Interplay of Conventional and Spin-Exchange Auger Recombination in Magnetically Doped Quantum Dots

Abstract

Auger recombination strongly influences the photophysics of colloidal quantum dots (QDs), limiting light-emission efficiency while enabling the generation and manipulation of hot carriers via Auger up-conversion. Recent work has shown that incorporating magnetic manganese (Mn) dopants accelerates multiexciton Auger decay by two to three orders of magnitudedown to subpicosecond time scalesyet the underlying mechanism has remained unclear. Here, we demonstrate that ultrafast Auger recombination arises only from hybrid multiexciton states comprising intrinsic QD excitons coupled to Mn-based excitations. In this regime, the Auger rates exhibit no QD-size dependence and are governed solely by QD exciton occupancy, with no appreciable dependence on the number of excited Mn ions. These observations are inconsistent with a conventional Auger recombination scenario but can be rationalized by a spin-exchange (SE) mechanism involving two concerted spin-transfer events coupled through a virtual intermediate state. In this framework, the process effectively preselects a single excited Mn ion, while all others remain inactive. Unlike conventional Auger recombination, where the hot-carrier spin is not well-defined, the SE-mediated process generates carriers with well-defined spin polarization linked to the spin state of the participating Mn ion. These findings establish spin-exchange Auger recombination as an exceptionally fast energy-transfer pathway, outpacing both conventional Auger decay and phonon-assisted cooling. By enabling efficient generation and control of hot carriers, SE-mediated Auger recombination has important implications for photoconversion and photochemistry.

Introduction

Auger recombination is a nonradiative process in which an electron recombines with a hole by transferring energy to a third (acceptor) charge carrier. , Due to the relaxation of the translational momentum conservation, Auger decay rates are greatly increased in zero-dimensional colloidal quantum dots (QDs) compared to bulk semiconductors. , Moreover, in the case of QDs, the Auger lifetimes are insensitive to the semiconductor bandgap or other details of the electronic structure and exhibit a surprisingly universal material-independent scaling with the QD volume, , varying from a few picoseconds for small QDs (∼1 nm radius) to ∼300 ps for large particles (∼4 nm radius).

Since Auger lifetimes are much shorter than the radiative time constants (typically, a few to tens of nanoseconds in II–VI and III–V QDs), Auger recombination is detrimental to applications requiring high emissivity of QDs, including light-emitting diodes , and especially lasers, , since biexcitons are typically the primary optical-gain species in such devices. To impede Auger decay in QDs and thus reduce its negative impact on light-emitting devices, strategies such as controlling Auger interactions through proper heterostructuring − and introducing compositional gradients have been developed.

On the other hand, there are promising applications of QDs that could benefit from high Auger recombination rates. Auger decay can be viewed as an up-conversion process in which an electron (or hole) is excited to a higher energy state by the transfer of energy from a recombining electron–hole pair. This process can facilitate photochemical reactions by harnessing the kinetic energy of unrelaxed hot carriers. , It can also be exploited for photoemission (PE) if an electron excited by Auger energy transfer is ejected from a QD. However, this usually requires at least two Auger excitation steps, as the electron affinity of a material (E _a, the energy difference between the band-edge electron state and the vacuum level) is typically greater than the bandgap, which determines the energy transferred to the acceptor electron during Auger recombination. Because of this, the Auger contribution to PE is usually weak. Indeed, although enhanced by quantum confinement, the rate of Auger energy transfer is still slower than the rate of energy loss due to phonon emission. Therefore, a hot electron created by the first Auger excitation step loses its energy via phonon emission before the second Auger energy-transfer step occurs.

Recent studies have shown that the rate of Auger upconversion is dramatically enhanced upon the incorporation of manganese (Mn) impurities into QDs. − This enhancement has enabled, for example, highly efficient PE via the direct ejection of a hot, unrelaxed electron from the QD, as well as via successive energy transfers from two excited Mn ions to a near-band-edge electron. Enhanced Auger upconversion in Mn-doped QDs has also been exploited to accelerate hot-electron-driven chemical reactions.

Despite this considerable practical utility for manipulating hot carriers on ultrafast (subpicosecond) time scales, the microscopic mechanism of Auger recombination in Mn-doped QDs remains poorly understood. The conventional picture invokes energy transfer from an excited Mn ion (Mn*)undergoing internal spin-flip relaxationto the intrinsic QD exciton, promoting it to a higher-energy “hot” state (Figure a).

1.

Schematic illustration of two Auger recombination scenarios in Mn-doped QDs. (a) Conventional energy-transfer mechanism of Auger recombination in Mn-doped QDs, depicted as an “excitonic” process. In this scenario, the energy of the internal spin-flip transition of an excited Mn ion (Mn*) is transferred to a band-edge electron or hole of a “cold” QD exciton (X), promoting it to a higher-energy “hot” exciton (X*). (b) Cross-relaxation via the spin-exchange (SE) mechanism. In this SE scenario, Auger recombination proceeds via two parallel pathways. In the s-d-exchange-driven pathway (left), a spin-down electron is transferred from Mn* (⁴T₁ state) to an excited QD conduction-band (CB) state, while a spin-up electron from the QD band-edge CB level is transferred back to the Mn ion, restoring its ⁶A₁ ground configuration. In contrast to conventional (spin-insensitive) energy-transfer mechanisms, the SE process generates a hot carrier with a well-defined spin polarization, opposite to that of the 3d electrons of the de-excited Mn ion. Furthermore, the SE process can be viewed as involving a short-lived virtual configuration that leads to preselection of a single Mn ion mediating the recombination, with other dopants acting as spectators. In the p-d-exchange-driven pathway (right), a preexisting spin-up electron from the QD valence band (VB) is transferred to the Mn ion, followed by the transfer of a spin-down electron from the Mn ion to the QD band-edge VB state. The first pathway generates a hot electron in the QD, whereas the second produces a hot hole. These two pathways are referred to as the CB and VB pathways, respectively.

An alternative scenario involves cross-relaxation mediated by spin-selective electron exchange between the QD and an excited Mn ion ,, (Figure b). In this spin-exchange (SE) mechanismdriven not by direct Coulomb coupling but by the sp-d exchange component of the Coulomb interaction − Auger recombination is mediated by two concerted spin-transfer events.

In the s-d-exchange-driven pathway, a spin-down electron is transferred from the Mn 3d shell in its excited (⁴T₁) state to a higher-energy QD conduction-band (CB) state, while a spin-up electron from the QD band-edge CB state is simultaneously transferred to the Mn ion, restoring its ⁶A₁ (“spin-up”) ground-state configuration (Figure b, left).

Alternatively, the SE–Auger process can proceed through a p-d-exchange-driven pathway, in which a preexisting spin-up electron from a lower-energy QD valence-band (VB) state is captured by the Mn ion, while a spin-down 3d electron is transferred to the QD band-edge VB state to fill the hole (Figure b, right). The first pathway generates a hot electron, whereas the second generates a hot hole in the QD. In what follows, we refer to these two SE–Auger channels as the CB and VB pathways, respectively.

While the energy-transfer and SE scenarios of Auger recombination are similar from the standpoint of energy conservationsince in both cases, the hot electron (or hot hole) acquires energy equal to the Mn spin-flip transition energy (E _Mn)they differ significantly in their spin-related aspects. In the energy-transfer mechanism, the spin state of the generated hot carrier is not well-defined. In contrast, in the SE-mediated process, the hot electron exhibits a well-defined spin polarization, oriented opposite to that of the 3d electron spin of the de-excited Mn ion at the completion of the Auger process (Figure b, left). Similarly, in the p-d-exchange-driven pathway, the hot-hole spin state is also well-defined with respect to the spin polarization of the Mn ion (Figure b, right).

Another important distinction of the SE pathway is that it can be viewed as involving a short-lived virtual configuration that effectively preselects a single excited Mn ion, while other excited dopants remain passive spectators. As discussed later in this work, this preselection plays a crucial role, making the SE–Auger rate largely insensitive to the total number of excited Mn ions.

Here, we investigate Auger recombination in size-tuned Mn-doped QDs to clarify its underlying mechanism and its potential dependence on QD size. We consider three regimes defined by the relation between the QD size-dependent band-edge exciton energy (E _X) and the Mn spin-flip energy: “resonant” (E _X ≈ E _Mn), “downhill” (E _X > E _Mn), and “uphill” (E _X < E _Mn).

Our measurements reveal two distinct recombination channels: a slower process on the tens-to-hundreds-of-picoseconds time scale, characteristic of conventional Auger recombination, and a much faster subpicosecond process. The ultrafast channel dominates in the resonant and downhill regimes, where multiexcitons form hybrid states composed of intrinsic and Mn-based excitations. In the uphill regime, subpicosecond Auger recombination emerges only at high excitation levels, when the band-edge 1S state becomes fully occupied and additional carriers populate higher-lying states with sufficient energy to excite the Mn* state. Under these conditions, a rapid initial decay due to the SE process is followed by slower conventional Auger recombination that governs the later time dynamics.

Importantly, the rate of the subpicosecond Auger process shows no appreciable size dependence and is independent of the number of excited Mn ions; instead, it is governed solely by the occupancy of intrinsic QD excitonic states. These features are inconsistent with a conventional energy-transfer Auger mechanism (Figure a) but are naturally explained within the SE-driven cross-relaxation framework (Figure b). In particular, the observed scaling of SE–Auger lifetimes with excitation number can be accounted for by the “preselection principle”, whereas the absence of size dependence in the subpicosecond rates reflects the short-range nature of the exchange Coulomb interactions underlying the SE process.

Results and Discussion

Quantum Dot Samples

For these studies, we synthesized four Mn-doped CdSe/CdS QD samples with mean CdSe core radii (r) ranging from 1.25 to 2.5 nm along with four similarly sized undoped reference samples. In all cases, the CdS shell thickness was approximately one semiconductor monolayer (see Figure a for a schematic representation of the QDs and Figure b for their transmission electron microscopy images). Beyond its protective role, the CdS shell passivates nonradiative surface sites, leading to an improved emission efficiency. Notably, although the photoluminescence (PL) is fully quenched immediately after the doping procedure, it recovers upon the CdS shell deposition. The resulting PL quantum yields range from 30% to 60% and show no systematic dependence on QD size.

2.

Optical spectra and structural and magnetic properties of undoped and Mn-doped QDs. (a) Schematic representation of a QD, consisting of a size-controlled CdSe core (red sphere), doped with Mn ions (yellow dots), and enclosed within a thin protective CdS shell (blue layer). The CdSe core radius (r) ranges from 1.25 to 2.5 nm, and the CdS shell thickness (h) is approximately one semiconductor monolayer. (b) Representative transmission electron microscopy (TEM) image of Mn-doped QDs with a core radius r = 2.5 nm. Inset: an enlarged image on an individual QD revealing the underlying crystal lattice. (c) Photoluminescence (left) and absorption (right) spectra of the samples studied in this work. Dashed and solid lines correspond to undoped and Mn-doped samples, respectively. The spectra of QDs of different sizes have been vertically shifted for clarity. The same color and style scheme for distinguishing between different samples is used throughout all figures in this work. A vertical orange stripe schematically represents a broadened Mn-ion spin-flip transition, with its center (E _Mn = 2.1 eV) indicated by a dashed orange line. (d) Representative magnetic field (H) dependence of magnetic circular dichroism (MCD) spectra of Mn-doped QDs with r = 1.75 nm (resonant QDs), measured at a temperature of T = 3.5 K with H varied from 0 to 6 T in 1 T steps (see Materials and Methods for details of the MCD measurements). (e) Zeeman splitting of the band-edge 1S QD transition, inferred from the measured MCD spectra, as a function of H, for sample temperatures from 3.5 to 40 K. Based on these data, the internal content of MCD-active Mn ions is determined to be 2.05%, corresponding to an average of 8.3 dopants per QD.

For both doped and undoped samples, PL is dominated by radiative recombination of intrinsic electron–hole pairs (excitons) (Figure c, left). The corresponding exciton energy can be inferred from the peak of the PL band, and for the QD sizes studied here, it varies from below (r = 2.5 nm) to above (r = 1.25 nm) the energy of the Mn spin-flip transition, E _Mn = 2.1 eV (Figure c, left). As shown previously, the energy difference Δ_X‑Mn = E _X – E _Mn governs the rate of energy exchange between intrinsic exciton- and Mn-based states, and their relative occupancies.

Optical absorption spectra of undoped samples show a sharp band-edge 1S peak, which shifts to higher energies with decreasing QD size (Figure c, right), following the same trend observed for the PL band. Upon Mn incorporation, both the 1S absorption peak and the PL band broadena typical consequence of diffusion-based doping, which increases size polydispersity. , In our samples, the size dispersion of the undoped (reference) QDs is ∼10–11%, increasing to ∼12–14% in the Mn-doped samples.

To prepare Mn-doped samples, we used a diffusion doping procedure introduced in refs , and later refined in ref (see Materials and Methods for synthesis details). In this method, Mn is initially incorporated into the QD surface layer as MnSe, after which Mn ions diffuse into the QD interior. As established in prior studies of Mn-doped bulk and QD forms of CdSe, the near-perfect chemical and structural compatibility between Mn²⁺ and the CdSe lattice leads to Mn incorporation almost exclusively as an isovalent substitutional dopant replacing Cd²⁺ ions. ,, According to elemental analysis using inductively coupled plasma optical emission spectroscopy (ICP-OES), the Mn content reaches 15–30%. This analytical technique detects both internally and surface-incorporated Mn ions. However, the latter exhibits only weak exchange coupling to QD electronic states, since the wave functions of the QD band-edge states decay rapidly toward the QD periphery.

To determine the content of internal Mn ions, which are strongly coupled to the intrinsic states of the QDs, we perform magnetic circular dichroism (MCD) measurements (see Materials and Methods for details). This technique probes the magnetic-field-induced difference in optical transmission between left- and right-circularly polarized light. Based on the MCD data (Figures d,e and S1–S4), the Mn content in the synthesized samples ranges from 1.7% to 2.9%, corresponding to an average of 2.5–16.3 internal Mn ions per QD (Table S1). As expected, these values are lower than those obtained from ICP-OES measurements. Importantly, however, even for the lowest Mn content estimated via MCD, the number of internal Mn ions is more than onesufficient to produce a pronounced effect of Mn-QD exchange interactions on carrier dynamics.

The structural, spectroscopic, and magnetic characteristics of all undoped and Mn-doped QD samples are summarized in Tables S1 and S2.

Multiexciton Recombination in Mn-Doped and Undoped QDs

We begin our analysis of multiexciton recombination with a QD sample of radius r = 1.75 nm, for which the band-edge excitonic transition E _X = 2.1 eV is resonant with the internal Mn spin-flip transition (see optical spectra in Figure c, second data set from the bottom). To monitor QD population dynamics, we use a transient absorption (TA) pump–probe technique, in which changes in the optical absorption coefficient (Δα) induced by a short 150 fs pump pulse are tracked as a function of time using a variably delayed broadband probe pulse of a femtosecond white-light continuum.

For all measurements, the pump photon energy was 2.41 eV. The QD samples were prepared as hexane solutions, loaded into 1 mm path length optical cells, and vigorously stirred throughout the measurements to prevent sample degradation and eliminate TA artifacts caused by uncontrolled photocharging. , All TA measurements were conducted at room temperature (see Materials and Methods for experimental details).

Figure compares the TA measurements of Mn-doped and undoped resonant samples. In Figure a, we show the pump-fluence-dependent TA dynamics of the Mn-doped QDs, recorded at the position of the lowest-energy 1S TA feature (see Figure S5). As established previously, this feature is dominated by state-filling-induced bleaching of the band-edge 1S_e electron state. , The hole contribution to the 1S TA signal is small because the band-edge absorption peak is associated with a higher-energy VB state (1S_h,U) that remains largely unoccupied under typical excitation conditions (hole energy increases downward from the top of the VB). Instead, photoexcited holes rapidly relax to the lower-energy VB state (1S_h,L) that is only weakly coupled to the 1S_e electron level. The corresponding optical transition (1S_e–1S_h,L) is responsible for emission and optical gain but does not contribute significantly to the band-edge absorption peak or to the 1S bleach in TA spectra. Both features are dominated by the higher-energy absorbing transition (1S_e–1S_h,U).

3.

Auger recombination in Mn-doped and undoped (reference) QDs in the resonant case. (a) Tail-normalized, pump-fluence-dependent 1S bleach dynamics obtained for Mn-doped resonant QDs with r = 1.75 nm, for which E _X ≈ E _Mn and hence Δ_X‑Mn ≈ 0 (bottom inset: schematic of Auger recombination occurring as a cross-relaxation SE process). The data are shown as −Δα_1S (pump-induced change in the 1S absorption coefficient) versus Δt (pump–probe time delay). Measurements were performed at progressively increasing pump fluences, with ⟨N⟩ varied from ∼0.02 to ∼21 (higher ⟨N⟩ corresponds to lighter-colored TA traces). Top-right inset: Ratio of zero-delay (A) to long-delay (B) bleaching amplitude, plotted as a function of ⟨N⟩, indicating the onset of Auger recombination at ⟨N⟩ ≈ 1. (b) A TA component arising solely from the ultrafast Auger process is obtained by subtracting the tail-normalized single-exciton dynamics, recorded at ⟨N⟩ ≪ 1, from the TA traces measured for ⟨N⟩ > 1 (the resulting quantities are denoted Δα_1S,diff). Inset: The time constant of ultrafast Auger recombination (τ_A,Mn) varies from ∼1 ps to ∼230 fs with increasing ⟨N⟩. (c) TA measurements of Auger recombination in undoped resonant QDs with r = 1.75 nm (reference sample). This panel uses the same representation of the TA data as for the Mn-doped sample in panel “a” with one notable distinctiondue to the much slower Auger recombination (∼90 ps time constant), a much longer time window is used (400 ps versus 12 ps in panel “a”). Bottom inset: Schematic of conventional Auger recombination. Top-right inset: Plot of the A/B ratio versus ⟨N⟩ indicates the onset of conventional Auger decay at ⟨N⟩ ≈ 1, similar to ultrafast Auger recombination in Mn-doped QDs.

Thermal broadening further distributes the hole population across a dense manifold of VB states, reducing the occupancy of the specific hole level involved in the absorbing transition. Consequently, the amplitude of the 1S TA signal (Δα_1S) provides a direct measure of the average per-dot occupancy of the band-edge electron state (1S_e), while the dynamics of Δα_1S track the temporal evolution of the 1S_e population. A detailed description of the VB structure and the notation used here can be found in ref .

For the data shown in Figure a, the per-pulse pump fluence (w _p) ranged from 0.9 to 945 μJ cm^–2, corresponding to average excitation levels of ⟨N⟩ = 0.02 to 21 excitations per QD. These values were calculated using ⟨N⟩ = (w _pσ_abs/hν _p), where hν _p = 2.41 eV is the pump photon energy and σ_abs = 9.1 × 10^–15 cm² is the QD absorption cross-section at that energy (see Materials and Methods for the experimental determination of σ_abs).

At low pump levels, corresponding to subsingle-exciton QD occupancies (⟨N⟩ ≪ 1), the TA traces show no noticeable decay over the 12 ps time window shown in Figure a. However, as ⟨N⟩ approaches and then exceeds 1, the TA dynamics develop a fast early time subpicosecond decay component, which emerges exactly at ⟨N⟩ of ∼1. The onset of this feature is reflected in the pump-fluence dependence of the ratio between the early time TA amplitude (A) and the slower single-exciton background (B) (Figure a, main panel and inset). The emergence of this fast signal therefore coincides with the regime in which more than one exciton is injected into the QD, leading us to conclude that the short-lived TA component originates from recombination mediated by carrier–carrier interactions in a multiexciton statea process typically referred to as Auger recombination.

To determine the Auger decay time constant (τ_A,Mn), we isolate multiexciton dynamics by subtracting the slow single-exciton background from the time transients measured at ⟨N⟩ > 1 (Figure b). The resulting traces are then fitted to a single-exponential decay convoluted with a Gaussian function representing the 150 fs-wide instrument response function of our TA setup. Using this approach, τ_A,Mn is found to be ∼1 ps for ⟨N⟩ of ∼2, and it gradually decreases to 230 fs at ⟨N⟩ = 21 (Figure b, inset).

The extracted time constants are in good agreement with those reported in a previous study of Auger recombination in Mn-doped QDs with nearly resonant E _X and E _Mn energies. In particular, that work yielded decay times ranging from ∼1 ps to 200–300 fs over a similar range of excitation levels. Importantly, this agreement is observed despite a substantial difference in the average number of Mn dopantsapproximately 13 in ref and ∼8 in the present work. This suggests a weak, or possibly negligible, dependence of τ_A,Mn on the number of incorporated Mn ions. The relationship between τ_A,Mn and the numbers of Mn ions (excited and unexcited) is discussed in more detail later in this work.

It is instructive to compare Auger dynamics in Mn-doped QDs with those in an undoped reference sample. In the latter case (Figures c and S6), Auger recombination also appears as a fast component in the TA decay, emerging at ⟨N⟩ > 1 (Figure c, top-right inset). However, its time constant (τ_A) is ∼90 psapproximately 2 orders of magnitude longer than τ_A,Mn.

This stark contrast highlights a fundamental mechanistic difference between carrier–carrier interactions in undoped and Mn-doped QDs: direct Coulomb coupling in the former versus exchange-mediated Coulomb coupling in the latter. Beyond their spin sensitivity (discussed later in this work), a key distinction is the much greater strength of the exchange Coulomb interactionparticularly in Mn-doped II–VI diluted magnetic semiconductors (DMS), where it is commonly described by sp-d exchange (with d referring to the 3d Mn orbital, and s and p denoting the CB and VB orbitals of the host II–VI semiconductor, respectively). This enhancement arises from the short-range nature of sp-d exchangeSE-mediated transitions occur within the compact Mn 3d shell (effective diameter ∼ 0.15 nm)and from the near absence of dielectric screening for such highly localized interactions (effective dielectric constant ε ≈ 1).

Early studies of impact excitation of Mn-doped ZnS in electroluminescent devices and Auger quenching of PL in similar materials demonstrated that both impact and Auger rates exceeded predictions based on direct Coulomb coupling by at least 2 orders of magnitude, but were quantitatively explained by invoking short-range exchange interactions. , Additional evidence for the unusually large exchange coupling in Mn-doped II–VI DMS materials comes from extensive magneto-optical studies, which revealed phenomena such as giant Zeeman splitting of excitonic levels and the formation of strongly bound excitonic magnetic polarons. ,, More recently, exchange interactions have been invoked to account for efficient Auger quenching induced by electrochemical electron injection into Mn-doped CdS QDs and for Auger-driven PE observed in similar DMS nanocrystals.

We propose that the ultrafast, subpicosecond component of Auger recombination in Mn-doped QDs arises from a similar SE-mediated mechanism driven by short-range sp-d Coulomb exchange. In the context of QDs, this process was previously analyzed theoretically and has more recently been invoked to explain QD ionization via direct Auger excitation from a hot-electron state, as well as the highly efficient generation of solvated electrons through two-step Auger up-conversion from the CB-edge state.

Relative Occupancies of Intrinsic QD and Mn-Based States

To investigate the scaling of SE-driven Auger recombination rates with exciton multiplicity, we analyze the dependence of τ_A,Mn on the average occupancies of QD- and Mn-based states, ⟨N _X⟩ and ⟨N _Mn⟩, respectively (⟨N _X⟩ + ⟨N _Mn⟩ = ⟨N⟩). As shown previously, in the low pump-intensity (single-exciton) regime, the probabilities for an excitation to reside in intrinsic (f _X = ⟨N _X⟩/⟨N⟩) or Mn-based (f _Mn = ⟨N _Mn⟩/⟨N⟩) states are governed by the rates of forward (QD → Mn) and backward (Mn → QD) transfer (k _f and k _b, respectively). These probabilities are further linked to the energetic detuning between the QD exciton and the Mn spin-flip transition (Δ_X‑Mn) through the relation f _X/f _Mn = k _b/k _f = exp­(−Δ_X‑Mn/δ₀), where δ₀ is the characteristic energy.

In Figure a, we schematically illustrate this process using both spin-transfer (left) and energy-transfer (right) representations. The spin-transfer depiction employs individual electron and hole states to emphasize the spin-conservation aspect of QD–Mn excitation exchange. Importantly, it is not intended to represent the absolute energies of QD or Mn levels or their alignment. Instead, the energetics relevant to the process are captured by the energy-transfer representation, which highlights that the forward and backward rates are governed by the relative detuning between E _X and E _Mn, rather than by the absolute positions of the QD and Mn states (e.g., with respect to the vacuum level).

4.

Spin-exchange (SE) mechanism of bidirectional QD–Mn excitation transfer and experimental determination of excitation partitioning between intrinsic excitonic and Mn-based states. (a) Spin-transfer (left) and energy-transfer (right) representations of QD–Mn excitation exchange. In the spin-transfer picture (left), forward QD → Mn transfer (black arrows; rate k _f) proceeds via two concerted spin transfer events: a spin-up electron from the Mn 3d shell fills a photogenerated hole in the QD valence band (VB), while a spin-down electron from the QD conduction band (CB) simultaneously fills the resulting vacancy in the Mn 3d shell. The backward (Mn → QD) transfer (blue arrows; rate k _b) reverses these steps. The energy-transfer representation (right) omits spin details but highlights the energetic aspect of the process, in particular that the ratio of backward and forward rates is governed by the energy detuning Δ_X‑Mn: k _b/k _f = exp­(−Δ_X‑Mn/δ₀), where δ₀ is the characteristic energy. (b) Dependence of q _1S = |Δα_1S|/α_0,1S on the average excitation level ⟨N⟩ for resonant undoped (open squares; q _1S,ref) and Mn-doped (solid squares; q _1S,Mn) QDs with r = 1.75 nm (α_0,1S is the 1S ground-state absorption coefficient). The solid line shows the dependence of q _1S on ⟨N⟩ calculated assuming a Poisson distribution of QD excitonic occupancies. These measurements are used to determine how ⟨N⟩ is distributed between the intrinsic QD and Mn-based states (⟨N _X⟩ and ⟨N _Mn⟩, respectively). Specifically, ⟨N _X⟩ is determined through three projections: ⟨N⟩ → q _1S,Mn → q _1S,ref → ⟨N _X⟩ (as indicated by arrows). Subsequently, ⟨N _Mn⟩ is found using ⟨N _Mn⟩ = ⟨N⟩ – ⟨N _X⟩.

Under resonant conditions (Δ_X‑Mn= 0), f _X = f _Mn, meaning that a photogenerated excitation spends equal time in intrinsic excitonic and Mn-based states. When the QD exciton is tuned to higher energy (Δ_X‑Mn > 0), the probability of occupying the intrinsic exciton state decreases exponentially with increasing detuning, following exp­(−Δ_X‑Mn/δ₀). According to ref , δ₀ = 103 meV in this regime. We note that this characteristic energy substantially exceeds the thermal energy at room temperature (∼25 meV), suggesting that the fast QD–Mn branching observed here does not correspond to a fully thermalized equilibrium, but rather to a nonequilibrium quasi-steady distribution established on the ultrafast time scale of SE interactions. The opposite trend, that is, an increase in f _X, is expected when E _X is tuned below E _Mn (Δ_X‑Mn < 0); however, the corresponding characteristic energy has not yet been experimentally determined.

The above expression for the branching ratio was derived for the single-exciton regime, and it is not immediately clear whether it remains valid under the multiexciton conditions relevant to SE–Auger recombination. In particular, previous work suggests that the forward transfer rate is enhanced in the biexciton case compared to a single exciton.

Motivated by these considerations, we chose to determine the excitation partitioning experimentally. This approach allows us, first, to verify that the partitioning follows the expected trend in the single-exciton regime and, second, to directly establish the partitioning behavior under multiexciton conditions explored in the present study. To this end, we determine how the total number of injected excitations, ⟨N⟩, partitions between these two types of states by comparing the early time 1S bleach amplitudesmeasured as a function of ⟨N⟩for Mn-doped QDs and undoped reference samples.

In Figure b, the 1S bleach magnitude is expressed as the normalized quantity q _1S = |Δα_1S|/α_0,1S, where α_0,1S is the ground-state 1S absorption coefficient. As discussed earlier, the 1S bleach is dominated by electrons; therefore, q _1S is directly related to the average occupancy of the 1S_e electron state, ⟨N _e,1S⟩, such that q _1S ≈ ⟨N _e,1S⟩/2. Because the 1S_e level is 2-fold degenerate, its maximum occupancy is 2, yielding a maximum q _1S of 1.

To relate q _1S to the average number of photoinjected excitons per QD, we assume that the QD excitonic occupancy follows Poisson statistics, which is typical for short-pulse excitation above the band-edge transition. In this case, the probabilities of a QD being occupied by exactly one exciton (p ₁) or two or more excitons (p _≥2) are given by p ₁ = ⟨N⟩e ^–⟨N⟩ and p _≥2 = 1 – p ₀ – p ₁ = 1 – e ^– ⟨N⟩ (1 + ⟨N⟩). Taking into account that ⟨N _e,1S⟩ = p ₁ + 2p _≥2, we derive the following relationship between q _1S and ⟨N⟩: q _1S = 1 + e ^–⟨N⟩ (⟨N⟩/2 – 1).

As shown in Figure b, the experimental dependence of q _1S on ⟨N⟩ measured for the undoped QDs (open squares) closely follows the Poisson prediction (solid line). In contrast, the q _1S values measured for the Mn-doped sample (Figure b, solid squares) lie systematically below both the theoretical curve and the data from the reference sample. This deviation indicates a partial loss of population from QD intrinsic states due to fast excitation transfer to Mn ions.

To quantify the distribution of photoinjected excitons between intrinsic and Mn-based states, we use the experimental q _1S-versus-⟨N⟩ dependence from the reference sample (q _1S,ref) as a calibration curve to relate the 1S bleach magnitude of the doped sample (q _1S,Mn) to the number of excitations in the intrinsic QD states, ⟨N _X⟩. This procedure is illustrated graphically in Figure b using three projections: ⟨N⟩ → q _1S,Mn → q _1S,ref → ⟨N _X⟩. Specifically, using projection 1 (vertical, upward-pointing arrow), we obtain q _1S,Mn for a given value of ⟨N⟩. Then, using projection 2 (horizontal, left-pointing arrow), we determine the point on the q _1S,ref (⟨N⟩) curve for which q _1S,ref = q _1S,Mn(⟨N⟩). Finally, projecting this point onto the ⟨N⟩ axis (vertical, downward-pointing arrow), we determine ⟨N _X⟩ for the doped sample.

Once ⟨N _X⟩ is determined, the number of excited Mn ions is calculated as ⟨N _Mn⟩ = ⟨N⟩ – ⟨N _X⟩, as indicated by the horizontal double arrow in Figure b. We then compute the relative fractions of intrinsic (f _X) and Mn-based (f _Mn) excitations (Figure a,b).

5.

Modeling of Auger recombination rates in Mn-doped QDs and the preselection principle. (a) The dependence of ⟨N _X⟩ and ⟨N _Mn⟩ on ⟨N⟩ shows close agreement for ⟨N⟩ < 1 but divergence at ⟨N⟩ > 1. This divergence reflects the increasing population of biexciton states, which exhibit a higher QD → Mn forward transfer rate than single excitons (bottom-right and top-left insets, respectively). (b) The corresponding dependences of the relative fractions of intrinsic and Mn-based excitations (f _X and f _Mn, respectively) on ⟨N⟩ also diverge at ⟨N⟩ > 1. (c) Open diamonds represent Auger rates (k _A,Mn= 1/τ_A,Mn) determined from the measured time constants τ_A,Mn for Mn-doped resonant QDs (Figure b, inset). The experimental trend is compared to modeling assuming k _A,Mn ∝ ⟨N _X⟩⟨N _Mn⟩ (dashed black line) or k _A,Mn = k _A,Mn‑X[⟨N _X⟩ (γ – 1) + 2 – γ] (solid red line). Here, k _A,Mn‑X = 0.95 ps^–1 is the Auger decay rate of a hybrid biexciton XMn* (from measurements), and γ=k _A,Mn‑XX/k _A,Mn‑X is a fitting parameter, where k _A,Mn‑XX is the Auger rate of a hybrid triexciton (XXMn*). The fit (red line) gives γ = 4.2, corresponding to k _A,Mn‑XX = 4 ps^–1 and τ_A,Mn‑XX = 250 fs. (d) Schematic illustration of the s-d-exchange-driven SE–Auger pathway (CB pathway). The initial state (left) consists of a QD exciton with a spin-up CB electron and two excited Mn ions, each with a spin-down 3d electron. Within the SE framework, Auger recombination proceeds through a short-lived virtual configuration (middle) formed by the transfer of a spin-down 3d electron from one of the excited Mn ions to a higher-energy (hot) CB state of the QD. This interaction effectively preselects a single Mn ion that mediates SE–Auger recombination. The coupled exchange-driven transition (transfer of a spin-up QD CB electron to the Mn ion) restores the spin- and energy-conserving configuration of the coupled QD–Mn system (right).

In Figure a,b, we present the dependence of the derived values of ⟨N _X⟩ and ⟨N _Mn⟩ on ⟨N⟩ (panel a), along with the corresponding dependence of f _X and f _Mn on ⟨N⟩ (panel b). At ⟨N⟩ < 1, ⟨N _X⟩ is approximately equal to ⟨N _Mn⟩, and both increase linearly with ⟨N⟩. This indicates that the excitation has an equal probability of occupying either an intrinsic or Mn-based state (f _X ≈ f _Mn ≈ 0.5, Figure b), as expected for the resonant case , (see earlier discussion).

This behavior changes once ⟨N⟩ exceeds 1. At this point, ⟨N _X⟩ begins to saturate, approaching a value of 2 as ⟨N⟩ increases to 21, while ⟨N _Mn⟩ continues to grow nearly linearly (Figure a). A similar trend is observed in the plots of f _X and f _Mn versus ⟨N⟩ (Figure b): while nearly identical at low excitation levels, the values of f _X and f _Mn begin to diverge sharply beyond ⟨N⟩ = 1, indicating that an increasing fraction of photoinjected excitons are transferred to Mn ions.

These trends suggest that the ratio of forward to backward transfer rates (k _f/k _b) increases with ⟨N⟩, as more QDs become populated with biexcitons and higher-order multiexcitons. This behavior is expected for SE-type spin-conserving QD → Mn excitation transfer. ,, As discussed in ref , only one of the four possible spin configurations of a single exciton (specifically, a spin-1 “dark” exciton) is suitable for transfer to the Mn ion (Figure a, top-left inset). By contrast, a biexciton (XX) state always contains one such suitable configuration (Figure a, bottom-right inset), implying that the forward transfer rate for a biexciton is four times higher than that for a single exciton. At the same time, the backward transfer rate is reduced because the presence of a preexisting exciton lowers the probability of finding a spin-conserving configuration. Altogether, these considerations imply that the k _f/k _b ratio increases with biexciton population, resulting in enhanced accumulation of excitations in the Mn-based states.

Scaling of SE–Auger Rates with Exciton Multiplicity

Next, we examine the measured dependence of the SE–Auger recombination rate k _A,Mn = 1/τ_A,Mn on ⟨N⟩ (Figure c, open diamonds). In the conventional Auger picture (Figure a), k _A,Mn is expected to scale with the product ⟨N _X⟩⟨N _Mn⟩, since all excited Mn ions and all QD-based excitons are presumed equally likely to participate in the recombination process. However, applying this model yields a predicted dependence (dashed black line in Figure c) that significantly overestimates the growth of k _A,Mn with increasing ⟨N⟩. This discrepancy arises from the nearly linear increase of ⟨N _Mn⟩ with ⟨N⟩ once ⟨N⟩ > 1, which produces a much steeper theoretical trend than is observed experimentally.

Our analysis of branching between QD- and Mn-based excitations shows that the number of excited Mn ions increased from ∼1 to ∼18 when ⟨N _X⟩ varies from ∼2 to ∼20. Even if the number of Mn* ions interacting strongly with QD excitons is restricted to ∼8 (the number on centrally located Mn ions derived from MCD measurements; Table S1), this would still increase the SE–Auger rate by at least a factor of ∼8and likely more when considering the concurrent increase in QD occupancy. Experimentally, however, the rate increases by only a factor of ∼4. This clearly indicates that the conventional ⟨N _X⟩⟨N _Mn⟩ scaling does not capture the observed behavior.

Importantly, a similar trend was reported in previous studies of Auger recombination in Mn-doped QDs, suggesting that the discrepancy reflects a fundamental limitation of the conventional Auger description when applied to SE-mediated processes.

As a next step, we model the observed behavior by assuming that the SE–Auger rate depends only on the number of intrinsic QD excitations and is independent of the number of excited Mn ions. This assumption is partly motivated by the apparent insensitivity of the SE–Auger rates to the total number of incorporated Mn ions, as indicated by the agreement between our present results and those of ref .

Under our experimental conditions, the average exciton occupancy per QD does not exceed two (⟨N _X⟩ ≤ 2; Figure a). Thus, the only multiexciton states contributing to Auger recombination are XMn* (hybrid biexciton; N _X = 1, N _Mn = 1) and XXMn* (hybrid triexciton; N _X = 2, N _Mn = 1). Let the Auger decay rates of these states be denoted as k _A,Mn‑X and k _A,Mn‑XX, respectively, and assume that ⟨N _X⟩ lies between 1 and 2. Then, the total SE–Auger decay rate can be expressed as k _A,Mn = s _X k _A,Mn‑X + s _XX k _A,Mn‑XX, where s _X = 2 – ⟨N _X⟩ and s _XX = ⟨N _X⟩ – 1 represent the probabilities that the QD is occupied by one or two intrinsic excitons, respectively. If we express k _A,Mn‑XX as k _A,Mn‑XX = γk _A,Mn‑X, the total Auger decay rate becomes k _A,Mn = k _A,Mn‑X [⟨N _X⟩ (γ – 1) + 2 – γ]. Here, γ is a scaling factor accounting for the increased Auger rate with higher exciton multiplicity.

To analyze the experimental dependence of τ_A,Mn versus ⟨N⟩ (Figure c, open diamonds), we apply this model using k _A,Mn‑X = 0.95 ps^–1, corresponding to a lifetime τ_A,Mn‑X = 1.05 ps observed at the onset of SE-type Auger decay. Fitting the data with γ as an adjustable parameter yields good agreement between the calculations and the experiment for γ = 4.2 (Figure c, solid red line). Based on this analysis, the Auger lifetimes of the XMn* and XXMn* states are τ_A,Mn‑X = 1.05 ps and τ_A,Mn‑XX = τ_A,Mn‑X/γ = 250 fs, respectively.

Thus, across the full range of pump intensities studied, the SE–Auger dynamics are accurately captured using only two statesXMn* and XXMn*regardless of the total number of photoinjected excitations. This strongly supports our hypothesis that SE–Auger rates are independent of the number of Mn-based excitations and depend solely on the occupancy of intrinsic QD states (N _X).

For the regime explored in this study (N _X ≤ 2), the scaling of the SE–Auger rate with N can be approximated as k _Mn‑NX = (N _X)² k _Mn‑X. This relation accurately captures the cases of N _X = 1 (hybrid biexciton, XMn*), and N _X = 2 (hybrid triexciton, XXMn*). We anticipate that future studies of SE–Auger recombination will test the generality of this scaling and determine whether it extends to higher-multiplicity states.

SE–Auger Recombination Model

Previously, Auger recombination in small Mn-doped CdS QDs (1.2–1.8 nm) was analyzed within first-order perturbation theory using Fermi’s golden rule, incorporating the Coulomb exchange interaction term. These calculations predicted sub-ps time constants for internally located dopants in the case of a single QD exciton interacting with a single excited Mn ionvalues consistent with those observed here. However, extending this conventional framework to SE-mediated Auger recombination would imply that the rate scales with the number of excited Mn ions, in clear contradiction with our experimental observations.

One possible explanation is that only a single Mn ion strongly couples to the QD exciton and therefore dominates the recombination process. This scenario, however, is inconsistent with our MCD measurements, which indicate that ∼8 Mn ions exhibit comparably strong coupling to the intrinsic QD exciton. A similar conclusion follows from the close quantitative agreement between Auger lifetimes obtained in this work and those reported in ref , despite a substantial difference in dopant concentration (∼8 vs ∼13 Mn ions per QD). It is therefore highly unlikely that only one Mn ion is active in all cases.

An alternative approach is to invoke a “truncated” version of first-order perturbation theory, in which Fermi’s golden rule is applied to a single Mn ion while all others are neglected. Rather than imposing such truncation ad hoc, we propose a phenomenological model in which it emerges naturally via a preselection principle. In this picture, SE–Auger recombination proceeds through two concerted spin-transfer events that involve a short-lived virtual configuration, similar to the mechanism proposed for excitation transfer in Mn-doped bulk semiconductors. Importantly, this intermediate configuration is not populated, that is, it does not correspond to a real charge-transfer state. Instead, it represents a transient virtual state that facilitates the overall exchange-driven transition, with its primary role being to select a single excited Mn ion that mediates the SE process from initiation to completion.

The proposed mechanism is illustrated in Figure d for the CB-mediated SE–Auger pathway. For simplicity, we represent both QD carriers and Mn ions using single-electron spin states with projections σ_z = +1/2 (spin-up) and σ_z = −1/2 (spin-down). For the Mn ion, these spin projections correspond to its ground (⁶A₁) and excited (⁴T₁) configurations, respectively. While simplified, this model captures the essential physics of the process.

We consider an initial QD–Mn configuration containing two excited Mn ions (each with a spin-down 3d electron) and a single QD exciton with a spin-up CB electron at the band edge (Figure d, left). The hole spin is not specified here, as it plays no active role in the CB pathway.

The SE process can be viewed as proceeding through a short-lived virtual configuration in which a spin-down electron from one of the excited Mn ions (which becomes effectively preselected) is promoted to a higher-energy QD CB state elevated above the band edge by E _Mn (Figure d, middle), while a spin-up electron from the QD CB is transferred to the Mn 3d shell, completing the process.

The final state consists of a hot spin-down electron in the QD and a de-excited Mn ion (Figure d, right). The intermediate configuration is not energy-conserving and is not populated; rather, it represents a transient virtual state enabled by the uncertainty principle. Its primary role is to enforce preselection, rendering all other Mn ions as spectators.

Access to the virtual configuration is enhanced by the high density of available higher-energy QD states and by the presence of multiple excited Mn ions serving as potential donors. Consequently, the overall probability of the process is governed by constraints associated with the transition from the virtual to the final state, which depends on the limited spin configurations of the QD exciton and the involvement of a single preselected Mn ion. As a result, the SE–Auger rate is determined primarily by the number of QD excitons and remains largely insensitive to the number of excited Mn ions. Such a response is unusual from the standpoint of a fully equilibrated multistate system and instead points to ultrafast, nonequilibrium SE dynamics that effectively single out one Mn ion during the recombination event.

This behavior fundamentally distinguishes SE–Auger recombination (Figure b) from the conventional Auger mechanism (Figure a) and arises directly from the proposed preselection principle. While a rigorous theoretical treatment is still needed, this principle appears to be a general feature of SE-mediated processes and, in particular, helps rationalize the PL lifetimes observed for the resonant sample (E _X ≈ E _Mn) in the single-exciton regime (Figure S7).

In the conventional model, the exciton is expected to be delocalized over all Mn ions (n _Mn, their total number), leading to a reduced intrinsic exciton fraction, f _X = 1/(1 + n _Mn), and a correspondingly slower PL lifetime τ_PL = τ_X,0(1 + n _Mn), since the decay is dominated by the excitonic transition with intrinsic lifetime τ_X,0. The internal Mn spin-flip transition is extremely slow (∼1 ms lifetime) and therefore contributes negligibly to the overall population decay.

For our resonant sample with n _Mn ≈ 8, this model predicts τ_PL ≈ 9τ_X,0. Experimentally, however, we observe only a 2-fold increase in PL lifetime (48 ns vs 25 ns; Figure S7), i.e., τ_PL ≈ 2τ_X,0. A similar result (PL lifetime doubling) was reported in ref for samples with two different Mn contents (∼4 and ∼13 ions per QD). These findings indicate that the exciton effectively interacts with only a single Mn ion, rendering n _Mn ≈ 1.

Within the SE framework, this behavior is naturally explained by the same preselection mechanism (Figure a, left). Exciton–Mn energy transfer proceeds via two concerted spin-transfer events involving a short-lived virtual configuration formed when a spin-up 3d electron from the Mn ion is transferred to the QD VB to fill a photohole. The exchange-driven transition is completed when a spin-down electron from the QD CB fills the vacancy in the 3d shell of the Mn ion selected during the formation of the virtual configuration. Although these two events occur within a single exchange-driven process, the overall rate is primarily constrained by the transition from the virtual to the final state, analogous to SE–Auger recombination. As a result, despite the presence of multiple dopants, the exchange interaction at any given time predominantly involves a single Mn ion, leading to an effective two-state picture. Consequently, the transfer rateand thus the PL lifetimeis largely independent of the total number of Mn ions, consistent with experimental observations.

Auger Recombination in the Downhill Transfer Regime

The preselection principle also accounts for the Auger dynamics observed in wider bandgap QDs with a radius of r = 1.25 nm, where the exciton energy (E _X = 2.23 eV) exceeds the Mn spin-flip transition energy (E _Mn = 2.1 eV), corresponding to the downhill energy-transfer regime (Figure a, inset). Optical absorption and PL spectra of Mn-doped and undoped QDs of this size are shown in the bottom row of Figure c, with the corresponding TA spectra presented in Figures S5 and S8.

6.

Auger recombination in Mn-doped QDs in the downhill case. (a) Tail-normalized, pump-fluence-dependent 1S bleach dynamics of Mn-doped QDs with r = 1.25 nm, obtained for ⟨N _X⟩ from ∼0.01 to ∼12. For this sample, E _X > E _Mn and hence Δ_X‑Mn > 0 (inset). This alignment of QD and Mn electronic levels favors forward QD → Mn excitation transfer over the backward Mn → QD transfer (indicated by thick and thin arrows, respectively, in the inset), reducing the occupancy of intrinsic QD states (⟨N _X⟩) relative to Mn-based states (⟨N _Mn⟩). (b) This trend is apparent from measurements of the ⟨N⟩-dependence of q _1S = |Δα_1S|/α_0,1S, where q _1S values for the Mn-doped sample (solid squares) are considerably lower than those for the reference undoped sample (open squares). The line corresponds to a theoretical q _1S-versus-⟨N⟩ dependence assuming a Poisson distribution of QD excitonic occupancies. (c) ⟨N⟩-dependences of ⟨N _X⟩ and ⟨N _Mn⟩, calculated based on the data in panel “b”. (d) The corresponding ⟨N⟩-dependences of the relative fractions of excitations residing in intrinsic QD states (f _X) and Mn-based states (f _Mn). (e) ⟨N⟩-dependent Auger recombination dynamics, obtained from TA traces in panel “a” by subtracting tail-normalized dynamics measured at ⟨N⟩ ≪ 1. These dynamics are fitted to a single exponential decay (solid black lines), yielding a time constant of ∼1.2 ps, which is virtually independent of ⟨N⟩ (inset).

Analysis of the early time amplitude of the 1S bleach as a function of pump fluence for ⟨N⟩ values up to ∼12 (Figure a,b) shows that at low excitation levels (⟨N⟩ < 1), both ⟨N _X⟩ and ⟨N _Mn⟩ increase nearly linearly with ⟨N⟩. The corresponding fractional occupancies remain approximately constant (f _X ≈ 0.25, f _Mn ≈ 0.75; Figure c,d), yielding a ratio f _Mn/f _X ≈ 3. This indicates preferential population of Mn-based states, as expected in the downhill regime, where forward QD → Mn transfer is favored over backward transfer (Figure a, inset).

It is instructive to compare this experimental ratio with the theoretical expectation discussed earlier, according to which f _Mn/f _X = exp­(Δ_X‑Mn/δ₀). For the present QDs, Δ_X‑Mn = 130 meV, which yields f _Mn/f _X = 3.5, in good agreement with the experimentally observed value (∼3).

At higher excitation levels (⟨N⟩ > 1), ⟨N _X⟩ saturates near unity, while ⟨N _Mn⟩ continues to increase (Figure c). This leads to a progressive increase in f _Mn and a corresponding decrease in f _X, reflecting the accumulation of excitations in Mn-based states, similar to the behavior observed in the resonant samples (Figure a,b). Despite the increasing number of excited Mn ions, the preselection model predicts that the Auger lifetime remains constant (equal to τ_A,Mn‑X), since ⟨N _X⟩ does not exceed 1.

This prediction is confirmed by lifetime measurements, which show an ⟨N⟩-independent Auger lifetime of ∼1.2 ps (Figure e, main panel and inset), in close agreement with τ_A,Mn‑X = 1.05 ps obtained for the resonant sample. The apparent insensitivity of the Auger recombination rate of the hybrid XMn* biexciton to QD size likely reflects the short-range, contact-like nature of the sp-d exchange Coulomb interaction underlying the SE-driven cross-relaxation process.

Uphill Transfer Regime: Coexistence of SE-Mediated and Conventional Auger Processes

An intriguing case of coexisting conventional and cross-relaxation Auger recombination processes arises in a larger QD sample (r = 2.25 nm), where the band-edge exciton energy (E _X = 2 eV) lies below the Mn spin-flip transition energy (E _Mn = 2.1 eV), resulting in a negative energetic driving force (Δ_X‑Mn = −100 meV; Figure a, insets). This corresponds to an uphill regime that energetically favors intrinsic band-edge exciton states over Mn-based states. As a result, near the onset of the multiexciton regime (1 < ⟨N⟩ < 2), the QD depopulation dynamics are governed primarily by conventional Auger decay, characterized by τ_A = 230 ps (Figure a, darker-colored traces). This time constant corresponds to a biexciton composed of two intrinsic 1S excitons (X_1SX_1S; Figure a, bottom-right inset).

7.

Coexistence of conventional and SE-type cross-relaxation Auger processes in the uphill case. (a) Tail-normalized, pump-fluence-dependent 1S bleach dynamics of Mn-doped QDs with r = 2.25 nm, obtained for ⟨N _X⟩ varied from ∼0.03 to 85 (note the time-axis break, separating an expanded view of short-time dynamics at Δt < 7 ps from the compressed view of long-time dynamics up to Δt = 700 ps). This sample corresponds to the uphill configuration, where E _X < E _Mn and Δ_X‑Mn < 0 (insets). At low pump levels (⟨N⟩ ≪ 1), TA traces are virtually flat across the entire time window (Δt = 700 ps), reflecting slow single-exciton decay. At intermediate pump levels (⟨N⟩ of around 1 or slightly more), the TA traces exhibit an additional ∼230 ps component (pronounced in the long-time dynamics after the time-axis break), characteristic of conventional Auger recombination. At these excitation levels, corresponding to the onset of the multiexciton regime, carriers are confined to the lowest-energy band-edge states, from which SE-type excitation transfer to Mn ions is not energetically feasible. Hence, multiexciton decay proceeds via regular Auger recombination (bottom-right inset). At ⟨N⟩ more than ∼3, a very fast (subpicosecond) component emerges in the TA traces (early time dynamics before the time-axis break), indicating the onset of SE–Auger recombination. The 1S bleach postgrowth (∼2 ps time constant) following the SE–Auger component results from the repopulation of band-edge QD states due to relaxation of hot carriers produced by the SE–Auger recombination. (b) Interestingly, when compared over a long time scale (Δt = 1.5 ns), pump-intensity-dependent multiexciton dynamics in undoped (dashed lines) and Mn-doped (solid lines) samples are virtually indistinguishable, both being governed by conventional Auger decay (in these measurements ⟨N _X⟩ varied from ∼0.8 to 75). Only careful examination of near-time-zero dynamics of the Mn-doped sample reveals a sharp SE–Auger-decay-related spike, which is absent in the undoped sample. (c) Schematic illustration of processes responsible for the various stages (subpanels 1 to 4) of the 1S bleach temporal evolution (regime of high excitation levels, where ⟨N⟩ > 3). Stage 1: Formation of a hybrid triexciton (X_1SX_1SMn*) via X_1P → Mn SE-type energy transfer. Stage 2: Sub-ps SE–Auger recombination of the hybrid X_1SX_1SMn* state, generating a hot electron in the QD. Stage 3: Repopulation of the 1S band-edge state through relaxation of the hot electron. Stage 4: Conventional Auger recombination of the X_1SX_1S biexciton.

Interestingly, a comparison of long-time TA dynamics (1.5 ns time window) between Mn-doped and undoped samples shows no significant differences across all pump levels up to ⟨N⟩ = 65 (Figure b), suggesting that conventional Auger recombination dominates in both cases. However, a closer look at the early time dynamics reveals a sharp, short-lived spike in the doped sample at higher pump levels. This feature becomes pronounced when ⟨N⟩ exceeds ∼3, as shown in the expanded early time TA dynamics (Figure a, lighter-colored traces), and is indicative of the SE-mediated cross-relaxation Auger process.

At these high pump fluences, the 1S_e electron level becomes fully occupied, forcing excess photogenerated electrons into the higher-energy 1P_e state, located over 200 meV above the 1S_e level. These 1P electrons, together with VB holes, form high-energy X_1P excitons capable of exciting Mn ions via SE energy transfer as the driving force becomes positive (Figure a, bottom-left inset). This leads to the formation of a hybrid triexciton (X_1SX_1SMn*), which undergoes rapid SE-type Auger recombination via a cross-relaxation process, resulting in the observed subpicosecond TA decay component. Notably, the lifetime of this component (∼200 fs) closely matches the SE–Auger decay time of a hybrid triexciton in the resonant sample (τ_A,Mn‑XX = 250 fs), again highlighting the lack of apparent dependence of SE–Auger lifetimes on QD size.

The coexistence of conventional and SE-type cross-relaxation Auger processes is also observed in another uphill sample (r = 2.5 nm and E _X = 1.98 eV; Figure S9). Over a 1.4 ns time window, the TA dynamics of doped and undoped QDs remain nearly identical for all pump levels up to ⟨N⟩ = 140 (Figure S9a). However, early time traces (Figure S9b) clearly reveal sub-ps SE–Auger recombination, indicating the formation of hybrid multiexcitons via SE energy transfer from high-energy excitonic states.

Another distinctive feature of high-fluence TA dynamics in Mn-doped uphill samplesabsent in undoped referencesis a pronounced postgrowth of the 1S bleach signal following the SE–Auger spike (Figures a,c and S9b). This postgrowth reflects the repopulation of the 1S_e level by hot carriers generated during the SE–Auger process. These carriers subsequently undergo intraband relaxation (cooling) on a time scale of a few picoseconds (Figure a,c), consistent with previously reported carrier cooling dynamics in CdSe QDs. ,

In addition to direct relaxation through the manifold of QD states (Figure c, subpanel 3), carrier cooling can also be mediated by Mn ions, which can temporarily trap a hot exciton and subsequently release it into a lower-energy QD state. Previous studies have shown that these processes occur on ultrafast time scales (∼100 fs) and therefore do not introduce a significant delay into the intrinsic picosecond-scale intraband dynamics.

Figure c presents a representative TA trace for the uphill sample accompanied by a schematic illustrating the sequence of processes that govern the observed relaxation dynamics. These include the following:

(1) QD-to-Mn excitation transfer once the 1P_e electron state becomes populated, leading to the formation of a hybrid triexciton (X_1SX_1SMn*); (2) SE–Auger recombination of X_1SX_1SMn* producing a hot electron; (3) Repopulation of the 1S_e band-edge state through intraband relaxation (carrier cooling); and (4) conventional Auger recombination of the band-edge biexciton (X_1SX_1S).

Direct visualization of these distinct relaxation steps within a single TA trace enables a clear side-by-side comparison of their time scales. This comparison shows unambiguously that SE–Auger recombination is the fastest pathway, outpacing both conventional Auger recombination and intraband cooling. Consequently, SE–Auger emerges as a particularly powerful mechanism for the generation and manipulation of the hot carriers.

Conclusions

Our studies reveal two distinct Auger recombination channels in Mn-doped QDs: a conventional process occurring on tens-to-hundreds-of-picoseconds time scales and an ultrafast (sub-ps) process mediated by SE interactions. The slower dynamics are consistent with direct Coulomb coupling, whereas the ultrafast component originates from sp-d Coulomb exchange involving hybrid multiexcitons composed of intrinsic QD excitons and Mn-based excitations.

Notably, the ultrafast Auger lifetimes show no dependence on the number of excited Mn ions and can be fully described by interactions between a single excited Mn ion and either one (XMn*) or two (XXMn*) intrinsic QD excitons. These processes are characterized by size-independent time constants of τ_A,Mn‑X = 1.05 ps and τ_A,Mn‑XX = 250 fs, respectively. This behavior departs from the conventional Auger picture (Figure a) and instead supports an SE-driven cross-relaxation mechanism governed by short-range Coulomb exchange interactions (Figure b). Within this framework, the Auger process is mediated by two concerted spin-transfer events involving a virtual intermediate state that effectively preselects a single excited Mn ion and thereby defines the dominant interaction channel of the SE process.

The preselection principle thus emerges as a central feature of SE-mediated dynamics and also provides a natural explanation for the observed independence of single-exciton dynamics from the total number of incorporated Mn ions. While the phenomenological model introduced here captures the essential physics of this behavior, a rigorous theoretical treatment of the preselection mechanism and its microscopic origin remains an important direction for future work.

Another important distinguishing feature of the SE-mediated pathway, compared to the conventional energy-transfer mechanism, is that it produces hot carriers with well-defined spin polarization. In particular, the hot electron generated via the SE–Auger process has a spin orientation opposite to that of the 3d electron spin of the Mn ion after its de-excitation. This spin selectivity represents a distinctive fingerprint of the SE mechanism and may open new opportunities for spin-controlled photophysical processes.

SE–Auger recombination represents the fastest relaxation pathway in Mn-doped QDs, outpacing both conventional Auger recombination and phonon-assisted cooling. Its ability to capture hot-carrier energy before dissipation underscores SE–Auger transfer as a powerful mechanism for high-efficiency PE, carrier multiplication, and potential future hot-carrier photochemistry.

These findings have important implications for the synthesis and optimization of QDs for SE–Auger-based applications. Prior synthetic strategies often prioritized achieving high Mn content. While beneficial for enhancing magneto-optical responses, this approach may not be optimal for SE-driven photoionization processes central to photocathodes and solvated electron generation. For single- and two-step SE–Auger ionization, the optimal numbers of Mn dopants per QD are approximately one and two, respectively. Additional dopants offer no benefit and can, in fact, reduce SE–Auger rates by depleting intrinsic QD states.

Similarly, increasing the QD bandgap has been viewed as advantageous for SE–Auger-based ionization because it raises the CB edge toward the vacuum level. However, our results indicate that this approach is not universally beneficial. Raising the exciton energy above E _Mn shifts the equilibrium between QD- and Mn-based states toward the latter, depleting intrinsic QD states and slowing SE–Auger recombination, potentially offsetting the gains from band-edge elevation.

Finally, an important direction for future research is the direct experimental verification of the predicted spin polarization of the SE-generated hot carriers. This could be achieved through spin-sensitive, magnetic-field-dependent measurements in which an external field is used to control the Mn spin polarization and probe its influence on the properties of the emitted hot carriers.

Together, these insights highlight the importance of understanding the SE–Auger mechanism for guiding future efforts to tailor and optimize QD properties through energetic alignment and informed doping strategies. This framework provides a blueprint for designing next-generation Mn-doped QDs for advanced photophysical, photochemical, and potentially spin-dependent applications.

Materials and Methods

Chemicals and Materials

We used chemicals as received without additional purification. Cadmium oxide (CdO, 99.99%), trioctylphosphine oxide (TOPO, 99%), trioctylphosphine (TOP, 97%), diphenylphosphine (DPP, 98%), 1-octadecene (ODE, 90%), oleic acid (90%), oleylamine (70%), sulfur powder (99.98%), and tributylphosphine (TBP, 95%) were purchased from Sigma-Aldrich. Octadecylphosphonic acid (ODPA, 99%) was purchased from PCI. Selenium (200 mesh, 99.999%) was purchased from Alfa Aesar. Manganese­(II) acetate tetrahydrate (Mn­(ac)₂·4H₂O, 99.999%) was purchased from Strem.

Synthesis of CdSe Quantum Dots (QDs)

CdSe QDs were prepared following the protocol reported in ref without modifications. Briefly, 60 mg of CdO, 280 mg of ODPA, and 3 g of TOPO were loaded into a 50 mL three-neck flask and degassed for 1 h at 150 °C. The mixture was then heated under an inert N₂ atmosphere to 320 °C and maintained at this temperature until it turned into a transparent solution, indicating full activation of the Cd precursors. Subsequently, 1.8 mL of TOP was injected, and the solution was further heated to 380 °C, at which point 0.433 mL of TOP-Se was rapidly injected. The reaction was allowed to proceed for 1 min at 380 °C and was then quenched by cooling to room temperature.

The synthetic conditions used herenamely high-temperature growth and the use of ODPA ligands, which stabilize nonpolar facets of hexagonal CdSe nanocrystalsare known to yield CdSe QDs with a wurtzite crystal structure. ,

QD size control was achieved by adjusting the amount of DPP added to the TOP used during the initial injection at 320 °C and the subsequent TOP-Se injection. The amounts of DPP used to prepare the “downhill”, “resonant”, and “uphill” QDs were 4%, 1%, and 0%, respectively.

Manganese Incorporation

To incorporate Mn ions into presynthesized CdSe QDs, we applied a diffusion doping procedure developed in ref without modification. Briefly, 5 mL of ODE, 0.433 mL of oleylamine, 0.20 mL of oleic acid, and 10 mg of Mn­(ac)₂·4H₂O were loaded into a three-neck flask and degassed for 1 h at 120 °C. The mixture was then heated under an N₂ atmosphere to 300 °C, and 8.3 mg of CdSe QDs along with 0.667 mL of TBP-Se in ODE were swiftly injected. The reaction was allowed to proceed at 300 °C for 20–30 min and was then quenched by cooling to room temperature.

CdS Shell Deposition

To enclose CdSe QDs (undoped and Mn-doped) within a protective CdS shell, we followed the procedure described in ref with slight modifications. Briefly, CdSe QDs were purified three times with ethanol and redispersed in toluene.

The Cd precursor was prepared by degassing a mixture of 36.0 mg of CdO, 735 μL of oleic acid, and 3.24 mL of ODE at 100 °C for 1 h, followed by heating to 250 °C under an N₂ atmosphere and maintaining this temperature for an additional hour. The resulting colorless solution of Cd-oleate in ODE was then cooled to 100 °C.

The S precursor was prepared in a glovebox by mixing 1.8 mL of TOP, 8.61 μL of DPP, and 4.43 mg of S powder, and stirring the mixture overnight.

Separately, 3.5 mL of ODE, 0.3 mL of oleylamine, and 0.15 mL of oleic acid were loaded into a three-neck flask and degassed at 100 °C for 1 h. The purified QDs were then swiftly injected into the reaction mixture under an N₂ atmosphere. The temperature was raised to 220 °C, and 0.05 mL of Cd-oleate solution was added dropwise. After allowing the reaction to proceed for 2.5 min at 220 °C, 0.05 mL of the TOP-S solution was added dropwise, and the reaction was allowed to proceed for an additional 2.5 min. The injections of Cd and S precursors were repeated once more, after which the reaction was quenched by cooling to room temperature.

Measurements of Optical Spectra

For spectroscopic measurements, a QD solution was loaded into a 1 mm path length quartz cuvette. Optical absorption spectra were acquired using a PerkinElmer Lambda 950 ultraviolet–visible-near-infrared spectrophotometer. Solvent-related background was subtracted from the measured spectra. Photoluminescence spectra were recorded using a Horiba Scientific FluoroMax+ spectrofluorimeter with excitation at 450 nm.

Magnetic Circular Dichroism (MCD) Measurements

For MCD measurements, solid-state samples were prepared by incorporating QDs into a poly­(lauryl methacrylate) matrix. The QD samples were placed into a variable-temperature insert (1.5–300 K) of a 7 T superconducting magnet with direct optical access (Oxford Spectromag). The samples were illuminated using a xenon lamp, with the incident light mechanically chopped at 90 Hz. Light polarization was controlled using a Glan-Taylor polarizer (Thorlabs, GT15) and modulated at 50 kHz between right- and left-circular polarizations using a photoelastic modulator (PEM; Hinds Instruments, FS50). Measurements were performed with a magnetic field of up to 6 T applied along the probe light propagation direction (Faraday configuration) at various sample temperatures.

The transmitted light was spectrally dispersed by an HRS300 Teledyne spectrometer equipped with a 1200 groove-per-mm diffraction grating and detected using a silicon avalanche photodiode. The MCD signal (ΔTr_MCD) was obtained by measuring the ratio of the difference and sum of the transmitted light intensities for right and left circular polarizations (Tr_R and Tr_L, respectively) using two separate lock-in amplifiers: one locked to the low-frequency mechanical chopper (sum signal) and the other to the PEM (difference signal). The MCD signal, calculated as ΔTr_MCD ∝ (Tr_L – Tr_R)/(Tr_L + Tr_R), is proportional to the Zeeman splitting (ΔE _Z) between spin-dependent light-absorbing transitions.

Analysis of MCD Data

MCD measurements were used to determine the magnetic field (H) -dependent Zeeman splitting (ΔE _Z) of the band-edge 1S optical transition. For undoped QDs, ΔE _Z is related to H by the following expression: $\mathrm{\Delta }{E}_{\mathrm{Z}}^{\mathrm{u}\mathrm{n}\mathrm{d}}=g_{\mathrm{e}\mathrm{x}}{\mu }_{\mathrm{B}}H$ , where g _ex is the exciton g-factor and μ_B is the Bohr magneton.

In Mn-doped QDs, the Mn ions act as magnetic dipoles that align under an external magnetic field, enhancing the total magnetic field experienced by the semiconductor host, thereby increasing the Zeeman splitting. In this case, it can be represented as $\mathrm{\Delta }{E}_{\mathrm{Z}}^{\mathrm{M}\mathrm{n}-\mathrm{doped}}=g_{\mathrm{e}\mathrm{f}\mathrm{f}}{\mu }_{\mathrm{B}}H+x_{\mathrm{M}\mathrm{n}}{N}_0(\alpha -\beta )⟨S_{\mathrm{J}}⟩$ where g _eff is the effective exciton g-factor, N ₀α = 0.23 eV and N ₀β = −1.27 eV are the s-d and p-d exchange coupling constants for CdMnSe, respectively, and ⟨S _J⟩ is the Brillouin function with the argument g _Mn S _Mnμ_B B(k _B T)⁻¹. Here, N ₀ is the total concentration of cation sites in the crystal lattice, x _Mn is the relative content of MCD-active internal Mn ions, S _Mn = 5/2 is the Mn angular momentum, g _Mn is the Mn g-factor, k _B is the Boltzmann constant, and T is the sample temperature.

The above formalism was used to analyze MCD data and, specifically, to determine the dopant contents and other magnetic characteristics of the undoped and Mn-doped QDs. The results of this analysis are summarized in Table S2.

Transient Absorption (TA) Spectroscopy

Purified QDs dissolved in hexane were loaded into a 1 mm path length quartz cuvette. The sample concentration was adjusted to an optical density of approximately 0.15 at the 1S exciton peak position. TA measurements were performed using a standard pump–probe setup based on a regeneratively amplified ytterbium-doped potassium gadolinium tungstate (Yb:KGW) femtosecond laser (Pharos, Light Conversion) generating ∼190 fs pulses at 1030 nm with a 500 Hz repetition rate.

The laser output was split into two arms. One arm seeded a second-harmonic generator (HIRO HHG, Light Conversion) to produce 515 nm (2.41 eV) pump pulses, whose duration was reduced to ∼150 fs as a result of nonlinear optical pulse narrowing. The second arm was directed toward a retroreflector mounted on a delay stage (maximum pump–probe delay, Δt = 4.5 ns) before exciting a YAG plate to generate broadband femtosecond white-light probe pulses. Pump–probe cross-correlation measurements yielded an overall instrumental response of ∼150 fs. The pump pulse repetition rate was reduced to 250 Hz using a mechanical chopper with a 50% duty cycle, synchronized with laser pulses.

The pump and probe beams were focused and spatially overlapped on the sample, with spot diameters of ∼120 μm and ∼90 μm, respectively, as measured using a BladeCam DataRay beam profiler. The transmitted white light was detected by a fiber-coupled Avantes AvaSpec-Fast ULS1350F-USB2 spectrometer.

To prevent photocharging, the QD solutions were continuously stirred during the measurements using a stainless-steel rod driven by an external rotating magnet.

TA data were acquired by scanning the delay stage mounted in the probe arm. At each time delay, the difference between the transmission of white light under pump-on and pump-off conditions was recorded. The measured TA data were corrected for “chirp” (spectro-temporal broadening characteristic of femtosecond white-light pulses) as described in ref .

Determination of Absorption Cross-Sections and Average QD Excitonic Occupancies

The average excitonic occupancy per QD (⟨N⟩) generated by a pump pulse was determined using the relation ⟨N⟩ = σ_abs(w _p/hν _p), where σ_abs is the sample-dependent absorption cross-section at the pump wavelength (λ_p = 515 nm), w _p is the per-pulse pump fluence, and hν _p = 2.41 eV is the pump photon energy (h is Planck’s constant and ν_p is the pump-photon frequency).

Absorption cross-sections were measured using QD samples before Mn doping, as in doped samples, the occupancy of intrinsic QD states (measured via the TA method) is influenced by bidirectional transfer involving Mn-based states.

To quantify σ_abs, we acquired a w _p-dependent late-time (Δt = 3.5–4 ns) 1S bleach signals (Δα_1S) for w _p varying from 0.9 μJ cm^–2 to 0.945 mJ cm^–2. At these time delays, all multiexcitonic species have already decayed via Auger recombination, so the measured TA signal is defined solely by the fraction of photoexcited QDs (p _exc) in the ensemble, independent of their initial excitonic occupancy. Under Poisson photon absorption statistics, p _exc = 1 – p ₀ = 1 – exp­(-⟨N⟩) = 1 – exp­(−σ_abs·w _p/hν _p), where p ₀ is the fraction of unexcited QDs. The absorption cross-section σ_abs was extracted by fitting the measured Δα_1S-versus-w _p dependence with this expression.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.6c06115.

• Magnetic circular dichroism measurements, additional transient absorption spectra and dynamics, photoluminescence dynamics, and summaries of spectroscopic, magnetic, and structural characteristics of quantum dot samples (PDF)

This project was supported by the Photochemistry and Radiation Chemistry Program of the Chemical Sciences, Biosciences and Geosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy (ultrafast spectroscopic studies of QD samples and mechanistic modeling of electronic dynamics) and the Laboratory Directed Research and Development (LDRD) program at the Los Alamos National Laboratory under project no. 20250126DR (synthesis, microstructural characterization, and magneto-optical studies of QD samples). V.P. acknowledges support by a LANL Director’s Postdoctoral Fellowship.

The authors declare no competing financial interest.