Size effect in the vortex-matter phase transition in Bi 2 Sr 2 CaCuO 8+  ? B. Kalisky, A. Shaulov and Y. Yeshurun Bar-Ilan University Israel T. Tamegai University of Tokyo Vortex Matter Workshop, Mombay, India February 2005

Khaykovich et al., PRL 76 (1996), 2555 Disordered Solid high j Ordered Solid (Abrikosov) low j Liquid Vortex Phase Diagram - Bi 2 Sr 2 CaCu 2 O 8+ 

SMP Melting line Ordered Solid (Abrikosov) low j Disordered Solid high j Liquid SMP Melting line Ordered Solid (Abrikosov) low j Disordered Solid high j Liquid SMP Melting line Large sample Small sample ThTh ? gap TT ? termination

Termination (low T) Y. Yeshurun et al., PRB (1994) B. K Khaykovich et al., PRL (1996) S.L. Li and H. H. Wen, PRB (2002) B. Kalisky et al., PRB (2003). Gap (high T) and effect of size Y. Kopelevich, P. Esquinazi et al., J. Low Temp. (1998, 1999) M. Wang, A.Zettl, T.Tamegai et al., PRL (2001) Large (70 microns) sample Small (30 microns) sample

Goals of this talk 1. Explain the origin of : Gap - high T Termination - low T 2. Understand the role of sample size

BSCCO samples 1225  m 700  m 500  m ~200  m~400  m S D D = 1225  m S d D = 200  m

2D image of induction distribution in a BSCCO sample Magneto-optical technique B 1D induction profile x m local = B(x) - H ext B

M vs. B at different T The SMP decreases with temperature

ThTh Peak height vs. T at 4 G/s Peak height =  m from onset to peak Large sample still demonstrates SMP at 27 K SDSD SdSd

m vs. B, different field sweep rates SMP increases with SR

Peak height vs. field sweep rate, 27 K Increase of peak height with sweep rate is a result of increase in the persistent current due to shorter time window of the experiment

Persistent current density vs. sweep rate Persistent current density is larger in larger sample j obtained by fit to Biot-Savart law

Why j is larger in larger samples? relaxation of j by a certain amount requires the entry of more fluxons in the larger sample and, consequently, longer time

Why j is larger in larger samples? A certain amount of vortices entering the samples causes stronger reduction of j in the small sample Time is scaled by t 0  d

Calculation of the size dependence of j in SR experiments SR and d appear only in the integration constant and boundary conditions

Numerically calculated j/j c vs. SR j increases with SR j increases with the sample size Results are qualitatively similar to experimental results H ext = 1000 G n=3 j c =10 6 A/cm 2

Summary of behavior at high temperatures Decay of persistent currents Disappearance of SMP above T h Small samples: Faster relaxation Disappearance of SMP at lower T h In comparing samples of different size, one should compensate for the reduction in the persistent current in the smaller samples by, e.g., adjusting the field SR

27 K – peak height increases with SR 21 K – peak height decreases with SR 27 K – peak height increases with SR 21 K – peak height decreases with SR maximum in the peak height at intermediate SR Effect of field sweep rate on the peak height at different T

TDVS are injected through the sample edges Paltiel, Zeldov et al., Nature 403, 398 (2000). “Edge contamination” Disorder is induced by inhomogeneous surface barriers H ext B od low-j high-j Appearance of TVS Short  As sweep rate increases, TVS with shorter lifetime play a role Transient Disordered Vortex States (TDVS)

For high sweep rates the SMP is masked by TDVS T=23 K Effectof TDVS on magnetization curves Effect of TDVS on magnetization curves

27 K – peak height increases with SR 21 K – peak height decreases with SR maximum in the peak height at intermediate SR Effect of SR on the peak height at different T

 (B) smallbig Transient disordered states Quasi-ordered phase B od B   time Effects of metastable states are more severe in the smaller sample Effects vortex state of states

Summary and conclusions Two mechanisms for the disappearance of the SMP: 1.High temperatures Decay of persistent currents SMP “disappears” with time 2. High temperatures Involvement of transient states Large M below SMP mask the peak

Sample size plays an important role: 1.Relaxation rate 2.Relative contribution of TDVS are enhanced in smaller samples Summary and conclusions (cont.)  T  and T h depend on sample size

Summary and conclusions (cont.) Our results question previous reports on size effect in the vortex matter phase transition Compensate experimentally for these effects : 1.Increasing SR- high T 2.Decreasing SR - low T

Peak height vs. SR at 25 K The maximum widens for the larger sample The SMP in the larger sample is less affected by relaxation of j and by the engagement of metastable states, for low and high field sweep rates

BSCCO samples 1225  m  m  m ~200  m~400  m S D D = 1225  m S d D = 200  m

BSCCO samples 1225  m 700  m 500  m ~200  m~400  m S D D = 1225  m S d D = 200  m

The sample size plays important role in superconductors, since the basic quantity, the magnetization, depends on sample size. Unlike in ferromagnetic materials, where the basic quantity is an intrinsic or uniform volume property.Introduction

=> The order-disorder phase transition depends on sample size Tc ??? [ ??? ] Irreversibility line [ ??? ] Critical current density [Qin 2004] Magnetic properties like relaxation rates rates [Weir 1991, ??? 0000, Yafit 2004] What else ??? The SMP disappears in samples with reduced size [Esquinazi 1998, Wang 2001] Effect of size in superconductors => “size effect” in SC

We start with the lower termination – below T l. קישור לשקף הבא

Injection through the sample edges Paltiel, Zeldov et al., Nature 403, 398 (2000). “Edge contamination” Disorder is induced by inhomogeneous surface barriers H ext B od low-j high-j Appearance of TVS Short  As sweep rate increases, TVS with shorter lifetime play a role MO imaging of generation of TVS

Effect of sweep rate Magnetization curves For high sweep rates the SMP is masked by TDVS T=23 K

Effect of temperature Magnetization curves For low temperatures the SMP is masked by TDVS 30 K 21 K 160 G/s

? Ordered Solid Disordered Solid Liquid - artifact caused by long living TDVS Transition masked by TDVS “Termination” of the transition line at low temperatures Khaykovich et al., PRL 76, 2555 (1996).

 (B 2 )  (B 1 )  (B 1 ) <  (B 2 ) smallbig Transient disordered states B od B   time=0

 (B) smallbig Transient disordered states Quasi-ordered phase B od B   time Effects of metastable states are more severe in the smaller sample Effects vortex state of states

smallbig Transient disordered states Quasi-ordered phase B od  (B) B od B   time

smallbig Transient disordered states Quasi-ordered phase B od  (B) B od B   time

Quasi-ordered phase smallbig B od B   (B)  time

Ferromagnets: Magnetization, M, is a uniform volume property  M is independent of sample size SIZE EFFECT ONLY IN NANO-SCALE REGIME Introduction: Size effects in ferromagnets and superconductors Bean model m  d 2 M  d In this talk: Special effects of size near vortex phase transition Superconductors: inhomogeneous distribution of the induction  M depends on sample size (e.g. Bean model: M  d) PRONOUNCED EFFECT OF SIZE IN ALL SCALES

Summary and conclusions Two mechanisms for the absence of the SMP: 1.Decay of persistent currents - high T 2.Involvement of metastable states - low T Sample size plays an important role: 1.Relaxation rate 2.Relative contribution of TDVS are enhanced in smaller samples