Probing photoinduced spin states in spin-crossover molecules with neutron scattering

K. Ridier,1 G. A. Craig,2 F. Damay,1 T. Fennell,3 M. Murrie,2 and G. Chaboussant1,* 1Laboratoire Léon Brillouin, UMR12 CEA-CNRS, F-91191 Gif-sur-Yvette, France 2WestCHEM, School of Chemistry, University of Glasgow, G12 8QQ Glasgow, United Kingdom 3Laboratory for Neutron Scattering, Paul Scherrer Institut, CH-5232 Villigen, Switzerland (Received 14 July 2016; revised manuscript received 25 November 2016; published 3 March 2017)


I. INTRODUCTION
Molecular or nanometer-size systems capable of changing their magnetic state through some external stimulus (magnetic field, electric field, light, or pressure) are subject to intense studies.Promising examples are photoswitchable materials based on the spin transition mechanism for future applications as optical memories or digital displays [1].The spin transition usually occurs with a temperature change, under pressure, or under visible or near-IR light irradiation.Molecules containing octahedral Fe(II) ions have been the most widely studied since the discovery of the light-induced excited spin-state trapping (LIESST) effect by Decurtins et al. [2,3] in [Fe(ptz) 6 ](BF 4 ) 2 (ptz = 1-propyltetrazole) which proved that the spin state could be switched reversibly from the low-spin (LS; S = 0) to the high-spin (HS; S = 2) state under visible light in a solid-state material.Since then [Fe(ptz) 6 ](BF 4 ) 2 has become one of the archetypal examples of photoswitchable molecular complexes with an abrupt thermal HS-to-LS spin transition at ∼135 K.At low temperature, green/blue light irradiation can switch the nonmagnetic LS Fe(II) ions to a metastable HS S = 2 state, which has a long lifetime (several weeks at 2 K).The LS ground state can be restored by thermal relaxation above the so-called T LI ESST temperature (T LI ESST ≈ 55 K) or under irradiation using near-infrared light (reverse LIESST effect).Despite several studies of the photoinduced HS magnetic state, there is relatively little information regarding its magnetic anisotropy.From magnetization curves, Goujon et al. [4,5] provided the first strong hint of the presence of a sizable zero-field splitting (ZFS).Using electron paramagnetic resonance (EPR) spectroscopy, Feng et al. [6] estimated both the axial D and rhombic E terms in the photoinduced high-symmetry HS state.Inelastic neutron scattering (INS) is a very efficient and proven technique to determine ZFS parameters [7], and unlike EPR, it does not rely on an external magnetic field to observe spin excitations.However, INS often requires a large amount of sample to reach reasonable counting times and statistics.It could thus be an extremely valuable tool for the study of photoswitchable magnetic molecular compounds, providing one succeeds in obtaining a significant fraction of HS magnetic sites over a large sample volume.So far, only small single crystals or thin layers of powder sample, up to 10-15 mm 3 , were considered in spectroscopic, diffraction, or bulk techniques due to light-penetration limits and laser-power damage.To best overcome this issue we have developed special setups tailored to combine neutron scattering (diffraction and INS) and in situ light irradiation for photomagnetic studies.The principal objective of the present study is to demonstrate the feasibility of such experiments with a large sample volume.We show that it is possible to determine by INS the ZFS parameters of the light-induced HS state of [Fe(ptz) 6 ](BF 4 ) 2 .Such a protocol could be easily implemented for other photomagnetic compounds.

II. EXPERIMENTAL AND SAMPLE
A fine powder of [Fe(ptz) 6 ](BF 4 ) 2 was synthesized following the method developed by Feng et al. [6].The powder neutron diffraction patterns were measured on the G4.1 diffractometer at LLB-Orphée (Commissariat à l'énergie atomique et aux énergies alternatives, Saclay), and the INS experiment was performed on the time-of-flight spectrometer FOCUS at the Swiss Spallation Neutron Source (SINQ, Paul Scherrer Institut, Villigen).An adapted sample holder designed to optimize the light irradiation over a large amount of powder sample was coupled to an optical fiber and fitted in the cryostat [8].The sample is flash cooled in liquid nitrogen below the HS-to-LS spin transition temperature (≈135 K) so as to stay in the rhombohedral R 3 phase, thus avoiding a disordered phase [9,10].The validity of such a procedure can easily be checked as the diffraction patterns of these two phases are completely different [11].Several previous x-ray diffraction studies have investigated the crystal structure in the HS [high temperature (HT), 150-300 K] and LS [low temperature (LT), 10-90 K] states [9,12].The lattice parameters of the photoexcited HS (LT) state at low temperature have also been reported.HS/LS fractions between 50% and 100% have been achieved under green light but only on tiny samples (volume ∼0.1-0.25 mm 3 ) [9,13,14].Green light sources (510-530 nm) were favored with the argument that choosing an excitation light energy slightly above the strong-absorption band, ( 1 T 1g ) ← ( 1 A 1g ) (maximum at 18 400 cm −1 ), will speed up the phototransformation.Another absorption band, ( 1 T 2g ) ← ( 1 A 1g ) (maximum at 26 600 cm −1 ), corresponds to blue/UV light.However, with blue light the process is more gradual, but the LIESST process remains very effective, as shown by Goujon et al. in polarized neutron diffraction (PND) experiments [4,5].PND was used to map out the spin density of the photoinduced HS vs LS state at 2 K under 5 T, with very encouraging results in terms of sample volume [15].

III. NEUTRON DIFFRACTION
The neutron diffraction data, obtained on the G4.1 diffractometer with a neutron wavelength λ = 2.423 Å and a detector coverage 2θ = 80 • , are shown in Fig. 1(a).They have been fitted using the FULLPROF package [16] to the rhombohedral R 3 space group using the atomic positions previously determined because the resolution of the instrument did not allow us to refine the atomic positions reliably.We find a,b = 10.832(1)Å and c = 31.850(2)Å in the HS (HT, 140 K) state and a,b = 10.657(2)Å and c = 31.902(5) Å in the LS (LT, 5 K) state.Under light irradiation (405 and 450 nm) we observe a progressive change in the Bragg peaks revealing the coexistence of the two spin states (HS and LS phases).During photoexcitation the temperature is stabilized at 10-15 K, well below the temperature of the thermally-driven relaxation process.After photoexcitation and return to 5 K the lattice parameters are a,b = 10.829(5) Å and c = 31.427(2)Å for the HS phase, while those of the LS phase remain unchanged.Moreover, the Bragg peaks do not show any broadening or loss in intensity, suggesting that we stayed in the R 3 phase during the whole process.The obtained values are perfectly in agreement with previous x-ray data, but extracting the HS/LS fraction from fitting the whole neutron diffraction pattern remains difficult.Instead, we chose to monitor the two Bragg peaks most sensitive to the Fe(II) spin state: (113) (Q 1 ≈ 1.31 Å−1 ) and ( 202) . As shown in Fig. 1(a), under blue light the two peaks clearly evolve towards four peaks, one pair for each spin state; thus, they were fitted assuming two sets of Bragg peaks.The comparison of Q 1 and Q 2 Bragg peak intensities in both LS and HS states yields a reliable estimate of the HS fraction γ H S assuming The HS fraction γ H S as a function of time and illumination Red: after rapid cooling in liquid nitrogen to 5 K (100% LS state); black: after irradiation at λ = 450 nm (400 mW, 32 h); orange: after irradiation at λ = 830 nm (150 mW, 13 h); green: after irradiation at λ = 450 nm (600 mW, 40 h); dark yellow: 5 K after warming to 80 K to restore full LS state; blue: after irradiation at λ = 405 nm (400 mW, 40 h).conditions is shown in Fig. 1(b).The first LIESST effect using a 450-nm laser at 400 mW power leads to γ H S ≈ 50% after 6-7 h, followed by a slower increase of γ H S up to 60%.This crossover between fast and slow kinetics has been systematically observed in our experiments, and we attribute it to a complex thickness-dependent process associated with light penetration and diffusion inside the powder material [14].The 450-nm laser is then replaced by an 830-nm laser (at 150 mW power), and a full reverse LIESST effect is observed after less than 5 h.As the sample was kept below 10-15 K during light irradiation, this observed decay is undoubtedly due to the reverse LIESST process rather than a thermal relaxation effect.The second LIESST effect, still using a 450-nm laser but with more power (600 mW), is less efficient than the first (γ H S ≈ 30% at saturation), probably due to a locally higher sample temperature arising from excessive heating.During the 405-450-nm irradiation processes, the temperature close to the laser entry point may have been higher than on the outer parts of the sample, but the balance between photoconversion (LS to HS) and thermally activated relaxation (HS to LS) remains, however, positive, and the saturation at about 60% arises also partially from limited light penetration.At higher power, the LS-to-HS conversion process saturates at a lower level due to a higher local temperature.The level of HS fraction that is achieved appears to be limited by two processes: local temperature increase (but not severe enough to trigger a full conversion back to LS) and limited penetration of light inside the powder.There is thus probably a sizable amount of sample which does not experience light irradiation.This is supported by the fact that the coexistence of both LS and photoinduced HS phases is evidenced in the diffraction patterns.After having reset the whole sample to the LS state by first warming it up to 80 K and then returning it to 5 K [see Fig. 1(b)], we obtained a maximum similar HS/LS fraction (60%) with 405-nm laser light (400 mW).With both laser wavelengths (405 and 450 nm) we approach saturation for γ H S after ∼15 h.In the course of the experiment, we did not reach a full HS state (γ H S = 1), even after 30 h.Despite only a fraction of the material being converted to HS, our neutron diffraction experiment demonstrates nevertheless that a large volume of powder sample (at least 175 mg) can be phototransformed using the present experimental setup.Such a positive outcome allowed us to perform INS experiments to probe the magnetic excitations of the light-induced metastable HS state as we expect no magnetic inelastic scattering at all in the LS phase.

IV. INELASTIC NEUTRON SCATTERING
INS spectra were recorded on FOCUS at low temperature on 400 mg of an undeuterated, microcrystalline powder sample of [Fe(ptz) 6 ](BF 4 ) 2 placed in our adapted sample holder.The FOCUS data were measured with an incident neutron energy E i = 9.108 meV with instrumental FWHM ≈ 0.45 meV at the elastic line position.The experimental resolution at finite-energy transfer is comparable (for hω ≈ E i /2, FWHM ≈0.6 ± 0.1 meV; see [17]) with possible broadening due to multiple scattering arising from scattering of hydrogen nuclei.The data, corrected for detector efficiency with vanadium metal standard, correspond to the sum of all of the central detectors (the upper and lower banks of the detectors are obstructed by the bulky metallic cryomagnet).Figure 2 shows the evolution with magnetic field of the INS spectra at 10 K after laser light irradiation (405 nm, 400 mW, 100 h).The INS spectrum obtained at 10 K and zero field prior to irradiation (100% LS nonmagnetic state) has been subtracted from the three data sets.At zero field, after light irradiation, we observe a clear extra inelastic scattering signal at ≈4.0 meV, compared to the initial spectrum.Since the LS state is nonmagnetic, the main source of extra scattering is magnetic, although modifications in the low-energy phonon modes could be invoked.Under magnetic field (up to 6 T) we observed a visible broadening and a slight shift towards higher energies of this extra scattering contribution, confirming its magnetic origin.
The ground state of the six-coordinated HS Fe(II) ions is the orbital triplet 5 T 2 state.The combined effect of spin-orbit coupling and additional ligand fields (e.g., tetragonal and/or rhombohedral distortions) has to be considered.These terms split the degeneracy of the ground term and quench, in many instances, the residual orbital contribution.Therefore, a "spin-only" Hamiltonian model has been conveniently, and successfully, used on various HS Fe(II) systems despite its approximative character (often taken care of in Landé factor shifts or "renormalization" of the anisotropy) [18][19][20][21].There are several instances where the pertinence of the ZFS spin Hamiltonian has been discussed, even setting out the conditions where a spin-only Hamiltonian can or cannot be used to describe the low-energy states of Fe(II) in distorted octahedral symmetry [20,21].In the present case, we have considered the model proposed by Feng et al. [6] used to describe their EPR data.
We assume that the six-coordinated Fe(II) ions in the HS state can be described using a S = 2 spin Hamiltonian that includes both the ZFS term due to magnetocrystalline anisotropy and the Zeeman interaction term: D and g are the ZFS tensor and the g matrix, respectively.Ŝ is the total spin moment of the molecule with components Ŝi .In the proper coordinates, for which D is diagonal, one obtains where D and E are the axial and rhombic ZFS parameters, respectively.In the present case, the eventual presence of a rhombic term is not foreseen due to symmetry arguments unless some further distortions and/or local variation in crystallographic environment come into play (see [22] and references therein).Indeed, the E term reported by Feng et al. [6] is rather small (|E/D| 0.06) and might be dominated by the existence of a random distribution of rhombic distortions.Introducing the reduced parameter u = √ 3E/D, the zero-field eigenvalues are For D < 0, E 2b is the lowest-energy state.The corresponding eigenfunctions are detailed in Ref. [23].In most cases we have u 2  1, and the states ψ 2a and ψ 2b (M s = ±2) are quasidegenerate E 2a = E 2b ≈ 2D.The next spin levels ψ 1a and ψ 1b (M s = ±1) at hω = 3|D| are split due to the possible rhombic term E. The energies of the allowed INS transitions M = ±1 between the low-lying states ψ 2a,2b and ψ 1a and ψ 1b are then hω ± ≈ 3|D| ± 3|E|.Finally, note that transitions between ψ 2a,2b and ψ 0 (hω ≈ 4|D|) are not allowed according to INS selection rules.
At zero field (see Fig. 2) we observe a broad INS peak centered around 3.9 meV, but its width is almost twice (0.9 ± 0.1 meV) the instrumental resolution, which suggests the presence of two peaks.The peaks shift slightly to higher energies with increasing field.Considering one single peak and keeping the resolution close to the instrumental one leads to a poor fit (not shown).If, instead, we use a double-Gaussian model with the same width as the resolution (or slightly larger) we obtain good agreement with two peaks centered at 3.6 ± and 4.1 ± 0.1 meV, but there is not resolution to clearly resolve the peaks.Taking into account these considerations, we tried to reproduce our INS data with ZFS parameters similar to those reported by EPR (D < 0 and E = 0) [6].Identifying these INS peaks with the magnetic transitions of energies hω ± ≈ 3|D| ± 3|E|, we obtain D = −1.28 ± 0.03 meV and |E| = 0.08 ± 0.03 meV.The ratio |E/D| = 0.062 is consistent with the initial assumption (u 2  1).As already shown by high-field (HF) EPR [6], the negative D value signals the existence of an easy-axis-type anisotropy for the photoinduced HS Fe(II) ions.The parameters derived from INS are consistent with HF-EPR results (D is negative, with |D| 15 cm −1 = 1.86 meV, and E = −0.95cm −1 = −0.12meV) with reasonably small error bars (no error bars are provided from the EPR study).
With increasing magnetic field, the magnetic INS contribution undergoes a clear broadening and a small global shift towards higher energies.The energy shift, due to the Zeeman splitting of both M s = ±2 and M s = ±1 states, depends on the field orientation with respect to the easy-axis direction z (see Ref. [24]).In the parallel direction (B z ), the Zeeman splitting , where 2 ≈ 3E 2 /D for small E/D.In such a situation, the overall splitting is essentially linear, δ , where 1 = 6E ≈ 3.8 cm −1 is comparable to the Zeeman term for B z 4 T.In the directions perpendicular to z, the Zeeman interaction induces almost no additional splitting; it barely shifts the energies of the M s states by  2), where we take D = −1.28meV, |E| = 0.08 meV (both inferred from zero-field estimates), and g z ≈ 2.3 (see [6]).From this set of data we certainly cannot unambiguously determine the g factors.We therefore considered some reasonable values and tried to account for the field-dependence of the INS peak of our powder sample.Three energy resolutions (0.45, 0.50, 0.65 meV) were considered to account for the combined effect of instrumental resolution and possible multiple scattering from hydrogen.In all cases, we find good agreement taking g z = 2.3 and g x = g y ≈ 1.6.Note that the sensitivity to g z (controlled by the high-energy bound of the INS peaks) is higher than to g x,y .This model is consistent with the observed broadening and the global shift of the INS peak under magnetic field.In particular, there is good agreement with the data at B = 0-4 T, regardless of the resolution changes, but some discrepancy is visible for B = 6 T, possibly due to magnetic torque effects that could substantially modify the statistical distribution of orientation in a powder.

V. CONCLUSION
In conclusion we have reported a neutron-scattering investigation of the photoinduced metastable HS S = 2 state of [Fe(ptz) 6 ](BF 4 ) 2 .Using a specially designed setup, we demonstrated the feasibility to induce by blue light (405 and 450 nm) irradiation a low-temperature spin transition (LIESST effect) over a large sample volume.In neutron diffraction, HS/LS ratios of up to 60% (≈200 mg of photoconverted material) are obtained during the LIESST effect, while a complete reverse LIESST is achieved using near-IR light (830 nm).The most important result is the INS study of the photoinduced HS state of a spin-crossover system.From INS magnetic transitions, we have interpreted our data in terms of a spin-only Hamiltonian model to describe the metastable S = 2 ground state and the presence of a zero-field splitting.Our scope was primarily to demonstrate that it is possible to perform inelastic neutron-scattering studies of photoinduced metastable states of photoswitchable materials.This result opens promising prospects for in situ magnetic inelastic neutron-scattering investigations of a broad range of photomagnetic materials.

≈
4g z μ B B z , down to B z ≡ 2 ≈ 0.1 T without giving rise to an INS peak due to INS selection rules.At 10 K and B z 4 T, only the lowest Zeeman branch (M s = −2) will be thermally populated.On the other hand, the splitting of the M s = ±1 states is given by δ

Figure 2
shows a crude attempt to reproduce the observed INS peaks under magnetic field.Solid lines in the right panels are calculations derived from Eqs. (1) and (