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We report the spatial and temporal dynamics of the photo-induced phase in the iron (II) spin crossover complex Fe(ptz)6(BF4)2 studied by image measurement under steady light irradiation and transient absorption measurement. The dynamic factors are derived from the spatial and temporal fluctuation of the image in the steady state under light irradiation between 65 and 100 K. The dynamic factors clearly indicate that the fluctuation has a resonant frequency that strongly depends on the temperature, and is proportional to the relaxation rate of the photo-induced phase. This oscillation of the speckle pattern under steady light irradiation is ascribed to the nonlinear interaction between the spin state and the lattice volume at the surface.
© 2013 Optical Society of America
1. Introduction
A material interacting with visible photons is an out-of-equilibrium dissipative system that is far from the ground state. Proper control of the out-of-equilibrium system gives a new opportunity to generate novel temporal or spatial structures called as “dissipative structures” that never appear in equilibrium system. One of typical examples is the laser system. In the general laser system, the combination of the laser medium and the feedback loop with a cavity realizes the laser oscillation where the photons have temporal and spatial coherence [1]. Optical delayed feedback using an external resonator leads to the chaotic fluctuation of the laser that shows temporal incoherence [1,2]. The chaotic laser oscillation is expected to be an encryption key in communication system [3,4]. The emergence of the laser oscillation and chaos can be controlled under the deep understanding of the nonlinear interaction between materials and photons. In the laser system, the nonlinearity comes from the electronic structures that are relevant to the laser oscillation. The population inversion in the two levels and the simulated emission from the excited state give rise to the coherent oscillation.
Here, we propose another class of “dissipative structures” driven by light irradiation, where only the macroscopic properties of the material oscillate. This kind of “dissipative structures” is ascribed to the nonlinear interaction between the macroscopic orders of the material, and the photons just supply the driving energy. Observation of these dissipative structures needs finding the materials having the light-induced change of the several macroscopic orders interacting with each other. Here, we adopt a proper material showing photo-induced structural phase transition phenomena.
Photo-induced phase transition (PIPT) phenomena are induced by the interaction of visible photons and materials having nonlinear cooperative interactions between molecules [5–7]. Because the photon energy of visible light is much larger than the thermal energy, visible photons can generate local non-equilibrium excited states that are far from the ground state. Such a local change may proliferate through cooperative interaction, giving rise to a global ordered state. In the PIPT process, nonlinear aspects originating in cooperative interactions, such as a threshold light intensity and an incubation period, are frequently observed [7–10].
We selected iron (II) spin crossover (SC) complexes as proper samples. The iron (II) SC complex exhibits the spin-state transition of the iron (II) ion between the 5T2 high-spin (HS) state and the 1A1 low-spin (LS) state under perturbations such as changes in temperature, pressure, and light. The spin-state transition by light is known as light-induced excited spin-state trapping (LIESST) [11]. In the PIPT process, many physical quantities change: the spin state, optical properties, magnetic susceptibility, and the size of the unit cell [11]. The SC complexes show PIPT under the irradiation of both continuous wave (cw) light and the short-pulse-width laser, while PIPT in many materials occur by only the short-pulse-width laser [5,7,12–16]. Experiments using cw light irradiation are suitable for observation of a novel state produced by the interplay between light and a material because the photons supply the driving energy continuously. These prosperities of the SC complexes are advantages for identifying “dissipative structures”.
In this work, we report the spatial and temporal dynamics of the photoinduced phase in the iron (II) SC complex Fe(ptz)6(BF4)2 studied by speckle pattern image measurement under stable cw laser illumination. Fe(ptz)6(BF4)2 is a well-known SC complex and exhibits strong cooperative effects [11,17–27]. We derived the dynamic factors from the temporal fluctuation of the image in the steady state under light irradiation between 65 and 100 K. The dynamic factors clearly indicate that the fluctuation has a resonant frequency that strongly depends on the temperature. This oscillation of the speckle intensities is governed by the nonlinear interaction between the spin state and lattice volume at the surface of the sample.
2. Experiment
The experimental setup for the imaging measurement is schematically shown in Fig. 1(a).We measured the image scattered at the surface of Fe(ptz)6(BF4)2 using a charge-coupled device (CCD) camera (Photometrics, CoolSNAP cf). The pair of lenses (objective lens, OL, and L1) is placed so as to fulfill the imaging condition. The spatial resolution and focal depth of this imaging system are 2 and 15 μm, respectively. The illumination source is a frequency-doubled Nd3+:YAG laser (cw, 2.33 eV, 50 mW/mm2). The photon energy of the laser is tuned to the broad absorption band of Fe(ptz)6(BF4)2 in the LS state. This absorption band is attributed to the d-d transition from the 1A1 to the 1T1 state of iron (II) ions [21]. Therefore, the laser provided not only illumination but also excitation. A sample was set in a helium gas-flow cryostat and irradiated through the objective lens (OL). The defocused spot necessary to produce wide-range irradiation and excitation was obtained using the pair of lenses (L2 and L3). The imaging spot of the sample is irradiated homogeneously because of the smaller imaging spot than the laser diameter and the short focal depth. Here, we emphasized that our observed phenomena is not ascribed to the sample inhomogeneity. To monitor the spin state, we also performed time-resolved transient absorption (TA) measurements. The probe light source is a halogen lamp. As shown in Fig. 1(b), the measured region is limited to within the pump region, which is the same as that in the imaging experiments. The probe light is detected by a single monochromator (Princeton Instruments) with a CCD camera system (InSight100A) instead of the camera used in the image measurements. The wavelength range covered by this system is 360—930 nm. The temporal resolutions of the imaging and TA measurements are 0.2 and 1 s, respectively.
Fig. 1 (a) Experimental setup for image measurement. The pair of lenses (OL and L1) is placed so as to fulfill the imaging condition. The sample is placed in a cryostat. To obtain the defocused spot necessary to produce wide-range irradiation, the collimated laser beam is focused in front of the microscopic objective lens by the lens pair of L2 and L3. (b) Arrangement of pump (2.33 eV cw laser) and probe (halogen lamp) lights in TA measurement. The pump light has a larger diameter than the probe light. These lights propagate in opposite directions. (c) Transmission picture of Fe(ptz)6(BF4)2 under illumination by the halogen lamp. Dotted area indicates the target of imaging and TA measurements.
Single crystals of Fe(ptz)6 (BF4)2 were prepared as described in a previous report [20]. The crystal was cleaved to obtain the proper optical density and decrease the internal pressure due to the change in the size of the unit cell. The typical single crystal is 0.2 × 0.2 × 0.1 mm3 in size. Figure 1(c) shows a transmission image of Fe(ptz)6(BF4)2 obtained by the above imaging system under illumination by the halogen lamp. In the area indicated by the square in Fig. 1(c), the sample is transparent, and no inhomogeneity is observed in this image. The target of the image measurement is in this regime. The absorption spectra in the visible region for Fe(ptz)6(BF4)2 were assigned by S. Decurtins et al. [21]. We estimated the HS fraction from the intensities of the absorption band of Fe(ptz)6(BF4)2 in the LS state. The single crystal was cooled from 300 to 60 K at a cooling rate of more than 10 K/min. When the cooling rate is greater than 10 K/min, Fe(ptz)6(BF4)2 shows a thermal spin-state transition without a crystallographic phase transition [23]. This guaranties that LIESST occurs without crystallographic phase transition in our experiments, where strong cooperative interaction is expected [23].
3. Results
Figure 2(a) shows an image of Fe(ptz)6(BF4)2 taken at 80 K under illumination by the cw laser with a photon energy of 2.33 eV. Higher intensities are represented by darker colors. One can see that Fe(ptz)6(BF4)2 has a grainy structure with a typical grain size of about 5 μm. These grainy structures are observed only under irradiation by coherent light. Note that these grainy structures appear irrespective of the spin state of the sample. Because the complete LS- and HS-state sample have spatial-homogeneous refractive index, these grainy structures are not ascribed to the scattering due to the fluctuation of reflective index. These grainy structures observed in the imaging setup are called subjective speckles [28]. They are ascribed to mutual interference of the coherent light, and sensitive to the surface roughness. The bright and dark spots in the speckle pattern correspond to smooth and rough surfaces, respectively.
Fig. 2 (a) Reflection image of Fe(ptz)6(BF4)2 at 80 K under cw laser illumination (2.33 eV, 50 mW/mm2). Gray scale shows counts per 100 ms. Open square indicates the region over which the intensity is integrated to evaluate the temporal evolution of the speckle pattern [see Fig. 3(a)]. (b) Dynamic structure factor calculated from the spatiotemporal fluctuation of the speckle pattern at 80 K. Intensity is normalized by the maximum intensity.
We found that these speckle patterns fluctuate temporally and spatially. Figure 3(a) shows the temporal evolution of the integrated intensity in the region indicated by the open square in Fig. 2(a). The intensity is normalized by the average intensity within 60 s. The intensity measured at 65 and 80 K fluctuates, and that measured at 100 K does not exhibit any fluctuation. Although the fluctuation of the intensity at 65 K stops, the fluctuation at 80 K seems to show oscillation with a defined frequency. To analyze the temporal and spatial fluctuations quantitatively, we calculated the dynamic structure factor of the speckle pattern. Here, the dynamic structure factor S(ω, k) is defined as the absolute value of the Fourier component of the speckle image,
where ω and k are the frequency and wavenumber vector, respectively. I(t, r) is the speckle intensity at time t and position r. The dynamic structure factor is equivalent to the Fourier transformation of the correlation function given by . Figure 2(b) shows the dynamic structure factor of the speckle pattern measured at 80 K. The dynamic structure factor has an intensity peak at 0.4 Hz along the frequency axis, indicating that the speckle pattern does not fluctuate randomly but has a defined oscillation frequency. At the peak frequency of 0.4 Hz, the intensity of the dynamic structure factor decreases along the wavenumber axis and follows a nonexponential decay. The wavenumber required for the intensity to fall to 1/e of the initial value at each frequency is around 1000 cm−1, which is equal to 10 μm. This indicates that the speckle has a strong spatial correlation with a range of 10 × 10 μm2. It is, however, not clear that iron (II) ions with the same spin state are correlated.To clarify the origin of the fluctuation of the temperature dependence, it is important to know how the spin state may change under photoirradiation. Figure 3(b) shows the temporal evolution of the HS fraction, γHS, which is estimated from the TA measurement under light irradiation. The condition of light irradiation is identical to that in the imaging measurement. At 65 K, the spin-state transition occurred within 20 s, and γHS reached 1. A comparison of Figs. 3(a) and 3(b) showed that the intensity of the speckle pattern fluctuated only when the spin state changed; no intensity fluctuation is observed in the absence of the spin-state transition. This suggests that these phenomena are correlated with each other. In contrast, no spin-state transition occurs at 80 and 100 K, although the fluctuations in the intensity of the speckle pattern behave differently in each case.
Fig. 3 (a) Temporal evolution of the integrated intensity in the region indicated by open square in Fig. 2(a) at 65, 80, and 100 K under cw laser illumination. Intensity is normalized by the average value, which is indicated by the broken line. The curve is offset for clarity. (b) Temporal evolution of HS fraction at 65, 80, and 100 K under cw laser illumination.
4. Discussion
Figures 3(a) and 3(b) show that there is a correlation between the spin-state transition and the fluctuation of the speckle pattern at 65 K; the spin-state transition and the fluctuation of the speckle pattern are observed at the same time. The fluctuation of the speckle pattern indicates a change in the surface roughness. The roughness change can be induced by changing the size of the unit cell. In SC complexes, the size of the molecule increases in the process of the spin-state transition from the LS to the HS state. These considerations indicate that the fluctuation of the speckle pattern corresponds to the spin-state transition. This indication is consistent with the observation that no spin-state transition and no fluctuation of the speckle pattern are observed at 100 K and in the temporal region above 20 s at 65 K [see Fig. 3]. However, at 80 K, the speckle pattern fluctuates in the absence of the spin-state transition. The reason for this is that the speckle pattern measurement is sensitive to surface changes, whereas the TA measurement reflects changes in the entire sample. Therefore, the spin-state transition occurred only at the surface of the sample at 80 K. At low temperatures, where the LS state is very stable, the light-induced spin-state transition occurs more easily at the surface than inside of the sample owing to a weaker internal pressure. The results obtained at 80 K indicate that the efficiency of the spin-state transition differs between the surface and inside of the sample.
The dynamic structure factor is traditionally measured using inelastic neutron, x-ray, or light scattering methods, and we adopted a similar method to analyze the temporal evolution of the speckle pattern. This provides dynamical information over a range of wavenumbers and frequencies. Figure 2(b) shows the dynamic structure factor of the speckle pattern observed at 80 K. The wavenumber shows no frequency dependence irrespective of the temperature between 65 and 100 K. There is a peak along the frequency axis. To investigate the frequency peak in detail, we integrated the intensity of the dynamic structure factor over the wavenumber axis, which is called the dynamic factor. This dynamic factor σ(ω) is given by
Figure 4(a) shows the temperature dependence of σ(ω). The dynamic factor exhibits almost no structure at 70 K, where the complete transition to the HS state occurred, as in the case of 65 K. With increasing temperature, the frequency peak appears and shifts to higher frequency. The peak structure suggests that the fluctuation of the speckle patterns has a defined oscillation frequency. After the peak intensity of the dynamic factor reaches the maximum at 80 K, the peak intensity decreases with increasing temperature. The peak structure disappears at 90 K, where no photoinduced phase transition occurred, as in the case of 100 K.Fig. 4 (a) Frequency dependence of the dynamic factor at different temperatures. Intensity is normalized by maximum intensity observed at 80 K. (b) Temperature dependence of HS fraction under cw laser illumination. The broken curve is guide to the eye (c) Peak frequency of the dynamic factor under cw laser illumination (left axis) and relaxation rate of HS phase in the dark (right axis) as a function of temperature. The solid curve is the fitting curve. The inset shows the correlation between the peak frequency and the relaxation rate. The solid line is the result of the linear fitting.
Figures 4(b) and 4(c) summarizes the temperature dependence of the HS fraction, peak frequency of the speckle pattern motion, and relaxation rate. The peak frequency of the speckle fluctuation, fs, is determined by the Gaussian fit of the dynamic factor σ(ω). The relaxation rate, kHS, is estimated from the TA measurement by fitting with an exponential function and corresponds to the inverse of the relaxation time. Although the typical relaxation dynamics from the light-induced HS to the LS state in Fe(ptz)6(BF4)2 show sigmoidal behaviors at low temperature, they are almost exponential functions in this temperature region [19]. The HS fraction decreases and the relaxation rate increases with increasing temperature. The temperature dependence of the relaxation rate is well reproduced by the Arrhenius thermal activation processes, where Ea is the energy barrier between the HS state and the LS state, and kB is the Boltzmann constant. This result indicates that the relaxation process is due to thermal relaxation. It is noteworthy that the peak frequency of the speckle pattern fluctuation and the relaxation rate show similar temperature dependence. The inset of Fig. 4(c) shows the correlation between the peak frequency and the relaxation rate. We found that there is almost a linear relationship between the peak frequency of the speckle pattern fluctuation and the relaxation rate. This result suggests that the fluctuation phenomena are related to the relaxation rate.
As shown in Fig. 2(b), spatial correlation as long as 10 μm is confirmed from the dynamical structure factor of the speckle pattern. This strong spatial correlation indicates that the spin state of a SC complex has a long-range order in space. In many SC complexes, strong cooperatively has been confirmed to promote photo-induced phase transition as well as the hysteresis in the thermal phase transition [23]. The origin of the cooperative interaction in the SC complexes has been attributed to the long-range elastic interaction. Relaxation dynamics of the photo-induced phase and the thermal spin transition have been well explained by the mean field approximation with elastic interaction between SC complexes [29]. Therefore, the spatial correlation observed in Fig. 2(b) should be originated from the long-range elastic interaction. The spatial correlation could be restricted by the relaxation rate derived above. S. Bedoui et al. reported domain motion under thermal phase transition in the surface region of [Fe(bapbpy)(NCS)2] system [10,30]. They observed the speed of the motion is ranged from 1 to 40 μm/s. One can estimate the coherent length as a product of the speed of motion by the relaxation time. This gives typically 2.5 to 100 μm at 80 K, which is in the same order of the coherent length observed in Fig. 2(b). This suggests that the dynamical aspect of the PIPT governs also the spatial structure of the photo-induced state under the steady excitation. To learn more about the dissipative structure, microscopic nature of long-range interaction should be resolved in more detail.
5. Phenomenological model
To summarize our findings, we observed the oscillation of the speckle pattern under steady cw light irradiation and found a linear relationship between the oscillation frequency and the relaxation rate. These results are explained by a phenomenological model with the nonlinear interaction between two order parameters, spin state and lattice volume that manifest in PIPT: The lattice-volume change at the surface of the sample is detected as the speckle pattern fluctuation in our imaging experiments. In the Fe(ptz)6(BF4)2 system, the light irradiation induces the spin-state transition from the LS to the HS state, that is accompanied by the volume change of unit cell. When the light intensity is weak enough, the volume change is limited only to unit cell where the spin-state transition from the LS to the HS state takes place. As increasing the light intensity, the number of the HS-state molecules increases. When the number of the HS-state molecules reaches to the critical values, macroscopic structure change, lattice-volume change, take place through cooperative interactions [11]. This is the photo-induced structural phase transition from the low temperature (LT) lattice phase to the high temperature (HT) lattice phase. It has been reported that this nonlinear interaction between the spin state and the lattice volume may induce different dynamics of the spin state and the lattice volume in the PIPT process of the Fe(ptz)6(BF4)2 system [26, 31]. Therefore, two order parameters such as the spin state and the lattice volume are necessary to describe dynamics the photo-induced phase transition of the Fe(ptz)6(BF4)2 system. The nonlinear interaction plays a key role in the “dissipative structure”. This is the reason why we consider the oscillation of the speckle pattern is due to the nonlinear interaction between the spin state and the lattice volume.
Figures 5(a)-5(d) illustrate our phenomenological model accounting for oscillation of the speckle pattern by the inhomogeneous lattice-volume change at surface: The Fe(ptz)6(BF4)2 system under light irradiation has the four states resulting from the combination of the spin state (HS or LS) and the lattice phase (HT or LT), LS-LT, LS-HT, HS-LT, and HS-HT. Because of size-mismatch, combinations of LS-HT and HS-LT are less stable than LS-LT and HS-HT [26,31]. In Fig. 5(a), at first, all molecules and lattices in the sample are in the LS state and the LT lattice, respectively. The light irradiation induces the spin-state transition from the LS to the HS state [Fig. 5(b)]. The LT lattice is small for the HS-state molecule, leading to the lattice-volume change from the LT to the HT lattice [Fig. 5(c)]. Note that the inside of the sample, which shows a bulk property, remains the LS state and the LT lattice because of more rigid structure than the surface of the sample. With an increase of the HT lattice at the surface, the lattice mismatch between the surface and the inside of the sample appears, resulting in the difficulty of the spin-state transition from the LS to the HS state and the lattice change from the LT to the HT lattice. When this suppression of the increase of the HS state and the HT lattice exceeds the light irradiation effect, the HS state and the HT lattice begin to decrease [Fig. 5(d)] and finally the system returns to the original state [Fig. 5(a)]. This cycle of the spin-state transition and the lattice-volume change is repeated as possible as long as the SC system is under light irradiation. This cycle can induce the oscillation of the speckle pattern observed in our experiment. In the real situation, the expanded area at the sample surface indicated in Figs. 5(c) and 5(d) should have spatially inhomogeneous distribution, which induces the speckle pattern under light irradiation. In the oscillation process, the lattice-volume change does not occur at the same position at the surface every time. Consideration of the inhomogeneous-spatial distribution is needed to describe the dynamics of the speckle pattern exactly, which forces the complicated calculations for formalism of the oscillation of the speckle pattern.
Fig. 5 (a)—(d) Schematic diagram of the mechanism of the speckle oscillation. The light irradiation induces the spin-state transition from the LS to the HS state (a→b), leading to the increase of the number of the HT lattices (b→c). The increase of the HT lattices causes the lattice mismatch between the surface and inside of the sample, leading to the decrease of the HS state (c→d) and the HT lattice (d→a). (e) Temporal evolution of the number of the LT lattices and HS-state molecules obtained from numerical solutions of Eqs. (3) and (4). The parameters used are J1 = J2 = 0.046, kLT = kLT = 0.46, NLT(0) = 10, NHS(0) = 11.
The numbers of the LT or HT lattices at the surface can reflect the degree of the lattice-volume change at the surface for first order approximation. The temporal change of the number of the LT or HT lattices should be relevant to the speckle oscillation. Therefore, we adopt the number of the LT lattices, NLT, and that of the HS-state molecules, NHS, at the surface as relevant parameters describing the oscillation of the speckle patterns. Our phenomenological model is given by following coupled rate equations including non-linear terms,
where J1 and J2 represent the interaction terms between the spin state and the lattice volume under light irradiation, and are equal to zero in the dark. Further, kLT and kHS are the generation rate of the LS lattice and the relaxation rate of the HS-state molecules in the dark, respectively. All the coefficients are positive. The nonlinear interaction terms, RLT and RHS play important roles to cause the oscillation. RLT represent the cooperative effect where the HS state favors not the LT lattice but HT lattice [see Fig. 5(b)→5(c)]. We also need to consider the lattice mismatch effect between the surface and the inside of the sample. RHS represent the lattice mismatch effect where the number of the LT lattice is related to the increase ratio of the number of the HS state [see Fig. 5(c)→5(d)]. The simultaneous differential equation given by Eqs. (3) and (4) is known as the Lotka-Volterra equation [32,33], and has an oscillation solution, as shown in Fig. 5(e). NLT and NHS oscillate with the same frequency, , and different phases; kHS is determined by the relaxation of the HS state. Although kLT cannot be experimentally evaluated, it is expected to show a similar temperature dependence to kHS. Thus, the oscillation frequency is simplified as kHS/2π, indicating the linear relationship between the oscillation frequency and the relaxation rate of the HS state. This simultaneous differential equation reproduces the experimental results very well. We propose that the oscillation phenomena observed in the SC complex under light irradiation should be ascribed to the nonlinear interaction between the spin state and the lattice volume at the surface.6. Conclusion
We studied the spatial and temporal dynamics of the photoinduced phase in the iron (II) spin crossover complex Fe(ptz)6(BF4)2 using speckle pattern image measurement and TA measurement. We observed the spatial and temporal fluctuation of the speckle patterns in the steady state under light irradiation between 65 and 100 K. A frequency analysis shows that the fluctuations have a frequency that strongly depends on the temperature. A linear relationship between the frequency and the relaxation rate is found. These phenomena are ascribed to the nonlinear interaction between the spin state and lattice volume at the surface. This oscillation structures originates from the inherent nonlinearity in the material itself. This unique dissipative structure opens up the possibility of discovering and developing new material states.
Acknowledgments
We thank Hiroshi Watanabe for stimulating discussions. This study was supported by KAKENHI (No. 23244065 and No. 20104007) from JSPS and MEXT of Japan.
References and links
1. H. Haken, Laser Light Dynamics (North-Holland Pub. Company, 1985).
2. J. R. Ackerhalt, P. W. Milonni, and M.-L. Shih, “Chaos in quantum optics,” Phys. Rep. 128(4-5), 205–300 (1985). [CrossRef]
3. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64(8), 821–824 (1990). [CrossRef] [PubMed]
4. A. Uchida, F. Rogister, J. García-Ojalvo, and R. Roy, “Synchronization and communication with chaotic laser systems,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2005), pp. 203–341.
5. S. Koshihara, Y. Tokura, T. Mitani, G. Saito, and T. Koda, “Photoinduced valence instability in the organic molecular compound tetrathiafulvalene-p-chloranil (TTF-CA),” Phys. Rev. B Condens. Matter 42(10), 6853–6856 (1990). [CrossRef] [PubMed]
6. S. Koshihara, Y. Tokura, K. Takeda, and T. Koda, “Reversible photoinduced phase transitions in single crystals of polydiacetylenes,” Phys. Rev. Lett. 68(8), 1148–1151 (1992). [CrossRef] [PubMed]
7. K. Nasu, Photoinduced Phase Transitions (World Scientific Publishing, 2004).
8. S. Koshihara, Y. Takahashi, H. Sakai, Y. Tokura, and T. Luty, “Photoinduced cooperative charge transfer in low-dimensional organic crystals,” J. Phys. Chem. B 103(14), 2592–2600 (1999). [CrossRef]
9. Y. Ogawa, S. Koshihara, K. Koshino, T. Ogawa, C. Urano, and H. Takagi, “Dynamical aspects of the photoinduced phase transition in spin-crossover complexes,” Phys. Rev. Lett. 84(14), 3181–3184 (2000). [CrossRef] [PubMed]
10. S. Bedoui, M. Lopes, W. Nicolazzi, S. Bonnet, S. Zheng, G. Molnár, and A. Bousseksou, “Triggering a phase transition by a spatially localized laser pulse: role of strain,” Phys. Rev. Lett. 109(13), 135702 (2012). [CrossRef] [PubMed]
11. P. Gütlich and H. A. Goodwin, “Topics in Current Chemistry 233–235,” in Spin Crossover in Transition Metal Compounds I –III (Springer, 2004).
12. S. Iwai, S. Tanaka, K. Fujinuma, H. Kishida, H. Okamoto, and Y. Tokura, “Ultrafast optical switching from an ionic to a neutral state in tetrathiafulvalene-p-chloranil (TTF-CA) observed in femtosecond reflection spectroscopy,” Phys. Rev. Lett. 88(5), 057402 (2002). [CrossRef] [PubMed]
13. E. Collet, M.-H. Lemée-Cailleau, M. Buron-Le Cointe, H. Cailleau, M. Wulff, T. Luty, S. Y. Koshihara, M. Meyer, L. Toupet, P. Rabiller, and S. Techert, “Laser-Induced Ferroelectric Structural Order in an Organic Charge-Transfer Crystal,” Science 300(5619), 612–615 (2003). [CrossRef] [PubMed]
14. H. Uemura and H. Okamoto, “Direct detection of the ultrafast response of charges and molecules in the photoinduced neutral-to-ionic transition of the organic tetrathiafulvalene-p-chloranil solid,” Phys. Rev. Lett. 105(25), 258302 (2010). [CrossRef] [PubMed]
15. A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001). [CrossRef] [PubMed]
16. M. Chollet, L. Guerin, N. Uchida, S. Fukaya, H. Shimoda, T. Ishikawa, K. Matsuda, T. Hasegawa, A. Ota, H. Yamochi, G. Saito, R. Tazaki, S. Adachi, and S. Y. Koshihara, “Gigantic photoresponse in 1/4-filled-band organic salt (EDO-TTF)2PF6.,” Science 307(5706), 86–89 (2005). [CrossRef] [PubMed]
17. A. Bousseksou, G. Molnár, J. Real, and K. Tanaka, “Spin crossover and photomagnetism in dinuclear iron(II) compounds,” Coord. Chem. Rev. 251(13-14), 1822–1833 (2007). [CrossRef]
18. A. Bousseksou, G. Molnár, L. Salmon, and W. Nicolazzi, “Molecular spin crossover phenomenon: recent achievements and prospects,” Chem. Soc. Rev. 40(6), 3313–3335 (2011). [CrossRef] [PubMed]
19. P. L. Franke, J. G. Haasnoot, and A. P. Zuur, “Tetrazoles as ligands. Part IV. Iron (II) complexes of monofunctional tetrazole ligands, showing high-spin ⇔ low-spin transitions,” Inorg. Chim. Acta 59, 5–9 (1982). [CrossRef]
20. S. Decurtins, P. Gütlich, C. P. Köhler, H. Spiering, and A. Hauser, “Light-induced excited spin state trapping in a transition-metal complex: The hexa-1-propyltetrazole-iron (II) tetrafluoroborate spin-crossover system,” Chem. Phys. Lett. 105(1), 1–4 (1984). [CrossRef]
21. S. Decurtins, P. Gütlich, K. M. Hasselbach, A. Hauser, and H. Spiering, “Light-induced excited-spin-state trapping in iron (II) spin-crossover systems - optical spectroscopic and magnetic susceptibility study,” Inorg. Chem. 24(14), 2174–2178 (1985). [CrossRef]
22. A. Ozarowski and B. R. McGarvey, “EPR study of manganese (II) and copper (II) in single crystals of the spin-crossover complex Fe(PTZ)6(BF4)2,” Inorg. Chem. 28, 2262–2266 (1989). [CrossRef]
23. A. Hauser, J. Jeftić, H. Romstedt, R. Hinek, and H. Spiering, “Cooperative phenomena and light-induced bistability in iron (II) spin-crossover compounds,” Coord. Chem. Rev. 190–192, 471–491 (1999). [CrossRef]
24. N. O. Moussa, G. Molnár, X. Ducros, A. Zwick, T. Tayagaki, K. Tanaka, and A. Bousseksou, “Decoupling of the molecular spin-state and the crystallographic phase in the spin-crossover complex [Fe(ptz)6](BF4)2 studied by Raman spectroscopy,” Chem. Phys. Lett. 402(4-6), 503–509 (2005). [CrossRef]
25. F. Varret, K. Boukheddaden, C. Chong, A. Goujon, B. Gillon, J. Jeftic, and A. Hauser, “Light-induced phase separation in the [Fe(ptz)6](BF4)2 spin-crossover single crystal,” Eur. Phys. Lett. 77(3), 30007 (2007). [CrossRef]
26. H. Watanabe, H. Hirori, G. Molnár, A. Bousseksou, and K. Tanaka, “Temporal decoupling of spin and crystallographic phase transitions in Fe(ptz)6(BF4)2,” Phys. Rev. B 79(18), 180405 (2009). [CrossRef]
27. C. Chong, H. Mishra, K. Boukheddaden, S. Denise, G. Bouchez, E. Collet, J.-C. Ameline, A. D. Naik, Y. Garcia, and F. Varret, “Electronic and structural aspects of spin transitions observed by optical microscopy. The Case of [Fe(ptz)6](BF4)2.,” J. Phys. Chem. B 114(5), 1975–1984 (2010). [CrossRef] [PubMed]
28. G. Cloud, “Optical Methods in Experimental Mechanics Part 26: Subjective speckle,” Exp. Tech. 31(2), 17–19 (2007). [CrossRef]
29. S. Miyashita, Y. Konishi, M. Nishino, H. Tokoro, and P. A. Rikvold, “Realization of the mean-field universality class in spin-crossover materials,” Phys. Rev. B 77(1), 014105 (2008). [CrossRef]
30. S. Bedoui, G. Molnár, S. Bonnet, C. Quintero, H. J. Shepherd, W. Nicolazzi, L. Salmon, and A. Bousseksou, “Raman spectroscopic and optical imaging of high spin/low spin domains in a spin crossover complex,” Chem. Phys. Lett. 499(1-3), 94–99 (2010). [CrossRef]
31. H. Watanabe, N. Brefuel, S. Mouri, J.-P. Tuchagues, E. Collet, and K. Tanaka, “Dynamical separation of spin and lattice degrees of freedom in the relaxation process from the photo-induced state,” Eur. Phys. Lett. 96(1), 17004 (2011). [CrossRef]
32. J. Lotka, “The growth of mixed populations: two species competing for a common food supply,” J. Wash. Acad. Sci. 22, 461–469 (1932).
33. V. Volterra, “Fluctuations in the Abundance of a Species considered Mathematically,” Nature 118(2972), 558–560 (1926). [CrossRef]
