Kinetics of Nonequilibrium Transition in Spin-Crossover Compounds

  • Iurii GudymaEmail author
  • Cristian Enachescu
  • Artur Maksymov
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 156)


This chapter is devoted to an analysis of spin-crossover system dynamics in the framework of Ising-like mechanoelastic model and macroscopic phenomenological model. Based on mechanoelastic model, the intermolecular interaction between spin-crossover sites and cooperative effects in materials has been studied. For light-induced spin-transition the relaxation curves has been calculated by Monte Carlo methods. The additive and multiplicative noise influence on transition phenomena following from system contact with environment was found within macroscopic description of spin-crossover system dynamics in Langevin framework and the corresponding Fokker-Planck equation. The mean first passage time from metastable state driven by colored noise was calculated by using the Kramers-like approximation. In addition, it is shown that transitions can be controlled by a parameter that governs relaxation flow, intensity of light and noise intensity.


Multiplicative Noise Colored Noise Spin Crossover Stationary Probability Distribution Mean First Passage Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Research of Iu. G. and A. M. was supported in part by the an Erasmus Mundus mobility program EMERGE, co-financed by the European Commission in the framework of the Erasmus Mundus programme. Iu. G. and A. M. thank the scientific group of Prof. Alexandru Stancu for the hospitality at the Alexandru Ioan Cuza University of Iasi while this work was in progress.


  1. 1.
    Cambi L, Szegö L (1931) Ber Deutsch Chem Ges 64:167Google Scholar
  2. 2.
    Cambi L, Malatesta L (1937) Ber Deutsch Chem Ges 70:2067Google Scholar
  3. 3.
    Orgel L (1956) in 10 ème Conseil de Chimie. Bruxelles, p 289Google Scholar
  4. 4.
    Figgins PE, Busch HD (1960) J Am Chem Soc 82:820Google Scholar
  5. 5.
    Robinson MA, Curry JD, Busch DH (1963) Inorg Chem 2:1178Google Scholar
  6. 6.
    König E, Madeja K (1966) Chem Comm 3:61Google Scholar
  7. 7.
    McGarvey J, Lawthers I, Chem J (1982) Chem Commun 1982:906Google Scholar
  8. 8.
    Decurtins S, Gütlich P, Köhler C, Spiering H (1984) Chem Phys Lett 105:1Google Scholar
  9. 9.
    Veen R van der, Kwon OH, Tissot A, Hauser A, Zewail AH (2013) Nat Chem 5:395Google Scholar
  10. 10.
    Bousseksou A, Molnár G, Salmon L, Nicolazzi W (2011) Chem Soc Rev 40:3313Google Scholar
  11. 11.
    Félix G, Abdul-Kader K, Mahfoud T, Gural’skiy I, Nicolazzi W, Salmon L, Molnár G Bousseksou A (2011) Surface plasmons reveal spin crossover in nanometric layers J Am Chem Soc 133:15342Google Scholar
  12. 12.
    Gütlich P, Goodwin H (eds) (2004) Spin crossover in transition metal compounds I. Topics in current Chemistry, vol 233. Springer, BerlinGoogle Scholar
  13. 13.
    Gütlich P, Goodwin H (eds) (2004) Spin crossover in transition metal compounds II. Topics in current chemistry, vol 234. Springer, BerlinGoogle Scholar
  14. 14.
    Gütlich P, Goodwin H (eds) (2004) Spin crossover in transition metal compounds III. Topics in current Chemistry, vol 235. Springer, BerlinGoogle Scholar
  15. 15.
    Halcrow M (ed) (2013) Spin-crossover materials properties and applications. Wiley, ChichesterGoogle Scholar
  16. 16.
    Kahn O, Martinez C (1998) Spin-transition polymers:from molecular materials toward memory devices. Science 279:44–48Google Scholar
  17. 17.
    Gudyma Yu, Semenko O (2004) Nonequilibrium kinetics in spin-crossover compounds. Phys Status Solidi B 241:370–376Google Scholar
  18. 18.
    Gudyma IV, Maksymov A (2010) Theoretical analysis of the states of spin-crossover solids under cross-correlated noises. Physica B 405:2534–2537Google Scholar
  19. 19.
    Gudyma Iu, Maksymov A (2011) High spin metastable state relaxation of spin-crossover solids driven by white noise. J Phys Chem Solids 72:73–77Google Scholar
  20. 20.
    Collet E, Buron-Lecointe M, Cailleau H (2006) X-ray diffraction investigation of the nature and the mechanism of photoinduced phase transition in molecular materials. J Phys Soc Jpn 75:011002Google Scholar
  21. 21.
    Lorenc M, Hébert J, Moisan N, Trzop E, Servol M, Buron-Le Cointe M, Cailleau H, Boillot ML, Pontecorvo E, Wulff M, Koshihara S, Collet E (2009) Successive dynamical steps of photoinduced switching of a molecular Fe(III) spin-crossover material by time-resolved X-ray diffraction. Phys Rev Lett 103:028301Google Scholar
  22. 22.
    Hauser A (1986) Reversibility of light-induced excited spin state trapping in the \({F}e(ptz)_{6}({BF_{4}})_{2}\) and the \({Z}n_{1-x}{F}e_{x}(ptz)_{6}({BF_{4}})_{2}\) spin-crossover systems Chem Phys Lett 124:543–548Google Scholar
  23. 23.
    Gütlich P, Hauser A, Spiering H (1994) Thermal and optical switching of iron(II) complexes. Angew Chem Int Ed 33:2024–2054Google Scholar
  24. 24.
    Hauser A (1992) Cooperative effects on the HS→LS relaxation in the \([Fe(ptz)_{6}](BF_{4})_{2}\) spin-crossover system.Chem Phys Lett 192:65–70Google Scholar
  25. 25.
    Wajnflasz J (1970) Etude de la transition „Low Spin“ – „High Spin“ dans les complexes octaédriques d'ion de transition. Phys Stat Sol 40:537–545Google Scholar
  26. 26.
    Boukheddaden K, Shteto I, Hoô B, Varret F (2000) Dynamical model for spin-crossover solids I. Relaxation effects in the mean-field approach. Phys Rev B 62:14796–14805Google Scholar
  27. 27.
    Boukheddaden K, Shteto I, Hoô B, Varret F (2000) Dynamical model for spin-crossover solids II. Static and dynamic effects of light in the mean-field approach. Phys Rev B 6214806–14817Google Scholar
  28. 28.
    Desaix A, Roubeau O, Jeftic J, Haasnoot JG, Boukheddaden K, Codjovi E, Linarès J, Noguès M, Varret F (1998) Light-induced bistability in spin transition solids leading to thermal and optical hysteresis. Eur Phys J B 6:183–193Google Scholar
  29. 29.
    Varret F, Boukheddaden K, Chong C, Goujon A, Gillon B, Jeftic J, Hauser A (2007) Light-induced phase separation in the \([{F}e(ptz)_{6}]({BF}_{4})_{2}\) spin-crossover single crystal. Europhys Lett 77:30007Google Scholar
  30. 30.
    Varret F, Bleuzen A, Boukheddaden K, Bousseksou A, Codjovi E, Enachescu C, Goujon A, Linares J, Menendez N, Verdaguer M (2002) Examples of molecular switching in inorganic solids, due to temperature, light, pressure, and magnetic field. Pure Appl Chem 74:2159–2168Google Scholar
  31. 31.
    Gudyma IuV, Maksymov AIu (2012) Optical induced switching in spin-crossover compounds: microscopic and macroscopic models and its relationship. Appl Opt 51:C55–C61Google Scholar
  32. 32.
    Gudyma Iu, Maksymov A, Enachescu C (2010) Decay of a metastable high-spin state in spin-crossover compounds: mean first passage time analysis. Eur Phys J B 78:167–172Google Scholar
  33. 33.
    Varret F, Boukheddaden K, Codjovi E, Maurin I, Tokoro H, Ohkoshi S, Hashimoto K (2005) Light-induced thermal hysteresis and intensity thresholds in molecular switcheable solids, by mean-field macroscopic master equation approach: Discussion of the experimental data obtained for Co -Fe Prussian Blue Analogues. Polyhedron 24:2857–2863Google Scholar
  34. 34.
    Enachescu C, Constant-Machado H, Codjovi E, Linares J, Boukheddaden K, Varret F (2001) Direct access to the photo-excitation and relaxation terms in photo-switchable solids: non-linear aspects. J Phys Chem Solids 62:1409–1422Google Scholar
  35. 35.
    Bousseksou A, Nasser J, Linares J, Boukheddaden K, Varret F (1992) Ising-like model for the two-step spin-crossove. J Phys I France 2:1381–1403Google Scholar
  36. 36.
    Boukheddaden K, Linares J, Spiering H, Varret F (2000) One-dimensional Ising-like systems: an analytical investigation of the static and dynamic properties, applied to spin-crossover relaxation. Eur Phys J B 15:317–326Google Scholar
  37. 37.
    Glauber RJ (1963) Time-dependent statistics of the Ising model. J Math Phys 4:294–307Google Scholar
  38. 38.
    Huang H (1973) Time-dependent statistics of the Ising model in a magnetic field. Phys Rev A 8:2553-2556Google Scholar
  39. 39.
    Huang H (1974) Dynamics of the Ising model. Phys Lett A 482553–2556Google Scholar
  40. 40.
    Gudyma Iu, Maksymov A, Miyashita S (2011) Noise effects in a finite-size Ising-like model. Phys Rev E 84:031126Google Scholar
  41. 41.
    Nasser JA (2005) Diluted spin conversion compounds behaviours in the atom-phonon coupling model: case of not too large dilution. Eur Phys J B 48:19–27Google Scholar
  42. 42.
    Nishino M, Boukheddaden K, Konishi Y, Miyashita S (2007) Simple two-dimensional model for the elastic origin of cooperativity among spin states of spin-crossover complexes. Phys Rev Lett 98:247203Google Scholar
  43. 43.
    Konishi Y, Tokoro H, Nishino M, Miyashita S (2008) Monte Carlo simulation of pressure-induced phase transitions in spin-crossover materials. Phys Rev Lett 100:067206Google Scholar
  44. 44.
    Stoleriu L, Enachescu C, Stancu A, Hauser A (2008) Elastic model for complex hysteretic processes in molecular magnets. IEEE Trans Magn 44:3052–3055Google Scholar
  45. 45.
    Enachescu C, Machado H, Menendez N, Codjovi E, Linares J, Varret F, Stancu A (2001) Static and light induced hysteresis in spin-crossover compounds: experimental data and application of Preisach-type models. Physica B 306:155–160Google Scholar
  46. 46.
    Enachescu C, Tanasa R, Stancu A, Varret F, Linares J, Codjovi E (2005) First-order reversal curves analysis of rate-dependent hysteresis: The example of light-induced thermal hysteresis in a spin-crossover solid. Phys Rev B 72:054413Google Scholar
  47. 47.
    Enachescu C, Stoleriu L, Stancu A (2009) Model for elastic relaxation phenomena in finite 2D hexagonal molecular lattices. Phys Rev Lett 102:257204Google Scholar
  48. 48.
    Enachescu C, Nishino M, Miyashita S, Hauser A, Stancu A, Stoleriu L (2010) Cluster evolution in spin crossover systems observed in the frame of a mechano-elastic model. Europhys Lett 91:27003Google Scholar
  49. 49.
    Enachescu C, Nishino M, Miyashita L, Stoleriu S, Stancu A (2012) Monte Carlo Metropolis study of cluster evolution in spin-crossover solids within the framework of a mechanoelastic model. Phys Rev B 86:054114Google Scholar
  50. 50.
    Chakraborty P, Enachescu C, Hauser A (2013) Analysis of the experimental data for pure and diluted \([FexZn_{1 -x}(bbtr)_{3}](ClO_{4})_{2}\) spin-crossover solids in the framework of a mechanoelastic model. Eur J Inorg Chem 2013:770–780Google Scholar
  51. 51.
    Koshino K, Ogawa T (2000) Theory of the photoinduced spin-state transitions in spin-crossover complexes. J Lumin 87–89:642–645Google Scholar
  52. 52.
    Enachescu C, Oetliker U, Hauser A (2002) Photoexcitation in the spin-crossover compound \([Fe(pic)_{3}]Cl_{2}\cdot EtOH (pic = 2-Picolylamine)\). J Phys Chem B 106:9540–9545Google Scholar
  53. 53.
    Chong C, Varret F, Boukheddaden K (2010) Evolution of self-organized spin domains under light in single-crystalline Phys Rev B 81:014104Google Scholar
  54. 54.
    Gudyma IuV, Semenko OM (2007) Noise-induced coupling and phase transition in initially homogeneous bistable system. Physica A 386:47–53Google Scholar
  55. 55.
    Gudyma AIu, Gudyma IuV (2010) Noise-induced collective regimes of complex system in contact with a random reservoir. Physica A 389:667–672Google Scholar
  56. 56.
    Hohenberg PC, Halperin BI (1977) Theory of dynamic critical phenomena. Rev Mod Phys 49:435–479Google Scholar
  57. 57.
    Ma Sk (2000) Modern theory of critical phenomena. Perseus Books, New YorkGoogle Scholar
  58. 58.
    Klyatskin V (2000) Dynamics of stochastic systems. Elsevier Science, AmsterdamGoogle Scholar
  59. 59.
    San Miguel M, Toral R (2000) Stochastic effects in Physical systems. In: Tirapegui E, Martínez J, Tiemann R (eds) Instabilities and nonequilibrium structures VI. Kluwer Academic, Dordrecht, pp 35–130Google Scholar
  60. 60.
    Wu D, Cao L, Ke S (1994) Bistable kinetic model driven by correlated noises: steady-state analysis. Phys Rev E 50:2496–2502Google Scholar
  61. 61.
    Gudyma Yu, Ivans’kii B (2006) Behavior of asymmetric bistable system under influence of cross-correlated noises. Mod Phys Lett B 20:1233–1239Google Scholar
  62. 62.
    Risken H (1989) The Fokker-Planck equation: methods of solution and applications. Springer, BerlinGoogle Scholar
  63. 63.
    Gardiner C (1986) Handbook of stochastic methods. Springer, BerlinGoogle Scholar
  64. 64.
    Gudyma Iu, Maksymov A (2010) Nonlinear stochastic relaxation dynamics in spin-crossover solid-state compounds. Semiconductor Physics, Quantum Electronics and Optoelectronics 13:357–362Google Scholar
  65. 65.
    Sang X, Zeng CH, Wang H (2013) Noise-induced optical bistability and state transitions in spin-crossover solids with delayed feedback. Eur Phys J B 86:229Google Scholar
  66. 66.
    Jung P, Hänggi P (1987) Dynamical systems: a unified colored-noise approximation. Phys Rev A 35:4464–4466Google Scholar
  67. 67.
    Hänggi P, Jung P (1995) Colored noise in dynamical systems. Adv Chem Phys 89:239–326Google Scholar
  68. 68.
    Hänggi P, Marchesoni F, Grigolini P (1984) Bistable flow driven by coloured Gaussian noise: AvCritical study. Z Phys B 56:333–339Google Scholar
  69. 69.
    Hänggi P (1986) Escape from a metastable state. J Stat Phys 42:105-148Google Scholar
  70. 70.
    Gudyma Iu, Maksymov A, Dimian M (2013) Stochastic kinetics of photoinduced phase transitions in spin-crossover solids. Phys Rev E 88:042111Google Scholar
  71. 71.
    Hänggi P, Talkner P, Borkovec M (1990) Reaction-rate theory: fifty years after Kramers. Rev Mod Phys 62:251–341Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Iurii Gudyma
    • 1
    Email author
  • Cristian Enachescu
    • 2
  • Artur Maksymov
    • 1
  1. 1.Chernivtsi National UniversityChernivtsiUkraine
  2. 2.Alexandru Ioan Cuza University of IasiIasiRomania

Personalised recommendations