Domain wall in a ferromagnetic Ising Co thin film
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1 Domain wall in a ferromagnetic Ising Co thin film Lemerle, Ferre, Chappert, Mathe, Giamarchi, PLD (Phys. Rev. Lett. 1998) D =1+1 interface (d=1,n=1) x
2 x D =1+1 interface (d=1,n=1) short-range disorder thermally equilibrated
3
4
5 Contact line of a fluid quasi-static depinning E. Rolley et al. (ENS)
6
7 Abrikosov vortex lattice (type II superconductors) vortex lattice = many parallel vortex lines aligned external field which order into a triangular lattice 7
8 Elasticity of a lattice of vortex lines Q: what are d,n? 8
9 Elasticity of a lattice of vortex lines 9
10 Vortex Lattice + Thermal fluctuations + quenched impurities 3 phases - phase diagram A: Vortex Liquid C C: Vortex glass strongly pinned amorphous A B: Bragg glass weakly pinned - quasi-lr transl order - no dislocations B YBaCuO BiSCCO 10
11 early decoration images of vortex lattice(seen from top) + delaunay triangulation dislocations and disclinations
12 Periodic object + weak disorder Abrikosov vortex lattice Bragg Glass: No dislocation decoration
13 divergent Bragg peaks Klein et al. KBaBiO Neutron diffraction
14 Vortex creep in the Bragg glass Zeldov et al. BSCCO velocity of vortex v <=> electric field E (Lorentz) force acting on vortex f <=> j super-current creep => zero linear resistivity = true superconductivity!
15 15
16 Avalanches
17 Avalanches Review PhD thesis (2013), A. Dobrinevski, arxiv ABBM model Nonstationary dynamics of the ABBM model! A. Dobrinevski, PLD, K. Wiese, PRE 85, (2012). BFM and beyond mean-field Avalanche dynamics of elastic interfaces! PLD, K. Wiese, arxiv: , PRE 88 (2013) Size distributions of shocks and static avalanches from the FRG! PLD, K. Wiese, arxiv: , PRE, 79, , (2009) Universality in the mean spatial shape of avalanches! T. Thiery, PLD, EPL (2016).
18 Contact line of a fluid quasi-static depinning E. Rolley et al. (ENS)
19 friction (overdamped dynamics) elastic restoring force (here non-local) driving contact line: gravity (capillary length) magnetic interface: demag. field (quenched) substrate disorder crack line: loading
20 Avalanches: reproducible
21 u(w) = center of mass of the contact line (over 2 Lc) avalanche
22 Barkhausen (magnetic) noise G. Durin (Torino) F. Bohn (Brazil) area proportional to total avalanche size S
23 - Fracture: peeling L. Ponson (UPMC-Paris) J. Chopin - Bursts of activity in collective cell migration Chepizhko et al. (Santucci, Zapperi..) PNAS (2016) Here we show that collective cell migration occurs in bursts that are similar to those recorded in the propagation of cracks, fluid fronts in porous media and ferromagnetic domain walls 23
24 Functional RG and field theory how to measure/define it? central object is renormalized disorder correlator PLD, EPL (2006), AnnalsPhys. (2010) PLD, KW, EPL (2007) it obeys differential FRG equation as m is varied
25 Functional RG and field theory how to measure/define it? central object is renormalized disorder correlator PLD, EPL (2006), AnnalsPhys. (2010) PLD, KW, EPL (2007) it obeys differential FRG equation as m is varied avalanche
26 Functional RG and field theory how to measure/define it? central object is renormalized disorder correlator PLD, EPL (2006), AnnalsPhys. (2010) PLD, KW, EPL (2007) it obeys differential FRG equation as m is varied 2-loop Chauve, PLD, KW, PRL (2000) 3-loop Huseman, PLD, KW unpub. - analytic correlator => Larkin - develops a cusp at Lc (Larkin length)
27 Functional RG and field theory how to measure/define it? central object is renormalized disorder correlator PLD, EPL (2006), AnnalsPhys. (2010) PLD, KW, EPL (2007) it obeys differential FRG equation as m is varied FRG fixed point: All universal observables can be obtained in perturbation in i.e. in Allows to calculate depinning critical exponents: two independent exponents SR SR d=1 Ferrero (2013) LR LR d=1 predicts 0.4 confirmed numerics Rosso, Krauth fracture: Ponson, Santucci,..
28 FRG fixed point at depinning: numerics and experiments numerics: interface cusp! driven quasi-statically by quadratic well A. Rosso,PLD,KW condmat/ contact line experiment: E. Rolley, S. Moulinet, PLD,KW EPL, 87 (2009) 56001
29 Barkhausen noise LR elasticity samples, comparison with MF Phys. Rev. Lett. (2016) is ONLY parameter! m = k0 demag. field
30 avalanche shape at fixed size: beyond mean-field samples with SR elasticity comparison with theory with epsilon=2 eddy currents ribbons! thick attempt to fit MF
31 Avalanche size distribution beyond mean-field recall: avalanche exponent: agrees to with Narayan-Fisher conjecture NF = 1.11
32 Additional topics 32
33 Front velocity 33
34
35
36 Q: is there translational order in the moving lattice? 36
37 Q: is there translational order in the moving lattice? Moving glass effect In lattice moving along principal axis direction x the Fourier modes (0, K_y) of the disorder are NOT averaged out by motion! Moving glass equation => transverse displacements u_y still see static disorder! is a pinning equation with additional convective term - upper critical dimension is d_uc=3 instead of 4 - there is a transverse pinning f_c 37
38 Moving Bragg glass and moving smectic 38
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