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New transition in the vortex liquid state of YBa2Cu3O7−δ
Physica C 437–438 (2006) 176–179 www.elsevier.com/locate/physc
New transition in the vortex liquid state of YBa2Cu3O7d Wai-Kwong Kwok a,b,c,*, Goran Karapetrov a,b,c, Ulrich Welp a,b,c, Andreas Rydh a,b,c, George W. Crabtree a, Lisa Paulius b, Jordi Figueras a,b,c, Teresa Puig a,b,c, X. Obradors
c
a
c
Materials Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA b Department of Physics, Western Michigan University, Kalamazoo, MI 49008, USA Institut de Cie`ncia de Materials de Barcelona, C.S.I.C., Campus U.A. Barcelona, 08193 Bellaterra, Catalunya, Spain Available online 3 February 2006
Abstract We have carried out angular dependent magneto-transport measurements on optimally doped, untwinned YBa2Cu3O7d crystals irradiated with high energy heavy ions to determine the onset of vortex line tension in the vortex liquid state. The dose matching field was controlled and kept at a low level to partially preserve the first order vortex lattice melting transition. A Bose glass transition is observed below the lower critical point which then transforms into a first order phase transition near 4 T. We find that the locus of points which indicates the onset of vortex line tension overlaps with the Bose glass transition line at low fields and then deviates at higher fields, indicating a new transition line in the vortex liquid state. This new line in the vortex liquid phase is dose independent and extends beyond the upper critical point. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Superconductivity; Vortex pinning; Phase transitions
1. Introduction High-temperature superconductors are rapidly emerging as the next generation of enhanced capability materials for microelectronics and power cable applications. However, despite the high superconducting critical temperatures of these extreme type II superconductors, their best performance is still limited to temperatures much below their critical temperatures. One of the key issues related to enhanced performance is the desirable ability to pin the magnetic flux lines at high-temperatures and magnetic fields. The main intrinsic barrier to vortex pinning at these elevated temperatures and magnetic fields is the ubiquitous vortex liquid phase which occupies a large portion of the magnetic phase diagram. Since the vortex shear modulus is absent in the liquid phase, vortices are free to move past individually-pinned neighboring vortices in contrast to the highly effective collective pinning state [1] found in the vortex solid phase. *
Corresponding author. Tel.: +1 630 252 5539; fax: +1 630 252 4748. E-mail address: [email protected] (W.-K. Kwok).
0921-4534/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.12.029
In this paper, we present our investigation of the vortex behavior in the liquid state. Vortex matter in high-temperature superconductors constitutes an ideal platform to investigate new phases and transitions since the energy scales that lead to competing phenomena such as vortex melting, pinning and glassy behavior can be experimentally controlled by tuning the temperature and tailoring the defect concentration via irradiation. We use high-energy heavy ions to create discrete pinning sites within pristine single crystals and study their vortex pinning behavior. We find an intrinsic phase transformation within the vortex liquid state [2] which can have strong ramifications on the upper limit of the irreversibility line for samples with correlated defects and hence strong implications for technological applications of these materials. 2. Experimental Two untwinned single crystals of optimally doped YBa2Cu3O7d (YBCO) were prepared for this study. Each crystal was cleaved into several pieces. One piece from each
W.-K. Kwok et al. / Physica C 437–438 (2006) 176–179
was used as a reference, with the rest irradiated along the c-axis with 1.38 GeV 208Pb56+ ions at Argonne’s ATLAS heavy ion irradiation facility. The cleaved crystals guarantee that the underlying intrinsic quality of the irradiated crystals are identical, a factor which becomes important when comparing crystals. We concentrated on two of the cleaved pieces which were irradiated to a dose matching field of BU = 2000 Oe and BU = 3500 Oe, respectively. At the dose matching field, the number of vortices matches the number of defects. Transport measurements were performed with current directed in the ab-plane of the crystal using the standard four probe method with both ac and dc techniques in magnetic fields up to 8 T at Argonne national laboratory and up to 17 T at the National high magnetic field laboratory. The zero field superconducting critical temperatures, Tc0, of the unirradiated, untwinned crystals are 93.5 K (reference for BU = 2000 Oe crystal) and 93.42 K (reference for BU = 3500 Oe crystal). Upon irradiation, the Tc’s of the BU = 2000 Oe and 3500 Oe samples decreased to 93.2 K and 92.26 K, respectively. Transport measurements with magnetic fields applied along the crystalline c-axis were used to determine the presence of a first order vortex melting transition through the associated sharp ‘kink’ in the temperature dependence of the resistivity [3]. In addition, current–voltage characteristics and the onset of nonlinear resistive behavior were used to determine the Bose glass transition associated with the columnar defects induced by heavy ion irradiation as described elsewhere [4]. Furthermore, we performed angular dependent magneto-transport measurements using a crossed-magnetic field superconducting magnet (8 T longitudinal and 1.5 T transverse) to investigate anisotropic pinning of the vortices in the presence of columnar defects.
177
Fig. 1. Temperature dependence of the normalized resistivity for the irradiated (BU = 2000 Oe) and reference crystals at magnetic fields of 0.5, 1, 2, 4, 6, and 8 T parallel to the c-axis.
Fig. 2. Angular dependence of the resistance at H = 0.5 T for several temperatures. Ha is the accommodation angle.
3. Results and discussions A set of typical resistance versus temperature curves in several magnetic fields is shown in Fig. 1 for the sample irradiated to a dose matching field of BU = 2000 Oe along with the reference (unirradiated) crystal. The sharp ‘kink’ in the resistive transition of the reference crystal is associated with a first order vortex melting transition [3]. Upon irradiation, the melting kink disappears for low fields (near 4 T and below), whereas a small vestige of the kink remains at high fields (6 T and 8 T). Similar behavior was reported in our earlier work [4] on crystals irradiated at lower dose matching fields where the irradiation induced disappearance of the kink was associated with the appearance of a lower critical point, Hlcp, below which a Bose glass transition [5] was observed. In this crystal, a Bose glass transition is observed only below about 4 T. Fig. 2 shows the angular dependent magneto-resistance of the BU = 2000 Oe crystal obtained in a magnetic field of H = 0.5 T. By performing the measurements at various temperatures, we could obtain the onset of anisotropic pinning, defined by the temperature where the resistance at
(h = 0°, i.e. Hkc and parallel to the induced columnar defects) first manifests a minimum (dip). From the data in Figs. 1 and 2, we constructed the H (T) vortex phase diagram shown in Fig. 3. The vortex melting curve for the crystal irradiated with a dose matching field of BU = 2000 Oe shows a Bose glass transition line at low magnetic fields, which smoothly transforms into a first order melting line near the lower critical point Hlcp. Once the first order transition (FOT) is recovered above Hlcp, the melting line conforms smoothly with the FOT line of the unirradiated reference crystal. In contrast, for the crystal irradiated to a dose matching field of BU = 3500 Oe, we observe the complete suppression of the FOT and the melting line is replaced with a Bose glass transition, although the shape of the curve above H = 4 T conforms with the FOT line of the reference crystal. The main result is the locus of points (solid symbols) making up the Hl (T) line which delineates the onset of anisotropic pinning of the irradiated crystals. Although the two irradiated crystals have different defect densities, the curves for both crystals lie virtually on top of each
178
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Fig. 4. Angular dependence of the resistance at H = 3 T for a melttextured twinned YBCO crystal.
Fig. 3. Magnetic phase diagram of the irradiated crystals. The solid symbols depict the onset of anisotropic pinning determined from measurements such as shown in Fig. 2. The open symbols depict the Bose glass transition for the two irradiated crystals. Dashed line shows the first order vortex melting transition (FOT) of the unirradiated reference crystal. The solid thick line shows the ‘recovered’ first order vortex melting line above the lower critical point, Hlcp, for the crystal irradiated with a dose matching field of BU = 2000 Oe.
other. Therefore, we speculate that the Hl (T) line represents an intrinsic transformation of the vortex state, related to the first appearance of a vortex line tension in the liquid state. At low fields, the nearly identical Hl (T) lines for both irradiated crystals follow the Bose glass transition lines. The Hl (T) curve for the BU = 3500 Oe crystal deviates from the Bose glass line at higher fields compared with the BU = 2000 Oe crystal. Our results further show that the Bose glass transition line tend to shift to higher fields with higher irradiation dose, but is limited by the Hl (T) line in the liquid state. In fact, even for crystals with higher irradiation dose, BU = 2 T, the irreversibility line does not extend beyond this Hl (T) line. In order to check if Hl (T) is an intrinsic feature, we conducted similar angular dependent magneto-transport measurements on a quite different twinned melt-textured YBCO sample. Fig. 4 shows a typical result. Similar to Fig. 2, the onset of anisotropic pinning was determined from the first dip in the resistivity at h = 0° (i.e., field parallel to the twin planes along c-axis). A comparison of the anisotropic pinning line for the heavy ion irradiated BU = 2000 Oe crystal and the twinned melt-textured crystal is shown in Fig. 5. Remarkably, the onset of anisotropic pinning for twin boundaries seems to coincide very closely with that for columnar defects, indicating that the Hl (T) line in the liquid state may be independent of the type and density of correlated disorder. The independence of the position of the onset of anisotropic pinning regardless of the type and density of correlated disorder indicates that Hl (T) reflects an intrinsic vortex transformation in the liquid state most probably associated with the onset of vortex line tension.
Fig. 5. Comparison of the onset of anisotropic pinning between twin boundaries and columnar defects (BU = 2000 Oe). Star represents data from Ref. [6] for BU = 2 T; Triangle represents data from Ref. [7] for splayed columnar defects.
The upward shift of the Bose glass line with increasing density of columnar defects was clearly observed in earlier works on crystals irradiated with higher doses [6]. For example, Samoilov et al. [6] reported an upper limit to the irreversibility line in 5.8 GeV Pb-ion irradiated YBCO crystals. They noticed that beyond a dose matching field of BU = 2 T, no enhancement of the irreversibility line was observed. The solid star symbol in Fig. 5 represents the data from their work. Furthermore, it was also demonstrated that splayed columnar defects could enhance the irreversibility line, shifting it to higher temperatures and fields [7,8]. The solid triangle in Fig. 5 represents the highest enhancement of the irreversibility line for splayed defects from Ref. [7]. Remarkably, both points above lie very close to our vortex line tension transformation line. The upper limit of the irreversibility line for columnar defects found by Samoilov et al. [6] was attributed to an entanglement/disentanglement transition. An analogous order–disorder transition [9] explanation has been presented for the vortex phase transition near the upper critical point in YBCO characterized by the appearance of a second magnetization peak [10]. If indeed, Hl (T) is related to an entanglement/disentanglement transition, one may
W.-K. Kwok et al. / Physica C 437–438 (2006) 176–179
179
In summary, by using correlated defects to probe the vortex behavior in the liquid state, we determined a vortex line tension transformation in the vortex phase diagram of YBCO which is independent of the type and density of the correlated defect. Our results suggest that the line tension transformation in the liquid state poses an upper limit to the enhancement of the irreversibility line with correlated disorder. Acknowledgements
Fig. 6. Field dependence of the accommodation angle for the BU = 2000 Oe crystal.
expect the Hl (T) line to terminate near the upper critical point. Furthermore, with increasing magnetic field, we expect the accommodation angle, ha, which is correlated with the strength of pinning to decrease to zero as the ratio of vortices to columnar defects increases. Indeed, we observe a sharp decrease in ha with increasing field for the BU = 2000 Oe crystal as shown in Fig. 6. However, following the sharp decrease with magnetic field, ha(H) saturates beyond the lower critical point, indicating that anisotropic pinning in the liquid state is present at magnetic fields far beyond the upper critical point which is near 10 T for this crystal. One explanation could be that the line tension transformation found here is the vortex line liquid transition predicted by Glazman and Koshelev [11]. In this case, Hl (T) should extend to even higher magnetic fields near the 3D to 2D vortex cross-over region where it should then join with the 2D melting line reported in Ref. [10]. Further measurements at higher fields are underway to clarify this issue.
This work was supported by the US Department of Energy, BES, Materials Science under Contract No. W31-109-ENG-38 at Argonne national laboratory. We acknowledge the support of the NHMFL for high field measurements. References [1] G. Blatter et al., Rev. Mod. Phys. 66 (1994) 1125. [2] F. Bouquet et al., Nature 411 (2001) 448. [3] J.A. Fendrich et al., Phys. Rev. Lett. 77 (1996) 2073; H. Safar et al., Phys. Rev. Lett. 69 (1992) 824; W.K. Kwok et al., Phys. Rev. Lett. 69 (1992) 3370. [4] W.K. Kwok et al., Phys. Rev. Lett. 84 (2000) 3706; R.J. Olsson et al., Phys. Rev. B 65 (2002) 104520. [5] D.R. Nelson, V.M. Vinokur, Phys. Rev. Lett. 68 (1992) 2398; Phys. Rev. B 61 (2000) 5917. [6] A. Samoilov et al., Phys. Rev. Lett. 77 (1996) 981; M. Konczykowski et al., Phys. Rev. B 44 (1991) 7167. [7] D. Lopez et al., Phys. Rev. Lett. 79 (1997) 2358; D. Lopez et al., Phys. Rev. Lett. 79 (1997) 4258; L. Civale et al., Phys. Rev. B (1994) 4102. [8] W.K. Kwok et al., Phys. Rev. B 58 (1998) 14594. [9] T. Giamarchi, P. Le Doussal, Phys. Rev. B 55 (1997) 6577; D. Ertas, D.R. Nelson, Physica C 272 (1996) 79. [10] K. Deligiannis et al., Phys. Rev. Lett. 79 (1997) 2121; T. Nishizaki et al., Phys. Rev. B 61 (2000) 3649; Y. Radzyner et al., Phys. Rev. B 61 (2000) 14362. [11] L.I. Glazman, A.E. Koshelev, Phys. Rev. B 43 (1991) 2835.
New transition in the vortex liquid state of YBa2Cu3O7d Wai-Kwong Kwok a,b,c,*, Goran Karapetrov a,b,c, Ulrich Welp a,b,c, Andreas Rydh a,b,c, George W. Crabtree a, Lisa Paulius b, Jordi Figueras a,b,c, Teresa Puig a,b,c, X. Obradors
c
a
c
Materials Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA b Department of Physics, Western Michigan University, Kalamazoo, MI 49008, USA Institut de Cie`ncia de Materials de Barcelona, C.S.I.C., Campus U.A. Barcelona, 08193 Bellaterra, Catalunya, Spain Available online 3 February 2006
Abstract We have carried out angular dependent magneto-transport measurements on optimally doped, untwinned YBa2Cu3O7d crystals irradiated with high energy heavy ions to determine the onset of vortex line tension in the vortex liquid state. The dose matching field was controlled and kept at a low level to partially preserve the first order vortex lattice melting transition. A Bose glass transition is observed below the lower critical point which then transforms into a first order phase transition near 4 T. We find that the locus of points which indicates the onset of vortex line tension overlaps with the Bose glass transition line at low fields and then deviates at higher fields, indicating a new transition line in the vortex liquid state. This new line in the vortex liquid phase is dose independent and extends beyond the upper critical point. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Superconductivity; Vortex pinning; Phase transitions
1. Introduction High-temperature superconductors are rapidly emerging as the next generation of enhanced capability materials for microelectronics and power cable applications. However, despite the high superconducting critical temperatures of these extreme type II superconductors, their best performance is still limited to temperatures much below their critical temperatures. One of the key issues related to enhanced performance is the desirable ability to pin the magnetic flux lines at high-temperatures and magnetic fields. The main intrinsic barrier to vortex pinning at these elevated temperatures and magnetic fields is the ubiquitous vortex liquid phase which occupies a large portion of the magnetic phase diagram. Since the vortex shear modulus is absent in the liquid phase, vortices are free to move past individually-pinned neighboring vortices in contrast to the highly effective collective pinning state [1] found in the vortex solid phase. *
Corresponding author. Tel.: +1 630 252 5539; fax: +1 630 252 4748. E-mail address: [email protected] (W.-K. Kwok).
0921-4534/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.12.029
In this paper, we present our investigation of the vortex behavior in the liquid state. Vortex matter in high-temperature superconductors constitutes an ideal platform to investigate new phases and transitions since the energy scales that lead to competing phenomena such as vortex melting, pinning and glassy behavior can be experimentally controlled by tuning the temperature and tailoring the defect concentration via irradiation. We use high-energy heavy ions to create discrete pinning sites within pristine single crystals and study their vortex pinning behavior. We find an intrinsic phase transformation within the vortex liquid state [2] which can have strong ramifications on the upper limit of the irreversibility line for samples with correlated defects and hence strong implications for technological applications of these materials. 2. Experimental Two untwinned single crystals of optimally doped YBa2Cu3O7d (YBCO) were prepared for this study. Each crystal was cleaved into several pieces. One piece from each
W.-K. Kwok et al. / Physica C 437–438 (2006) 176–179
was used as a reference, with the rest irradiated along the c-axis with 1.38 GeV 208Pb56+ ions at Argonne’s ATLAS heavy ion irradiation facility. The cleaved crystals guarantee that the underlying intrinsic quality of the irradiated crystals are identical, a factor which becomes important when comparing crystals. We concentrated on two of the cleaved pieces which were irradiated to a dose matching field of BU = 2000 Oe and BU = 3500 Oe, respectively. At the dose matching field, the number of vortices matches the number of defects. Transport measurements were performed with current directed in the ab-plane of the crystal using the standard four probe method with both ac and dc techniques in magnetic fields up to 8 T at Argonne national laboratory and up to 17 T at the National high magnetic field laboratory. The zero field superconducting critical temperatures, Tc0, of the unirradiated, untwinned crystals are 93.5 K (reference for BU = 2000 Oe crystal) and 93.42 K (reference for BU = 3500 Oe crystal). Upon irradiation, the Tc’s of the BU = 2000 Oe and 3500 Oe samples decreased to 93.2 K and 92.26 K, respectively. Transport measurements with magnetic fields applied along the crystalline c-axis were used to determine the presence of a first order vortex melting transition through the associated sharp ‘kink’ in the temperature dependence of the resistivity [3]. In addition, current–voltage characteristics and the onset of nonlinear resistive behavior were used to determine the Bose glass transition associated with the columnar defects induced by heavy ion irradiation as described elsewhere [4]. Furthermore, we performed angular dependent magneto-transport measurements using a crossed-magnetic field superconducting magnet (8 T longitudinal and 1.5 T transverse) to investigate anisotropic pinning of the vortices in the presence of columnar defects.
177
Fig. 1. Temperature dependence of the normalized resistivity for the irradiated (BU = 2000 Oe) and reference crystals at magnetic fields of 0.5, 1, 2, 4, 6, and 8 T parallel to the c-axis.
Fig. 2. Angular dependence of the resistance at H = 0.5 T for several temperatures. Ha is the accommodation angle.
3. Results and discussions A set of typical resistance versus temperature curves in several magnetic fields is shown in Fig. 1 for the sample irradiated to a dose matching field of BU = 2000 Oe along with the reference (unirradiated) crystal. The sharp ‘kink’ in the resistive transition of the reference crystal is associated with a first order vortex melting transition [3]. Upon irradiation, the melting kink disappears for low fields (near 4 T and below), whereas a small vestige of the kink remains at high fields (6 T and 8 T). Similar behavior was reported in our earlier work [4] on crystals irradiated at lower dose matching fields where the irradiation induced disappearance of the kink was associated with the appearance of a lower critical point, Hlcp, below which a Bose glass transition [5] was observed. In this crystal, a Bose glass transition is observed only below about 4 T. Fig. 2 shows the angular dependent magneto-resistance of the BU = 2000 Oe crystal obtained in a magnetic field of H = 0.5 T. By performing the measurements at various temperatures, we could obtain the onset of anisotropic pinning, defined by the temperature where the resistance at
(h = 0°, i.e. Hkc and parallel to the induced columnar defects) first manifests a minimum (dip). From the data in Figs. 1 and 2, we constructed the H (T) vortex phase diagram shown in Fig. 3. The vortex melting curve for the crystal irradiated with a dose matching field of BU = 2000 Oe shows a Bose glass transition line at low magnetic fields, which smoothly transforms into a first order melting line near the lower critical point Hlcp. Once the first order transition (FOT) is recovered above Hlcp, the melting line conforms smoothly with the FOT line of the unirradiated reference crystal. In contrast, for the crystal irradiated to a dose matching field of BU = 3500 Oe, we observe the complete suppression of the FOT and the melting line is replaced with a Bose glass transition, although the shape of the curve above H = 4 T conforms with the FOT line of the reference crystal. The main result is the locus of points (solid symbols) making up the Hl (T) line which delineates the onset of anisotropic pinning of the irradiated crystals. Although the two irradiated crystals have different defect densities, the curves for both crystals lie virtually on top of each
178
W.-K. Kwok et al. / Physica C 437–438 (2006) 176–179
Fig. 4. Angular dependence of the resistance at H = 3 T for a melttextured twinned YBCO crystal.
Fig. 3. Magnetic phase diagram of the irradiated crystals. The solid symbols depict the onset of anisotropic pinning determined from measurements such as shown in Fig. 2. The open symbols depict the Bose glass transition for the two irradiated crystals. Dashed line shows the first order vortex melting transition (FOT) of the unirradiated reference crystal. The solid thick line shows the ‘recovered’ first order vortex melting line above the lower critical point, Hlcp, for the crystal irradiated with a dose matching field of BU = 2000 Oe.
other. Therefore, we speculate that the Hl (T) line represents an intrinsic transformation of the vortex state, related to the first appearance of a vortex line tension in the liquid state. At low fields, the nearly identical Hl (T) lines for both irradiated crystals follow the Bose glass transition lines. The Hl (T) curve for the BU = 3500 Oe crystal deviates from the Bose glass line at higher fields compared with the BU = 2000 Oe crystal. Our results further show that the Bose glass transition line tend to shift to higher fields with higher irradiation dose, but is limited by the Hl (T) line in the liquid state. In fact, even for crystals with higher irradiation dose, BU = 2 T, the irreversibility line does not extend beyond this Hl (T) line. In order to check if Hl (T) is an intrinsic feature, we conducted similar angular dependent magneto-transport measurements on a quite different twinned melt-textured YBCO sample. Fig. 4 shows a typical result. Similar to Fig. 2, the onset of anisotropic pinning was determined from the first dip in the resistivity at h = 0° (i.e., field parallel to the twin planes along c-axis). A comparison of the anisotropic pinning line for the heavy ion irradiated BU = 2000 Oe crystal and the twinned melt-textured crystal is shown in Fig. 5. Remarkably, the onset of anisotropic pinning for twin boundaries seems to coincide very closely with that for columnar defects, indicating that the Hl (T) line in the liquid state may be independent of the type and density of correlated disorder. The independence of the position of the onset of anisotropic pinning regardless of the type and density of correlated disorder indicates that Hl (T) reflects an intrinsic vortex transformation in the liquid state most probably associated with the onset of vortex line tension.
Fig. 5. Comparison of the onset of anisotropic pinning between twin boundaries and columnar defects (BU = 2000 Oe). Star represents data from Ref. [6] for BU = 2 T; Triangle represents data from Ref. [7] for splayed columnar defects.
The upward shift of the Bose glass line with increasing density of columnar defects was clearly observed in earlier works on crystals irradiated with higher doses [6]. For example, Samoilov et al. [6] reported an upper limit to the irreversibility line in 5.8 GeV Pb-ion irradiated YBCO crystals. They noticed that beyond a dose matching field of BU = 2 T, no enhancement of the irreversibility line was observed. The solid star symbol in Fig. 5 represents the data from their work. Furthermore, it was also demonstrated that splayed columnar defects could enhance the irreversibility line, shifting it to higher temperatures and fields [7,8]. The solid triangle in Fig. 5 represents the highest enhancement of the irreversibility line for splayed defects from Ref. [7]. Remarkably, both points above lie very close to our vortex line tension transformation line. The upper limit of the irreversibility line for columnar defects found by Samoilov et al. [6] was attributed to an entanglement/disentanglement transition. An analogous order–disorder transition [9] explanation has been presented for the vortex phase transition near the upper critical point in YBCO characterized by the appearance of a second magnetization peak [10]. If indeed, Hl (T) is related to an entanglement/disentanglement transition, one may
W.-K. Kwok et al. / Physica C 437–438 (2006) 176–179
179
In summary, by using correlated defects to probe the vortex behavior in the liquid state, we determined a vortex line tension transformation in the vortex phase diagram of YBCO which is independent of the type and density of the correlated defect. Our results suggest that the line tension transformation in the liquid state poses an upper limit to the enhancement of the irreversibility line with correlated disorder. Acknowledgements
Fig. 6. Field dependence of the accommodation angle for the BU = 2000 Oe crystal.
expect the Hl (T) line to terminate near the upper critical point. Furthermore, with increasing magnetic field, we expect the accommodation angle, ha, which is correlated with the strength of pinning to decrease to zero as the ratio of vortices to columnar defects increases. Indeed, we observe a sharp decrease in ha with increasing field for the BU = 2000 Oe crystal as shown in Fig. 6. However, following the sharp decrease with magnetic field, ha(H) saturates beyond the lower critical point, indicating that anisotropic pinning in the liquid state is present at magnetic fields far beyond the upper critical point which is near 10 T for this crystal. One explanation could be that the line tension transformation found here is the vortex line liquid transition predicted by Glazman and Koshelev [11]. In this case, Hl (T) should extend to even higher magnetic fields near the 3D to 2D vortex cross-over region where it should then join with the 2D melting line reported in Ref. [10]. Further measurements at higher fields are underway to clarify this issue.
This work was supported by the US Department of Energy, BES, Materials Science under Contract No. W31-109-ENG-38 at Argonne national laboratory. We acknowledge the support of the NHMFL for high field measurements. References [1] G. Blatter et al., Rev. Mod. Phys. 66 (1994) 1125. [2] F. Bouquet et al., Nature 411 (2001) 448. [3] J.A. Fendrich et al., Phys. Rev. Lett. 77 (1996) 2073; H. Safar et al., Phys. Rev. Lett. 69 (1992) 824; W.K. Kwok et al., Phys. Rev. Lett. 69 (1992) 3370. [4] W.K. Kwok et al., Phys. Rev. Lett. 84 (2000) 3706; R.J. Olsson et al., Phys. Rev. B 65 (2002) 104520. [5] D.R. Nelson, V.M. Vinokur, Phys. Rev. Lett. 68 (1992) 2398; Phys. Rev. B 61 (2000) 5917. [6] A. Samoilov et al., Phys. Rev. Lett. 77 (1996) 981; M. Konczykowski et al., Phys. Rev. B 44 (1991) 7167. [7] D. Lopez et al., Phys. Rev. Lett. 79 (1997) 2358; D. Lopez et al., Phys. Rev. Lett. 79 (1997) 4258; L. Civale et al., Phys. Rev. B (1994) 4102. [8] W.K. Kwok et al., Phys. Rev. B 58 (1998) 14594. [9] T. Giamarchi, P. Le Doussal, Phys. Rev. B 55 (1997) 6577; D. Ertas, D.R. Nelson, Physica C 272 (1996) 79. [10] K. Deligiannis et al., Phys. Rev. Lett. 79 (1997) 2121; T. Nishizaki et al., Phys. Rev. B 61 (2000) 3649; Y. Radzyner et al., Phys. Rev. B 61 (2000) 14362. [11] L.I. Glazman, A.E. Koshelev, Phys. Rev. B 43 (1991) 2835.