Probing Charge-Transfer with Infrared Spectroscopy

Femtosecond Infrared spectroscopy (IR) is a relevant technique to study ultrafast photoinduced phenomena, especially in molecular-based materials, for which electronic state and vibration modes are strongly coupled.¹⁴ In the case of heterobimetallic cyano-bridged materials, IR spectroscopy is known to be particularly sensitive to the intermetallic CT, due to the frequency shift of the IR active N−C stretching mode.^{11d, 15} For our time-resolved IR spectroscopy measurements, the IR probe beam was generated with a Coherent Astrella amplifier seeding an optical parametric amplifier and difference frequency generation set-up. The ≃90 fs broadband spectrum of the infrared beam was centred at 2105 cm⁻¹ (Figure S2). We pumped the material on the red edge of the absorption band. This Mn-centred (d–d) excitation drives a reverse Jahn–Teller distortion, through the population of antibonding Mn−N orbitals, which induces the intermetallic CT within ≃200 fs.^12a The pump wavelength was set to 560 nm where the optical penetration depth is ≃0.6 μm.¹⁶ Since excited crystals may reach a permanent photoinduced state, we used a sample powder streaming set-up (Figure 1a), whereby sub-micrometric RbMn_0.94Co_0.06Fe crystals in the LT phase are dispersed in ethanol and streamed through a free-flowing jet (300 μm thick—6 mm large, Figure S3). The IR optical density (OD) spectral analysis was carried out in transmission geometry, with a monochromator coupled to a Mercury Cadmium Telluride (MCT) photodiode from Infrared Associates and a lock-in amplifier from Stanford Research Systems. The IR probe was focused to a spot size of 130×120 μm² on the sample.

The larger laser spot size of the pump beam (190×240 μm²) ensures a homogeneous excitation of the sample in the volume probed by the IR beam. The experimental time resolution achieved in this setup is ≃140 fs. The crystal-solvent weight ratio was 1 : 270 with a jet velocity of 0.3 m s⁻¹ at the interaction region. We varied the pump fluence between 0 and 27 mJ cm⁻². Figure 1b and S2c show the IR absorption spectra for the LT and HT phases of RbMn_0.94Co_0.06Fe, in the N−C stretching region. These spectra, measured with our femtosecond IR spectroscopy set-up, are similar to the ones measured with conventional FTIR (Figure S5). This experimental approach was important to use the same spectral resolution for measuring the IR absorption of the steady LT and HT states and out-of-equilibrium dynamics. In the HT phase, the sharp peak at 2157 cm⁻¹ (8 cm⁻¹ full width at half maximum) is assigned to the IR active N−C stretching mode of the Mn²⁺−N−C−Fe³⁺ valence state (Figure 2).¹⁵ This mode is triply degenerate (T₂, x,y,z) in the $$ point group of the cubic HT phase. In the LT phase, the band shifts around 2100 cm⁻¹ as CT decreases the bonding strength.⁸ Due to the symmetry breaking in the tetragonal phase ($$ point group), the IR active N−C stretching mode of the Mn³⁺−N−C−Fe²⁺ valence state (Figure 2) splits in two: a B₂ (z) mode and a doubly degenerate E mode (x,y).¹⁵ Due to the formation of boundaries and ferroelastic domains in the LT tetragonal phase, the infrared N−C band is quite broad (Figure 1b), as usually observed for RbMnFe samples and derivatives.⁸ The black curve in Figure 1c shows the differential IR spectrum upon thermal conversion (HT phase spectrum minus LT phase spectrum), resulting from coupled symmetry change and CT. It is characterized by the disappearance of the broad LT band centred around 2100 cm⁻¹ (negative signal) and the appearance of the sharp HT band around 2157 cm⁻¹ (positive signal). On the other hand, the orange curve shows the photo-induced ΔOD change for high pump fluence (17.6 mJ cm⁻²), measured 1 ns after photo-excitation of the LT phase at room temperature (within the thermal hysteresis). It is characteristic of the PIPT from the LT Mn³⁺−N−C−Fe²⁺ tetragonal phase to the HT Mn²⁺−N−C−Fe³⁺ cubic phase. The amplitude of the orange curve is multiplied by 3, which means that about one third of the crystals in the stream are photo-converted at this pump fluence.

The partial increase of intensity and the spectral shift of the photoinduced Mn²⁺−N−C−Fe³⁺ band, compared to HT phase, indicates that the macroscopic dynamics is not complete after 1 ns, as observed by X-ray diffraction.⁷ Hereafter, we present time-resolved IR measurements and discuss the non-equilibrium electronic and structural dynamics towards the persistent PIPT, inside the thermal hysteresis at room temperature.

Out-of-Equilibrium Dynamics

Figure 3 shows the evolution of the differential IR spectra with time delays for different pump fluences. At high fluence (17.6 mJ cm⁻² Figure 3a) the disappearance of the broad LT band and the appearance of the sharp HT Mn²⁺−N−C−Fe³⁺ band is characteristic of the LT→HT PIPT. This agrees with the X-ray diffraction study, which evidenced that above a threshold fluence of about 10 mJ cm⁻² the Mn³⁺−N−C−Fe²⁺ tetragonal→Mn²⁺−N−C−Fe³⁺ cubic PIPT occurs within ≃100 ps.⁷ Our time-resolved IR data confirm that the HT phase forms within this timescale, as directly monitored through the characteristic IR band of the Mn²⁺−N−C−Fe³⁺ species (inset Figure 3a).

However, another IR band appears on shorter timescale around 2073 cm⁻¹. It disappears within 100 ps at high fluence as the HT phase forms, but it persists at 1 ns at low fluence (Figure 3c). The frequency of this IR band is characteristic of the N−C stretching mode of the Mn²⁺−N−C−Fe²⁺ electronic configuration (Figure S4), observed in the IR spectra of the Rb₂Mn²⁺[Fe²⁺(CN)₆] ⋅ 3.5H₂O material, made of passive Mn²⁺−N−C−Fe²⁺ bridges. This band, which was also observed by time-resolved IR spectroscopy at low excitation density for the Rb_0.94Mn[Fe(CN)₆]_0.98 ⋅ 1.3H₂O sample, is known to be characteristic of the local structural trapping of the photoinduced CT.^11d As shown in Figure 2a, photoexcitation of the homogeneous LT Mn³⁺−N−C−Fe²⁺ phase can result in a single intermetallic CT, forming an isolated excited bridge [Mn²⁺−N−C−Fe³⁺]*. It is surrounded by five Mn²⁺−N−C−Fe²⁺ and Mn³⁺−N−C−Fe³⁺ bridges. The detection of the characteristic Mn²⁺−N−C−Fe²⁺ IR band after photoexcitation constitutes a direct proof of the local nature of the structural trapping of the intermetallic CT, forming small CT polarons [Mn²⁺−N−C−Fe³⁺]*. The local structural trapping of these CT states, due to the spin transition on the Mn sites, is responsible for the macroscopic lattice expansion, which was directly monitored by time-resolved X-ray diffraction.^{7, 12a} The strong oscillator strength of the Mn²⁺−N−C−Fe²⁺ band, about six times greater than that of the Mn²⁺−N−C−Fe³⁺ band,⁷ makes femtosecond IR spectroscopy particularly relevant to study the role of the small CT-polaron in the macroscopic dynamics of the photoinduced phase transition.

Figure 4a shows the photoinduced spectral change at 2 ps, scaled to laser fluence. The superposition of the spectral changes at 3.1 and 5.3 mJ cm⁻², with a clear common isosbestic point at 2090 cm⁻¹, shows that the differential spectrum changes linearly with the laser fluence at low excitation density. The decrease of intensity of the ground state Mn³⁺−N−C−Fe²⁺ band and increase of the Mn²⁺−N−C−Fe²⁺ band are linear with pump fluence, as expected for the formation of the small CT polaron.

A femtosecond X-ray spectroscopy study of the photoinduced CT process in the Co−Fe material revealed that the mechanism corresponds to a spin-transition-induced CT process.^6m Another femtosecond optical spectroscopy study, supported by DFT calculations, on a Mn−Fe material has shown that the optical excitation promotes a Mn (d–d) centered electronic transition. The coupled reverse Jahn–Teller distortion drives intermetallic CT within ≃200 fs.^12a Consequently, we consider that the evolution of the ΔOD(t) time traces in Figure 4 should be described through an exponential depopulation of the LT Mn³⁺−N−C−Fe²⁺ state and a simultaneous exponential population of the polaronic Mn²⁺−N−C−Fe²⁺ band. The fit of these time traces ΔOD(t) (Figures S6–S9) are consistent with this mechanism and indicates that the Mn³⁺−N−C−Fe²⁺→[Mn²⁺−N−C−Fe³⁺]* electron transfer process occurs within $$ ≃250 fs. Indeed, in the case of a direct photoinduced CT, an instantaneous decrease of OD of the LT Mn³⁺−N−C−Fe²⁺ band and an instantaneous increase of the polaronic Mn²⁺−N−C−Fe²⁺ band should be observed.

At higher fluence (17.6 mJ cm⁻²), the ΔOD decrease at 2 ps on the LT band is still scaling with laser fluence (Figure 4a), due to the bleaching of the ground LT phase. However, the ΔOD change on the Mn²⁺−N−C−Fe²⁺ band (2075 cm⁻¹) is lower than at lower pump fluence. In addition, the isosbestic point at low fluence (2090 cm⁻¹_, Figure 4c) shifts to 2083 cm⁻¹ at higher fluence. These observations highlight that the spectral changes strongly deviate from the linear response at high pump fluence.

Figure 5 shows the normalized ΔOD(t) for the LT Mn³⁺−N−C−Fe²⁺ (2109 cm⁻¹), the polaronic Mn²⁺−N−C−Fe²⁺ (2073 cm⁻¹) and the HT Mn²⁺−N−C−Fe³⁺ (2152 cm⁻¹) species for low and high pump fluences. In agreement with X-ray diffraction,⁷ we can distinguish two regimes. In the low fluence polaronic regime (bottom) the CT remains local. The photoexcited LT Mn³⁺−N−C−Fe²⁺ bridges disappear to form small CT polarons [Mn²⁺−N−C−Fe³⁺]*, surrounded by Mn²⁺−N−C−Fe²⁺ bridges. These small CT polarons live ≃15 μs, as characterized by time-resolved optical spectroscopy and X-ray diffraction studies.^{12a, 13} In this polaronic regime, the HT phase does not form and the partial decay of the Mn²⁺−N−C−Fe²⁺ band and the associated increase of the LT Mn³⁺−N−C−Fe²⁺ band may be interpreted as a partial decay of the small CT polarons towards the ground LT state within 100 ps, which is characteristic of the equilibration timescale of the polarons with the crystalline lattice.^{7, 13} In the high fluence PIPT regime (top) the macroscopic CT phase transition occurs. The photoexcited LT Mn³⁺−N−C−Fe²⁺ phase disappears as small CT polarons [Mn²⁺−N−C−Fe³⁺]* form, which is witnessed through the increase of the surrounding Mn²⁺−N−C−Fe²⁺ bridges (Figure 4). Then, the Mn²⁺−N−C−Fe²⁺ species decay (Figures 3a & 5) while the IR band of the HT Mn²⁺−N−C−Fe³⁺ phase grows, indicating a cooperative PIPT process. When a sufficient amount of small CT polarons are initially created, the remaining Mn³⁺−N−C−Fe²⁺ sites are further converted because of internal pressure. Our time-resolved IR spectra indicate that this cooperative PIPT occurs within ≃100 ps. This result is in very nice agreement with the recent time-resolved X-ray study, which monitored the growing of the cubic HT phase on a similar timescale.⁷

The change from a local polaronic regime to a macroscopic and cooperative PIPT regime above a threshold fluence is also described in Figure 6, which shows the fluence dependence of the three IR bands at different delays. Figure 6a shows that the LT Mn³⁺−N−C−Fe²⁺ species decay almost linearly with laser fluence up to ≃10 mJ cm⁻², where their number remains constant up to ≃30 ps and photoexcitation remains local. At higher fluence, the signal saturates below 30 ps as the laser penetration depth (0.6 μm) is a limiting factor, given the size of the crystals (0.9 μm). However, for higher fluence, looking on the amplitude of this depopulation band, it is clear that a cooperative transformation starts around the 100 ps as seen by further decrease of the signal.

Figure 6b also shows that the low fraction of photoinduced Mn²⁺−N−C−Fe³⁺ species increases almost linearly with laser fluence below 10 ps, which agrees with the local nature of the photoinduced CT. However, above ≃6 mJ cm⁻² the photoinduced Mn²⁺−N−C−Fe³⁺ species strongly increase with delay and saturate around 1 ns. This is the signature of the cooperative and self-amplified PIPT. Figure 6c shows a more complex evolution with laser fluence of the Mn²⁺−N−C−Fe²⁺ species. For time delays shorter than 10 ps the amplitude of the Mn²⁺−N−C−Fe²⁺ band increases almost linearly with pump fluence up to ≃6 mJ cm⁻². Above, the amplitude of this band decreases within ≃100 ps as the PIPT occurs. This decrease includes both the decaying photoinduced small CT polaron and the disappearance of the ferroelastic domain walls, containing Mn²⁺−N−C−Fe²⁺ species. Figure 2a shows different 3D electronic configurations of the crystalline lattice in the LT phase made of Mn³⁺−N−C−Fe²⁺ bridges (blue) and in the HT phase made of Mn²⁺−N−C−Fe³⁺ bridges (red).

When a single CT occurs around one site, $$ , $$ and $$ . When CT occur on two adjacent sites, $$ , $$ and $$ per site, etc. The ΔOD around 2075 cm⁻¹ scales linearly with the total number $$ of photoinduced

In a rough approximation, considering a homogeneous excitation, the fraction of photoexcited sites is $$ where ϕ corresponds to the laser fluence and $$ is related to penetration depth. The cyan line in Figure 6c shows the evolution of the number $$ of Mn²⁺−N−C−Fe²⁺ bridges calculated with this model and scaled to OD. This model accounts only for the photoinduced change of electronic configuration on picosecond timescale, i.e. when the cooperative elastic effects are not activated yet. This simple model can qualitatively reproduce the measurements, as it explains the almost linear increase of ΔOD on the Mn²⁺−N−C−Fe²⁺ band with low laser fluence and its decrease when CT occurs statistically over adjacent crystalline sites. For the Mn²⁺−N−C−Fe²⁺ band, the ΔOD is maximum for X=0.3. A more advanced model, such as the mechano-elastic one,¹⁷ would be required to describe the cooperative PIPT occurring on the 100 ps acoustic timescale, which corresponds to the time required for the macroscopic expansion of the sub-micrometric crystals. Such an elastically-driven process, associated with elastic deformation waves propagating at the speed of sound, can account for the cooperative conversion of the Mn²⁺−N−C−Fe²⁺ species towards the higher volume Mn²⁺−N−C−Fe³⁺ ones.