VOLUME 89, NUMBER 25 PHYSICAL REVIEW LETTERS 16DECEMBER 2002

Comment on ‘‘Superheating and Supercooling of 1 Vortex Matter in a Nb Single Crystal: Direct Evidence for a Phase Transition at the Peak Effect H ≈ H m c2 from Neutron Diffraction’’ 0.8

H ( ν < 1 ) In a recent Letter [1], Ling et al. by neutron scattering dis 0.6 observed a first-order phase transition in the vortex lattice (0) ν c2 H ( >>1 ) of superconducting Nb well below the upper critical field dis

Hc2T: At a magnetic field H 0:5Hc20, the tempera- H / 0.4 ture of the transition is 200 mK below the appropriate Tc2H. At this transition, which Ling et al. interpreted as vortex melting, the regular vortex lattice transforms into 0.2 a disordered phase. Using the results of Ref. [2], we argue 0 here that the observed transition is not thermal melting of 0 0.2 0.4 0.6 0.8 1 order-disorder transition t = T / T the vortex lattice, but is an c caused by pinning. A similar conclusion on the absence of vortex melting FIG. 1. Schematic phase diagram of Nb. The solid lines show well below Tc2H was drawn from experiments by the order-disorder lines Hdist for <1 and  1.The Forgan et al. [3] using a cleaner Nb crystal. In the same dashed line is the vortex-lattice melting line Hm Hc2.The range of magnetic fields, no phase transition was observed HmT probably terminates slightly below Ti [2]. up to a temperature T within 20 mK of the upper critical field line. From this they concluded that the phase tran- netic field (see Fig. 1).We think just this line was detected sition of Ref. [1] is due to pinning effects. Using our in Ref. [1]. The position of HdisT relative to Hc2T is results [2], we qualitatively explain here how the H-T now determined by the parameter D, phase diagram for pure Nb [3] evolves to that found in 2 Ref. [1] when the quenched disorder in the vortex lattice Hc2THdisT/Hc20D ; (2) increases. 2 1=3 We interpret the situation as follows. For type-II super- and depends on the type of pinning (note that D Gi conductors with pinning two phase transition lines exist since  1). Interestingly, although HdisT lies in the in the H-T plane: The line H T corresponds to the bundle pinning region, its position in the H-T plane dis closely correlates with the boundary of the upper single order-disorder transition from the Bragg glass to the up vortex pinning region, Hsv t: disordered amorphous vortex phase, and the line HmT to the vortex melting from the Bragg glass to the vortex up Hc2THdisT/Hc2THsv T : liquid. These lines intersect at a temperature Ti which is 3=2 3 an increasing function of the parameter  2 D = This upper region occurs near Hc2T due to the softening Gi1=2. Here the Ginzburg number Gi measures the ther- of the vortex lattice, as discussed by Larkin and 1=2 mal fluctuations, the parameter D jc0=j00 de- Ovchinnikov [4] to explain the peak effect in the scribes the strength of the quenched disorder in the low-Tc superconductors. flux-line lattice, and jc0 and j00 are the critical and depairing current densities at low temperatures and mag- 1,2 2 10 G. P. Mikitik and E. H. Brandt netic fields. According to Ref. [3], Gi 10 for Nb. If 1B. Verkin Institute for Low Temperature the crystal is very clean, it is possible that <1.Inthis Physics & Engineering case the temperature T 0:2T lies far below T . National Ukrainian Academy of Sciences i c c Kharkov 61103, Ukraine Hence, at H 0:5Hc20 one can observe only the melt- 2Max-Planck-Institut fu¨r Metallforschung ing line, Fig. 1. For small Gi, this melting line practically D-70506 Stuttgart, Germany coincides with the mean-field theory Hc2T, 1=3 Received 24 January 2002; published 3 December 2002 Hc2THmT/Hc20Gi : (1) DOI: 10.1103/PhysRevLett.89.259701 PACS numbers: 74.60.Ge, 61.12.Ex In particular, for Nb we obtain the estimate, Hc2T H T=H 0T HT H=T 103, which m c2 c2 m c [1] X. S. Ling et al., Phys. Rev. Lett. 86, 712 (2001). agrees with the data of Ref. [3]. [2] G. P. Mikitik and E. H. Brandt, Phys. Rev. B 64, 184514 In crystals with noticeable quenched disorder, one finds (2001). 1=2  1 due to the large Gi .InthiscaseTi practically [3] E. M. Forgan et al., Phys. Rev. Lett. 88, 167003 (2002). coincides with Tc, and the order-disorder transition line [4] A. I. Larkin and Yu. N. Ovchinnikov, J. Low Temp. Phys. HdisT should be observable below Hc2T at any mag- 34, 409 (1979).

259701-1 0031-9007=02=89(25)=259701(1)$20.00  2002 The American Physical Society 259701-1