Abstract
We report recent work on the competition between opposite kinetic processes: (i) photo-excitation (LIESST) and relaxation processes, and (ii) direct and reverse LIESST. The light-induced instability eventually occurring at the light-induced equilibrium temperature is attributed to a cooperative origin. The subsequent light-induced thermal hysteresis (LITH) and intensity threshold effect (LIOH) are adequately described through a mean-field macroscopic master equation assuming a linear photo-excitation term and a self-accelerated term for cooperative relaxation. Further analysis provides evidence for non-linear character of the photo-excitation terms, capable of inducing bistability in the light-driven quasi-static regime when the direct and reverse LIESST regimes compete. The behaviour of correlations under permanent photo-irradiation is also considered, both experimentally and theoretically, through a kinetic Ising-model including a photo-excitation term and accounting for both long- and short-range interactions. Paradoxical effects of light are reported, with various experimental features and theoretical model providing a qualitative explanation.
A novel instability effect is introduced, due to the non-linear competition between direct and reverse LIESST, for which the expected hysteresis with respect to wavelength is denoted Light Induced Spectral Hysteresis (LISH).
Preview
Unable to display preview. Download preview PDF.
Abbreviations
- SCO:
-
Spin crossover
- btr:
-
4,4′-Bis(1,2,4-triazole)
- LIESST:
-
Light-induced excited spin state trapping
- LIMH:
-
Light-induced magnetic hysteresis
- LIOH:
-
Light-induced optical hysteresis
- LIPH:
-
Light-induced pressure hysteresis
- LISH:
-
Light-induced spectral hysteresis
- LITH:
-
Light-induced thermal hysteresis
- LPTH:
-
Light-perturbed thermal hysteresis
- T 1/2 :
-
Spin transition temperature
- T 1/2 * :
-
Light-driven equilibrium temperature
- α :
-
Self-acceleration factor of the relaxation rate (Hauser factor)
References
Létard JF, Guionneau P, Rabardel L, Howard JAK, Goeta AE, Chasseau D, Kahn O (1998) Inorg Chem 37:4432
Désaix A, Roubeau O, Jeftic J, Haasnoot JG, Boukheddaden K, Codjovi E, Linarès J, Nogués M, Varret F (1998) Eur Phys J B 6:183
Menendez N, Varret F, Codjovi E, Boukheddaden K, Haasnoot JG (2000) Third TMR-TOSS meeting (Leiden, May 2000)
Boukheddaden K, Shteto I, Hoo B, Varret F (2000) Phys Rev B 62:14,806
Varret F, Boukheddaden K, Jeftic J, Roubeau O (1999) ICMM ‘98 (Seignosse, France, Sept 1998). Proceedings: Mol Cryst Liq Cryst 335:561
Hauser A (1986) Chem Phys Lett 124:543
Hauser A, Gütlich P, Spiering H (1986) Inorg Chem 25:4245
Hauser A (1992) Chem Phys Lett 192:65
Hauser A, Jeftic J, Romstedt H, Hinek R, Spiering H (1999) Coor Chem Rev 190/192:471–491
Decurtins S, Gütlich P, Köhler CP, Spiering H, Hauser A (1984) Chem Phys Lett 139:1
Decurtins S, Gütlich P, Hasselbach KM, Spiering H, Hauser A (1985) Inorg Chem 24:2174
Gütlich P, Hauser A, Spiering H (1994) Angew Chem Int Ed 33:2024
Hauser A (1991) Coord Chem Rev 111:275
Hauser A (1991) J Chem Phys 94:2741
Gütlich P, Garcia Y, Woike T (2001) Coord Chem Rev 219/221:839
McGarvey JJ, Lawthers I (1982) J Chem Soc 906
Enachescu C, Linarès J, Varret F (2001) J Phys Condens Matter 13:2481
Ogawa Y, Koshihara S, Koshino K, Ogawa T, Urano C, Takagi H (2000) Phys Rev Lett 84:3181
Enachescu C, Constant H, Codjovi E, Linarès J, Boukheddaden K, Varret F (2001) J Phys Chem Solids 62:1409
Enachescu C, Oetliker U, Hauser A (2002) J Phys Chem 37:9540
Varret F, Boukheddaden K, Codjovi E, Linarès J (2000) 4th TMR-TOSS meeting (Bordeaux, May 2000)
Hoo B, Boukheddaden K, Varret F (2000) Eur Phys J B 17:449
Boukheddaden K, Shteto I, Hoo B, Varret F (2000) Phys Rev B 62:14,796
Boukheddaden K (2000), Thèse d’Habilitation, Université de Versailles
Boukheddaden K, Varret F, Salunke S, Linarès J, Codjovi E (2002) International Conference on Photo-Induced Phase Transitions (Tsukuba, Japan, Nov 2001), Proceedings: Phase Transitions 75:733
Ogawa Y, Ishikawa T, Koshihara S, Boukheddaden K, Varret F (2002) Phys Rev B 66:073104
Renz F, Spiering H, Goodwin H, Gütlich P (2000) Hyperfine Interact 126:155
Montant S, Chastanet G, Létard S, Marcen S, Létard JF, Freysz E (2002) Fifth TMR-TOSS Meeting (Seeheim, March 2002)
Shimamoto N, Ohkosi SK, Sato O, Hashimoto K (2002) Chem Lett 4:486
Hauser A (1995) Comments Inorg Chem 17:17
Martin JP, Zarembowitch J, Bousseksou A, Dworkin A, Haasnoot JG, Varret F (1994) Inorg Chem 18:2617
Constant-Machado H, Linarès J, Varret F, Haasnoot JG, Martin JP, Zarembowitch J, Dworkin A, Bousseksou A (1996) J Phys I France 6:1203
Jeftic J, Matsarki M, Hauser A, Goujon A, Codjovi E, Linarès J, Varret F (2001) Polyhedron 20:1599
Létard JF, Chastanet G, Nguyen O, Marcen S, Marchivie M, Guionneau P, Chasseau D, Gütlich P (2002) In: Verdaguer M, Linert W (eds) Monatshefte für Chemie. Springer, Berlin Heidelberg New York
Chastanet G, Enachescu C, Varret F, Ader JP, Létard JF (2002) Fifth TOSS Meeting (Seeheim, March 2002)
Varret F, Constant-Machado H, Dormann JL, Goujon A, Jeftic J, Nogués M, Bousseksou A, Klokishner S, Dolbecq A, Verdaguer M (1998) International Conference on Applied Mossbauer Effect, ICAME ‘97, Proceedings. Hyperfine Interact 113:37
Codjovi E, Morscheidt W, Jeftic J, Linarès J, Nogués M, Goujon A, Roubeau O, Constant-Machado H, Desaix A, Bousseksou A, Verdaguer M, Varret F (1999) Proceedings of ICMM ‘98 (Seignosse, France) Mol Cryst Liq Cryst 335:1295
Varret F, Nogués M, Goujon A (2001) In: Miller J, Drillon M (eds) Magnetism: molecules to materials, vol 2. Wiley WCH, pp 257–291
Roubeau O, Haasnoot JG, Codjovi E, Varret F, Reedjik J (2002) Chem Mater 14:2559
Spiering H, Kohlhaas T, Romstedt H, Hauser A, Bruns-Yilmas C, Kusz J, Gütlich P (1999) Coord Chem Rev 190/192:629
a) Wajnflasz J, Pick R (1971) J Phys Coll 32:C1–91; b) Bousseksou A, Nasser J, Linarès J, Boukheddaden K, Varret F (1992) J Phys I 2:1381
Real JA, Bolvin H, Bousseksou A, Dworkin A, Kahn O, Varret F, Zarembowitch J (1992) J Am Chem Soc 114:4650
Linarès J, Spiering H, Varret F (1999) Eur Phys J B 10:271
Doniach S (1978) J Chem Phys 68:11
Goujon A, Roubeau O, Varret F, Dolbecq A, Bleuzen A, Verdaguer M (2000) Eur Phys J B 14:115
Varret F, Goujon A, Boukheddaden K, Nogués M, Bleuzen A, Verdaguer M (2002) International Symposium on Cooperative Phenomena of Assembled Metal Complexes (Osaka, Japan, Nov 2001) Proceedings (2002). Mol Cryst Liq Cryst 379:333
Goujon A, Varret F, Escax V, Bleuzen A, Verdaguer M (2001) ICMM’00 (San Antonio, Texas) Proceedings (2001). Polyhedron 20:1347
Hôo B (2001) Thèse de Doctorat, Université de Versailles
Hauser A (1998) J Phys Chem Solids 59:1353
Garcia Y, Ksenofontov V, Levchenko G, Schmitt G, Gütlich P (2000) J Phys Chem B 104:5046
Codjovi E, Menendez N, Jeftic J, Varret F (2001) C R Acad Sci Paris 4:181
Varret F, Enachescu C, Boukheddaden K, Codjovi E, Linarès J (2002) Final TMR-TOSS Meeting (Seeheim, March 2002)
Koshihara S, Takahashi Y, Sakai H, Tokura Y, Luty T (1999) J Phys Chem B 103:2592
Romstedt H, Hauser A, Spiering H (1998) J Phys Chem Solids 59:265
Linarès J, Enachesu C, Boukheddaden K, Varret F (2003) Proceedings ICMM’02 (Valencia, Spain), Polyhedron 22:2453
Jeftic J, Hauser A (1997) J Phys Chem B 101:10,262
Bousseksou A, Molnar G, Tuchagues JP, Menendez N, Codjovi E, Varret F (2003) Compt Rend Acad Sci Paris (Chimie) 6:329
Varret F, Bleuzen A, Boukheddaden K, Bousseksou A, Codjovi E, Enachescu C, Goujon A, Linarès J, Menendez N, Verdaguer M (2003) Pure Appl Chem 74:2159
Boukheddaden K, Linarès J, Spiering H, Varret F (2000) Eur Phys J B 15:317
Willenbacher N, Spiering H (1988) J Phys C 21:1423; Spiering H, Willenbacher N (1989) J Phys Cond Matter 1:10,089
Bousseksou A, Constant-Machado H, Varret F (1995) J Phys I 5:747
Glauber RJ (1968) J Math Phys 4:294
Ludwig KF, Park B (1992) Phys Rev B 46:5079
Mamada H, Takano S (1968) J Phys Soc Japan 25:675
Acknowledgements
We are indebted to A. Wack (LMOV) for technical assistance, to CNRS and Université for financial support, to NATO for the collaborative linkage grant between the Iasi and Versailles Universities, to the EC for Socrates Erasmus grants, for TRM-TOSS program (ERB-FMRX-CT98–0199), and for ESF action Molecular Magnetism.
Author information
Authors and Affiliations
Corresponding author
Appendix. The dynamic Ising model in the presence of photo-excitation
Appendix. The dynamic Ising model in the presence of photo-excitation
1.1 Introduction
The aim of this section is to present the Ising-like model which is very often used to describe the static and dynamic properties of the spin-crossover (SC) systems. We are interested here in these properties under photo-excitation. In particular we will study the photo-excitation effect on the relaxation curve of the HS fraction in order to analyze their effect on the developments of the correlations during the relaxation.
1.2 Ising-Like Model
The microscopic models developed for cooperative spin-crossover solids are based on the Ising-like hamiltonian, following the pioneering works of Wajnsflasz and Pick and Bousseksou et al. [41a, 41b]. Such a two-state model can be viewed as a simple Ising model under a temperature-dependant ‘‘effective’’ field which accounts for the different degeneracies of the levels [44].
In the Ising like model, the two states associated with the eigenstates of the fictitious spin ±1, have different degeneracies, denoted respectively, g+ and g- . In the spin crossover systems, the eigenvalues +1 and −1 of the fictitious spin correspond to the high-spin (HS) and low-spin (LS) molecular states respectively.
The Ising-like hamiltonian including long- and short-range interactions [59] writes:
where: Δ eff =(1/2) k B T ln(g + /g − ) −Δ+G <s> is the effective field, <s>= m is the net fictitious magnetization, J and G are the short- and long-range interactions associated with short- and long-range elastic effects [60] respectively. 2Δ is the energy difference E(HS)-E(LS) for isolated molecules. g + /g − is the degeneracy ratio between the HS and LS states and T the temperature. The ratio g + /g − may be quite large (up to a few thousands) because it involves both the spin degeneracies and the density of vibrational levels [61] in the two spin states.
The static properties of this model in the case J>0 and J<0 have been studied analytically in [59]: thermal hysteresis loops with simple and double transitions can occur, due to the competing effect of short-range ‘‘ferro-’’ or ‘‘anti-ferromagnetic’’ interaction and long-range ‘‘ferromagnetic’’ interactions. The phase diagram of this model has been obtained in [59, 41a], where the conditions of the occurrence of the first order transitions of the Ising-like model have been analyzed.
1.3 Master Equation
Now, we are interested in the dynamical properties of such cooperative SC systems. So as to do it, we use the well known general stochastic formalism developed by Glauber [62]. In this stochastic approach, the spin-flips s i →−s i are induced by the thermal bath, with transition rates W(s i ).
Following Glauber we consider P({s};t) the probability of observing the system in the configuration (s 1 , ..., s N )={s} at time t. The time evolution P({s};t) is given by the master equation:
In the last formula, {s}j denotes the configuration of all spins excepted spin s j and the expectation value of the j-th spin is defined as: \( {\left\langle {s_{j} } \right\rangle } = {\mathop \Sigma \limits_{{\left\{ s \right\}}} }s_{j} P{\left( {{\left\{ s \right\}};t} \right)}, \), where the sum is taken over all spin configurations.
The detailed balance condition at equilibrium writes as:
where P e (s 1 ,s 2 , ...s N ) ~ exp[-β E(s 1 ,...,s i , ...,s N ) ] is the equilibrium probability of finding the system with the energy E(s 1 ,...,s i , ...,s N ), i.e. in the spin configuration (s 1 ,s 2 , ...s N ).
1.4 The dynamic choice
Several dynamic choices leading to the same equilibrium states are possible according to Eq. 13 which only provides the ratio of the probabilities of opposite transition rates. We have established recently [4] that the choice suited to the spin-crossover systems (above the tunneling regime) was of the Arrhenius-type [63], because the dynamical process in these systems is thermally activated over an intra- and/or inter-molecular energy barrier (see Fig. 18), and this fact is strongly correlated to the sigmoidal character of the relaxation curves in these systems.
Let’s assume that E a 0 is the energy barrier corresponding to the saddle point energy of the double well configurational energy diagram of Fig. 18 when the HS and the LS fractions are equal, i.e. at equilibrium temperature. Therefore, we can re-write the Eq. 13 under the following form, which obeys the detailed balance equation:
where βE(s i ) = - g s i Σ α=1,q s i+α - b s i , with g=βJ, b=βΔ eff , and α runs over the neighbours. We choose for the transition rate the general form W Therm (s i ) ~ exp[-β (E a 0 – E(s i )], which can be re-written as:
with the following notations: x= coshb, y = coshg, x’ = sinhb, y’ = sinhg.
Under photo-excitation, which is assumed to induce only the LS→HS transitions, we must introduce an additional optical transition rate W Opt given by:
where I 0 is the intensity of the incident radiation and σ is the absorption cross-section, related to the quantum photo-process. σ is considered as independent of the lattice configuration {s}. Photo-excitation is considered here as a non-cooperative process, since it is written as a single site term. The exact formulation of the dynamic equations leads to the following evolution equations for the fictitious magnetization and the equal-time correlation:
and
The right-hand sides of Eqs. 17, 18 involve the average of clusters of spins. In the present work, we are interested by the correlations effect during the transition, therefore we perform all calculations in the pair approximation. Indeed, in that case our approach represents the dynamical extension of the well known Bethe-Peierls approach of the equilibrium statistical mechanics. We now have to choose an explicit form for the probabilities P({s},t) as a function of the order parameters of the model and the spin variables (s 1 , s 2 ,...,s N ) ={s}.
1.5 Pair Approximation
In the pair approximation, the probabilities (or the density matrix operators) P 1 (s j ; t) for the single spin s j , and the pair probability P 2 (s i ; s j ; t) associated with a pair of neighbouring spins s i ; s j ; are given by:
and
with m i = <s i > and r i,j = <s i s j >.
We now have to examine the probabilities of occupation of the configuration of clusters of q+1 spins, which are formed by the central spin surrounded by its q neighbours. The probability P q+1 (s i , {s i+α }; t), of such a cluster is approximated by using an elegant formulation due to Mamada and Takano [64], in which the authors considered P q+1 (s i , {s i+α }; t) ≈ P 1 (s i ,; t) ×...× P (s i+α ,∣s j ; t) ×...× P (s i+qα ,∣s j ; t), where P (s i ∣s j ; t) is the conditional probability at time t of s j at fixed value of spin s i . Using the identity P 2 (s i , s j ; t) =P 1 (s j ; t) × P(s j ∣s i ; t), we obtain:
where the subscript α runs over the neighbouring spins of s i . Inserting Eq. 21 in the right-hand side of Eqs. 17, 18, we obtain the closed set of motion equations of the system, presented in the next section.
1.6 Relaxation under photo-excitation
For this first attempt, the lattice is assumed to be spatially invariant; then we put m i = m and r ij = r | i-j| = r. Substituting now the probability of flipping site i, W i Therm (s i ), W i Opt (s i ) and P q+1 (s i , {s i+α }; t) for their corresponding expressions (15–21), we obtain, after some calculations, the following evolution equations for the long- and short-range order parameters, respectively:
and
with (x+x’) = exp(b) and (x-x’) = exp(-b), where b, y and y’ are given by: b = β [Gm+(1/2)kT ln (g+/g-) - Δ], y = coshβJ, and y’ = sinhβJ.
For convenience, it is useful to re-express the latter equations in terms of the fractions of the high spin molecules (n H) and the pairs HS-LS molecules (n HL), respectively n H (t) = (1+m(t))/2 and n HL (t)=(1-r(t))/4 [59]. They give, in the low-temperature region in which we are looking for the relaxation of the HS fraction, the following non-linear equations:
and
The photo-excitation effect depends on the time t w at which the light is switched on. This time has to be compared with the characteristic time t c at which the correlation onsets in sizeable amount. t c should be considered as an incubation time, defined as the time at which the transition rate exhibits a sizeable departure from the linear mean-field behaviour. The t c value is of course determined numerically. We obtain the following results:
-
1.
t w <t c : the lifetime of the metastable HS state is increased; however, the relaxation tail is reduced. The light drives the system to the mean-field behavior. We stress on the paradoxical effect that finally light speeds up relaxation in the late stage of the relaxation.
-
2.
t w >t c : in a first stage, light slows down relaxation; even, above a threshold value of intensity, an increase of the HS population may be observed. In a further stage, i.e. after some incubation process, the light starts destroying the already established correlations and the final effect is to speed up relaxation.
(Figure 10 curves (b), (c)). The paradoxical effect is remarkably rapid and efficient.
Systematic computations have shown that the above effects are exclusively associated with the short-range interaction. An extensive investigation including short- and long-range interactions is under progress.
Rights and permissions
About this chapter
Cite this chapter
Varret, F., Boukheddaden, K., Codjovi, E., Enachescu, C., Linarès, J. On the Competition Between Relaxation and Photoexcitations in Spin Crossover Solids under Continuous Irradiation. In: Spin Crossover in Transition Metal Compounds II. Topics in Current Chemistry, vol 234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b95417
Download citation
DOI: https://doi.org/10.1007/b95417
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40396-8
Online ISBN: 978-3-540-36774-1
eBook Packages: Springer Book Archive