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Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona Structure and magnetism in the premartensitic and martensitic states in.

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Presentation on theme: "Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona Structure and magnetism in the premartensitic and martensitic states in."— Presentation transcript:

1 Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona Structure and magnetism in the premartensitic and martensitic states in Heusler shape-memory alloys Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Antoni Planes Collaborators: E. Bonnot, T. Castán, Ll. Mañosa, X. Moya, M. Porta, E. Vives (UB), A. Saxena, T. Lookman, J. Lashley (Los Alamos), M. Acet, T. Krenke, E.F. Wassermann, S. Aksoy (Duisburg), M. Morin (INSA). T.A. Lograsso, J.L. Zarestky (Ames)

2 Introduction Magnetic shape-memory effect refers to the change of shape (deformation) of a magnetic material undergoing a martensitic transition caused by either:  inducing the transition or  rearranging the martensitic variants by means of an applied magnetic field Prototypical shape-memory alloy: Ni-Mn-Ga Maximum induced deformation ~ 10% with an applied field ~ 10 kOe  two orders of magnitude larger than in magnetosrictive Terfenol-D (Tb 0.27 Dy 0.73 Fe 2 ) Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

3 Shape-memory properties Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Superelasticity Shape-memory effect Elastic Superelastic Elastic

4 Magnetic shape-memory properties Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Magnetic superelasticity Magnetic shape-memory effect H H Elastic Superelastic Elastic

5 La 2-x Sr x CuO 4 Lavrov et al., Nature, 418, 385 (2002) (antiferro) Magnetic shape-memory materials HEUSLER IRON-BASED OTHER Ni-Mn-XUllakko et al., APL, 69, 1966 (1996) (Ga) (X= Ga, Al, In, Sn, …)Fujita et al., APL, 77, 3054 (2000) (Al) Sutou et al., APL, 85, 4358 (2004); Krenke et al., PRB, 72, (2005); 73, (2006) (In,Sn) Co-Ni-AlOikawa et al., APL, 79, 2472 (2001) Ni-Fe-GaMorito et al., APL, 81, 5201 (2002); 83, 4993 (2003) Fe-PdJames & Wuttig, PMA, 77, 1273 (1998) Fe-PtKakeshita et al., APL, 77, 1502, (2000) Co-NiZhou et al., APL, 82, 760 (2003) Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

6 Interplay Structural degrees of freedom Magnetic degrees of freedom Unique pretransitional behaviour Mesoscopic scale Elastic domains (variants) Magnetic domains Microscopic scale (spin-phonon interplay) Magnetic shape-memory Magnetic superelasticity Magnetocaloric effect Magnetostructural interplay Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

7 Outline  Phase diagram and general properties  Pretransitional effects: Phonon anomalies and the intermediate transition  Conclusions Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

8 Magnetic properties Heusler, L2 1 (Fm3m) Ni Mn Ga Ni 2 MnGa Ferromagnetic order (T c ~ 370 K) Total magnetic moment: µ total  4.1 µ B per f.u. Non-stoichiometric Ni 2 Mn 1+x Ga 1-x (µ Ni  0.3 µ B per f.u.) Weak magnetic anisotropy Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

9 Phase diagram Ni 2+x Mn 1-x Ga Intermediate Martensite L2 1 -ferro L2 1 -para From: Vasil’ev et al., Physics-Uspekhi, 46, 559 (2003) Phase diagram at constant Ga concentration Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

10 Phase diagram Relative phase stability controlled (to a large extent) by the average number of valence electrons per atom, e/a Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

11 Other effects From: Khan et al., J. Phys. Condens. Matter, 16, 5259 (2004) Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

12 Cubic Martensitic transition mechanism Transformation mechanism: Shear + Shuffle on {110} planes along directions Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, M ([32] 2 ) 14M ([52])

13 Martensitic structure From: Lanska et al., J. Appl. Phys., 95, 8074 (2004) Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 By increasing e/a the following structures occur: 10M14MNM (L1 0 )

14 Entropy change Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Ni-Mn-Sn Ni-Mn-InNi-Mn-Ga para ferro para ferro paraferro

15 Magnetic properties e/a From: Enkovaara et al., PRB, 67, (2003). From: Albertini et al., APL, 81, 4032 (2002). Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

16 Ni 49.5 Mn 24.5 Ga 25.1 Ni 56.2 Mn 18.2 Ga 25.5 Ni 50 Mn 35 Sn 15 Ni 50 Mn 34 In 16 ΔS independent of H Effect of a magnetic field Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

17 Precursors in phase transitions Nanoscale structures which occur above phase transitions. They announce that a system is preparing for the phase transition before it actually takes place. Often observed in ferroic and multiferroic materials. Revealed by high-resolution imaging techniques well above the (expected) phase transition. Detected as anomalies in diffraction experiments (intense diffuse scattering) and in the response to certain exitations. Not expected in systems undergoing first-order transions (which are expected to occur abruptly). In martensites, related to low restoring forces in specific lattice directions (transition path). Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

18 Structural precursors in Ni-Al (similar phenomenology in Fe-Pd, ….., shape-memory alloys) TEM Neutron Diffraction From, S.M. Shapiro et al., PRL, 57, 3199 (1986) Cross-hatched striations (tweed) parallel to {110} planes observed above T M. (020) Example: tweed (60 nm) Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

19 Phonons in Ni-Mn-Ga L2 1  5ML2 1  7M Acoustic-phonon dispersion curves for the cubic phase of Ni 2 MnGa. From: Zheludev et al., 54, (1996). TA2 branch at selected temperatures. The position of the dip depends on the selected martensite structure. From: Mañosa et al. PRB, 64, (2001) Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

20 The softening is enhanced at the Curie point. For systems transforming to the 5M structure, the softening is nearly complete at T I > T M. Upon further cooling the frequency increases. At T I the system undergoes the intermediate transition. TMTM L2 1 → 5M (low e/a) TITI (higher e/a) Ni-Al (from Shapiro et al., PRL, 62, 1298 (1989); PRB, 44, 9301 (1991) Slopes in the two phases Phonon softening Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

21 Elastic constants L2 1  5M L2 1  7M Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

22 Diffraction experiments (100) J. Pons, private communication T > T I T < T I (111) T < T I TEM Neutrons From A. Zheludev et al., PRB, 54, (1996) Elastic scattering along the (ξξ0) direction The transition at T I is associated with the lock-in of the pseudoperiodic tweed phase into a commensurate phase due to the freezing of the anomalous phonon. Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Modulation of {110} planes with wave number 1/3 along direction. Preserve cubic symmetry.

23 Magnetic and thermal anomalies Further results which prove the existance of the premartensitic transition. A.c. magnetic susceptibilityCalorimetry Latent heat= 9 J/mol (Martensitic transition:~ 100 J/mol) A. Planes et al., PRL 79, 3926 (1997) TITI The intermediate transition is first-order Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

24 Effect of external fields Elastic constant Transition temperatures: STRESS MAGNETIC FIELD From: W.H. Wang et al., J. Phys. Condens. Matter, 13, 2607 (2001) From: Gozàlez-Comas et al., PRB, 60, 7085 (1999) [001] direction [1-10] direction 0 MPa 1 MPa 4.5 MPa T I ~ M 2 Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

25 Comparison with non-magnetic SMA High temperature phase (cubic) T tw ? Tweed T I Modulated (or intermediate) phase T M Martensite Ni-Mn-Ga Ni-Al Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

26 Amplitude of the relevant phonon mode  Order parameters: Magnetization M Free energy: Expansions: Landau model Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

27 Minimization with respect to M gives the following effective free-energy: where: M 0 is the magnetization of the high temperature phase (  = 0): T c is the Curie temperature Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Landau model

28 If  1 2 /B is large, can be negative, and a first-order transition is possible. The transition temperature is: The temperature dependence of the anomalous phonon frequency:  1 > 0  softening is enhanced. Clausius-Clapeyron equation: Results in agreement with the experiments if  1 > 0 Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Landau model: results

29 When an intermediate transition occurs? Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Results for Ni-Mn-Ga(Fe) TcTc MsMs

30 In Heusler alloys the relative phase stability is (to a large extent) controlled by e/a. Compared to other shape-memory alloys, Ni-Mn-Ga shows unique pretransitional behaviour which is a consequence of spin-phonon coupling. Strong softening of the 1/3[110]TA 2 phonon and large magnetisation is required for a first-order intermediate transition to occur. The intermediate phase almost preserves cubic symmetry and results from the freezing of 1/3[110]TA 2 phonon. Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Conclusions

31 Transition at zero-field: Formation of twin related variant. The magnetic easy axis changes from one twin to the other Cubic → Martensite (twinned) Effect of a magnetic field Twin related variants and magnetic stripe domains inside From: Ge et al., JAP, 96, 2159 (2004). Weak anisitropyStrong anisitropy In systems with strong anisotropy and highly mobile boundaries, field induced rearrangement of martensitic variants is possible  Magnetic Shape-Memory Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Magnetic shape-memory effect

32 Field induced deformation in a Ni-Mn-Ga alloy The residual deformation remaining when the field is removed can be removed by: 1.Heating up through the transition 2.Application of a magnetic field perpendicular to the original 3.Application of a stress that opposes the applied field From: Likhachev et al., Proc SPIE, 4333, 197 (2001) Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Example

33 Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Magnetic superelasticity From: Krenke et al., PRB, (2007) Magnetic superelasticity in Ni-Mn-In alloy

34 Adiabatic Temperature change,  T adi Isothermal Entropy change,  S iso when a magnetic field H is applied/removed It is given by: ∆T e is the range over which the transition extends. Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Magnetocaloric effect Controlled by the change of magnetization at the transition ΔM = M M – M P > 0, Conventional magnetocaloric effect ΔM = M M – M P < 0, Inverse magnetocaloric effect

35 Ni 49.5 Mn 25.4 Ga 25.1 ∆M = M M - M P Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Magnetocaloric effect in Ni 2 MnGa Inverse magnetocaloric effect

36 (a)(b)(c) Cubic Tetragonal Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007 Physical picture

37 Historical Magnetostructural characterization, Ziebeck’s group [Philos.Mag. B, 49, 295 (1984)] Martensitic Transformation and Shape-Memory Properties (Martynov, Kokorin, …) Phonon anom. & Intermediate trans., Shapiro’s group PRB, 51, (1995) Magnetic Shape-Memory Effect, O´Handley’s group at MIT, APL, 69, 1966 (1996) Magnetoelastic coupling. Vordervisch, Trivisono, UB group (phonons/elas. cnts, 1997) Modelling: O’Handley (JAP, 1998), James & Wuttig (PMB, 1998), ….. First.Principles Calculations: Helsinski group, Duisburg group, … Further developments, MIT group, Helsinki group, ….. Development of other M-SMA: Ishida’s group, Kakeshita’s group, …. Magnetic superelasticity: Duisburg & Barcelona, PRB, 2007 Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007


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