Devil s staircase and multi-step transitions

Transcription

1 Devil s staircase and multi-step transitions Eric COLLET, 1 Elzbieta TRZOP 1, Hervé CAILLEAU 1, José A. REAL 2, Seiji MIYASHITA 3 1 Institute de Physique de Rennes UMR 6251 CNRS - University Rennes 1, France 2 Instituto de Ciencia Molecular (ICMol) Universidad de Valencia, Paterna, Valencia, Spain 3 Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo-Ku, Tokyo, Japan.

2 Devil s staircase in material science n/m Devil's staircase theoretically introduced to explain the rich variety of spatially modulated phases, in a vast variety of systems: - charge density waves, - spin density waves, - atomic concentration waves in alloys, - ferroelectric materials - spin-valve systems - Spin-crossover!!! 1 Out-of-plane magnetization of Sr1 xbaxco6o11 Physical parameter 1/2 Artificial nanostructures open the possibility to create completely new electronic functionalities for technological applications. 0 Field P. Bak, J. von Boehm, Phys. Rev. 1980, 21, 5297 M. E. Fisher and W. Selke, PRL 1980, 44, 1502 S. Aubry, J. Physique 1983, 44,

3 Universal description of long-range ordering of Spin-crossover molecules Fe II,Fe III, Mn, Co HS S=+ LS S= - Charge order and charge density waves e - rich S=+ e - poor S= - Spin density waves e - rich S=+ e - poor S= - Concentration waves atom A S=+ atom B S= -

4 Single step Spin Cross-over and phase transition M. Buron-Le Cointe et al. Phys Rev.B (2016) Low Spin S= - Governed by entropy, shaped by elastic interactions High Spin S=+ Dark side vs Light side Entropic effect governed by g the degeneracy ratio between HS and LS states g = g HS g LS

5 Cooperative Elastic Coupling between molecules: Photoresponse of nano-crystals to different excitation densities Self-amplification occurs The SCO crystal is an active medium elastic deformation wave up to 10 molecules switched / photon R. Bertoni et al, Nat. Mat 15, 606 (2016)

6 4 Different types of stepwise spin-crossover conversion Type 1: crystallography independent sites: different ligand fields, two T 1/2 g B A B A B HS A B g HS g HS A Type 2: 3-states molecules: ex HS-LS/LS-HS g HS = ½ + ½ Type 3: Long-range ordering of HS/LS states: symmetry breaking T N. Bréfuel et al., Angew.Chem. (2009 ), N. Moussa, Phys. Rev B 75 (2007), N. Bréfuel, Chem. Eur. J (2010), D. Chernyshov, Angew. Chem. 42 (2003), S. Bonnet, Chem. Commun. (2008), Nakano, Chem Com (2004), M. Klingele, Chem com (2005), J.A. Real, D a l t o n T r a n s. ( ), Simaan, Chem. Eur. J. (2005)

7 HS-LS ordering Several descriptions in the literature: theory and/or experiment 2016

8 Symmetry breaking and HS-LS order: Spin State Concentration Waves Stepwise LS to HS switching H. Watanabe et al, Phys Rev. B (2016) Symmetry Breaking loss of translation symmetry E. Trzop Angew. Chem. Int. Ed. 55,8675 (2016)

9 How can we describe multi-step SCO? Landau theory of phase transition. 2 STEPS TRANSITION : what are the order parameters? g HS : Concentration of HS h : ordering between sites : h = <g HS 2i g HS 2i+1 > HS HS HS HS g HS = 1 and h = 0 HS x LS HS LS g HS = 0.5 and h = 1 LS LS LS LS g HS = 0 and h = 0 Measuring the temperature dependence of the OP? g HS known from SQUID what about h? A. Marino et al, Faraday discussion 177 (2015)

10 HS fraction What are the order parameters? Symmetric OP: High spin fraction g HS same as density for liquid/gas is related to -the magnetic susceptibility -the intramolecular structure: <Fe-N> <Fe-N> length (Å) average of <Fe-N> <Fe-N>length HS fraction h Temperature(K) g HS Symmetry breaking OP: h: ordering between sites Formation of Spin-State Concentration Wave Different HS population between previously equivalent sites h = <g HS 2i g HS 2i+1 > g HS (r)=g HS +h cos(q.r) E. Collet et al, Phys. Rev. Lett (2012)

11 HS fraction What are the order parameters? Symmetric OP: High spin fraction g HS same as density for liquid/gas is related to -the magnetic susceptibility -the intramolecular structure: <Fe-N> <Fe-N> length (Å) average of <Fe-N> <Fe-N>length HS fraction h Temperature(K) g HS Symmetry breaking OP: h: ordering between sites Formation of Spin-State Concentration Wave Different HS population between previously equivalent sites h = <g HS 2i g HS 2i+1 > g HS (r)=g HS +h cos(q.r) E. Collet et al, Phys. Rev. Lett (2012)

12 How can we describe the intermediate phase? Landau theory of phase transition. 2 STEPS TRANSITION : what are the order parameters? g HS : Concentration of HS h : ordering between sites : h = <g HS 2i g HS 2i+1 > HS c LS HS LS g HS = 0.5 and h = 1 X-ray diffraction: superstructure Bragg peaks <F hkl > = g HS1 *F HS + (1- g HS1 )*F LS +[g HS2 *F HS + (1- g HS2 )*F LS ] e -ipl For l odd: <F hk l > = [ g HS1 - g HS2 ] * [F HS F LS ] Can we observe <F hk l the > = [ temperature h ] * [F HS Fdependence LS ] of the OP from experimental data? Ordering means g HS1 # g HS2 The measured diffracted intensity I h 2 A. Marino et al, Faraday discussion 177 (2015)

13 Elastic frustration responsible for stepwise transitions described with anisotropic next-nearest neighbor Ising model J J J J J c J A J HS LS A H. Watanabe Phys Rev.B (2016) LS s i =-1 = - HS s i =+1 = + Can generate stepwise transitions with one or several intermediate phases

14 Elastic frustration Such frustration can generate stepwise transitions with one or several intermediates phases HS + LS - and ultimately generate a Devil s staircase Devil s flower - For each step, there is a wavevector describing the wave - No group-subgroup relationship betweent the steps - 1st order phase transition between each step

15 Elastic frustration responsible for stepwise transitions described with anisotropic next-nearest neighbor Ising model J J J J J c J A J HS LS A H. Watanabe Phys Rev.B (2016) LS s i =-1 = - HS s i =+1 = + Such frustration can generate stepwise transitions with one or several intermediates phases and ultimately generate a Devil s staircase E. Trzop Angew.Chem. Int. Ed. 55,8675 (2016) Any value between 0 and 1

16 Elastic frustration - For each step, there is a wavevector Q describing the wave - No group-subgroup relationship betweent the steps - 1 st order phase transition between each step Such frustration can generate stepwise transitions with one or several intermediates phases and ultimately generate a Devil s staircase Any value between 0 and 1

17 Incomplete Devil s staircase n/m? ½ 17/50? Reciprocal space view: HS-LS sequences of form on the steps Periodicity change = new Bragg peaks at:

18 Incomplete Devil s staircase Real space view: Different sequences of HS-LS order form on the steps: HS and LS stripes The change of periodicity generates new Bragg peaks g HS (r)=g HS +h cos(q c.r) g HS (r)=g HS +h cos(q i.r) E. Trzop et al Angew.Chem. Int.Ed. 55,8675 (2016)

19 Commensurate SSCW E. Trzop et al Angew.Chem. Int.Ed. 55,8675 (2016) g HS (r)=g HS +h cos(q c.r)

20 Incommensurate SSCW E. Trzop et al Angew.Chem. Int.Ed. 55,8675 (2016) g HS (r)=g HS +h cos(q i.r)

21 More complicated g HS g HS A g HS B Fe III SCO Murnaghan Chem. Eur. J. 2014, 20,

22 More recently Clements, Angew. Chem. 128, 1 6 (2016) Q 3 Q 2 Q 1

23 Devil s Staircase-type phase transition in Materials Universality of the description: competing interactions/frustration k n/m spin-crossover, Th, hn, (Brefuel, Real) Fe 2 -Co 2 (Oshio) Neutral-ionic transition (Miyasaka) 1 Physical parameter 1/2 0 X(r)=X 0 +h cos(q.r) Field P. Bak, J. von Boehm, Phys. Rev. 1980, 21, 5297 M. E. Fisher and W. Selke, PRL 1980, 44, 1502 S. Aubry, J. Physique 1983, 44,