1. Peak effect in Superconductors - Experimental aspects G. Ravikumar Technical Physics & Prototype Engineering Division, Bhabha Atomic Research Centre, Mumbai

2. Type II superconductivity – Mixed state Abrikosov Vortex solid H c2  0  2.01 × 10 -7 G. cm 2 B = n  0 a 0  (  0 /B) 1/2 H c1  100 Oe H c1 Meissner State B = 0 U el   (  0 /4  ) 2 ln (a 0 / ) (a 0 < )  (  0 /4  ) 2 exp(  a 0 / ) (a 0 > ) - M H

3. Lorentz Force F = J × B Causes vortex motion Electric field E = v X B Can not carry any bulk current Current transport through Abrikosov Vortex lattice

4. Vortex pinning by lattice defects and impurities U pin =  0 H c 2  3 V = 0 below I = I c (critical current) IcIc H / T Usually I c is a monotonically decreasing function of H / T

5. vortex lattice imaged by bitter decoration Conventional view: Unique solid vortex phase – disordered solid with various kinds of vortex lattice defects. Increase in material disorder leads to more defective vortex solid. Current view: Two distinct solid phases in weakly pinned superconductors Bragg Glass: Quasi-ordered (or weakly disordered) solid without lattice defects. Lattice correlations decay with distance as a power law. Vortex Glass: Highly disordered solid

6. Peak effect in NbSe 2 H c2 Measurement at different T Autler et al, PRL 1962. H T Peak effect Low T c materials

7. Neutron beam H X. S. Ling et al, PRL Small Angle Neutron Scattering (SANS) gives structure of the vortex lattice Below peak – Long range order exists Correlation volume V c is large Above peak – No long range order V c is small

8. Peak effect is seen only for weak pinning In V 3 Si defects introduced by fast neutron irradiation. At low dose pinning weak – peak is sharp Peak broadens with increasing dose (increase in pinning) For strong pinning J c – H is monotonic Küpfer et al

9. J c from Magnetization hysteresis measurements – Critical State Model Resistivity  = 0 For J < J c,   0 For J > J c Persistent currents of density J c induced in response to field variation Direction of currents depends on the direction of field scan M (H  ) = –  0 J c R M (H  ) =  0 J c R J c (H) = { M (H  ) – M (H  ) } / 2  0 R

10. Peak effect in magnetization measurements J c (H) ~  M (H)/  0 R MM NbSe2 T = 6.8K H c2

11. Pick-up coil in a SQUID magnetometer

12. Peak effect in LaSrCaCuO (T c  38 K) – Peak is broad – Anisotropic

13. Peak effect in YBCO (T c  90 K) Nishizaki et al PRB 58, 11169 Vortex lattice melting at high Temperatures in YBCO A sharp kink in  vs T A sharp jump in reversible Magnetization It is established that vortex lattice melts through a first order transition

14. Phase diagram in YBCO (T c  90 K) kT is important in the peak effect regime in addition to U el and U pin Bragg Glass Bragg Glass – Vortex Liquid Transition is a First order transition Onset peak Plastically deformed vortex lattice

15. Peak effect in Bi 2 Sr 2 CaCu 2 O 8 (Highly anisotropic) Melting – Peak occurs at very low fields – Peak field is almost constant – Peak effect line and melting line meet at a critical point Khaykovich et al, PRL 76 (1996) 2555

16. Over-doped : Weakest pinning Optimally doped : Strongest pinning Surprisingly Melting line follows the peak effect line

17. Not the Final Summary H T Peak effect in Low T c Sharp & Just below H c2 BSCCO YBCO

18. Nomenclature Peak effect (low Tc) Second Magnetization Peak (SMP) or just second peak (high T c ) Fishtail Effect Bragg Glass Phase (Dislocation free) Quasi-Ordered Vortex Solid Ordered Solid Phase Bragg Glass – Vortex Glass Transition Bragg Glass – Disordered Solid Transition Solid – Solid Transition Order – Disorder transition

19. History dependence in the peak region J c depends on how a particular point (H,T) in the phase diagram is approached ZFC FC HpHp Henderson et al PRL (1996) NbSe 2

20. Strong history dependence observed below H p Above H p, J c is unique T H FC ZFC HpHp J c FC (H,T) > J c ZFC (H,T)

21. History dependence in magnetization History dependence due to metastability

22. Metastability Repeated field cycling drives a metastable state towards equilibrium Minor Hysteresis Loops A large number of metastable states are possible Each metastable state can be macroscopically characterized by a J c

23. Just belowJust above No Metastability No History effect

24. Model to describe History dependent J c Each J c corresponds to a metastable vortex configuration Transformation from one configuration to another is governed by J c (B+  B) = J c (B) + |  B | (J c st – J c )/B r G. Ravikumar et al, Phys. Rev. B, 61, 6479 (2000)

25. History dependence of the vortex state

27. G. Ravikumar et al, Phys. Rev. B 63, 24505 (2001) Equilibrium state by Repeated field cycling J c < J c eq J c > J c eq

28. G. Ravikumar et al, Phys. Rev. B 63, 24505 (2001) M eq shows “melting - like” change across the order-disorder transition

29. Avraham et al Nature 411 (2001) 451 Equilibration by transverse AC magnetic field H H ac Peak effect – First order transition

30. Magnetization measurements of spherical V 3 Si crystal Sample experiences B(t) = Const  time + Oscillatory field due to sample vibration in non- uniform field

31. Order/disorder transition step in the reversible region of the BG step in m(B)step in m(B)

32. Summary History dependence and metastability near order-disorder transition. “Repeated field cycling” to access the equilibrium state Order-disorder transition is a first order transition.

34. History dependence Near Peak effect Many metastable states (multiple J c ’s) Disorder and low kT - difficult to access equilibrium state M eq (H) = [ M (H  ) + M(H  ) ]/2 Assuming J c (microscopic vortex state) is same in the increasing and decreasing field branches V 3 Si / 9.5 K