Directly probing spin dynamics in a molecular magnet with femtosecond time-resolution† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c6sc01105e Click here for additional data file.

Femtosecond magneto-optical measurements detect the formation of a spin-excited state in the vanadium–chromium Prussian blue analogue, which is a molecule-based magnet.


Introduction
The ability to optically switch the spin conguration of molecular magnets 1-3 could contribute to the development of applications such as quantum computers, spintronic devices, and high-capacity information-storage devices. Femtosecond laser pulses currently form the only technology able to function beyond one terahertz (10 12 Hz), allowing for potentially faster switching than the 10-100 gigahertz capabilities of electronic transistors. To study switching processes, a method is needed that is directly sensitive to the spin state and is fast enough to probe on the sub-picosecond timescale relevant for optical excitation. To this end, ultrafast magneto-optical (MO) techniques, 4,5 such as Faraday rotation, are the only optical methods capable of directly probing spin dynamics on these timescales, as reported in various magnetic metals, 6 dielectrics 7 and nanoparticles. 8 Applying these techniques to molecular materials therefore offers exciting possibilities since optical spinmanipulation has been achieved in a range of molecule-based magnets [9][10][11][12][13][14][15][16] and spin-crossover (SCO) systems [17][18][19][20][21][22][23][24][25][26][27][28][29] but so far only X-ray uorescence using free-electron lasers has provided a direct probe of the sub-ps spin dynamics. 30 Faraday rotation is closely related to magnetic circular dichroism (MCD) and occurs due to a difference in the index of refraction for le and right circularly polarised light in a magnetised material. 31 The difference arises because the circular polarisation components interact differently with Zeeman-shifted electronic states whose spin and orbital angular momenta align differently in a magnetic eld. Importantly, the Faraday rotation angle is proportional to the sample magnetisation. In time-resolved measurements, the MO signal is obtained by carefully measuring the change in polarisation state of the probe pulse as a function of time delay aer exciting the sample with a pump pulse. Ultrafast MO methods have made it possible to untangle spin dynamics from charge and lattice dynamics in ferromagnets aer femtosecond laser pulse excitation. 6 They therefore show great potential to be able to distinguish spin and nuclear dynamics in SCO materials, where high-spin and lowspin states are typically distinguished based on changes in optical spectra 18,23,25,32 and/or bond-lengths, 21,22,24,[33][34][35] which are not explicitly sensitive to spin dynamics. The power of ultrafast MO Faraday measurements is that they can give details of magnetisation dynamics on the fs timescale.
In this article, we explore the ultrafast MO and transmission dynamics of thin lms of the V II/III -Cr III Prussian Blue Analogue (PBA), which was chosen as a model system because it is a roomtemperature magnet 36 with a pronounced static MO response in the visible spectrum. 37,38 We demonstrate that a change in the spin conguration on the metal ions leads to a sub-picosecond change in the MO signal due to the super-exchange interaction between the metallic ions in the lms.

Materials
The sample and a typical transmittance spectrum are shown in Fig. 1(a). The V II/III -Cr III PBA is composed of Cr ions in their third oxidation state (Cr III , 3d 3 electrons in the conguration t 3 2g e 0 g ) octahedrally surrounded by cyanide ligands (CN À ) with the carbon end (grey spheres) towards the Cr ions (yellow spheres) and the V ions (green spheres) bound to the nitrogen (blue spheres) end of the ligands (see Fig. 1(b)). In the lm, V is present in two different oxidation states, V II (t 3 2g e 0 g ) and V III (t 2 2g e 0 g ), and the corresponding ratio is determined by the electrochemical conditions used during deposition. 37 The electrons are only partially localised on the metal ions and there is some orbital overlap between adjacent ions via the cyanide ligands. This leads to a coupling of the spins via the ligand bridge and the magnetic properties of the PBA therefore arise from the super-exchange interaction between the metal ions through the cyanide ligand ( Fig. 1(b)). Due to the stoichiometry of the materials, vacant sites, and the presence of both V II (S ¼ 3/2) and V III (S ¼ 1) there is not a complete cancellation of the V spins with respect to the Cr III spins (S ¼ 3/2) and consequently the V-Cr PBA is a ferrimagnet.
We electrochemically synthesised thin lms of the V II/III -Cr III PBA on 3 mm thick uorine-doped tin oxide (FTO) coated glass substrates under potentiostatic conditions as outlined in ref. 37 and 38. Aqueous solutions of VCl 3 and K 3 [Cr(CN) 6 ] from Sigma-Aldrich were used without further purication at concentrations of 15 and 10 mM and KCl was used as the electrolyte at a concentration of 0.5 M. The substrates were cleaned in an ultrasonic bath using three different solvents (clean substrates were critically important in order to produce lms of good optical quality and thus reduce the amount of scattered pump light in the time-resolved experiments). A potential of À1.2 V w.r.t. a Pt pseudo-reference electrode was applied for 10 minutes, producing blue-coloured lms, which showed transmittance spectra in accordance with the literature. 37,44 Inductively coupled plasma optical emission spectrometry showed a Cr/V ratio of 0.89 and the IR spectrum showed an intense peak at 2106 cm À1 assigned to the asymmetric CN À stretching frequency (ESI †). The V-Cr PBAs are air sensitive and so the electrochemistry was performed under a ow of N 2 . The lms were rinsed with N 2 -bubbled H 2 O and allowed to dry under a ow of N 2 . Once dried, they were sealed with cyanoacrylate glue and a 0.18 mm thick glass microscope coverslip.

Time-resolved conguration
The pump-probe MO conguration is sketched in Fig. 1(d). The laser system is an amplied titanium sapphire laser delivering 50 fs pulses at 5 kHz, with a central wavelength at 800 nm. Part of the beam is used to generate the pump pulses by frequency doubling (400 nm) in a b-barium borate crystal. The pump power was adjusted using a combination of a half waveplate and a polariser in order to achieve a pulse energy of 100 nJ. The beam was focused with a 25 cm achromatic lens to achieve a uence of 0.5 mJ cm À2 . At this pump energy, the samples were stable for ca. 10 min aer which some degree of photodegradation was observed. For this reason, all experiments were performed on the same sample but at a different sample position for each measurement. The transmittance was checked before and aer each measurement and because of the good sample homogeneity it was possible to measure at different spots with the same transmittance. The pump wavelength spectrally overlapped with the ligand-to-metal charge transfer (LMCT) UV bands, where an electron transfers from a CN À ligand onto the Cr ion ( Fig. 1(b)). Another part of the beam is used to generate a supercontinuum (l ¼ 480-690 nm) in a sapphire crystal by self-phase modulation. The supercontinuum is used to measure the time-dependent differential transmission (DT/T) and MO response (Faraday rotation, Dq F ). A folded dispersive optical line allows for partial compensation of the chirp of the probe pulses. A variable slit in this dispersive line allows the narrower spectral probe wavelengths to be selected. In total eight wavelength-specic kinetics traces were recorded in the range of 480-690 nm with a 15 nm bandwidth. The uence in the 15 nm spectral band was ca. a factor of 1000 lower than the pump energy. The pump and probe delay line is moved by a stepper motor. The overall pump and probe temporal resolution is $250 fs. The Faraday rotation is measured with a balanced polarisation bridge analysis. The signal-to-noise ratio in the transmission is minimised by an appropriate reference signal selected from the incoming probe beam. All signals are detected using a modulation and lock-in synchronous detection scheme. 4,5 The temperature T s of the sample is controlled with a cryostat and the magnetic eld, applied perpendicular to the sample plane, is provided by a superconducting magnet.

Computational methods
TD-DFT computations were carried out in order to give further support to the assignment of the optical transitions. Due to the complexity of the PBA system, we carried out the calculations for a single monomeric unit comprising one V with ve CN À ligands (with N pointing toward V), one Cr with ve CN À ligands (with C pointing toward Cr) and one bridging CN À ligand (with N toward V and C toward Cr). Gaussian 09 (ref. 39) was employed to perform the TD-DFT calculations using the PBE0 hybrid functional. 40 The calculations were performed at a xed geometry and the 6-311G(d) basis set 41 was used for V and Cr ions, and the 6-31G(d) basis set 42,43 for C and N atoms. The symmetry of the monomeric unit was C 4V . The calculations for the V III -Cr III PBA showed two transitions with non-zero oscillator strengths in the UV/VIS spectrum, namely a LMCT from the CN À ligand to the Cr t 2g orbital at 401 nm and a metal-tometal charge-transfer (MM 0 CT) transition at 780 nm from the Cr t 2g to the V t 2g orbital. For the V II -Cr III PBA system, the transitions were mixed. Here two degenerate LMCT transitions were identied at 324 nm and showed a mix of transfer from the CN À ligand to both the Cr and V t 2g orbitals. The MM 0 CT transition was also mixed between transitions between t 2g orbitals from Cr to V and V to Cr and occurred at 572 nm. The red-shi of the MM 0 CT from lower to higher oxidation state of the V (572 and 780 nm, respectively) is in qualitative agreement with experiments. 37 Results and discussion Fig. 2(a) shows Dq F at T s ¼ 50 and 300 K for l ¼ 660 nm. The signals are recorded for antiparallel magnetic eld directions, perpendicular to the sample plane (H ¼ AE0.5 T), and the difference between the two signals is shown in Fig. 2(b). As is seen in Fig. 2(a) and (b), a change in the MO signal occurs on a sub-picosecond timescale. It should be noted that Dq F has not been normalised for the static Faraday signal q F . The dynamics are tted with a causal exponential decay, taking into account the Gaussian temporal prole of the pump laser. Aer a fast rising part, relaxation occurs with the time-constants s Dq (50 K) ¼ 0.64 ps and s Dq (300 K) ¼ 1.31 ps at l ¼ 660 nm. The corresponding dynamics of the transmission are displayed in Fig. 2(c) with similar time constants of s DT (50 K) ¼ 0.76 ps and s DT (300 K) ¼ 1.05 ps. The fast decay reaches a plateau that slowly decays over several hundreds of picoseconds (shown in ESI †). For l ¼ 480 nm (Fig. 2(d)) the dynamics of both Dq F and DT/T are different at 50 K, where only the plateau is observed. For this wavelength, a negative signal around zero time delay is also observed at both temperatures. Fig. 3, obtained by interpolation of wavelength-specic kinetic traces, summarises the spectro-temporal dynamics of DT/T and Dq F over the whole probe supercontinuum for T s ¼ 50 and 300 K. The maxima of the dynamical spectra are shied for the two temperatures. The temperature is clearly important for the dynamics aer pumping at the LMCT and can be seen to also play a role in the static transmittance spectra of nonphotoexcited lms (Fig. 3(e)). Fig. 3(a)-(d) show that the fast initial decay reaches a plateau (although for l ¼ 480 nm at 50 K, the signal immediately reaches the plateau). This is shown in detail in Fig. 2(b) and (c). Fig. 3(f) shows the tted time constants from the wavelength-specic kinetic traces for the decays over the probe spectrum. The decays are faster at T s ¼ 50 K than at 300 K for both s Dq and s DT .
The overall spin and charge dynamics aer the LMCT to Cr are interpreted by considering that the probe pulses overlap with the MM 0 CT band ( Fig. 1(c) and 4(a)). Because of the different oxidation states of the V ions, more energy is required to transfer an electron from a Cr ion to a V II site than to a V III site due to the Coulomb repulsion. This difference results in the splitting of the MM 0 CT band into two peaks in the transmittance spectrum at 660 nm (Cr III / V III ) and at 540 nm (Cr III / V II ), which is barely seen as a shoulder in the transmittance spectrum shown in Fig. 1(a). Such a peak was observed at 550 nm by Garde et al. for V II -Cr III PBA molecules in suspension who also assigned it to the MM 0 CT band. 44 The static Faraday ellipticity spectrum reported by Ohkoshi et al. 37 gives further support for the two types of charge-transfer. Indeed, in their PBA lms the predominance of V II ions strongly reduces the resonance at 660 nm associated with the V III ions.
The increase in transmission of the MM 0 CT states and subsequent fast decay has to be interpreted by considering that we are pumping at the LMCT transition. In contrast to metallic materials, where the excitation energy is quickly redistributed among all electrons on a femtosecond timescale, the electron dynamics in transition metal complexes depend on the pump wavelength which may excite transitions that are (i) localised ligand-ligand or metal-centred ligand-eld (LF) transitions or (ii) partially delocalised LMCT/MLCT or MM 0 CT transitions. Ultrafast relaxation dynamics aer fs excitation in Cr III (acac) 3 (acac ¼ deprotonated monoanion of acetylacetone) complexes in solution at both LF and LMCT pumping have been extensively studied by Juban and McCusker. 32,45 They found that the excited 4 LMCT state quickly decays via intersystem crossing (ISC) to the 2 E state of the Cr ion with a 50 fs time constant. Subsequent decay kinetics of the signal on a 1.1 ps timescale was attributed to vibrational cooling in the 2 E state. The 2 E state eventually decays back via ISC to the 4 A 2 ground state on a ns timescale. ISC on timescales shorter than 100 fs aer MLCT excitation is known to occur in Fe II SCO complexes in solution 23 and it has been reported that similar dynamics, localised on the Fe sites in the lattice, can be observed in SCO crystals. 21,25 It is therefore plausible that the decay processes described by Juban and McCusker 32,45 are applicable to the dynamics of the Cr ions in the V II/III -Cr III PBA lattice. It should be noted that for the shortest wavelength (l ¼ 480 nm, Fig. 2(d)) we observe a very fast transient  decrease of the transmission, which we attribute to an excitedstate absorption (ESA) from the 4 LMCT state. The subsequent fast decay of the ESA at 480 nm (180 AE 30 fs at 50 K and 110 AE 10 fs at 300 K, both time constants shorter than the experimental time resolution), which occurs at the very beginning of the pumpprobe DT/T signal, further supports the short life-time of the 4 LMCT state. The subsequent formation of the excited 2 E state corresponds to a spin ip of one of the electrons in a t 2g orbital and for this reason we will hereaer name the metal-to-metal charge-transfer process M*M 0 CT instead of MM 0 CT, where M* indicates an excited state of the Cr ion. The new spin conguration on the Cr site will affect the M*M 0 CT transition leading to a reduction in the MM 0 CT absorption causing the increase in the transmission that we observe experimentally. The vibrational cooling in the 2 E state is responsible for the $0.8 ps at 50 K and $1.1 ps at 300 K decay of the transient transmission that we observe ( Fig. 4(b)). We do not observe any ESA from the 2 E state, 45 presumably because changes to the visible spectrum are completely dominated by the much stronger M*M 0 CT transition.
The propensity to optically transfer to either V II or V III from the excited-state potential, and the corresponding timescale for which this occurs, depends on the sample temperature, as observed in Fig. 3(a), (b) and (f). The temperature dependence of the M*M 0 CT absorption band should therefore be different from the temperature dependence of the ground-state MM 0 CT band as displayed in the static spectrum of Fig. 3(e). The above interpretation of a temperature-dependent decay pathway aer the LMCT excitation is further sustained by the results of Bozdag et al. 46 who identied a hidden metastable state that caused a decrease in the magnetisation aer illuminating a sample of V-Cr PBA for 60 h at the LMCT transition at 10 K (l ¼ 350 nm). In their results, the metastable state survives heating up to 250 K and disappears at higher temperatures, indicating the efficient role played by thermal excitations in PBAs.
Let us now focus on the differential magneto-optical Faraday signal Dq F measured at temperatures T s ¼ 50 and 300 K. Electronic optical transitions that affect exchange-coupled electrons give rise to a MO signal whose magnitude and sign depend on the nature of the transition. 31 Ohkoshi et al. have shown that the MO signal from the MM 0 CT transition in V-Cr PBA is proportional to the magnetisation. 37 This arises because the spins on the Cr ions are connected to the spins on the V ions via the super-exchange interaction. In contrast, there is no static MO signal from the LMCT transition, 37 which is probably due to the fully occupied orbital of the ligand and so there is no exchange interaction between the electrons on the ligand and the Cr ion. In our experiments, we observe similar decay constants as for DT/T, which is shown in Fig. 3(f). Aer the fast ISC to the 2 E state on the Cr ion, the new spin conguration is changed from S ¼ 3/2 to S ¼ 1/2 (Fig. 4(c)). The local change in spin conguration modies the super-exchange interaction between the Cr and V ions and therefore gives rise to the change in MO signal for the M*M 0 CT transition. The time-resolved MO signal can therefore detect changes in the strength of the super-exchange interaction on a sub-ps timescale.
Besides from the large range of studies on SCO compounds mentioned previously, where fast ISC occurs accompanied by structural changes, other molecular magnetic systems also display fast dynamics. For example, fast sub-50 fs three-state dynamics, involving partly spin-allowed steps, have been observed in breathing crystals using transient absorption. 12 In Prussian blue, both ultrafast back-electron transfer and trapping of charge-transfer (CT) states occur aer exciting at the MM 0 CT transition. 47,48 This has also been observed in related dinuclear cyano-bridged mixed-valence systems. 49 Trapping of long-lived CT states (ns) in the photomagnetic Co II -Fe III PBA was also observed aer both MM 0 CT and LMCT pumping. 50

Conclusions
In conclusion, we have observed the ultrafast dynamics of charge and spin transfer in the molecule-based magnet V-Cr PBA at room temperature and 50 K. It has been carried out by performing time-resolved femtosecond transmission and magneto-optical Faraday measurements with frequency nondegenerate pumping (400 nm) and probing (super-continuum in the visible). We show that upon exciting the ligand-to-metal charge-transfer transition at 400 nm, the 2 E state on the Cr sites is populated in less than 250 fs, resulting in an increase in the transmission associated with the M*M 0 CT transition. Vibrational cooling in the 2 E state occurs with a time constant of 0.78 AE 0.05 ps at 50 K and 1.1 AE 0.1 ps at 300 K. Correspondingly the time-dependent MO Faraday signal follows the same dynamics and the associated change in spin-conguration of the 2 E state is observable in the MO signal of the M*M 0 CT transition. The results show that this method can be used to directly observe changes to spin congurations, and therefore the exchange interaction, on a fs timescale in magnetic molecular materials. The signature from both V oxidation states implies that the present approach of studying site-specic dynamics using ultrafast laser spectroscopy together with time-resolved magneto-optics is a powerful and underexplored technique for the eld of molecular magnetism, especially when selective pumping and broad-band spectral probing are employed. This in turn will allow for new chemistry to be developed in the process of optimising magneto-optical properties and spin switching rates by chemically tuning the molecular properties. A sudden change in spin conguration can lead to a large structural change, as in the case of spin-crossover materials, which typically leads to vibrational dynamics involving stretching and bending modes. 21,23,25 The proposed method here is fast enough to follow the vibrational dynamics of magneto-structural correlations by simultaneously recording the transmission and MO signals. Faraday MO techniques can therefore provide an attractive alternative approach to directly probe the spin dynamics in molecule-based magnets, singlemolecule magnets, and spin-crossover materials. These studies show the large potential of femtomagnetism for studying and monitoring molecular magnets.