Melting of “Porous” Vortex Matter

Abstract

Bitter decoration and magneto-optical studies reveal that in heavy-ion irradiated superconductors, a 'porous' vortex matter is formed when vortices outnumber columnar defects (CDs). In this state ordered vortex crystallites are embedded in the 'pores' of a rigid matrix of vortices pinned on CDs. The crystallites melt through a first-order transition while the matrix remains solid. The melting temperature increases with density of CDs and eventually turns into a continuous transition. At high temperatures a sharp kink in the melting line is found, signaling an abrupt change from crystallite melting to melting of the rigid matrix.PACS numbers: 74.60. Ec, 74.60.Ge, 74.72.Hs Melting of heterogeneous systems, and in particular of nanocrystals embedded in porous rigid matrices, is a complex process with many uncontrolled parameters. Metal and semiconductor nanocrystals with free surfaces, for example, usually show a decrease in their melting temperature with decreasing size [1], whereas nanocrystals encapsulated in a porous matrix often display an increase in melting temperature [2]. Although the contribution of the different factors is still a matter of debate, the melting process is known to depend on the size, dimensionality, material properties of the nanocrystals and the matrix, as well as the interface energies between the materials [1,2]. In this work we investigate an analogous, but a more controllable composite system, which is a 'porous' vortex matter consisting of vortex nanocrystals encapsulated in a matrix of strongly pinned vortices. As shown below, this system is present in the commonly heavy-ion irradiated superconductors when the vortices outnumber the columnar defects (CDs). The rigid matrix is created by vortices localized on the network of random CDs, while the softer nanocrystals are formed within the 'pores' of this matrix by the interstitial vortices. The size of the nanocrystals can be readily varied from several hundred down to a few vortices by changing the applied field or the density of CDs. We find that this composite vortex matter reveals a number of intriguing mechanisms: Similarly to the metallic nanocrystals in a matrix, we observe for the first time a pronounced upward shift in the vortex melting temperature T m , while preserving the first-order nature of the transition (FOT). With increasing density of CDs, the size of the pores decreases, resulting in a larger shift in T m . We also find a critical point at which the FOT changes into a continuous melting. Moreover, the crystallites can melt while the matrix remains rigid. As a result, at high temperatures we find an abrupt breakdown in the upward shift of T m and a sharp kink in the FOT line, which apparently result from the collapse of the matrix due to vortex depinning from the CDs.The reported findings were obtained using Bitter decoration and differential magneto-optical (MO) [3] techniques. High quality Bi 2 Sr 2 CaCu 2 O 8 (BSCCO) crystals (T c ≈ 89 K) were covered by various patterned masks and irradiated at GANIL by 1 Ge...

Melting and structure of the vortex solid in strongly anisotropic layered superconductors with random columnar pins

“…Both the BrG to BoG and the BoG to IL transitions are found to be first-order. We also find that a local melting temperature can be suitably defined using a criterion based on the degree of localization of the vortices, and that its behavior (in particular, its spatial variation) is quite consistent with what is seen in experiments 18,28 . The value of the local melting temperature is strongly correlated with the presence of topological defects (dislocations) in the vortex solid which, in turn, is correlated with the local arrangement of the pinning centers.…”

“…Since several experimental studies 17,18,19 of the effects of irradiationinduced columnar pinning on the mixed state of BSCCO exist in the literature, we have used parameter values appropriate for this system. For other layered superconductors, the BoG phase might occur over a wider or narrower (even vanishing) range.…”

“…In this subsection, we show that this inhomogeneity leads to a spatial variation of a "local melting temperature", defined below. As mentioned in the Introduction, such spatial variations of a local melting temperature have been deduced from measurements of the local magnetization in BSCCO samples with random point 28 and columnar pinning 18 . Since we are dealing with time averaged densities, it is clear that the value of ρ i at a local peak of the density field provides a measure of the degree of localization of the vortex whose average position corresponds to the location of the density peak.…”

Vortex matter freezing inBi2Sr2CaCu2O8samples with a very dense distribution of columnar defects

“…A complete destruction of the positional and orientational order of the vortex structure is reported. [19][20][21][22][23][24][25][26] However, for very low CD densities of tens of Gauss, the short-range order of the vortex structure is recovered 20 and a polycristalline structure is observed in magnetic decoration snapshots [21][22][23][24][25][26] indicating inter-vortex repulsion remains important even in the presence of such strong pins. As mentioned, the vortex configurations imaged by field-cooling decorations correspond to the state frozen at T freez at which vortex mobility is strongly reduced by the effect of pinning.…”

Biography of Francisco de la Cruz

“…In high-temperature superconductors, however, the lattices melt into a vortex liquid through a first-order thermodynamic transition (6). In this liquid state, the superconductor cannot sustain electrical currents without dissipation, and technical applications require research to overcome this problem (7)(8)(9).…”