Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor
Identifieur interne : 000C85 ( Istex/Corpus ); précédent : 000C84; suivant : 000C86Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor
Auteurs : V F Kozhevnikov ; M J Van Bael ; P K Sahoo ; K. Temst ; C. Van Haesendonck ; A. Vantomme ; J O IndekeuSource :
- New Journal of Physics [ 1367-2630 ] ; 2007.
Abstract
Superconductivity in single crystal Sn samples with surface-enhanced order parameter is studied experimentally. Controllable surface enhancement is achieved by mechanical polishing or by ion irradiation. A first-order surface superconductivity transition is found in parallel magnetic fields close to the bulk critical field Hc(T) and for temperatures above 0.8Tc up till a surface critical temperature Tcs > Tc, where Tc is the bulk critical temperature. The resulting phase diagram agrees with that predicted for interface-delocalization or wetting transitions in type-I superconductors, based on the GinzburgLandau theory.
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DOI: 10.1088/1367-2630/9/3/075
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</title><author><name sortKey="Kozhevnikov, V F" sort="Kozhevnikov, V F" uniqKey="Kozhevnikov V" first="V F" last="Kozhevnikov">V F Kozhevnikov</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Van Bael, M J" sort="Van Bael, M J" uniqKey="Van Bael M" first="M J" last="Van Bael">M J Van Bael</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Sahoo, P K" sort="Sahoo, P K" uniqKey="Sahoo P" first="P K" last="Sahoo">P K Sahoo</name><affiliation><mods:affiliation>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Temst, K" sort="Temst, K" uniqKey="Temst K" first="K" last="Temst">K. Temst</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Van Haesendonck, C" sort="Van Haesendonck, C" uniqKey="Van Haesendonck C" first="C" last="Van Haesendonck">C. Van Haesendonck</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Vantomme, A" sort="Vantomme, A" uniqKey="Vantomme A" first="A" last="Vantomme">A. Vantomme</name><affiliation><mods:affiliation>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Indekeu, J O" sort="Indekeu, J O" uniqKey="Indekeu J" first="J O" last="Indekeu">J O Indekeu</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: joseph.indekeu@fys.kuleuven.be</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:9F4F6191803E5A4C3FAD530A19C484031E0BB01C</idno><date when="2007" year="2007">2007</date><idno type="doi">10.1088/1367-2630/9/3/075</idno><idno type="url">https://api.istex.fr/document/9F4F6191803E5A4C3FAD530A19C484031E0BB01C/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000C85</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</title><author><name sortKey="Kozhevnikov, V F" sort="Kozhevnikov, V F" uniqKey="Kozhevnikov V" first="V F" last="Kozhevnikov">V F Kozhevnikov</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Van Bael, M J" sort="Van Bael, M J" uniqKey="Van Bael M" first="M J" last="Van Bael">M J Van Bael</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Sahoo, P K" sort="Sahoo, P K" uniqKey="Sahoo P" first="P K" last="Sahoo">P K Sahoo</name><affiliation><mods:affiliation>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Temst, K" sort="Temst, K" uniqKey="Temst K" first="K" last="Temst">K. Temst</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Van Haesendonck, C" sort="Van Haesendonck, C" uniqKey="Van Haesendonck C" first="C" last="Van Haesendonck">C. Van Haesendonck</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Vantomme, A" sort="Vantomme, A" uniqKey="Vantomme A" first="A" last="Vantomme">A. Vantomme</name><affiliation><mods:affiliation>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation></author><author><name sortKey="Indekeu, J O" sort="Indekeu, J O" uniqKey="Indekeu J" first="J O" last="Indekeu">J O Indekeu</name><affiliation><mods:affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: joseph.indekeu@fys.kuleuven.be</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">New Journal of Physics</title><title level="j" type="abbrev">New J. Phys.</title><idno type="ISSN">1367-2630</idno><idno type="eISSN">1367-2630</idno><imprint><publisher>Institute of Physics Publishing</publisher><date type="published" when="2007">2007</date><biblScope unit="volume">9</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="75">75</biblScope><biblScope unit="page" to="75">75</biblScope></imprint><idno type="ISSN">1367-2630</idno></series><idno type="istex">9F4F6191803E5A4C3FAD530A19C484031E0BB01C</idno><idno type="DOI">10.1088/1367-2630/9/3/075</idno><idno type="PII">S1367-2630(07)37905-6</idno><idno type="articleID">237905</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1367-2630</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">Superconductivity in single crystal Sn samples with surface-enhanced order parameter is studied experimentally. Controllable surface enhancement is achieved by mechanical polishing or by ion irradiation. A first-order surface superconductivity transition is found in parallel magnetic fields close to the bulk critical field Hc(T) and for temperatures above 0.8Tc up till a surface critical temperature Tcs > Tc, where Tc is the bulk critical temperature. The resulting phase diagram agrees with that predicted for interface-delocalization or wetting transitions in type-I superconductors, based on the GinzburgLandau theory.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>V F Kozhevnikov</name><affiliations><json:string>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</json:string></affiliations></json:item><json:item><name>M J Van Bael</name><affiliations><json:string>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</json:string></affiliations></json:item><json:item><name>P K Sahoo</name><affiliations><json:string>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</json:string></affiliations></json:item><json:item><name>K Temst</name><affiliations><json:string>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</json:string></affiliations></json:item><json:item><name>C Van Haesendonck</name><affiliations><json:string>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</json:string></affiliations></json:item><json:item><name>A Vantomme</name><affiliations><json:string>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</json:string></affiliations></json:item><json:item><name>J O Indekeu</name><affiliations><json:string>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</json:string><json:string>E-mail: joseph.indekeu@fys.kuleuven.be</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>paper</json:string></originalGenre><abstract>Superconductivity in single crystal Sn samples with surface-enhanced order parameter is studied experimentally. 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Phys.</title><idno type="pISSN">1367-2630</idno><idno type="eISSN">1367-2630</idno><imprint><publisher>Institute of Physics Publishing</publisher><date type="published" when="2007"></date><biblScope unit="volume">9</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="75">75</biblScope><biblScope unit="page" to="75">75</biblScope></imprint></monogr><idno type="istex">9F4F6191803E5A4C3FAD530A19C484031E0BB01C</idno><idno type="DOI">10.1088/1367-2630/9/3/075</idno><idno type="PII">S1367-2630(07)37905-6</idno><idno type="articleID">237905</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2007</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>Superconductivity in single crystal Sn samples with surface-enhanced order parameter is studied experimentally. Controllable surface enhancement is achieved by mechanical polishing or by ion irradiation. A first-order surface superconductivity transition is found in parallel magnetic fields close to the bulk critical field Hc(T) and for temperatures above 0.8Tc up till a surface critical temperature Tcs > Tc, where Tc is the bulk critical temperature. The resulting phase diagram agrees with that predicted for interface-delocalization or wetting transitions in type-I superconductors, based on the GinzburgLandau theory.</p></abstract></profileDesc><revisionDesc><change when="2007">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/9F4F6191803E5A4C3FAD530A19C484031E0BB01C/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1"</istex:xmlDeclaration><istex:docType SYSTEM="http://ej.iop.org/dtd/iopv1_5_1.dtd" name="istex:docType"></istex:docType><istex:document><article artid="nj237905"><article-metadata><jnl-data jnlid="nj"><jnl-fullname>New Journal of Physics</jnl-fullname><jnl-abbreviation>New J. Phys.</jnl-abbreviation><jnl-shortname>NJP</jnl-shortname><jnl-issn>1367-2630</jnl-issn><jnl-coden>NJOPFM</jnl-coden><jnl-imprint>Institute of Physics Publishing</jnl-imprint><jnl-web-address>stacks.iop.org/NJP</jnl-web-address></jnl-data><volume-data><year-publication>2007</year-publication><volume-number>9</volume-number></volume-data><issue-data><issue-number>3</issue-number><coverdate>March 2007</coverdate></issue-data><article-data><article-type type="paper" sort="regular"></article-type><type-number type="paper">75</type-number><article-number>237905</article-number><first-page>75</first-page><last-page>75</last-page><length>1</length><pii>S1367-2630(07)37905-6</pii><doi>10.1088/1367-2630/9/3/075</doi><copyright>IOP Publishing and Deutsche Physikalische Gesellschaft</copyright><ccc>1367-2630/07/010075+7$30.00</ccc><printed></printed></article-data></article-metadata><header><title-group><title>Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</title><short-title>Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</short-title><ej-title>Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</ej-title></title-group><author-group><author address="nj237905ad1"><first-names>V F</first-names><second-name>Kozhevnikov</second-name></author><author address="nj237905ad1"><first-names>M J</first-names><second-name>Van Bael</second-name></author><author address="nj237905ad2"><first-names>P K</first-names><second-name>Sahoo</second-name></author><author address="nj237905ad1"><first-names>K</first-names><second-name>Temst</second-name></author><author address="nj237905ad1"><first-names>C</first-names><second-name>Van Haesendonck</second-name></author><author address="nj237905ad2"><first-names>A</first-names><second-name>Vantomme</second-name></author><author address="nj237905ad1" email="nj237905ea1"><first-names>J O</first-names><second-name>Indekeu</second-name></author><short-author-list>V F Kozhevnikov <italic>et al</italic></short-author-list></author-group><address-group><address id="nj237905ad1" showid="yes">Laboratorium voor Vaste-Stoffysica en Magnetisme, <orgname>Katholieke Universiteit Leuven</orgname>, B-3001 Leuven, <country>Belgium</country></address><address id="nj237905ad2" showid="yes">Instituut voor Kern-en Stralingsfysica, <orgname>Katholieke Universiteit Leuven</orgname>, B-3001 Leuven, <country>Belgium</country></address><e-address id="nj237905ea1"><email mailto="joseph.indekeu@fys.kuleuven.be">joseph.indekeu@fys.kuleuven.be</email></e-address></address-group><history received="24 November 2007" online="27 March 2007"></history><abstract-group><abstract><heading>Abstract</heading><p indent="no">Superconductivity in single crystal Sn samples with surface-enhanced order parameter is studied experimentally. Controllable surface enhancement is achieved by mechanical polishing or by ion irradiation. A first-order surface superconductivity transition is found in parallel magnetic fields close to the bulk critical field <italic>H</italic><sub>c</sub>(<italic>T</italic>) and for temperatures above 0.8<italic>T</italic><sub>c</sub> up till a surface critical temperature <italic>T</italic><sub>cs</sub> > <italic>T</italic><sub>c</sub>, where <italic>T</italic><sub>c</sub> is the bulk critical temperature. The resulting phase diagram agrees with that predicted for interface-delocalization or wetting transitions in type-I superconductors, based on the Ginzburg–Landau theory.</p></abstract></abstract-group></header><body refstyle="numeric"><sec-level1 id="nj237905s1"><p indent="no">In this paper, we address the following fundamental issues. What is the nature of surface superconductivity? Is it possible that the superconducting phase ‘wets’ the specimen surface, meaning that a macroscopic superconducting sheath intrudes between the surface and the normal phase? Can the interface delocalization or ‘wetting’ phase diagram, predicted for surface-enhanced type-I superconductors, be verified experimentally? If so, what is the character of the phase transitions involved? How can surface enhancement of superconductivity be achieved in a controlled and systematic way?</p><p>Surface superconductivity has continued to intrigue experimentalists and theorists alike since its prediction in 1963 [<cite linkend="nj237905bib1">1</cite>]. Continuous nucleation of superconductivity occurs at the sample surface below a parallel magnetic field known as <italic>H</italic><sub>c3</sub>(<italic>T</italic>), with <italic>T</italic> < <italic>T</italic><sub>c</sub>, provided the Ginzburg–Landau (GL) parameter κ exceeds 0.41. This effect arises for surfaces in contact with vacuum or an insulator. For materials with κ < 0.41, <italic>H</italic><sub>c3</sub> lies below the bulk critical field <italic>H</italic><sub>c</sub>. Then there is no stable surface superconductivity above <italic>H</italic><sub>c</sub> and, decreasing <italic>H</italic> below <italic>H</italic><sub>c</sub>, <italic>H</italic><sub>c3</sub> is the metastability limit of the normal state.</p><p>A surprising transformation of surface superconductivity, in which the superconducting surface sheath can develop ‘bulk’ proportions, was predicted in 1995 for different surfaces, endowed with enhancement of the superconducting order parameter [<cite linkend="nj237905bib2">2</cite>]. In this interface delocalization or ‘wetting’ scenario the sheath thickness becomes macroscopic when <italic>H</italic> is lowered to <italic>H</italic><sub>c</sub> for temperatures above a ‘wetting’ temperature <italic>T</italic><sub>w</sub>. Further, surface superconductivity extends to a surface critical temperature <italic>T</italic><sub>cs</sub> > <italic>T</italic><sub>c</sub>. This equilibrium phenomenon is very different from fluctuation conductivity [<cite linkend="nj237905bib3">3</cite>]. The phase diagram for κ < 0.374 features a first-order surface ‘prewetting’ transition from the normal state to a superconducting surface sheath, for <italic>T</italic><sub>w</sub> < <italic>T</italic> < <italic>T</italic><sub>cs</sub>. For 0.374 < κ < 0.707 the predicted wetting transition is critical instead of first order [<cite linkend="nj237905bib2">2</cite>]. For mesoscopic samples the theory predicts a significant increase of <italic>T</italic><sub>c</sub> [<cite linkend="nj237905bib4">4</cite>] on the basis of which new applications can be expected.</p><p>The similarity between ‘wetting’ phenomena in type-I superconductors and those in fluids or Ising magnets ([<cite linkend="nj237905bib5">5</cite>, <cite linkend="nj237905bib6">6</cite>]; for a recent review, see [<cite linkend="nj237905bib7">7</cite>]) comes from the fact that there is a positive excess free energy γ<sub>0</sub> associated with the interface between the coexisting bulk phases, in our case the normal phase and the superconducting Meissner phase. In addition, there is preferential adsorption of one bulk phase at the surface, in our case the superconducting phase. For κ > 0.41 and surfaces in contact with an insulator this leads to nucleation at <italic>H</italic><sub>c3</sub>(<italic>T</italic>) but this is not quite sufficient to induce wetting. Complete wetting is possible only if the difference of surface free energies of normal and superconducting phases, γ<sub>n</sub> − γ<sub>s</sub>, is large enough to match the interfacial tension γ<sub>0</sub>. This requires other surfaces, with enhancement of the order parameter, i.e., negative surface extrapolation length <italic>b</italic> in the GL theory [<cite linkend="nj237905bib2">2</cite>].</p><p>Phase transitions from partial to complete wetting have been observed in various liquid–liquid and liquid–gas systems in a broad temperature range, from cryogenic (see, e.g., [<cite linkend="nj237905bib8">8</cite>]) to thousands of degrees [<cite linkend="nj237905bib9">9</cite>]. However, in spite of continuing interest in the phenomenon [<cite linkend="nj237905bib10">10</cite>], no experimental study has yet been dedicated to verify the theory of interface delocalization transitions in superconductors. Note that the so-called ‘twinning-plane superconductivity’ in Sn [<cite linkend="nj237905bib11">11</cite>], which was <italic>a posteriori</italic> interpreted as prewetting [<cite linkend="nj237905bib2">2</cite>, <cite linkend="nj237905bib12">12</cite>], originates from internal defects. These cannot be manipulated systematically, and certainly not reversibly, in contrast with the outer surface of the sample [<cite linkend="nj237905bib13">13</cite>].</p><p>Pure Sn is a classical type-I superconductor with κ ≈ 0.15 [<cite linkend="nj237905bib14">14</cite>]. <italic>T</italic><sub>c</sub> as measured by us is 3.73 ± 0.005 K, consistent with previous work [<cite linkend="nj237905bib15">15</cite>]. As was recently shown [<cite linkend="nj237905bib13">13</cite>], mechanical polishing (surface cold working) induces reversible surface enhancement of the order parameter in single crystal Sn samples. Enhancement of superconductivity by surface cold working was demonstrated long ago on an InBi alloy [<cite linkend="nj237905bib16">16</cite>]. Possible origins of this effect in Sn are discussed in [<cite linkend="nj237905bib13">13</cite>]. One of the samples we use is a polished single crystal Sn sample described in [<cite linkend="nj237905bib13">13</cite>] (sample no. 2), below referred to as ‘polished’. Another single crystal sample from the same supplier (Alfa Aesar) has the same shape (spark cut disk, 7 mm diameter and 1 mm thickness) and purity (99.9999%) as the polished sample. We refer to it as ‘plain’. Its quality was checked by measuring dc magnetization at supercritical temperatures 3.74 and 3.76 K, yielding the same diamagnetic response as for the annealed samples described in [<cite linkend="nj237905bib13">13</cite>], which is an order of magnitude lower than for the polished sample. Upon completing a full set of measurements, one side of the plain sample was modified via irradiation with Xe ions (using the Leuven ion separator), and hence is referred to as ‘implanted’.</p><p>Irradiation with noble gas ions can be viewed as precision surface cold working, by far more controllable and uniform than polishing. If so, ion irradiation should induce enhanced surface superconductivity. Indeed, irradiation by Xe<sup>++</sup> ions with energy 160 keV and a fluence of 10<sup>16</sup> cm<sup>−2</sup> yielded an increase in supercritical diamagnetic response of about 50% with respect to the magnetization in the plain sample. Consecutive irradiation with a ten times larger fluence of 80 keV Xe<sup>+</sup> ions resulted in an enhancement of supercritical diamagnetism by a factor of 5. This is about half of the surface diamagnetism of the polished sample (see figure <figref linkend="nj237905fig1">1</figref>). Taking into account that polishing was applied to both sides [<cite linkend="nj237905bib13">13</cite>], this means that the implanted and polished samples possess approximately the same effective surface enhancement. Upon irradiation the sample surface became smoother: roughness probed by atomic force microscopy (AFM, Veeco Autoprobe M5) on a scale of 1 μm yielded 15 and 6 nm rms for the plain and implanted samples, respectively. Note that for niobium the effect is opposite [<cite linkend="nj237905bib17">17</cite>]. On the other hand, the irradiation did not change the large-scale profile formed by the spark cutting: average valley-to-hill height and distance were 0.2 and 2 μm, respectively. Using Rutherford backscattering and channelling spectrometry with a 1.57 MeV He<sup>+</sup> beam, the damage accumulation in the sample was analysed. It was found that due to the Xe irradiation, the crystalline structure is degraded in a surface layer with thickness of approximately 50 nm.</p><figure id="nj237905fig1" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="19.6pc" printcolour="no" filename="images/nj237905fig1.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj237905fig1.jpg"></graphic-file></graphic><caption type="figure" id="nj237905fc1" label="Figure 1"><p indent="no">Magnetization at supercritical temperature 3.74 K. Open and closed circles are for the implanted sample for decreasing and increasing field, respectively; <italic>H</italic><sub>s</sub> is the maximum field for surface superconductivity. In the inset, −<italic>M</italic> is shown on a semi-log scale.</p></caption></figure><p>To construct the phase diagram of the surface-enhanced samples, dc magnetization was measured versus in-plane magnetic field at temperatures from 3.76 K down to 2 K, using a Quantum Design SQUID magnetometer. Magnetization data of the plain sample served as a reference. The data for the implanted sample for decreasing and increasing magnetic field at supercritical temperature 3.74 K are shown in figure <figref linkend="nj237905fig1">1</figref>. Experimental curves for the plain and polished samples, for decreasing field, are shown for comparison. The supercritical magnetization is much greater than fluctuation diamagnetism [<cite linkend="nj237905bib13">13</cite>]; on the other hand, it is three orders of magnitude smaller than the magnetization measured at 3.72 K. The standard deviation of the temperature and magnetic field readings is 0.005 K and 0.005 Oe, respectively. The inhomogeneity of the magnetic field on a 3 cm scan length, used in the measurements, is 0.05%. The uncertainty on the data for the magnetic moment <italic>M</italic> is ± 1 × 10<sup>−7</sup> emu.</p><p>Onset and vanishing of surface superconductivity occur with noticeable hysteresis (see also [<cite linkend="nj237905bib13">13</cite>]), which is consistent with an underlying first-order phase transition. This can be seen more clearly in the data shown on semi-log scale in the insert of figure <figref linkend="nj237905fig1">1</figref>. The origin in figure <figref linkend="nj237905fig1">1</figref> is shifted with respect to zero field due to a small residual field in the magnetometer. For consistency only data obtained at positive fields are discussed. A maximum field, at which surface superconductivity is recognizable, is reached for increasing field and marked as <italic>H</italic><sub>s</sub>. Note the difference with respect to conventional surface superconductivity at <italic>H</italic><sub>c3</sub>; the latter develops as a second-order phase transition and does not involve hysteresis.</p><p>The subcritical <italic>M</italic>(<italic>H</italic>) isotherms can be divided into high- and low-temperature groups, with and without surface superconductivity, respectively. The absence of the surface sheath at low temperatures and its presence at higher ones is a hallmark of the wetting transition.</p><p>Typical magnetization data near the bulk critical field for two isotherms from the high- and low-temperature groups are shown in figures <figref linkend="nj237905fig2">2</figref>(a) and (b), respectively. <italic>H</italic><sub>c</sub> marks the field of the bulk transition to the normal state. This transition takes place at the same field for all three samples. There is no apparent metastable continuation of bulk superconductivity, so <italic>H</italic><sub>c</sub> is the thermodynamic critical field. <italic>H</italic><sub>s</sub> for the implanted sample is only barely different from that for the polished sample.</p><figure id="nj237905fig2" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="23.6pc" printcolour="no" filename="images/nj237905fig2.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj237905fig2.jpg"></graphic-file></graphic><caption type="figure" id="nj237905fc2" label="Figure 2"><p indent="no">Magnetization near the bulk critical field (a) at high temperatures, and (b) at low temperatures. Diamonds, triangles and circles are for the plain, polished and implanted samples, respectively. Directions of change of the magnetic field are shown with dashed arrows; down arrows indicate decreasing field, up arrows increasing field.</p></caption></figure><p>In figure <figref linkend="nj237905fig2">2</figref>(a), surface superconductivity in the polished and implanted samples is clearly noticeable for increasing field (<italic>H</italic><sub>c</sub> < <italic>H</italic> < <italic>H</italic><sub>s</sub>). For decreasing field the range of metastable continuation of the <italic>surface</italic> normal state increases with decreasing temperature; at <italic>T</italic> = 3.64 K the surface normal state in the implanted samples persists down to <italic>H</italic><sub>c</sub>, and at 3.54 K the normal state metastability in both surface-enhanced samples extends below <italic>H</italic><sub>c</sub>. No surface superconductivity was recorded for the plain sample. The range of normal state metastability for the plain sample is larger than that for the surface-enhanced samples. The difference &Dgr;<italic>H</italic> = <italic>H</italic><sub>s</sub> − <italic>H</italic><sub>c</sub> gradually decreases with decreasing <italic>T</italic>.</p><p>As is seen from figure <figref linkend="nj237905fig2">2</figref>(b), at low <italic>T</italic> no surface superconductivity was recorded. The normal state metastability range in the plain sample increases with decreasing <italic>T</italic>; the same occurs in the polished sample, but for a smaller range. Normal state metastability is barely noticeable in the implanted sample. This may be due to the greater uniformity of surface defects created by irradiation.</p><p>The phase diagram of the implanted sample constructed from the magnetization data is shown in figure <figref linkend="nj237905fig3">3</figref>. First, we compare our results for <italic>H</italic><sub>c</sub>(<italic>T</italic>) with classic data [<cite linkend="nj237905bib18">18</cite>], depicted with crosses. There is a systematic shift of less than 2 Oe in field and, correspondingly, 0.01 K in temperature between the coexistence curve (solid line) and those data.</p><figure id="nj237905fig3" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="20.9pc" printcolour="no" filename="images/nj237905fig3.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj237905fig3.jpg"></graphic-file></graphic><caption type="figure" id="nj237905fc3" label="Figure 3"><p indent="no">Phase diagram of the surface-enhanced Sn samples. The solid line is the bulk coexistence curve <italic>H</italic><sub>c</sub>(<italic>T</italic>); the dashed line is the surface transition <italic>H</italic><sub>s</sub>(<italic>T</italic>). The line in the inset is a theoretical curve fitted to the &Dgr;<italic>H</italic>(<italic>T</italic>) data for the implanted sample.</p></caption></figure><p>As figure <figref linkend="nj237905fig3">3</figref> shows, the phase diagram of surface-enhanced Sn is different from the standard phase diagram of low-κ type-I superconductors and consistent with that predicted in [<cite linkend="nj237905bib2">2</cite>]. The critical temperature for surface superconductivity in zero field is <italic>T</italic><sub>cs</sub> ≈ 3.78 K. Linear extrapolation of the <italic>H</italic><sub>s</sub> data towards low <italic>T</italic> yields a location <italic>W</italic> of the wetting transition at <italic>T</italic><sub>w</sub> ≈ 3.25 K.</p><p>In the inset <italic>H</italic><sub>s</sub>(<italic>T</italic>) for implanted and polished samples are shown as &Dgr;<italic>H</italic> ≡ <italic>H</italic><sub>s</sub> − <italic>H</italic><sub>c</sub> versus <italic>T</italic>. The curve is the well-known theoretical dependence &Dgr;<italic>H</italic> ∝ −(<italic>T</italic> − <italic>T</italic><sub>w</sub>)/ln (<italic>T</italic>−<italic>T</italic><sub>w</sub>) for the prewetting curve close to <italic>W</italic>, for systems with short-range interactions, <fnref linkend="nj237905fn1"><sup>3</sup></fnref> originally derived in [<cite linkend="nj237905bib19">19</cite>] and confirmed for superconductors in [<cite linkend="nj237905bib10">10</cite>]. The fit to &Dgr;<italic>H</italic>(<italic>T</italic>) for the implanted sample yields the improved estimate <italic>T</italic><sub>w</sub> ≈ 3.10 K.</p><p>The global phase diagram (κ versus ξ(<italic>T</italic>)/<italic>b</italic>, with ξ(<italic>T</italic>) the GL coherence length) derived in [<cite linkend="nj237905bib2">2</cite>] allows one to infer κ from parameters of surface and bulk superconductivity. To check this prediction, we first calculate κ for the implanted sample, using the standard procedure following the well-known formula [<cite linkend="nj237905bib21">21</cite>] κ = κ<sub>p</sub>(1 + 0.78 ξ<sub>0</sub>/l), where κ<sub>p</sub> is the GL parameter in the pure limit, ξ<sub>0</sub> the Pippard or Bardeen–Cooper–Schrieffer (BCS) coherence length, and <italic>l</italic> the electron mean free path. The latter was obtained from the residual resistivity ratio (RRR) at 293 K and 6 K, measured using the van der Pauw technique. RRR for the plain sample is 120, and RRR measured for the modified side of the implanted sample is close to 40. Since surface superconductivity develops in a much thicker layer than just the layer with degraded crystalline structure, we have to use the mean free path for the bulk, i.e., the value found for the plain sample. Other quantities used are: 1.03 × 10<sup>−11</sup> &OHgr; cm<sup>2</sup> for <italic>l</italic>/σ [<cite linkend="nj237905bib14">14</cite>], 8.9 × 10<sup>4</sup> (&OHgr; cm)<sup>−1</sup> for the electrical conductivity σ at room temperature [<cite linkend="nj237905bib15">15</cite>], 3100 Å for ξ<sub>0</sub> [<cite linkend="nj237905bib11">11</cite>], and 0.15 for κ<sub>p</sub> [<cite linkend="nj237905bib14">14</cite>]. We find <italic>l</italic> = 1.2 × 10<sup>4</sup> Å, and κ ≈ 0.18.</p><p>Next, we deduce κ from the global phase diagram (see figure <figref linkend="nj237905fig2">2</figref> of the first paper of[<cite linkend="nj237905bib2">2</cite>]). We need to calculate ξ(<italic>T</italic><sub>w</sub>)/<italic>b</italic>. According to the theory <italic>b</italic> = −ξ(<italic>T</italic><sub>cs</sub>), so <inline-eqn></inline-eqn>. Taking for <italic>T</italic><sub>c</sub>, <italic>T</italic><sub>cs</sub>, and <italic>T</italic><sub>w</sub>, 3.73, 3.78 and 3.25 K, respectively, we obtain κ ≈ 0.18, while, taking <italic>T</italic><sub>w</sub> = 3.10 K, we find κ ≈ 0.20. Both estimates agree well with that found by the standard procedure. Moreover, we find that assuming κ ≈ 0.2 the entire prewetting line closely follows the calculated one shown in figure <figref linkend="nj237905fig3">3</figref> in the first paper of [<cite linkend="nj237905bib2">2</cite>].</p><p>Thus, the theory [<cite linkend="nj237905bib2">2</cite>] agrees quantitatively with experiment as regards the first-order prewetting line and the value of κ. The magnetization data at <italic>T</italic> > <italic>T</italic><sub>c</sub> (e.g., figure <figref linkend="nj237905fig1">1</figref>) allow us to make one more estimate. The slope ∂ <italic>M</italic>/∂<italic>H</italic> at zero field is proportional to the volume of the superconducting sheath, and therefore to its effective thickness <italic>d</italic>. Calculations for the implanted sample yield <italic>d</italic> ≈ 10 μm for 3.74 K and <italic>d</italic> ≈ 1 μm for 3.76 K. These thicknesses are of the order of ξ(<italic>T</italic>) and largely exceed that of the damaged layer (50 nm). The sheath disappears at <italic>T</italic><sub>cs</sub>. Our findings are consistent with the prediction that, for <italic>T</italic> > <italic>T</italic><sub>c</sub>, the superconducting order parameter decays into the sample on the scale of ξ(<italic>T</italic>) ∝ (<italic>T</italic> − <italic>T</italic><sub>c</sub>)<sup>−1/2</sup>, and its amplitude vanishes at <italic>T</italic><sub>cs</sub>.</p><p>Below <italic>T</italic><sub>c</sub>, in the complete wetting regime <italic>T</italic> > <italic>T</italic><sub>w</sub>, theory predicts a very weak divergence of the sheath thickness upon lowering <italic>H</italic> towards <italic>H</italic><sub>c</sub>, of the form ln(1/(<italic>H</italic> − <italic>H</italic><sub>c</sub>)) [<cite linkend="nj237905bib2">2</cite>]. The data (figure <figref linkend="nj237905fig2">2</figref>(a)) allow us to detect wetting layer thicknesses up till about a few μm, slightly larger than ξ(<italic>T</italic>) at the temperatures under consideration. Fits to our data agree better with the predicted logarithmic divergence than with a power law.</p><p>Finally we estimate <italic>b</italic>, using <inline-eqn></inline-eqn>, where ξ<sub>p</sub>(<italic>T</italic>) is the pure limit of ξ(<italic>T</italic>) [<cite linkend="nj237905bib3">3</cite>]. We obtain <italic>b</italic> = −1.4 μm ≈ −5 ξ<sub>0</sub>.</p><p>We arrive at the following conclusions. (1) The observed <italic>H</italic>–<italic>T</italic> phase diagram for a surface-enhanced Sn type-I superconductor differs qualitatively from the standard phase diagram for surface superconductivity and is consistent with that predicted for low-κ type-I superconductors undergoing an interface delocalization transition. (2) Onset of surface superconductivity in surface-enhanced samples occurs as a <italic>first-order</italic> phase transition at <italic>T</italic> > <italic>T</italic><sub>w</sub>. There is no surface superconductivity at <italic>T</italic> < <italic>T</italic><sub>w</sub>. The surface transition <italic>H</italic><sub>s</sub>(<italic>T</italic>) disappears at a surface critical temperature <italic>T</italic><sub>cs</sub> > <italic>T</italic><sub>c</sub>. (3) Surface enhancement of superconductivity in Sn can be induced in a controllable way by different kinds of surface cold working, such as irradiation by ions of, e.g., heavy noble gases, or mechanical polishing.</p></sec-level1><acknowledgment><heading>Acknowledgments</heading><p indent="no">We thank Stijn Vandezande for performing the electrical measurements and Alexander Volodin for the AFM measurements. 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See [<cite linkend="nj237905bib20">20</cite>].</p></footnote></footnotes></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="eng"><title>Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</title></titleInfo><titleInfo type="abbreviated"><title>Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</title></titleInfo><titleInfo type="alternative" lang="eng"><title>Observation of wetting-like phase transitions in a surface-enhanced type-I superconductor</title></titleInfo><name type="personal"><namePart type="given">V F</namePart><namePart type="family">Kozhevnikov</namePart><affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M J</namePart><namePart type="family">Van Bael</namePart><affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">P K</namePart><namePart type="family">Sahoo</namePart><affiliation>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">K</namePart><namePart type="family">Temst</namePart><affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C</namePart><namePart type="family">Van Haesendonck</namePart><affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A</namePart><namePart type="family">Vantomme</namePart><affiliation>Instituut voor Kern-en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J O</namePart><namePart type="family">Indekeu</namePart><affiliation>Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium</affiliation><affiliation>E-mail: joseph.indekeu@fys.kuleuven.be</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="paper">paper</genre><originInfo><publisher>Institute of Physics Publishing</publisher><dateIssued encoding="w3cdtf">2007</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract>Superconductivity in single crystal Sn samples with surface-enhanced order parameter is studied experimentally. Controllable surface enhancement is achieved by mechanical polishing or by ion irradiation. A first-order surface superconductivity transition is found in parallel magnetic fields close to the bulk critical field Hc(T) and for temperatures above 0.8Tc up till a surface critical temperature Tcs > Tc, where Tc is the bulk critical temperature. The resulting phase diagram agrees with that predicted for interface-delocalization or wetting transitions in type-I superconductors, based on the GinzburgLandau theory.</abstract><relatedItem type="host"><titleInfo><title>New Journal of Physics</title></titleInfo><titleInfo type="abbreviated"><title>New J. Phys.</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">1367-2630</identifier><identifier type="eISSN">1367-2630</identifier><identifier type="PublisherID">nj</identifier><identifier type="CODEN">NJOPFM</identifier><identifier type="URL">stacks.iop.org/NJP</identifier><part><date>2007</date><detail type="volume"><caption>vol.</caption><number>9</number></detail><detail type="issue"><caption>no.</caption><number>3</number></detail><extent unit="pages"><start>75</start><end>75</end><total>1</total></extent></part></relatedItem><identifier type="istex">9F4F6191803E5A4C3FAD530A19C484031E0BB01C</identifier><identifier type="DOI">10.1088/1367-2630/9/3/075</identifier><identifier type="PII">S1367-2630(07)37905-6</identifier><identifier type="articleID">237905</identifier><accessCondition type="use and reproduction" contentType="copyright">IOP Publishing and Deutsche Physikalische Gesellschaft</accessCondition><recordInfo><recordContentSource>IOP</recordContentSource><recordOrigin>IOP Publishing and Deutsche Physikalische Gesellschaft</recordOrigin></recordInfo></mods></metadata><enrichments><json:item><type>multicat</type><uri>https://api.istex.fr/document/9F4F6191803E5A4C3FAD530A19C484031E0BB01C/enrichments/multicat</uri></json:item></enrichments><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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