Peak effect in Superconductors - Experimental aspects

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

2. Hc2 0  2.01 × 10-7 G. cm2 B = n0 a0  (0 /B)1/2 Hc1 100 Oe Abrikosov Vortex solid Hc1 Type II superconductivity – Mixed state Uel  (0 /4) 2ln (a0/ ) (a0 < )  (0 /4) 2exp(  a0/ ) (a0 > ) Meissner StateB = 0 - M H

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

4. Vortex pinning by lattice defects and impurities Upin = 0Hc23 V = 0 below I = Ic (critical current) Ic H / T Usually Ic is a monotonically decreasing function of H / T

5. 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 vortex lattice imaged by bitter decoration

6. Peak effect Low Tc materials H T Peak effect in NbSe2 Measurement at different T Hc2 Autler et al, PRL 1962.

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

8. Peak effect is seen only for weak pinning • In V3Si 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 Jc – H is monotonic Küpfer et al

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

10. Peak effect in magnetization measurements Jc(H) ~ M (H)/0R M NbSe2 T = 6.8K Hc2

11. Pick-up coil in a SQUID magnetometer

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

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

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

15. Peak effect in Bi2Sr2CaCu2O8 (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. Peak effect in Low Tc H T Not the Final Summary YBCO BSCCO Sharp & Just below Hc2

18. Nomenclature Peak effect (low Tc) Second Magnetization Peak (SMP) or just second peak (high Tc) 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 regionJc depends on how a particular point (H,T) in the phase diagram is approached Hp FC NbSe2 ZFC Henderson et al PRL (1996)

20. Strong history dependence observed below HpAbove Hp , Jc is unique H JcFC (H,T) > JcZFC (H,T) Hp FC ZFC T

21. History dependence in magnetization History dependence due to metastability

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

23. Just below Just above No Metastability No History effect

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

25. History dependence of the vortex state G. Ravikumar et al, Phys. Rev. B, 61, 6479 (2000)

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

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

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

30. Magnetization measurements of spherical V3Si crystal Sample experiences B(t) = Const  time + Oscillatory field due to sample vibration in non-uniform field

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

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. V3Si / 9.5 K • History dependence Near Peak effect • Many metastable states (multiple Jc’s) • Disorder and low kT - difficult to access equilibrium state Meq(H) = [ M (H) + M(H) ]/2 Assuming Jc (microscopic vortex state) is same in the increasing and decreasing field branches