1. Studies on supercooled metastable states of vortex matter P Chaddah Cryogenics & Superconductivity Section, Centre for Advanced Technology, Indore 452013 S. B. Roy M K Chattopadhyay, M A Manekar, K J Singh Sokhey

2. This talk is motivated by a 1 st order solid-to-solid phase transition in kinetically hindered vortex matter. We claimed, in 1997, that the onset of peak-effect in CeRu2, was associated with a 1 st order phase transition. There was a hysteresis in the onset of hysteresis, but we performed many cross-checks on the metastable states. Metastable states are encountered due to supercooling/superheating, but also due to hindered kinetics. How can one determine the origin of metastability?

3. Hysteresis due to hindered kinetics: Bean’s CSM

4. Supercooling and/or superheating is the origin of hysteresis across a 1 st order transition S=0 state supercools as T falls from (a) to (d), where it shatters. Ordered state superheats

5. Roy & Chaddah, J. Phys.: Condens. Matter 9 (1997) L625–L632. Hysteresis in M vs H is caused by ‘hindered kinetics’. This hysteresis is opening at a higher field, and closes at a lower field. Hysteresis of hysteresis is attributed to a first order transition.

6. On signatures of first order phase transitions To report a FOPT along a (T,H) line, one needs to observe a discontinuous change in entropy (i.e. observe a latent heat L), or in magnetization (i.e. in vortex volume), as one crosses the (T,H) line by varying either of the control variables T or H. The FOPT is firmly established if the magnetization jump and latent heat satisfy the Clausius–Clapeyron relation.

7. Vortex melting – a 1 st Order Transition Jump in magnetization occurred over a field range. This width has been understood as an effect of sample geometry in these bulk measurements of magnetization; Zeldov et al. showed in their studies (BiSrCaCuO-2212) that the width becomes negligible when local measurements are made using microhall probes. Schilling et al. measured the latent heat across the transition (YBCO), in conjunction with measuring the jump in magnetization. Both these measurements were made over a wide region of the melting line, and they showed that over this entire region the Clausius– Clapeyron relation was valid. Vortex lattice melting was thus firmly established as a FOPT.

8. Vortex melting – a 1 st Order Transition Transition is broad when seen in a bulk measurement, but is a sharp over a local region. (Zeldov et al ’95) broad due to hindered kinetics? Sharp transition occurs over as small as 7X7 vortex regions. (Soibel et al ’00) broad due to disorder? Vortex matter provides physical realization of ‘broad 1 st Order’ transitions (Imry & Wortis ‘80)

9. Chattopadhyay et al Hysteresis due to supercooling & superheating

10. Less rigorous, possible indicator, of a FOPT Supercooling/superheating presents itself as hysteresis when locating the phase boundary (as a function of H or T) via a sharp change in a physical property. Can hysteresis be seen without a FOPT? Pressure-cycle a material which is very viscous and has a pressure range where the volume changes very strongly with pressure, but not discontinuously. If we change pressure fast then observed volume lags behind the equilibrium volume because of high viscosity. Similar effect is expected when pressure is reduced. Thus we would observe a hysteresis loop that is purely kinetic in origin. Kinetic hysteresis is seen when equilibrium can be reached only over times much longer than experimental time scales. (Copper shows an ellipse as the M-H loop in an ac measurement.) This is very relevant for vortex matter in hard superconductors where M–H hysteresis is understood using Bean’s critical state model. Hysteresis and metastability, by themselves, are arguable signatures of a FOPT.

11. MHL’s: a new experimental technique for disorder broadened first-order transitions: Latent heat in broadened first order transition is not easy to measure. Detection of hysteresis and metastability (supercooling/superheating) can be used as an indicator of a 1 st Order transition. But, such hysteresis needs to be distinguished from the hysteresis arising from hindered kinetics

12. MHLs are straight lines if hysteresis is due to surface currents. The left circle displays minor loops when hysteresis is due to bulk pinning, as in critical state model. The minor loops are then continuously nonlinear, Minor hysteresis loops and harmonic generation calculation in generalized critical state model, P. Chaddah, et al, Phys. Rev. B46, 11737 (1992).

14. First order vortex solid-solid transition in vortex state of Type-II Superconductors: CeRu 2 a case study

16. Shattering is more when supercooling is deeper

18. Supercooling with two control variables : Path-dependence

19. Roy et al, JPCM 10 (1998) 8327 (a) MD1 (b) ICND

21. First order vortex solid-solid transition in vortex state of Type-II Superconductors: CeRu 2 a case study

22. J Phys Cond Matt 10 (1998)4885; 10(1998)8327.

23. Path-dependence – theoretical prediction & experimental data

24. Barrier for shattering satisfies predicted inequalities ( Chaddah & Roy Pramana 2000)

25. Chaudhary et al Solid State Communications 114 (2000) 5–8

26. Kinetic arrest or Supercooling? A supercooled liquid is different from a glass

27. Kinetic arrest OR Supercooling (hindered growth vs hindered nucleation) Keep cooling. Kinetically arrested state survives, supercooled state does not. Path dependence – Cool-in-field vs lower field isothermally. FC is farther from equilibrium in supercooling. Apply H ac – and raise frequency. Supercooled state goes to equilibrium; kinetically hindered state moves towards arrest (nucleation of vortices hindered). (hindered nucleation vs hindered growth) Relaxation rate as one lowers (T/H) behaves differently.

28. Supercooled states are metastable; shatter as T  0

29. (a) Kinetic arrest under CSM, and path 2 gives a remanent critical state, while path 1 gives state closest to equilibrium. (b) 1 st order phase transition, and path 1 gives state farthest from equilibrium.

30. Chattopadhyay, Roy & Chaddah, Phys Rev B (in press) Peak at 29kOe at 4.5K; Peak at 22.5 kOe at 5K. CeRu(Nd)2

31. Chattopadhyay et al

32. M. A. MANEKAR et al. Phys Rev B 64 104416 F is partially arrested, G is fully arrested

33. CeFe(Al)2

34. Chattopadhyay et al Phys Rev B 70 214421 (2004) on Gd5Ge4

35. CeFe2

38. Phase coexistence across a disorder-broadened first-order transition

41. MHLs are non-linear; arise from bulk, not from surface.

43. H

44. Chaddah & Roy PRB 60 (1999) 11926

45. Radzyner et al, PRB (2000)