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Multiple phase transformations in weakly pinned vortex matter S. Ramakrishnan and A. K. Grover S. Ramakrishnan and A. K. Grover Department of Condensed Matter Physics and Materials Science Tata Institute of Fundamental Research, Mumbai, India In collaboration with S. Bhattacharya, K. Ghosh, S. Banerjee, D. Pal, S. Sarkar, A. Tulapurkar, A. Thakur, D. Jaiswal (TIFR), T.V. C. Rao, G. Ravikumar, P.K. Mishra, V.C. Sahni (TPPED, BARC) C.V. Tomy (Department of Physics, IIT Mumbai) McK. Paul, G. Balakrishnan (Univ. Warwick) M. Higgins (NEC, NY)

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Motivation: To understand the vortex lattice transformations via the occurrence of anomalous variations in Jc in a variety of low Tc superconductors and compare them with a HTSC. 2. Basic premises: Plateau effect: Transformation from individual or single bundle pinning to collective pinning (single domains) Second Magnetization Peak : Transformation from single domain to multidomain vortex system Classical PE effect: (Multidomain vortex system to maximally disordered /amorphous)

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Plan of the talk 1. Brief recap on vortex lattice transformations (a) Plateau effect (b) Second magnetization peak (SMP) (c) Classical Peak effect (PE) (c) Classical Peak effect (PE) 2. Effect of disorder in 2H-NbSe 2 3. Comparison of SMP and PE in YBCO and Ca 3 Rh 4 Sn 13 4. SMP and PE in Borocarbides(LuNi 2 B 2 C and YNi 2 B 2 C) and 2H-NbX 2 (X=Se, S) 5. Compare the phase diagram and dynamics in two samples of 2H-NbSe 2

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( i) 2H-NbSe 2 crystals with varying disorder (Tc- 7.1 to 6 K) (Uni. Warwick and NEC, NY) ( ii) 2H-NbS 2 crystal (Tc ~ 6.6 K) (J.N.U, India) ( iii) Ca 3 Rh 4 Sn 13 (Tc~8.2 K), Yb 3 Rh 4 Sn 13 crystals(Tc~7.6 K) (Uni. Warwick) ( iv) LuNi 2 B 2 C (Tc~16 K) (Ames) and YNi 2 B 2 C (Tc~15.4 K) (NIMS, Japan) crystals (v) CeRu2 Crystal (Tc~6.4 K) (Uni. Osaka,Toyanaka) (vi) YBCO (few twins, Tc~93 K) (Uni. Wisconsin, Milawauke.) Systems under study using ac and dc magnetization, transport measurements

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T pl Tp Ordered state shrinks as T approaches T cOrdered state shrinks as T approaches T c. Anomalous change in Jc in two crossover regimes. High field is PE and the low field end is Plateau effect. K. Ghosh PRL 76,4600 (1996). Tc~7.17 K S. S. Banerjee et al, PRB 62, 11838 (2000)

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Peak Effect and Effect of Increasing disorder Ordered phase is sandwitched between disordered phases. It shrinks with increasing pinning.Ordered phase is sandwitched between disordered phases. It shrinks with increasing pinning. Reentrance in PE related to pinning.Reentrance in PE related to pinning. K. Ghosh et al, PRL, 76,4600 (1996) S. Banerjee et al, PRB 62, 11838 (2000)

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2H-NbSe 2 (C) Paltiel et al, PRL,85,3712 (2000)

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Observation second magnetization peak and classical peak effect in the same isothermal scan in a low T c superconductor Ca 3 Rh 4 Sn 13 (T c =8.18 K) S. Sarkar, D. Pal et al. Phys. Rev. B 64, 144510 (2001) From magnetization SMP cannot be distinguished at high temperatures

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Observation of the second magnetization peak and peak effect in the same isothermal scan in YBa 2 Cu 3 O 7- (H || c) YBCO with few twins Tc~93 K D. Pal et al. Phys. Rev. B 63, 132505 (2001)

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S. Sarkar, D. Pal et al. Phys. Rev. B 64, 144510 (2001) Comparison of SMP and PE in low Tc and high Tc superconductors SMP and PE are well separated. SMP occupies larger (H,T) space in YBCO as compared to Ca 3 Rh 4 Sn 13

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D. Pal et al PRB 65, 965202, (2002) SMP and PE Deligiannis et al PRL, 79, 2121 (1997) Extensive studies Nishizaki et al PRB 58, 11169 (1998) PRB 53, 82 (1996) PRB 61, 3649 (2000)

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Observation of the second magnetization peak and peak effect in the same isothermal scan in YBa 2 Cu 3 O 7- (H || c) YBCO with few twins Tc~93 K D. Pal et al. Phys. Rev. B 63, 132505 (2001)

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Bi 2 Sr 2 CaCu 2 O 8 Avraham et al Nature, 409, 451 (2001) D. Pal Phys. Rev. B, 64, 144510 (2001), PRB 65, 965202, (2002) D. Pal Phys. Rev. B, 62, 6699 (2000)

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Both crystals A and B show similar Tc and exhibit dHvA Oscillations upto 8 K D. Jaiswal (Physica B, 2004 and un published work) Poster P25, P26 IVW 2005

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Peak Effect and Effect of Increasing disorder Ordered phase is sandwitched between disordered phases. It shrinks with increasing pinning.Ordered phase is sandwitched between disordered phases. It shrinks with increasing pinning. Reentrance in PE related to pinning.Reentrance in PE related to pinning. S. S. Banerjee et al, PRB 62, 11838 (2000)

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Ajay Thakur et al (unpublished.) A. D. Thakur (unpublished)

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NO SMP

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In crystal A, the PE relaxesfaster as compared to disordered crystal C. In crystal A, the PE relaxes faster as compared to disordered crystal C. However, the SMP in C relaxes faster than the PE in the same sample. Caution: SMP is affected by the ripple effect (Kuepfer IVW 2005) P66 IVW 2005

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A. D. Thakur (unpublished) P66 IVW 2005

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A.D. Thakur etal P66 IVW 2005 Both SMP and PE are present at intermediate fields but at higher fields move closer and A broad peak emerges Broadening of the PE is maximum in The FCC response. First observation of SMP in a temperature dependent scan

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Phase diagram Two 2H-NbSe 2 crystals Crystal AB2 Similar to B K. Ghosh et al PRL76, 4600 (1996) Banerjee et al Euro Phys. Lett 46, 91 (1998) Crystal CC2 similar to sample C Banerjee et al PRB 11838 (2000)

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Anistropy ~68 Tc~ 6.6 K, Magnetic response ~2H-NbSe2 crystal C (a)Tulapurkar etal, Physica B200 (b)A. Thakur et al (2004, unpublished)

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A. D. Thakur (unpublished)

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To Summarize 1. SMP and CPE are two distinct anomalies which can be observed in weakly pinned samples of both LTSC and HTSC systems. They relate to order- disorder transformation in the pinned vortex matter. 2. However, both anomalies per se could have different temporal behavior. History and metatstability associated with them depends on times scales involved which are influenced not only by the pinning but also by field (a 0 ). 3. In very weakly pinned sample CPE is sharp but with disorder CPE broadens with emergence of another (SMP) broad peak prior to CPE. Further disorder makes a single broad anomaly commencing well below Hc 2. 4. The absence of reports on SMP distinct from CPE in 2H-NbSe 2 presumably due to the fact that currents associated with SMP decay dies faster than those due to CPE. Commercial Squid magnetometers unable to resolve this. 6. Recent results on various samples are in agreement with our premises 7. In order to substantiate one needs to go beyond macroscopic measurements (eg. STM (Leiden group) experiments on high quality samples or neutron scattering)

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D. Pal et al. Phys. Rev. B 63, 132505 (2001)

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Like Atomic solids, the Vortex Matter responds like an elastic medium It costs energy to distort a Flux line in FLL. For hexagonal lattice, three independent elastic moduli are adequate at B = 1 T, c 66 ~5x10 4 dynes/cm 2 Vortex Matter Physics belongs to the realm of Soft Condensed Matter Weak elasticity of the vortex matter makes it easily susceptible to disordering effects: 1)Disordering effect of thermal energy (kT) (e.g. melting of atomic solid 2)Disorder produced by sample Inhomogenities (impurites, voids, dislocations), Irradiations

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Multiple phase transformations in weakly pinned vortex matter S. Ramakrishnan and A. K. Grover S. Ramakrishnan and A. K. Grover Department of Condensed Matter Physics and Materials Science Tata Institute of Fundamental Research, Mumbai, India In collaboration with Technical Physics Prototype Engineering Division, Bhabha Atomic Research centre, Mumbai, India S. Bhattacharya, K. Ghosh, S. Banerjee, D. Pal, S. Sarkar, A. Tulapurkar, A. Thakur, D. Jaiswal (TIFR), T.V. C. Rao, G. Ravikumar, P.K. Mishra, V.C. Sahni (BARC) C.V. Tomy (Department of Physics, IIT Mumbai) McK. Paul, G. Balakrishnan (Univ. Warwick)

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Pinning Centers in Vortex Matter For example: Point Pins Point pins distort flux line such that it does not remain straight over the entire thickness of the sample. This could lead to loss of long range translational order in FLL. LcLc Produced by sample Inhomogenities, atomic defects, etc. Random distribution of point defects inside the sample give rise to statistical fluctuations in the defect density, which in turn act as weak pinning agents

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Different possible phases of Vortex Matter Weak Pinning Bragg glass (Solid) Vortex Liquid Vortex Glass Thermal Fluctuations

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Peak Effect Phenomenon in J c & the Different Phases of Vortex Matter PE first observed in 1961 in NbZr alloy Almost all weakly pinned superconductors show the Peak Effect. 2H-NbSe 2 crystals: most studied over years Current Carrying capacity in a superconductor (J c ) is related to the extent of order in the FLL as well as strength of pinning Larkin - Ovchinnikov theory (1979)

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Reentrant characteristic of Order-Disorder Phase Boundary Flux Line Soft lattice is very soft at low and high feild Reentrance. (kT) T. Giamarchi and P. Le Doussal (1995); M. Gingras and D. A. Huse (1996). D. R. Nelson (1998) Temperature and/or pinning could induce re-entrant characteristic