSe shells, E_Z has opposite sign, yet still exhibits a significant sp–d coupling: E_Z still saturates at low temperatures and high fields and is significantly larger than in non-magnetic nanocrystals. Carrier–Mn²⁺ sp–d exchange coupling is clearly still appreciable; however, its sign has inverted. A clear inversion of the sp–d exchange is seen in Fig. 3a, which shows E_Z versus H at 1.6 K for one series of Mn²⁺-doped ZnSe–CdSe nanocrystals. In this series, the 1S absorption edge drops from 2.9 eV (red trace) to 2.2 eV (purple trace) as h increases to 8 Å. For all nanocrystals in this magnetic series, E_Z exhibits saturation at high magnetic fields (and also reveals a Brillouin-function temperature dependence; not shown), indicating significant sp–d interactions. E_Z inverts when h2 Å. For comparison, the small, linear E_Z from non-magnetic nanocrystals is also shown (black trace). Effective exciton g-factors derived from the low-field Zeeman splitting, g_eff, along with g_eff from all other nanocrystal series, are plotted in Fig. 3b versus the absorption energy. With increasing h, g_eff is tuned from -200 to +30.

Figure 3: Field-dependent Zeeman splitting of the 1S absorption peak, E_Z, and corresponding effective exciton g-factors at T=1.6 K.

a, The measured E_Z for one series of Mn²⁺-doped ZnSe–CdSe nanocrystals having different CdSe shell thickness h ranging from h<1 Å (red) to h8 Å (purple). The black symbols show E_Z for non-magnetic 'reference' core–shell nanocrystals. b, Effective exciton g-factors, g_eff, derived from the low-field Zeeman splitting at 1.6 K, plotted as a function of the 1S absorption edge energy. Also shown are g_eff from the non-magnetic 'reference' core–shell nanocrystals (black symbols). g_eff inverts when h2 Å.

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Although elegant experiments in DMS quantum wells have shown that the net sp–d interaction's magnitude is tunable through wavefunction engineering²², to our knowledge its sign has never been shown to invert, which is unexpected in the traditional framework of sp–d exchange (discussed below) and which points to new physics in these core–shell nanocrystal materials. In the following, we show that the inversion of E_Z can arise, in part, from the strong 'zero-dimensional' quantum confinement realized in nanocrystals, which exceeds that typically found in two-dimensional heterostructures, and which can invert the sign of , the electron–Mn²⁺ exchange parameter.

Although a single Mn²⁺ spin interacting with a single exciton will generate—even in zero field—a measurable E_Z in a single quantum dot^{10, 12}, our colloidal nanocrystal cores each contain 2 Mn²⁺ spins on average, in which the overlap-weighted average magnetization determines E_Z in any given nanocrystal. Furthermore, we study ensembles of nanocrystals. The Mn²⁺ in the ZnSe cores are positioned randomly, and the number of Mn²⁺ per core fluctuates statistically, enabling us to discuss sp–d exchange interactions in these nanocrystal ensembles in terms of a pseudo-bulk model. Here, spin splittings of the conduction and valence band edges in the nanocrystals have two contributions: (1) a small splitting from the 'intrinsic' electron and hole g-factors in the host semiconductor, g_e,h (of order unity in CdSe and ZnSe), and (2) a potentially much larger splitting from the s–d (p–d) exchange interaction between the s_e=1/2, s-like electrons (j_h=3/2, p-like holes) and the S=5/2 d-shell moments of the Mn²⁺. The s–d and p–d character of the electron–Mn²⁺ and hole–Mn²⁺ interaction are characterized by the exchange energies N₀ and N₀, respectively, where N₀ is the density of unit cells. In bulk II–VI DMSs (refs 3,23), N₀ arises from potential (ferromagnetic) s–d exchange and is positive, whereas N₀ derives predominantly from kinetic-type (antiferromagnetic) p–d exchange and is larger and negative. In bulk Zn_1-xMn_xSe (Cd_1-xMn_xSe), N₀=+0.29 eV (+0.23 eV) and N₀=-1.4 eV (-1.27 eV (ref. 23)).

In analogy with bulk DMS materials^{3, 23}, s–d and p–d exchange in our core–shell nanocrystals generates a spin splitting between the s_z=1/2 electrons and the j_z=3/2 holes equal to f_eN₀S_z and f_hN₀S_z, respectively. In our nanocrystals, f_e and f_h characterize the degree of spatial overlap between the Mn²⁺ ions in the core and the modulus-square of the wavefunctions _e(r) and _h(r) (in bulk DMSs, f_e and f_h simply equal the average percentage of Mn²⁺ cations). In an ensemble of nanocrystals, f_e and f_h can therefore be regarded as the average probability that the electron and hole reside in the core, multiplied by the average percentage of Mn²⁺ cations per core. The last quantity, S_z, is the average spin projection per Mn²⁺ along H. For low Mn²⁺ doping, S_z follows a Brillouin function, which describes the magnetization of paramagnetic Mn²⁺ moments; that is, S_zsaturates at low temperatures and high magnetic fields. By convention S_z is negative, being oriented antiparallel to H.

In colloidal II–VI nanocrystals, experiments and theory have established²⁴ that band-edge, 1S excitons (nominally composed of twofold degenerate s_e=1/2 electrons and fourfold degenerate j_h=3/2 holes) are split by the effects of strong electron–hole exchange, crystal field and shape asymmetry into five distinct levels labelled by F, the total angular momentum projection on the nanocrystal symmetry axis: F=2, 1^L, 0^L, 1^U and 0^U, where 'U/L' denotes upper/lower manifold levels. Figure 4a shows the ordering of these levels in nearly spherical nanocrystals. Exciton photoluminescence originates primarily from the lower optically active state (1^L), whereas the band-edge absorption peak derives from the upper 1^U transition, which has much larger oscillator strength. The energy separating the 1^L,U states gives the large 'global' Stokes shift typically observed in nanocrystals (see Fig. 1). Both 1^U and 1^L excitons are twofold degenerate with respect to total angular momentum (F=1^L,U). Thus, the MCD originates in the Zeeman spin splitting of the absorbing 1^U states, which couple to photons respectively.

Figure 4: Energy level diagrams illustrating the Zeeman splitting at the nanocrystal absorption edge, in both an exciton and an electron–hole picture.

a, The five exciton levels of the 1S band-edge exciton in nanocrystals. The 1^L and 1^U exciton states are primarily responsible for photoluminescence and absorption, respectively, and their separation gives the 'global' Stokes shift. MCD derives from the Zeeman splitting of the absorbing 1^U states. According to the experimental data, the order of the +1^U and -1^U states changes on introduction of Mn²⁺ ions into nanocrystals with thin shells, but remains unchanged for the case of nanocrystals with thick shells. In both cases, however, the Zeeman splitting in doped nanocrystals greatly exceeds that in undoped nanocrystals. b, Representation of the Zeeman splitting of the 1^U excitonic state in terms of the individual splittings of the s_z=1/2 electron and j_z=3/2 hole states that comprise the 1^U exciton, for the case of (i) non-magnetic nanocrystals, (ii) Mn²⁺-doped nanocrystals with thin CdSe shells and (iii) Mn²⁺-doped nanocrystals with thick CdSe shells. Independent of shell thickness, introduction of Mn²⁺ ions into nanocrystals changes the order of the +1/2 and -1/2 electron states, assuming that the sign of is inverted in nanocrystals compared with the bulk. For thin shells, however, the 'excitonic' exchange is still dominated by hole–Mn²⁺ interactions; therefore, the resulting Zeeman splitting observed in MCD is qualitatively similar to that in bulk DMS materials. Alternatively, for thick shells the strength of the Mn²⁺–hole interaction is decreased because holes become primarily shell-localized. As a result, the measured excitonic splitting is dominated by the 'sign-inverted' electron–Mn²⁺ interaction. c, A diagram showing the relative energies of quantum-confined electron and hole levels in the nanocrystal (E_e and E_h) and the occupied and unoccupied Mn 3d levels (⁺ and ^-). Red arrows show the virtual transitions that enter into calculations of the confinement-induced contribution of kinetic exchange to (described in the text).

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In our ZnSe cores, the 1^U transition is composed largely (75%) of transitions from j_z=3/2 hole states, with a small (25%) admixture from j_z=1/2 hole transitions²⁴. Neglecting the latter contribution and using the standard selection rules for the absorption of circularly polarized light, we can express E_Z measured in these nanocrystal ensembles as:

which is very similar to that in conventional DMS materials. Note that in bulk DMSs, where >0 and , the small 'intrinsic' contribution to E_Z (first term; of order +0.1 meV T^-1 in ZnSe) is typically overwhelmed by the large and negative sp–d contribution, which can exceed -100 meV at low temperatures and a few tesla.

Equation (1) provides a good description of the average E_Z in these ensembles of Mn²⁺-doped nanocrystals, and hence the observed inversion of E_Z for h>2 Å indicates a sign reversal of the average exchange term, (f_e-f_h). Clearly, simply modifying the overlap integrals f_e,h by wavefunction engineering cannot invert this quantity if and retain the same sign as in the bulk (positive and negative, respectively). Rather, the sign of or in these nanocrystals must be different than in the bulk. Such a possibility is indeed expected on the basis of recent experiments in DMS quantum wells^{25, 26, 27} and by theory^{26, 28}, which established that changes with quantum confinement and may even invert (become negative) in strongly confined II–VI quantum dots (although this has never yet been observed). This effect results from an admixture of p-type valence band states into the electron's Bloch wavefunction, causing a negative kinetic-exchange contribution to that increases with confinement energy ( remains largely unaffected, being already dominated by kinetic exchange).

Following the work of Merkulov et al.²⁶, in quantum-confined systems can be approximated as =_bulk+|C_v|²(E)_bulk, where the coefficient |C_v|²E_e/E_g describes the valence-band contribution to the electron's Bloch wavefunction, which scales as the ratio of the electron confinement energy, E_e, to the bulk bandgap E_g. The kinetic-exchange parameter (E) is calculated in second-order perturbation theory and depends strongly (resonantly) on the proximity of the confined electron and hole energies (E_e, E_h) to the occupied and unoccupied levels of the Mn²⁺ 3d electrons (⁺, ^-): (E)=(E_h-⁺)(^--E_h)/(E_e-⁺)(^--E_e) (see Fig. 4c). Strong confinement in ZnSe nanocrystals influences (E) primarily through the resonant (^--E_e)^-1 term, because E_e shifts much closer to ^- than in the bulk. Using literature values²⁹ (⁺ is 3.5 eV below the valence band edge and ^- is 3.5–4.0 eV above it), we estimate that inverts sign (becomes negative) when E_e>200–300 meV. In our 17-Å-radius ZnSe cores, the 1S absorption edge blueshifts by 400 meV with respect to bulk ZnSe (see Fig. 1), indicating that N₀ is probably negative and of order -0.2 eV.

However, without a significant disparity between the carrier–Mn²⁺ overlap integrals f_e,h, a small negative value of alone will not invert E_Z. In nanocrystals with thin CdSe shells, _e(r) and _h(r) reside primarily in the core, so that f_ef_h and E_Z remains dominated by the large hole–Mn²⁺ coupling and is negative, as experimentally observed (Fig. 2c). Inverting E_z requires a marked and preferential reduction of hole–Mn²⁺ overlap, such that f_hf_e. Precisely this situation occurs in nanocrystals with thicker CdSe shells (h>2 Å), where _h(r) migrates to the non-magnetic shell more rapidly than _e(r) (see Fig. 1), effectively 'turning off ' the hole–Mn²⁺ coupling. Although not expected to occur in a model of S-like envelope wavefunctions alone⁷, this disparity between f_e and f_h arises because, unlike _e(r), _h(r) has both S- and D-like spatial symmetry²⁴ (its radial wavefunction has both j₀ and j₂ spherical Bessel components; the latter vanishes at the nanocrystal centre and concentrates near the nanocrystal surface even in core-only nanocrystals). The relative contribution from j₂ increases with h because thicker shells favour localization of holes with D-type symmetry. Thus, f_h rapidly decreases to zero with increasing shell thickness, suppressing p–d exchange and inverting the sp–d exchange, N₀(f_e-f_h), as experimentally measured. Figure 4a,b explicitly illustrates how the relevant energy levels evolve with increasing h, in both an exciton (1^U) and in a separate electron–hole (s_e, j_h) picture (see figure caption for details). As demonstrated here, the extremely strong 'zero-dimensional' quantum confinement afforded in heterostructured nanocrystals leads to new regimes of tunable carrier–Mn²⁺ spin exchange in these materials, and future measurements are aimed at resolving, separately, the electron and hole exchange parameters.

Acknowledgements

We thank B. Prall for technical assistance. This work was supported by Los Alamos LDRD Funds and the Chemical Sciences, Biosciences, and Geosciences Division of the Office of Basic Energy Sciences, Office of Science, US Department of Energy (DOE). D.A.B. and V.I.K. are partially supported by the DOE Center for Integrated Nanotechnologies jointly operated by Los Alamos and Sandia National Laboratories. A.L.E. acknowledges financial support from ONR.

Received 19 June 2008; Accepted 12 November 2008; Published online 14 December 2008.

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