Ferromagnetic excited-state Mn${}^{2+}$ dimers in Zn${}_{1-x}$Mn_xSe quantum dots observed by time-resolved magnetophotoluminescence

Colloidal Mn${}^{2+}$-doped semiconductor nanocrystals are solution processable analogs of classic phosphor and diluted magnetic semiconductor materials with promising applications ranging from fluorescence microscopy to spintronic information processing. At doping levels of only a few cation mole percent, Mn${}^{2+}$ dimers form in appreciable concentration and cause shortened photoluminescence decay times and reduced luminescence circular polarization under applied magnetic fields. Here, we show that these differences allow the use of time-resolved magnetophotoluminescence measurements to investigate the magnetic properties of the luminescent dimer excited state in Zn${}_{1-x}$Mn${}_x$Se nanocrystals. These measurements reveal that Mn${}^{2+}$-Mn${}^{2+}$ dimers are coupled ferromagnetically in their luminescent excited state, in contrast with the antiferromagnetic coupling of their ground state. We find that Mn${}^{2+}$-Mn${}^{2+}$ dimers also luminesce with much purer circular polarization than Mn${}^{2+}$ monomers under applied magnetic fields. These results are explained well by perturbation theory and density functional theory analyses of the microscopic orbital exchange interactions within the photoexcited Mn${}^{2+}$-Mn${}^{2+}$ dimers. This discovery of photoswitchable dimer magnetism (from $S$ = 0 to $S$ = 4) with strong associated circularly polarized luminescence raises intriguing possibilities for optical spin manipulation in doped semiconductors.

Figure 1

(a) Room-temperature absorption (left axis, black) and 1.7 K, 6 T magnetic circularly polarized luminescence spectra of 1.5% Zn${}_{1-x}$Mn${}_x$Se/ZnS nanocrystals. Inset: Magnetic-field dependence of the MCPL ratio, Δ$I/I$. (b) Room-temperature TR PL traces for Zn${}_{1-x}$Mn${}_x$Se/ZnS NCs with Mn${}^{2+}$ concentrations from 0.1 to 3.5% as indicated. All nanocrystals have core $d$ ∼ 3 nm and shell thickness ∼0.5 nm.

Figure 2

Time-resolved ${\sigma }^{+}$ and ${\sigma }^{-}$ PL decay traces from (a) 0.46% and (b) 3.5% Zn${}_{1-x}$Mn${}_x$Se/ZnS NCs (core $d$ = 3 nm, respectively), both measured at 1.7 K, 6 T in the Faraday geometry. (c) Time-resolved MCPL (Δ$I/I$ vs $t$) traces for the same samples measured under the same conditions.

Figure 3

Mn${}^{2+}$ concentration dependence of $P_{\mathrm{TD}}/P_{\mathrm{TI}}$ (left axis, blue circles) and time-integrated $\Delta I/I$ (right axis, red squares), measured at 1.7 K and 6 T. Note the negative axes. The solid curve plots the calculated probability that a Mn${}^{2+}$ ion is part of a nearest-neighbor dimer, scaled arbitrarily to overlay the data. The solid curve runs from zero at 0% Mn${}^{2+}$ to 0.22 at 3.5% Mn${}^{2+}$.

Figure 4

(a) Time-resolved MCPL of 0.52% Zn${}_{1-x}$Mn${}_x$Se/ZnS NCs, measured from 0 to 4.5 T at 1.7 K. (b) $P_{\mathrm{TD}}$ (blue triangle) and $P_{\mathrm{TI}}$ (red circle) values from the traces in (a) plotted vs applied magnetic field and normalized at 0.25 T. The dashed lines plot Brillouin magnetization functions calculated for $S$ = 1/2 to 5 ($g$ = 2, 1.7 K), also normalized at 0.25 T.

Figure 5

(a) Simulated circularly polarized PL decay curves for monomers [blue, ${\tau }_m$ = 800 μs, ${(\Delta I/I)}_m$ = −0.32] and dimers [red, ${\tau }_d$ = 300 μs, ${(\Delta I/I)}_d$ = +1.00). Here, ${\sigma }^{-}$ and ${\sigma }^{+}$ components are shown as dashed and solid lines, respectively. The integrated dimer PL accounts for 5% of the overall PL in this simulation. Inset: The simulated summed ${\sigma }^{-}$ and ${\sigma }^{+}$ PL intensities overlaid with the experimental data from Fig. 2. (b) The simulated MCPL ratio from (a) as a function of time (solid red line), overlaid with the experimental data from Fig. 2. (c) Simulated magnetic field dependence of $P_{\mathrm{TD}}$ obtained by scaling the monomer and dimer MCPL polarization ratios by the $S$ = 3/2 and $S$ = 4 Brillouin functions, respectively.

Figure 6

Schematic depictions of the transitions defining MCPL ratios for monomers and dimers in Zn${}_{1-x}$Mn${}_x$Se and related systems in the spin-only limit. In monomers (left), MCPL is determined by the relative transition moment probabilities of $\Delta m_s$ = −1 (${\sigma }^{-}$, blue arrow) and $\Delta m_s$ = +1 (${\sigma }^{+}$, red arrow). In dimers (right), the ground state is antiferromagnetically coupled, and the luminescent excited state is ferromagnetically coupled. The dimer luminescence intensity is dominated by the spin-allowed Δ$S$ = 0 transition. In the dimer MCPL, only the $\Delta m_s$ = +1(${\sigma }^{+}$) component of this transition conserves angular momentum, leading to 100% circular polarization with the opposite sign as in the monomers. Splittings are not to scale.

Figure 7

(a) Schematic summary of spin-transfer processes responsible for ground- and excited-state magnetic exchange coupling of Mn${}^{2+}$-Mn${}^{2+}$ dimers in ZnSe. The dashed red arrows denote spin-transfer processes favoring antiferromagnetic Mn${}^{2+}$-Mn${}^{2+}$ coupling, and the solid blue arrows denote spin-transfer processes favoring ferromagnetic coupling. (b) Two possible Jahn-Teller distortions of the Mn${}^{2+}$ ${}^4$T${}_1$ excited state ($C_{3v}$ and $D_{2d}$), and the corresponding $d$-orbital splitting patterns.

Figure 8

Results from DFT calculations on Zn${}_{84}$Mn${}_2$Se${}_{86}$ nanocrystals. Density of states diagrams for (a) the antiferromagnetically coupled $|{}^6{\mathrm{A}}_1,{}^6{\mathrm{A}}_1\rangle$ ground state and (b) the ferromagnetically coupled $|{}^4{\mathrm{T}}_1,{}^6{\mathrm{A}}_1\rangle$ excited state. The top and bottom of each plot denote α and β spins, respectively. (c) and (d) Structural changes upon photoexcitation of Mn${}^{2+}$ monomer and Mn${}^{2+}$-Mn${}^{2+}$ dimer. Ground-state (black) and excited-state (red) structures are illustrated, and the most significant changes in bond lengths and angles upon excitation are indicated. (e) Electron density contours of the Mn${}^{2+}$-Mn${}^{2+}$ dimer LUMO and HOMO in the ferromagnetically coupled $|{}^4{\mathrm{T}}_1,{}^6{\mathrm{A}}_1\rangle$ excited state, which correspond primarily to the empty and doubly occupied orbitals of the photoexcited Mn${}^{2+}$ ion, respectively. Mn${}^{2+}$ ions are shown in purple, Zn${}^{2+}$ in blue, and Se${}^{2-}$ in yellow.