Ngoc Minh Tran

Marlène Palluel

Nathalie Daro

Guillaume Chastanet

Eric Freysz
email: eric.freysz@u-bordeaux.fr

Time-Resolved Study of the Photoswitching of Gold Nanorods Coated with a Spin-Crossover Compound Shell

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Introduction

Spin crossover (SCO) is a phenomenon that occurs in families of transition metal complex in the center of which a metallic ion such as Fe(II), Co(II) is inserted. [START_REF] Cambi | Über die magnetische Susceptibilität der komplexen Verbindungen[END_REF][START_REF] Stoufer | UNUSUAL MAGNETIC PROPERTIES OF SOME SIX-CO ÖRDINATE COBALT(II) COMPLEXES1 -ELECTRONIC ISO-MERS[END_REF][START_REF] König | 5T2-1A1 Equilibriums in some iron(II)-bis(1,10-phenanthroline) complexes[END_REF] Upon variations of temperature, pressure or light intensity, the spin state of the metallic center may change, giving rise to a mechanism called spin crossover. [START_REF] Gütlich | Spin Crossover in Transition Metal Compounds I[END_REF] It results in sizable modifications of the mechanical, magnetic, electrical and optical properties of the complexes. [START_REF] Gütlich | Spin Crossover in Transition Metal Compounds I[END_REF][START_REF] Bousseksou | Molecular spin crossover phenomenon: recent achievements and prospects[END_REF][START_REF] Murray | Spin-crossover complexes[END_REF][START_REF] Gütlich | Spin state switching in iron coordination compounds[END_REF][START_REF] Halcrow | Spin-crossover materials: properties and applications[END_REF][START_REF] Hayami | Spin-state switches in molecular materials chemistry[END_REF] At the macroscopic scale, this change may be accompanied by a first-order phase transition which is often associated with a thermal hysteresis loop. Within the hysteresis loop and depending on its cycling history, the sample may remain in its high temperature (high spin -HS) or low temperature (low spin -LS) state as long as the temperature is kept within the thermal hysteresis loop.

The potential application of this phenomenon in displays, indicators, data recording, and sensors, has triggered a lot of attention 5,10-14 and numerous efforts have been made to design SCO compounds with well-suited properties. For that purpose, much attention has been driven towards polymeric triazole based Fe(II) complexes such as [Fe(Htrz) 2 trz] (BF 4 ). [START_REF] Kahn | Spin transition molecular materials for displays and data recording[END_REF][START_REF] Kroeber | Spin transitions and thermal hysteresis in the molecular-based materials [Fe (Htrz) 2 (trz)](BF4) and [Fe (Htrz) 3](BF4) 2. cntdot. H2O (Htrz= 1, 2, 4-4H-triazole; trz= 1, 2, 4-triazolato)[END_REF][START_REF] Roubeau | Triazole-Based One-Dimensional Spin-Crossover Coordination Polymers[END_REF] The latter exhibits a broad thermal hysteresis loop centered above room temperature. Small nanostructures of these compounds can be synthesized while maintaining the cooperativity. [START_REF] Herrera | Studies on bifunctional Fe(II)-triazole spin crossover nanoparticles: time-dependent luminescence, surface grafting and the effect of a silica shell and hydrostatic pressure on the magnetic properties[END_REF][START_REF] Coronado | Bistable spin-crossover nanoparticles showing magnetic thermal hysteresis near room temperature[END_REF][START_REF] Herrera | Bifunctional Hybrid SiO2 Nanoparticles Showing Synergy between Core Spin Crossover and Shell Luminescence Properties[END_REF][START_REF] Herrera | Studies on bifunctional Fe (II)-triazole spin crossover nanoparticles: time-dependent luminescence, surface grafting and the effect of a silica shell and hydrostatic pressure on the magnetic properties[END_REF][START_REF] Torres-Cavanillas | Downsizing of robust Fe-triazole@SiO2 spin-crossover nanoparticles with ultrathin shells[END_REF][START_REF] Li | Integrating spin-crossover nanoparticles with silver nanowires: toward magnetic and conductive bifunctional nanomaterials[END_REF] Besides, it is possible to obtain plenty of different and exotic nanostructures based on such systems. [START_REF] Salmon | Spin-crossover nanoparticles and nanocomposite materials[END_REF] However, for a lot of applications, an improvement in the response time of SCO compounds is required. Through conventional heating, it is usually difficult to record a spin state transition on a short time scale. To circumvent this problem attempts have been made using the light-induced excited spin-state trapping (LIESST) effect [START_REF] Hauser | Reversibility of light-induced excited spin state trapping in the Fe(ptz)6(BF4)2, and the Zn1-xFex(ptz)6(BF4)2 spin-crossover systems[END_REF] or local shockwave excitation. [START_REF] Parpiiev | Ultrafast non-thermal laser excitation of gigahertz longitudinal and shear acoustic waves in spin-crossover molecular crystals [Fe (PM-AzA) 2 (NCS)[END_REF] However, the LIESST effect is usually recorded at low temperatures [START_REF] Létard | Structural, magnetic, and photomagnetic studies of a mononuclear iron (II) derivative exhibiting an exceptionally abrupt spin transition. Light-induced thermal hysteresis phenomenon[END_REF] and forbiddens applications at room temperature. Besides, the shock waves are usually induced through absorption of the laser pulse exciting the medium and therefore difficult to control and optimize. [START_REF] Marino | Femtosecond optical pump-probe reflectivity studies of spin-state photo-switching in the spin-crossover molecular crystals [Fe(PM-AzA)2(NCS)2[END_REF] To go further, we have used the photo-thermal effect to rapidly switch a spin crossover compound between the LS and HS states. [START_REF] Fouché | Laser induced spin state transition: Spectral and temporal evolution[END_REF] A fast photo-switching is recorded exciting the duration and energy of the optical pulse, as well as the thermal diffusion within and between the particles. [START_REF] Gallé | Room temperature study of the optical switching of a spin crossover compound inside its thermal hysteresis loop[END_REF][START_REF] Gallé | Nanosecond study of spin state transition induced by a single nanosecond laser shot on [Fe(NH2trz)3] compounds inside and outside their thermal hysteresis loops[END_REF] This photo-switching is fastened in SCO nanoparticles (NPs). [START_REF] Gallé | Study of the fast photoswitching of spin crossover nanoparticles outside and inside their thermal hysteresis loop[END_REF] To further minimize the laser pulse energy required to photo-switch SCO NPs, a new approach based on a combination of gold and SCO NPs has been recently proposed. [START_REF] Moulet | Grafting of gold onto spin-crossover nanoparticles: SCO@ Au[END_REF][START_REF] Qiu | SCO@ SiO 2@ Au core-shell nanomaterials: enhanced photo-thermal plasmonic effect and spin-crossover properties[END_REF][START_REF] Suleimanov | The photothermal plasmonic effect in spin crossover@silica-gold nanocomposites[END_REF][START_REF] Palluel | The Interplay between Surface Plasmon Resonance and Switching Properties in Gold@Spin Crossover Nanocomposites[END_REF][START_REF] Torres-Cavanillas | Design of Bistable Gold@Spin-Crossover Core-Shell[END_REF] Along this line, we have recently demonstrated that insertion of gold nanorods (AuNRs) in [Fe(Htrz) 2 trz] (BF 4 ) NPs largely reduces the optical peak power required to induce the spin-state transition in these SCO nanohybrids. [START_REF] Suleimanov | The photothermal plasmonic effect in spin crossover@silica-gold nanocomposites[END_REF][START_REF] Palluel | The Interplay between Surface Plasmon Resonance and Switching Properties in Gold@Spin Crossover Nanocomposites[END_REF] For simplicity we will hereby refer the NPs of [Fe(Htrz) 2 trz] (BF 4 ) and AuNRs embedded in [Fe(Htrz) 2 trz] (BF 4 ) as SCONP and Au@SCO, respectively.

Embedding AuNRs inside the SCONP provides a robust structure and good core/shell contact. [START_REF] Palluel | The Interplay between Surface Plasmon Resonance and Switching Properties in Gold@Spin Crossover Nanocomposites[END_REF][START_REF] Torres-Cavanillas | Design of Bistable Gold@Spin-Crossover Core-Shell[END_REF] The high and broad optical absorption of Au@SCO in the visible range results in burgundy color and permits to excite the Au@SCO in a large spectral range. Besides an optical excitation at 770 nm, near the longitudinal SPR absorption peak of the AuNRs provides a means of selectively heating the core of the AuNRs. These Au@SCO are therefore expected to have optimized response time and low power consumption. [START_REF] Palluel | The Interplay between Surface Plasmon Resonance and Switching Properties in Gold@Spin Crossover Nanocomposites[END_REF] In this paper we investigate the photoswitching process in these Au@SCO nanohybrids. The study is performed exciting the samples with near-infrared quasi-continuous wave (QCW) or nanosecond pulse tunable from visible to near-infrared range. These QCW and nanosecond pulse excitations permit studying the growing of the HS state within the samples under Heaviside's or Dirac's excitations, respectively. Upon Dirac excitation with nanosecond pulses a photo-switching time down to 20 ns is recorded in Au@SCO. We also show these nanosecond experiments give power to analyze the growing of the HS state fraction within an ensemble of individual SCONP and Au@SCO. Besides, we evidence that compared to the SCONP of the same size, the energy of the optical pulses required to induce the spin state transition in Au@SCO is overall reduced. A more remarkable reduction is recorded around the surface plasmon resonance (SPR) of the AuNRs.

Methods

General

Transmission electron microscopy (TEM) images are acquired using a JEOL 1400+ (Japan), with a high-resolution mode and a tension of 60 kV. Each compound is analyzed separately and the measurements of 100 particles are done in order to give the average dimensions.

Magnetic measurements are performed using a MPMS-5S Quantum Design SQUID magnetometer operating at 20 kOe. The powder samples are prepared in a thin layer ( 0.9 mg on around 100 µm thickness). The sample is weighted before any measurement and the diamagnetic contributions of the sample and the sample holder are removed. The thermal cycles are performed at around 0.7 Kmn -1 scan rate. The absorption measurements are carried out shining the sample with a broadband halogen light (Thorlabs OSL1-EC) source and recording the spectra of the transmitted light with and without the sample with a compact spectrometer (Ocean Optics, Flame Vis-NIR) versus the temperature. The relative optical density is evaluated by computing the logarithmic ratio of the sample spectra over the reference spectra transmitted by a microscope glass slide.

Millisecond photoswitching set-up

The set-up used to record photoswitching kinetic of the samples at the millisecond time scale is displayed in Fig. 1a. The sample is kept in a thermally regulated oven and excited by a continuous wave (CW) laser diode (Thorlabs FPL785S) that central wavelength is about 785 nm. The latter is almost within the longitudinal SPR absorption mode of Au@SCO. A mechanical shutter is used to generate optical pulses of steady state intensity with duration between 2 ms and 500 ms. The exciting pulse is focused on the sample on slightly elliptical spot which diameter is about 0.8 mm. The probe light is provided by a high-intensity halogen lamp (Thorlabs OSL1-EC) which spectrum ranges from 350 nm to 800 nm. On the sample, the halogen light is also focused on a spot of about 0.8 mm in diameter. The light transmitted by the sample is collimated and focused on entrance slit of a monochromator (CVI CM110 1/8m). The monochromator is set to transmit light centered at 770 nm where the change in absorption of the sample induced by the LS and HS state switching is large.

It is equipped with a grating (1200 grooves/mm) blazed at 600 nm and 600 µm input and output slits. The output of the monochromator is focused on a fast photodiode connected to a numerical oscilloscope. The transmission signals are averaged over about 120 shots.

Nanosecond photoswitching set-up

Figure 1b displays the optical setup used to record the time-resolved photoswitching of the samples at the nanosecond time scale. The sample kept in a thermally regulated oven is excited by nanosecond pulses provided by an optical parametric oscillator (Continuum OPO Panther EX). The central wavelength of these pulses is tunable from 410 nm to 2700 nm.

The pulse duration and energy are about ∼ 6 ns and 40 mJ, respectively. These pulses are slightly focused on the sample on a beam spot of Φ ∼ 1.5 mm in diameter. The transmission of the sample is probed at normal incidence, using the Thorlabs CW laser diode (FPL785S).

The probe beam transmitted by the sample is collimated and focused on the entrance slit of a monochromator (CVI CM110). The signal at the output of the monochromator is further filtered by a laser-line filter (Thorlabs), collected by a high-speed silicon photodiode and then recorded on a 1 GHz numerical oscilloscope (Tektronik) which triggered the nanosecond pump pulses. The transmission signals are averaged over about 120 shots.

Sample preparation

The synthesis method of the SCONP and the hybrid Au@SCO has been discussed elsewhere. [START_REF] Palluel | The Interplay between Surface Plasmon Resonance and Switching Properties in Gold@Spin Crossover Nanocomposites[END_REF] The AU@SCO as prepared have high filling factor: about 90% of the SCONP contain at least one gold nanorod. As shown in the transmission electron microscopy (TEM) image (Fig. 2a), the average size of Au@SCO along the longitudinal and transverse axis is 212±30 nm by 106±24 nm. The embedded AuNRs have an average dimension of 60±8 nm The samples used to record the photoswitching kinetics are prepared as follows. A powder of either SCONP or Au@SCO is dispersed in ethanol, drop-casted, and then dried on a microscope glass slide. The thickness l s = 4.0±2.0 µm of the sample is measured over a 100 µm * 100 µm area with an AFM in tapping mode and averaged. The dried sample is then covered by an other microscope glass slide and inserted in an oven that temperature can be finely controlled (±0.1 • C) from 300 K to 490 K.

Results and discussions

Absorption spectra of the samples in the visible and near infrared.

Figure 2b displays the absorbance of the samples in the LS and HS states in the 400 nm to 850 nm spectral range. As its temperature increases the SCONP sample switches from the LS to the HS state and its color turns from pink (T∼300 K) to white (T ∼ 410 K). The change in color of SCONP results in a decrease of their absorbance in the HS state. The absorbance spectra of the Au@SCO exhibits two broad peaks, related to the transverse ( ∼520 nm) and longitudinal (in between 600 nm and 850 nm) surface plasmon modes of the AuNRs. The latter is more marked and its maximum shifts from ∼ 750 nm to ∼ 710 nm when the temperature is increased from 300 K to 410 K. Comparison between the magnetic and absorption measurements (Fig. 3a) indicates this shift of the longitudinal SPR is associated to the switching from the LS to the HS state of the spin crossover shell within the Au@SCO.

Figure 3b also indicates the switching from the LS to HS state results in a decrease of the normalized absorbance of both SCO and Au@SCO samples at 750 nm.

Study of the photoswitching at the millisecond time scale

Experimental results

Figure 4a shows the temporal evolution transmission upon QCW excitation of Au@SCO (blue dots) and SCONP (red dots) samples by an optical pulse of power and duration of I p = 270 mW and t p = 490 ms, respectively.

Upon excitation, the increase in transmission is fitted using a simple mono-exponential model

S(t) = S 0 (1 -exp (-t/τ c ))
, where the rate of change is expressed by the characteristic time τ c . The fitted values of τ c are 60 ms and 300 ms for Au@SCO and SCONP, respectively.

After the pulse excitation, the transmission of the samples remains constant and it does not relax back to its initial value. To recover its initial transmission, the sample has to be cooled down below 330 K. In Figure 4a, we have also estimated the ratio of converted NPs during the photoswitching experiment (Fig. 4b). The way we estimated the change in the HS fraction ∆γ HS is as follows. Before exciting the sample, we recorded the change in amplitude ∆V of the signal recorded by the photodiode at the exit of the monochromator when the sample is set at T=300 K and at T=430 K in the HS state. We consider this change in amplitude ∆V is associated to ∆γ HS = 1. Then we consider that upon laser excitation the change in ∆γ HS (t) scales with respect to the signal V(t) recorded by the photodiode: ∆γ HS (t) = ∆V (t) ∆V . Accordingly, we estimate that a QCW optical pulse of I p = 270 mW switches about 28% (∆γ HS = 0.28) of Au@SCO NPs from LS to HS states while it is less than 10% for SCONP.

Regarding the photoswitching time, the conversion is achieved within ∼250 ms for Au@SCO when the pulse duration is t p = 490 ms. Note that when the pump pulse ends the slope of the signal is almost zero indicating we reached a steady state regime. On the contrary, upon excitation the SCONP sample does not reach such a steady state even after 490 ms.

We also recorded transmission of the Au@SCO upon excitation by a 1 Hz pump train (Fig. 4c). The exciting pulses have the same peak power (I p1 = 160 mW) and duration (t p = 100 ms). Note that only the first pulse induces a change in transmission (red curve in Fig. 4c). When another pulse excites the sample, the transmission does not further change.

To further increase the transmission of the sample, one has to increase temperature of the sample or laser peak power as illustrated in Fig. 4c where pump peak power was increased from I p1 = 160 mW to I p2 = 270 mW.

Finally, to evidence the impact of the change in ∆γ HS on the photoswitching kinetics, we normalize the transmission of the sample under different pulse powers for given pulse duration. One can notice that for a given pulse duration, the higher the peak power density, the faster the photoswitching (Fig. 5a). Besides for short pulse duration t p = 100 ms, the kinetics remains almost unchanged whatever the pulse power (Fig. 5b) while a noticeable change is observed for longer pulse duration (Fig. 5a).

Hereafter, we will assume that upon QWC excitation the change in temperature can result almost instantaneously in an increase of ∆γ HS in both the Au@SCO and SCONP samples.

In our QCW experiments, the change in ∆γ HS versus ∆T can be estimated from Fig. 3.

Note that in the latter figure at the rising edge of the hysteresis loop (T∼370K), γ HS (and therefore ∆γ HS ) scales almost linearly with ∆T along the ascending branch of the thermal hysteresis. Hence to model our experimental data one has to account for the temperature evolution within our sample upon laser excitation.

Upon QCW pulse excitation, the change in temperature of the sample ∆T is governed by the heat equation that writes:

∂∆T ∂t = D th ∇ 2 (∆T ) + Q ρC p (1)
where D th , ρ, C p and Q are heat diffusivity, initial mass density, heat capacity and the heat deposited in the sample, respectively. The latter equation is valid for a homogeneous solid whose thermal conductivity is independent of the temperature. For QCW pulse excitation Q = α(λ p )I p /V where α(λ p ), I p and V are the absorption coefficient of the sample at a pump wavelength λ p , the power density of optical pump pulse and the excited volume, respectively. The resolution of Eq. 1 along with the boundaries, initial conditions and used main approximations are given in the supplementary material. Under our experimental conditions where the thickness l s of the sample is small compared to the diameter (d=2a) of the photo-excited area, the temperature at the center of our very thin sample writes:

∆T 0 ≈ A 0 l 2 s 8D th (2)
where A 0 = α(λ p )I p /(V ρC p ). The mean temperature of the sample at steady state writes:

∆T m ≈ 2 3 ∆T 0 (3)
Since ∆T m ∝ ∆T 0 ∝ I p , the mean temperature of the sample increases linearly with the power of the exciting laser. One can also evaluate the kinetic for temperature rise. The latter writes:

∆T (r, z, t) ≈ ∆T (r, z) 1 -exp - t τ c,z × 1 -exp - t τ c,r (4)
where the time constants τ c,z = 1

D th l 2 π 2 and τ c,r ≈ 1 D th a 2.4 2
account for diffusion of heat along the thickness and diameter of the sample, respectively. According to Eq. 2-4 and knowing the radius a of the beam spot of the pump pulse, the thickness l s , the thermal diffusivity D th , the density ρ and the specific heat C p of the sample, one can compute the temperature at the center of the disk ∆T 0 (Eq. 2), the mean temperature at steady state ∆T m (Eq. 3) and the time constant. The heat capacity of the [Fe(Htrz) 2 trz] (BF 4 ) is

C p ∼ 1 J•g -1 •K -1 . 39
The bulk thermal diffusivity of this material has not been reported, but

we will consider that it behaves like a conventional polymer with D th ∼ 1.2 × 10 -7 m 2 /s.

The density of the [Fe(Htrz) 2 trz] (BF 4 ) is ρ ∼ 1.8 g/cm 3 . 39 However, the technique used to prepare our samples makes the SCO NPs randomly packed. Their actual density is therefore lesser because it depends on the way the different nanorods are arranged in the powder. It has been shown that the occupied volume fraction scales at most like φ ≈ D L where D and L are the diameter and length of the rods, respectively. Since for our sample D L ≈ 0.5 we estimate ρ ∼ 0.9 g/cm 3 . 40 Knowing these parameters, we can readily compute the steady state temperature in the center of the SCONP and Au@SCO samples upon excitation by a QCW pump pulse. In these computations, the main difference between SCONP and Au@SCO samples is their absorption α(λ p ) at the pump wavelength. We will consider that ∼60% and ∼ 20% of the pump power is absorbed by the Au@SCO and SCONP sample, respectively. Accordingly, considering the pump power I p = 160 mW is focused on beam spot of Φ ∼ 0.8 mm, one finds ∆T 0 (Au@SCO)∼ 1.38 K and ∆T m (Au@SCO)∼ 0.92 K. whereas for SCONP ∆T 0 (SCONP)∼ 0.45 K and ∆T m (SCONP)∼ 0.3 K.

When the peak power of the pump is increased from 160 mW to 270 mW: ∆T m (Au@SCO)∼ 1.55 K and ∆T m (SCONP)∼ 0.52 K. One can notice that in agreement with Fig. 4b, the latter peak power gives rise to a measurable change in transmission for both SCONP and Au@SCO samples.

Finally, we evaluate the characteristic time τ c necessary for the sample to be at a quasisteady temperature. The characteristic times related to diffusion of heat along the thickness The HS fraction can be further increased by a second more energetic optical pulse which brings the system to a higher temperature (∆T 2 > ∆T 1 ).

duration will bring the sample back to point B. However, if the peak power is increased (I p 2 > I p 1 ), the sample will be brought at a higher temperature T = T 0 + ∆T 2 that will further increase γ HS (point D). Then the sample will cool down (point E). Of course further increase of γ HS can be achieved increasing the pump peak power. This process stops when γ HS =1. The described phenomenon accounts for all the observations reported in Fig. 4c.

It is worth noticing that the spin state transition responsible for the increase γ HS results in a modification of the absorption of the sample α(λ p ) as well as most of the thermodynamic constants of the sample such as ρ, C p , D th . Hence the computation we performed holds only if the change of γ HS is small and lower than ∼ 0.1. For larger increase in γ HS , the photoswitching kinetics is expected to be modified. This likely accounts for the change in kinetics displayed in Fig. 5a.

Study of the photoswitching at the nanosecond time scale Experimental results

Figure 7 displays a typical evolution of the transmission signal S(t) of the Au@SCO sample initially set at T 0 = 333 K upon excitation by a nanosecond laser pulse centered at 520 nm that fluence is F p ∼ 34 mJ/cm 2 . The evolution of S(t) indicates the transmission of the sample increases rapidly within few tens of nanoseconds and remains constant for ∼ 20 µs.

It then slowly relaxes within few milliseconds (Fig. 7b). Using the following function S(t) = S 0 (1 -exp (-t/τ s )) where τ s is the switching time constant, we are able to fit the rapid increase of S(t) considering τ s = 20 ± 2 ns (Fig. 7b). Similarly, we are able to nicely fit the relaxation of S(t) considering a mono-exponential decay law with a time constant τ rel = 410 ± 10 µs (Fig. 7c).

This experiment was also performed for four different lesser laser fluences (Fig. 8a). The increase in transmission is well fitted using the same switching time of τ s = 300 ± 80 ns (Fig. 8b). Similarly, the relaxation is also well fitted using the same relaxation time of τ rel = 60 ± 6 µs regardless of the excitation fluence (Fig. 8c). The sample is also excited using nanosecond laser pulses centered at 470 nm (Fig. 8d-e-f).

However in this case, we vary the initial temperature while keeping the laser fluence constant.

The Figure 8d displays the evolution of the transmission signal recorded at constant pump fluence F p = 10 mJ/cm 2 and different initial temperatures ranging from 313 K to 333 K. The amplitude of the signal decreases as the initial temperature is decreased. We are able to fit the rising and relaxation times of the signal applying mono-exponential functions. Here again whatever the initial temperature of the sample, we find that the characteristic switching time is τ s = 200 ± 50 ns (Fig. 8e), whereas the relaxation time is τ rel = 80 ± 8 µs (Fig. 8f). As displayed in Fig. 9, the threshold fluence remains almost constant in the 420 nm to 570 nm spectral range and is about F th ∼ 28 ± 2 mJ/cm 2 and F th ∼ 22 ± 2 mJ/cm 2 for SCONP and Au@SCO sample, respectively. It rapidly increases at longer wavelengths. Above 700 nm, the laser fluence required to record such change in transmission is too high and always damage the SCONP sample. Regarding Au@SCO at 620 nm, the laser fluence threshold is F th ∼ 44 ± 2 mJ/cm 2 and slightly drops towards 42 ± 2 mJ/cm 2 as one set the pump wavelength at 750 nm close to the plasmon resonance of the Au@SCO.

Equation ( 1) also describes the photoswitching upon excitation of the sample by nanosecond pulses. However Fig. 7a reveals that photoswitching of the nanohybrids takes place on a time scale ∼ 20 ns that is about three orders of magnitude smaller that ∼ 13 µs the time it takes for heat to diffuse within our 4 µm thick sample. In fact, in the time t∼20 ns the heat diffuses over a length L c = 2π √ D th T ∼310 nm that is about the characteristic length of our NPs. This indicates, we can neglect the diffusion of heat in between the NPs during the first tens of nanoseconds. Neglecting the heat diffusion in Eq.( 1), the rise in temperature ∆T upon excitation of the sample by a nanosecond pulse writes:

∆T = Q ρC p ( 5
)
where Q is the generated heat. The latter writes Q = α(λp)Ep e where α(λ p ), E p and e are absorption of the sample at the pump wavelength, the pump laser fluence and the thickness of the sample, respectively. [START_REF] Fouché | Mechanism for optical switching of the spin crossover [Fe (NH 2-trz)[END_REF] Contrary to the QCW pulse excitation (see Eq.( 2)), ∆T does not depend on the thermal diffusivity. Besides, at variance with the approximations used to analyze QCW pulse excitation, all the particles, even those lying on the top and bottom surfaces, are heated.

To evaluate the rise in temperature ∆T of the Au@SCO sample displayed in Fig. 7, we will here again consider this sample has the following characteristic parameters: ρ ∼ 0.9 g/cm 3 ,

C p ∼ 1 J•g -1 •K -1 .
Since at λ p = 520 nm, ∼ 60% of the pump fluence F p = 34 mJ/cm 2 is absorbed within the sample thickness of e ∼ 4 µm when ∆T ∼ 56 K. If the initial temperature of the sample is T 0 = 333 K, close to the end of the descending branch of the thermal hysteresis loop, upon excitation its temperature becomes T = T 0 + ∆T ∼ 389 K and the sample is set ∼ 10 K above the ascending branch of the thermal hysteresis loop (see Fig. 3). Therefore, the HS fraction rapidly grows within each NPs. This accounts for the τ s ∼ 20 ns nanosecond photo-switching time. This switching time likely depends on the size of the NPs. [START_REF] Gallé | Study of the fast photoswitching of spin crossover nanoparticles outside and inside their thermal hysteresis loop[END_REF] We have also evaluated the increase in temperature upon excitation of the sample in the experiment displayed in Fig. 8a. Before excitation, the temperature of sample is set at T 0 = 333 K. The computed rise in temperature ∆T is ∼ 9.3 K, 12 K, 14.5 K and 18.5 K for laser fluence of 9.6 mJ/cm 2 , 12 mJ/cm 2 , 15 mJ/cm 2 and 19 mJ/cm 2 , respectively. Since the temperature of sample T = T 0 + ∆T is always ≤ 352 K, it should remain below the ascending branch of the thermal hysteresis (see Fig. 3). Therefore, it is surprising to record a photoswitching of a non-negligible amount of NPs. However, the simple computation we performed neglects the attenuation of the pump pulse during its propagation within the sample. In fact, as the pulse propagates within the sample, it drops less and less energy.

The increase of temperature is therefore not homogeneous along the sample thickness. It is more important at the top of the sample and likely above 30 K. Besides, the increase and saturation of the HS fraction happen on time scale of about τ s ∼ 300 ns. This time scale is about ten times larger than the time it takes for heat to diffuse within a single NP (∼ 20 ns). During 300 ns heat diffuses over a characteristic length

L d = 2π √ D th τ s ∼ 1 µm
which is large compared to the size of the Au@SCO. Therefore, while during the first tens of nanoseconds, it is mostly the NPs at the top of the sample that are photoswitched, as time goes on and thermal diffusion takes place, the temperature of NPs beneath the top surface further increases and they are brought along the ascending branch of the thermal hysteresis loop giving rise to an increase of the HS fraction. Afterwards the heat generated within the NPs further diffuses within the whole sample.

As previously mentioned, the characteristic time for thermalization of our 4 µm thick sample is τ c,z ∼ 13 µs. After this characteristic time, we do not expect to record any further increase of the HS fraction. This latter behavior is indeed in good agreement with the time scale of the plateau (∼ 20 µs) displayed in Fig. 7a, Fig. 8c-f. At longer time scale, relaxation from the HS to the LS spin state should proceed and the higher ∆γ HS the longer the relaxation time. Here again, this agrees with the data displayed in Fig. 78.

As we noticed above, the initial temperature of the sample matters. By keeping the laser fluence constant while reducing the initial temperature, the sample is moved away from the ascending branch of the thermal hysteresis loop and the amplitude of the transmitted signal is reduced. This is in agreement with the data displayed in Fig. 8d-e-f where a nanosecond pulse centered at 470 nm is used to excite the sample. At this wavelength the sample is more absorbing. Hence, even if the E p = 10 mJ/cm 2 considering ∼85 % of the pump energy is absorbed by the sample, the rise in temperature is ∆T ∼23 K. Therefore upon excitation, the sample is quenched at the edge of ascending branch of the thermal hysteresis loop. Besides, in agreement with the evolution recorded exciting the sample at 520 nm, as the HS switching happens on shorter time scale (τ s ∼ 200 ± 100 ns), the relaxation is recorded on a smaller time scale (τ rel ∼ 80 ± 10 µs).

The processes described above can take place in both SCONP and Au@SCO samples. The main difference between these samples is their difference in absorption at a given wavelength.

The latter directly impacts the temperature at which the sample is quenched upon excitation.

At fixed laser fluence F p , the higher the absorption the higher the rise in temperature.

Conversely, one can also fix the change in transmission and record the evolution pump fluence threshold F th (λ p ) required to induce such change in transmission at a given pump wavelength λ p . The pump fluence threshold F th (λ p ) scales with the amount of energy absorbed by the sample and is proportional to the absorbance A(λ p ) of the sample at the exciting wavelength.

Thanks to the inclusion of Au nanorod in the SCO NPs, whatever the wavelength, absorption of the Au@SCO is larger than the SCONP. Therefore, in agreement with data displayed in Fig. 9, F th (λ p ) is larger for the SCONP sample. For the SCONP in the LS state, absorption rapidly decreases in the near IR spectral range, thus F th (λ p ) should also rapidly increase in the visible range, whereas for the Au@SCO, it should decrease thanks to the plasmon resonance. While for the SCO the reduction of F th is lower than expected, these trends are evidenced in Fig. 9.

We have previously shown the evolution of signal recorded upon excitation by a nanosec-ond laser pulse is related to the evolution of the position of the sample within its (T, γ HS ) phase diagram. [START_REF] Fouché | Mechanism for optical switching of the spin crossover [Fe (NH 2-trz)[END_REF] This scenario is depicted in Fig. 10a along with the evolution of transmission signal (Fig. 10b). The sample is initially set below the thermal hysteresis loop (γ HS ∼ 0) near the ascending branch of the thermal hysteresis loop (point A). Upon excitation and absorption of the laser light by the sample, the temperature of the sample rapidly increases while most of the SCONP remain in their initial state (Point B). When the fluence is high enough, the SCO sample is over heated and the HS fraction rapidly growths. Then as heat diffuses, the average temperature lowers due to the endothermic nature of the LS to HS transition process. This process stops when the temperature of the sample reached the ascending branch of the thermal hysteresis loop (Point C). Beyond this temperature, the HS state fraction remains constant whereas the temperature further decreases. This lasts as long as the temperature of the sample has not reached the descending branch of the thermal hysteresis loop (Point D). Below that latter temperature both the LS fraction and temperature relax back to their initial position within the (T, γ HS ) phase diagram.

General discussion

The experiments performed on a thin layer of AuSCO and SCONP and the analysis presented above provide a lot of information about laser-induced LS to HS state thermal photoswtiching of an ensemble of NPs we are going to summarize hereafter.

The first important result that our study convey is that insertion of AuNRs in an SCO NP is an interesting mean to increase the absorption of the Au@SCO in a very broad spectral range. But for a sample made out of an ensemble of Au@SCO, it does not guarantee a fast photoswitching or a very large increase in temperature of a sample . These latter depend on parameters which strongly impact the solutions of the heat equation. If one considers heat diffusion within a thin disk that surfaces are kept at room temperature, they are two kinds of parameters. The first ones we will consider as intrinsic parameters are related to the studied material. These are the mass density ρ, the heat capacity C p , the thermal diffusivity D th , V ρCp . At variance with the increase of temperature upon instantaneous heating, ∆T QCW is not linked to the pulse duration t p but depends on the thickness and the thermal diffusivity of the sample. The fact that the rise in temperature scales like ∆T QCW ∼ e 2 may account for the large increase in ∆γ HS we reported previously shinning a 1 mm thick sample with laser power density of 15 mW cm -2 . 37 Indeed considering that the experimental conditions are very similar and that only the thickness of the sample is increased from 4 µm to 1 mm, then ∆T QCW (1 mm) ∼ 10 5 ∆T QCW (4 µm)! We have also evaluated the typical time τ QCW ∼ φ 2 D th it takes to achieve the ∆T QCW . The expression of τ QCW emphasizes the size of the laser beam directly impacting the LS to HS photoswitching kinetics. For beam diameter of about 1 mm and conventional heat diffusivity of SCO compound the constant time for the temperature rise is τ QCW ∼ 300 ms. The latter is usually very large compared to the time it takes for the HS to grow within a NP. Hence, we can consider the growing of the HS state is due to an ensemble of NP coupled to each other by diffusion of heat within the sample. It is noteworthy to mention that as soon as the pump beam is stopped the temperature readily relaxes with the constant time τ relax ∼ τ e . If the sample was initially within the thermal hysteresis loop ∆γ HS achieved during photoexcitation remains otherwise ∆γ HS relaxes back towards zero.

Finally, we compare the ratio between the temperature increase achieved upon nanoseconds or QCW pulse excitation with laser pulses having the same peak power. The latter ratio writes ∆Tns ∆T QCW ∼ tpD th e 2

∼ tp τe where t p is the duration of the nanosecond pulse. Since in the experiment we carried out t p ∼ 10 -8 s and τ e ∼ 10 -4 s then ∆Tns ∆T QCW ∼ 10 -4 . This indicates that recording fast photoswitching requires nanosecond laser pulses with high peak power, the latter being limited by the optical damage threshold of the material.

Conclusions

We have investigated the photoswitching process between the LS and HS states taking place in a thin layer of SCO of polymeric triazole based iron(II) complexes of [Fe(Htrz) 2 trz] (BF 4 ) and nanohybrid made of AuNRs coated in a shell of this SCO polymeric [Fe(Htrz) 2 trz] (BF 4 ).

The experiments were performed setting the sample in the LS state and exciting the samples with near-infrared quasi-continuous wave or nanosecond pulses, tunable in visible to nearinfrared range. The photoswitching experiments were performed recording the evolution of transmission of the sample near the SPR of the AuNRs. When a QCW pulse with peak power of few hundreds of milliwatts excites the sample close to the SPR of the AuNRs, the photoswitching happens on few hundreds of millisecond time. However, the latter process is only recorded when the temperature of the samples is set near the ascending branch of the hysteresis loop. Hence, upon excitation the sample is brought in a HS-LS mixture state within the thermal hysteresis loop. We also run similar experiments setting the temperature of the samples below the thermal hysteresis and exciting them with a nanosecond pulse.

Under these conditions, we recorded both the photoswitching from the LS to HS state as well as the relaxation from the HS to LS state. The photoswitching amplitude and time constant depend on the laser fluence and absorption of the samples at the exciting pulse wavelength. A photoswitching time constant down to 20 ns has been recorded, indicating that, as expected one can very rapidly switch a non-negligible amount of the studied samples from the LS to HS state. For the nanohybrid, it was shown that the nanosecond pulse energy required to switch the sample from the LS to HS state decreases as one tune the central frequency of the nanosecond laser pulse toward the SPR of the AuNRs. We have also proposed a simple model that accounts well for this ensemble of results. It makes it possible to evaluate the kinetics and rise in temperature within the sample upon QCW or nanosecond pulsed excitation. The amplitude of the temperature rises nicely accounts for the change upon LS to HS photoswitching. The evolution and rise in temperature within the sample were also used to propose a scenario that accounts for the reported experiments.

This simple model also shines some light on some parameters of the sample such as the thicknesses and absorption that impact the rise and relaxation in temperature and therefore on the photoswitching kinetics. It happens within tens of nanoseconds for nanosecond pulses.

We have also shown that the experiment using nanosecond pulse make it possible to analyze the photo-switching within individual NPs whereas the ones with quasi-continuous wave excitation reveal the photo-switching within an ensemble of NPs.

Figure 1 :

 1 Figure 1: (a) Scheme of time-resolved transmission set-up using quasi continuous-wave light source. (b) Scheme of the time-resolved transmission set-up excited by nanosecond pulses.

Figure 2 :

 2 Figure 2: (a) Transmission electron microscopy (TEM) image of Au@SCO (b) Absorbance spectra of SCO and Au@SCO in their low spin (LS) and high spin (HS) states

25 HSFigure 3 :

 253 Figure 3: (a) Evolution of the product of χ M T measured using a SQUID magnetometer (gray square) versus the position of longitudinal plasmon absorption peak (orange circle) within the thermal hysteresis loop of Au@SCO. The solid lines are guidelines. (b) Thermal hysteresis loop of SCO (red triangle) and Au@SCO (blue circle) based on the normalized absorbance at 750 nm. The solid lines are guidelines.

Figure 4 :

 4 Figure4: (a) Evolution of the transmitted signal during the photoswitching of Au@SCO (blue dots) and SCONP (red dots) induced at T = 370 K by an optical pulse that peak power and pulse duration are I p = 270 mW and t p = 490 ms. The dashed lines indicate the start and end of the pump pulse. The solid lines are mono-exponential fits considering the transmission writes S(t) = S 0 (1 -exp (-t/τ c )), where τ c are 60 ms and 300 ms for Au@SCO and SCONP, respectively. (b) Evolution of the transmitted signal of the Au@SCO sample upon excitation by a 400 ms optical pulse at various peak powers I p . The inset evidences the linear increase of the maximum signal on the pump power. (c) Step photoswitching in Au@SCO induced by two consecutive 100 ms pump pulses with different peak powers.

Figure 5 :

 5 Figure 5: Normalized transmission signal over the pulse duration of (a) t p = 400 ms and (b) t p = 100 ms.

l s ∼ 4 Figure 6 :

 46 Figure6: The evolution of HS fraction induced by QCW pulsed excitation is illustrated in the (T ,γ HS ) hysteresis loop of the sample. The HS fraction can be further increased by a second more energetic optical pulse which brings the system to a higher temperature (∆T 2 > ∆T 1 ).

Figure 7 :

 7 Figure 7: (a) Evolution of the transmitted signal S(t) of Au@SCO sample set at T 0 = 333 K upon excitation by 6 ns pulse which central frequency is 520 nm and fluence 34 mJ/cm 2 . The orange line stands for the mono-exponential fit which writes S(t) = S 0 (1 -exp (-t/τ s )). (b) Relaxation of the transmitted signal S(t) at microsecond time scale. The orange line stands for the mono-exponential fit which writes S(t) = S 0 exp (-t/τ rel )).

Figure 8 :

 8 Figure 8: (a-b-c) Temporal evolution of transmission in Au@SCO sample at initial temperature T 0 =333 K excited by a 520 nm optical pulse at different pump fluence from 9.6 mJ/cm 2 to 19.1 mJ/cm 2 . Mono-exponential fits show characteristic rise time τ s = 300 ± 100 ns and relaxation time τ rel = 60 ± 10 µs independent of pump fluence. (d-e-f) Temporal evolution of transmission in Au@SCO sample at different initial temperature T 0 ranging from 313 K to 333 K, excited by a 470 nm optical pulse at fluence of 10 mJ/cm 2 . Mono-exponential fits of the characteristic rise time τ s = 200 ± 100 ns and relaxation time τ rel = 80 ± 10 µs which are independent of initial temperature T 0 .

Figure 9 :

 9 Figure 9: The wavelength dependence of the pump fluence threshold required to achieve ∆γ HS = 0.1 in Au@SCO and SCO samples.

Figure 10 :L 2 c 4π 2

 1022 Figure 10: (a) Evolution of HS fraction in the (γ HS ,T ) hysteresis loop upon nanosecond pulsed excitation. (b) Evolution of the transmission signal during the evolution of γ HS in the (γ HS ,T ) hysteresis loop upon nanosecond pulsed excitation. The logarithm plot of the transmission signal is extracted from Fig. 8a.

Table . 1Table 1 :

 .1 The dependence of photo-switching time, temperature increase and relaxation time on the relation between the pulse duration t p and the heat diffusion characteristic time in a single SCO NP τ N P d . Instantaneous heating Occurs after t ≥ τ e = e 2 4π 2 D th Rise time ∼ t p ∼ 10 -8 s τ e ∼ 10 -4 s Temperature ∆T ns ∼ α(λp)tpIp Non-instantaneous heating Instantaneous relaxation Rise time τ φ = φ 2 2.4 2 D th Temperature ∆T QCW ∼ e 2

		Photo-switching	Relaxation outside the
			thermal hysteresis loop
	t p ≤ τ N P d
		V ρCp
	t p	τ N P d
			α(λp)Ip
		D th	V ρCp

Acknowledgement

CNRS, University of Bordeaux, Nouvelle Aquitaine Region and the ANR program (HEROES ANR-17-CE09-0010-01) are acknowledged for the fundings.

Supporting Information Available

Solution of the heat equation of a thin disk photo excited by a quasi continuous wave.