- Email: [email protected]
Elucidation of the stable vortex state across the peak effect region in CeRu2
Physica C 355 (2001) 59±64
www.elsevier.nl/locate/physc
Elucidation of the stable vortex state across the peak eect region in CeRu2 A.A. Tulapurkar a,*, D. Heidarian a, S. Sarkar a, S. Ramakrishnan a, A.K. Grover a, E. Yamamoto b, Y. Haga b, M. Hedo c, Y. Inada c, Y. Onuki b,c a
Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Colaba, Mumbai 400005, India b ASRC Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan c Faculty of Science, Osaka University, Toyonaka 560, Japan Received 11 October 2000; accepted 31 October 2000
Abstract We present magnetization data on a weakly pinned single crystal of CeRu2 , showing the existence of a stable state of the vortex matter in the peak eect (PE) region. The stable state is achieved by cycling the magnetic ®eld by a small amplitude. It is characterized by a unique value of the critical current density, independent of the magnetic history of the sample. The results support a recent phenomenological model proposed by Ravikumar et al. [Phys. Rev. B 61 (2000) R6479] which postulates a speci®c recipe to incorporate the history dependence of the current density. Our data also shows the occurrence of a ®rst order phase transition from an ordered vortex phase to a disordered phase across the PE. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.25.Ha; 74.60.Ge; 74.60.Jg Keywords: Peak eect; Stable vortex state; Step change in equilibrium magnetization; CeRu2
1. Introduction The critical current density (Jc ) of a type II superconductor usually decreases monotonically with increasing H or T. However, in weakly pinned superconductors, the interplay between the intervortex interaction and the ¯ux pinning produces an anomalous peak in Jc , before Jc decreases to zero at (or just before) the superconductornormal phase boundary Hc2 =Tc H line [1]. This eect is known as the peak eect (PE) and it sig-
*
Corresponding author. Fax: +91-22-215-2110. E-mail address: [email protected] (A.A. Tulapurkar).
ni®es that the vortex phase undergoes a transition from an ordered phase to a disordered phase [1±5]. The PE in weakly pinned superconductors is accompanied by metastable vortex states [2,6±11]. Each metastable vortex con®guration is characterized by a dierent Jc , which depends on the thermomagnetic history of the superconductor. However, the critical state model (CSM) due to Bean [12,13], which is usually invoked to describe the hysteretic magnetic response of a superconductor, assumes a unique value of Jc , independent of the thermomagnetic history. It, therefore, does not capture many of the interesting characteristics [11] in the magnetic hysteretic response of weakly pinned superconductors in the PE region. Recently,
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 0 ) 0 1 7 7 2 - X
60
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
Ravikumar et al. [5] have proposed a phenomenological model to incorporate the history dependence of the critical current density which reduces to the Bean's critical state model in the limit that Jc H is a single valued function of H. This model postulates a stable state of vortex lattice with a critical current density Jcst , which is determined uniquely by the ®eld and temperature and is independent of the past magnetic history. This stable state ought to be reached from any metastable vortex state by cycling the applied ®eld by a small amplitude. Ravikumar et al. have further [14] elucidated the existence of such a stable state in a specimen of 2H-NbSe2 via repeated tracings of the minor hysteresis loops (MHLs) across the PE region. In addition, they have asserted that the equilibrium magnetization curve across the PE region can be ascertained from the determined values of `stable' hysteresis loop. We report in this paper the results of an investigation aimed at unravelling the stable state and determining the equilibrium magnetization behaviour across the PE region in a single crystal sample of the superconductor CeRu2 Tc 0 6:2 K. The PE phenomenon in this system has been under investigation by a number of groups in recent years [15±26] and there have been con¯icting reports regarding the behaviour of equilibrium magnetization in it [15,26]. 2. Phenomenological model for history eects and metastability in weakly pinned superconductors An important assumption of the model due to Ravikumar et al. [5] is the existence of a stable vortex state with a critical current density Jcst , which is unique for a given temperature and ®eld. They have postulated the following equation to describe how the Jc changes when the magnetic ®eld is varied from B to B DB : Jc B DB Jc B jDBj=Br Jcst
Jc
1
where Br is a macroscopic measure of the metastability and it describes how strongly Jc is history dependent. Physically, we may imagine that in the absence of thermal ¯uctuations, it is the change in local ®eld B that can move the vortices from their
metastable con®guration to a nearby stable state. It can be seen from the above equation that a metastable vortex state with Jc 6 Jcst can be driven into the stable state by cycling the ®eld by a small amplitude [14]. 3. Experimental results and discussion DC magnetization measurements have been carried out using a 12 T vibrating sample magnetometer (VSM) (Oxford Instruments, UK) on a single crystal sample of cubic (C15) CeRu2 compound (Tc 6:2 K). The sample was vibrated with an amplitude of 1.5 mm at a frequency of 55 Hz. The dc ®eld was swept at the rate of 0.02 T/min, while recording the magnetization hysteresis loops at 4.5 K. All the measurements were carried out by cooling the sample to 4.5 K in zero ®eld (ZFC mode) and then applying the magnetic ®eld parallel to the cube edge. Fig. 1(a) shows a portion of the magnetization hysteresis loop, comprising the M vs: H curves in the increasing (forward) and decreasing (reverse) ®eld cycles. According to the CSM, the hysteresis in magnetization, DM H M H" M H#, provides a measure of the critical current density (Jc / DM) [27]. Thus, an anomalous increase in the width of the hysteresis loop is a distinct indicator of the occurrence of the PE. We identify Hpl as the onset ®eld of the PE on the forward leg, where M begins to decrease sharply (see Fig. 1(a)). The onset ®eld for the PE on the reverse leg is marked as Hpl , which is less than Hpl . The ®eld value where the magnetization hysteresis bubble is the widest identi®es the peak ®eld Hp , and the collapse of the hysteresis loop locates the irreversibility ®eld Hirr , above which the critical current density falls below the measurable limit of the present data. Fig. 1(a) and (b) also show the MHLs initiated from dierent ®elds within the PE region lying on the forward and reverse legs. As per the CSM, all the MHLs should lie within the envelope curve and saturate by overlapping with the envelope curve. However, it can be seen from Fig. 1(a) that the MHLs starting from points, Hpl < H < Hp , on the forward cycle saturate without meeting the reverse envelope curve, although they remain well
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
61
reverse curve overshoot the forward envelope curve. These observations cannot be understood within the CSM and indicate that Jc is magnetic history dependent across the PE region [11]. Moreover, they also imply that the critical current density in the forward cycle (Jcfor ) is less than the critical current density in the reverse cycle (Jcrev ). Using the saturation points of the MHLs, in principle the magnetization hysteresis loops corresponding to Jcfor and Jcrev can be generated. Jcfor H and Jcrev H can then be obtained [10] from the width of the hysteresis loops (see for instance Fig. 2). In the top panel of Fig. 3, we show the MHLs obtained by repeatedly cycling the ®eld starting from a point in the PE region on the forward leg. The cycling amplitude DH is chosen such that it is above the threshold ®eld required to reverse the direction of shielding currents throughout the sample. From Fig. 3(a), it is clear that the MHLs show expansion with ®eld cycling and after few
Fig. 1. Magnetization hysteresis data across the PE region in a single crystal of CeRu2 (H parallel to the cube edge) at 4.5 K. Panel (a) shows the MHLs starting from the forward leg and panel (b) shows MHLs starting from the reverse leg. The ®eld at which the PE commences on the forward leg and terminates on the reverse leg have been marked as Hpl and Hpl , respectively. The peak ®eld (Hp ) of the PE and the irreversiblity ®eld (Hirr ) have also been indicated in panel (a).
within the envelope curve. On the other hand, the MHLs starting from points, Hpl < H < Hp , on the
Fig. 2. Critical current densities Jcfor and Jcrev in the increasing and decreasing ®eld cases respectively (continuous lines) at 4.5 K in CeRu2 . Dotted line shows the stable state critical current density Jcst (cf. Fig. 4).
62
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
Fig. 3. The top panel (a) shows the MHLs obtained by repeatedly cycling the ®eld starting from a point in the PE region on the forward leg. The outer most MHL corresponds to the stable state. The bottom panel (b) shows the outcome of the same procedure when the starting point lies on the reverse leg.
®eld cycles, the MHLs retrace each other indicating that Jc does not change further more with ®eld cycling. We, therefore, conclude that the vortex state attains a stable con®guration. On the reverse cycle, the MHLs starting within the PE region show shrinkage with ®eld cycling, and ®nally the MHLs retrace each other indicating the approach to the stable vortex state, as shown in the bottom panel of Fig. 3. From Fig. 3 it is also clear that the stable state magnetization value does not depend on whether the starting point is on the forward or on the reverse leg. This rearms the basic assumption of the phenomenological model [5] that there exists a unique stable state, independent of the initial vortex con®guration. Fig. 4 shows the construction of the stable magnetization hysteresis loop obtained from the saturated values of the
Fig. 4. The stable magnetization hysteresis loop corresponding to the saturated magnetization values as determined via repeated ®eld cyclings (cf. Fig. 3) at 4.5 K. The dotted curve represents the forward and reverse legs of the usual envelope hysteresis loop as shown in Fig. 1.
stable MHLs as depicted in Fig. 3. The critical current density in the stable state (Jcst ) can be obtained from the width of the stable state hysteresis loop. Jcst H across the PE region along with the Jc values in the forward and reverse cycles are shown in Fig. 2. It can be noted that they follow the relation: Jcrev > Jcst > Jcfor . The equilibrium magnetization (Meq ) can be obtained from the stable state magnetization hysteresis loop using the relation, Meq M st H" M st H#=2 (see Fig. 5). It can be seen that Meq shows a sharp increase above the onset position of the PE region (cf. Meq H and Jcst H data in Figs. 2 and 5 respectively), implying the occurrence of a ®rst order phase transition from an ordered vortex phase to a disordered phase. The DMeq value of 0.75 Oe obtained in the present case compares favourably with the values reported in the literature for the ¯ux line lattice (FLL) melting transition in cuprate superconductors [28] and for the
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
63
Acknowledgements We thank Dr. G. Ravikumar for sharing insights on the principles of his phenomenological model. We also gratefully acknowledge Prof. S. Bhattacharya and other members of the vortex state studies group at TIFR/BARC, Mumbai for numerous discussions. This work was presented at The Joint Vortex-Physics and ESF-Vortex Matter Workshop held at Lunteren, The Netherlands, 27 August to 1 September, 2000.
References
Fig. 5. The dotted curve shows the stable state hysteresis loop across the PE region at 4.5 K. The solid line corresponds to the equilibrium magnetization, which shows a step change DMeq just above the onset position Hpl of the PE phenomenon along the forward leg (cf. Fig. 1).
amorphization transition across the PE in weakly pinned single crystals of 2H-NbSe2 [14,29] and Nb [4].
4. Conclusions In this paper, we have studied dierent metastable vortex con®gurations in the PE region of a weakly pinned single crystal of the superconductor CeRu2 . These states have been characterized by dierent values of critical current densities, which were obtained by dc magnetization measurements. Our new data con®rms the existence of a stable state across the PE region and reveals the occurrence of a step change in the equilibrium magnetization near the onset position of the PE. The results in CeRu2 thus rearm the notion of the stable state evident in the magnetic [14] and transport [30, Fig. 3(a)] experiments performed on 2H-NbSe2 and the structural studies carried out in Nb [4], and thereby establish the generic nature of this feature in weakly pinned systems exhibiting PE phenomenon.
[1] M.J. Higgins, S. Bhattacharya, Physica C 257 (1996) 232. [2] S.S. Banerjee, N.G. Patil, S. Saha, S. Ramakrishnan, A.K. Grover, S. Bhattacharya, G. Ravikumar, P.K. Mishra, T.V.C. Rao, V.C. Sahni, M.J. Higgins, E. Yamamoto, Y. Haga, M. Hedo, Y. Inada, Y. Onuki, Phys. Rev. B 58 (1998) 995. [3] P.L. Gammel, U. Yaron, A.P. Ramirez, D.J. Bishop, A.M. Chang, R. Ruel, L.N. Pfeier, E. Bucher, Phys. Rev. Lett. 80 (1998) 833. [4] X.S. Ling, S.R. Park, B.A. McClain, S.M. Choi, D.C. Dender, J.W. Lynn, cond-mat/0008353. [5] G. Ravikumar, K.V. Bhagwat, V.C. Sahni, A.K. Grover, S. Ramakrishnan, S. Bhattacharya, Phys. Rev. B 61 (2000) R6479. [6] M. Steingart, A.G. Putz, E.J. Kramer, J. Appl. Phys. 44 (1973) 5580. [7] R. Wordenweber, P.H. Kes, C.C. Tsuei, Phys. Rev. B 33 (1986) 3172. [8] W. Henderson, E.Y. Andrei, M.J. Higgins, S. Bhattacharya, Phys. Rev. Lett. 77 (1996) 2077. [9] W. Henderson, E.Y. Andrei, M.J. Higgins, S. Bhattacharya, Phys. Rev. Lett. 80 (1998) 381. [10] S.S. Banerjee, S. Ramakrishnan, A.K. Grover, G. Ravikumar, P.K. Mishra, V.C. Sahni, C.V. Tomy, G. Balakrishnan, D.Mck. Paul, M.J. Higgins, S. Bhattacharya, Physica C 332 (2000) 135. [11] G. Ravikumar, P.K. Mishra, V.C. Sahni, S.S. Banerjee, A.K. Grover, S. Ramakrishnan, P.L. Gammel, D.J. Bishop, E. B ucher, M.J. Higgins, S. Bhattacharya, Phys. Rev. B 61 (2000) 12490. [12] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [13] C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. [14] G. Ravikumar, V.C. Sahani, A.K. Grover, S. Ramakrishnan, P.L. Gammel, D.J. Bishop, E. B ucher, M.J. Higgins, S. Bhattacharya, cond-mat/0007436. [15] S.B. Roy, P. Chaddah, J. Phys.: Condens. Matter 9 (1997) L625. [16] S.B. Roy, P. Chaddah, S. Chaudhary, J. Phys.: Condens. Matter 10 (1998) 4885.
64
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
[17] S.B. Roy, P. Chaddah, S. Chaudhary, J. Phys.: Condens. Matter 10 (1998) 8327. [18] R. Modler, P. Gegenwart, M. Deppe, M. Weiden, T. Luhmann, C. Geibel, F. Steglich, C. Paulsen, J.L. Tholence, N. Sato, T. Komatsubara, Y. Onuki, M. Tachiki, S. Takahashi, Phys. Rev. Lett. 76 (1996) 1292. [19] F. Steglich, R. Modler, P. Gegenwart, M. Deppe, M. Weiden, M. Lang, C. Geibel, T. Luhmann, C. Paulsen, J.L. Tholence, Y. Onuki, M. Tachiki, S. Takahashi, Physica C 263 (1996) 498. [20] A. Yamashita, K. Ishii, T. Yokoo, J. Akimitsu, M. Hedo, Y. Inada, Y. Onuki, E. Yamamoto, Y. Haga, R. Kadono, Phys. Rev. Lett. 79 (1997) 3771. [21] M. Tachiki, S. Takahashi, P. Genenwart, M. Weiden, C. Geibel, F. Steglich, R. Modler, C. Paulsen, Y. Onuki, Z. Phys. B 100 (1996) 369. [22] K. Kadowaki, H. Takeya, K. Hirata, Phys. Rev. B 54 (1996) 462.
[23] N.R. Dilley, M.B. Maple, Physica C 278 (1997) 207. [24] R. Modler, Czech. J. Phys. 46 (1996) 3123. [25] A.D. Huxley, C. Paulsen, O. Laborde, J.L. Tholence, D. Sanchez, A. Junod, R. Calemczuk, J. Phys.: Condens. Matter 5 (1993) 7709. [26] K. Tenya, S. Yasunami, T. Tayama, H. Amitsuka, T. Sakakibara, M. Hedo, Y. Inada, E. Yamamoto, Y. Haga, Y. Onuki, J. Phys. Soc. Jpn. 68 (1999) 224. [27] W.A. Fietz, W.W. Webb, Phys. Rev. 178 (1969) 657. [28] M.J.W. Dodgson, V.B. Geshkenbein, H. Nordborg, G. Blatter, Phys. Rev. Lett. 80 (1998) 837. [29] G. Ravikumar, P.K. Mishra, V.C. Sahni, S.S. Banerjee, S. Ramakrishnan, A.K. Grover, P.L. Gammel, D.J. Bishop, E. B ucher, M.J. Higgins, S. Bhattacharya, Physica C 322 (1999) 145. [30] Z.L. Xiao, E.Y. Andrei, P. Shuk, M. Greenblatt, condmat/0006197.
www.elsevier.nl/locate/physc
Elucidation of the stable vortex state across the peak eect region in CeRu2 A.A. Tulapurkar a,*, D. Heidarian a, S. Sarkar a, S. Ramakrishnan a, A.K. Grover a, E. Yamamoto b, Y. Haga b, M. Hedo c, Y. Inada c, Y. Onuki b,c a
Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Colaba, Mumbai 400005, India b ASRC Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan c Faculty of Science, Osaka University, Toyonaka 560, Japan Received 11 October 2000; accepted 31 October 2000
Abstract We present magnetization data on a weakly pinned single crystal of CeRu2 , showing the existence of a stable state of the vortex matter in the peak eect (PE) region. The stable state is achieved by cycling the magnetic ®eld by a small amplitude. It is characterized by a unique value of the critical current density, independent of the magnetic history of the sample. The results support a recent phenomenological model proposed by Ravikumar et al. [Phys. Rev. B 61 (2000) R6479] which postulates a speci®c recipe to incorporate the history dependence of the current density. Our data also shows the occurrence of a ®rst order phase transition from an ordered vortex phase to a disordered phase across the PE. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.25.Ha; 74.60.Ge; 74.60.Jg Keywords: Peak eect; Stable vortex state; Step change in equilibrium magnetization; CeRu2
1. Introduction The critical current density (Jc ) of a type II superconductor usually decreases monotonically with increasing H or T. However, in weakly pinned superconductors, the interplay between the intervortex interaction and the ¯ux pinning produces an anomalous peak in Jc , before Jc decreases to zero at (or just before) the superconductornormal phase boundary Hc2 =Tc H line [1]. This eect is known as the peak eect (PE) and it sig-
*
Corresponding author. Fax: +91-22-215-2110. E-mail address: [email protected] (A.A. Tulapurkar).
ni®es that the vortex phase undergoes a transition from an ordered phase to a disordered phase [1±5]. The PE in weakly pinned superconductors is accompanied by metastable vortex states [2,6±11]. Each metastable vortex con®guration is characterized by a dierent Jc , which depends on the thermomagnetic history of the superconductor. However, the critical state model (CSM) due to Bean [12,13], which is usually invoked to describe the hysteretic magnetic response of a superconductor, assumes a unique value of Jc , independent of the thermomagnetic history. It, therefore, does not capture many of the interesting characteristics [11] in the magnetic hysteretic response of weakly pinned superconductors in the PE region. Recently,
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 0 ) 0 1 7 7 2 - X
60
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
Ravikumar et al. [5] have proposed a phenomenological model to incorporate the history dependence of the critical current density which reduces to the Bean's critical state model in the limit that Jc H is a single valued function of H. This model postulates a stable state of vortex lattice with a critical current density Jcst , which is determined uniquely by the ®eld and temperature and is independent of the past magnetic history. This stable state ought to be reached from any metastable vortex state by cycling the applied ®eld by a small amplitude. Ravikumar et al. have further [14] elucidated the existence of such a stable state in a specimen of 2H-NbSe2 via repeated tracings of the minor hysteresis loops (MHLs) across the PE region. In addition, they have asserted that the equilibrium magnetization curve across the PE region can be ascertained from the determined values of `stable' hysteresis loop. We report in this paper the results of an investigation aimed at unravelling the stable state and determining the equilibrium magnetization behaviour across the PE region in a single crystal sample of the superconductor CeRu2 Tc 0 6:2 K. The PE phenomenon in this system has been under investigation by a number of groups in recent years [15±26] and there have been con¯icting reports regarding the behaviour of equilibrium magnetization in it [15,26]. 2. Phenomenological model for history eects and metastability in weakly pinned superconductors An important assumption of the model due to Ravikumar et al. [5] is the existence of a stable vortex state with a critical current density Jcst , which is unique for a given temperature and ®eld. They have postulated the following equation to describe how the Jc changes when the magnetic ®eld is varied from B to B DB : Jc B DB Jc B jDBj=Br Jcst
Jc
1
where Br is a macroscopic measure of the metastability and it describes how strongly Jc is history dependent. Physically, we may imagine that in the absence of thermal ¯uctuations, it is the change in local ®eld B that can move the vortices from their
metastable con®guration to a nearby stable state. It can be seen from the above equation that a metastable vortex state with Jc 6 Jcst can be driven into the stable state by cycling the ®eld by a small amplitude [14]. 3. Experimental results and discussion DC magnetization measurements have been carried out using a 12 T vibrating sample magnetometer (VSM) (Oxford Instruments, UK) on a single crystal sample of cubic (C15) CeRu2 compound (Tc 6:2 K). The sample was vibrated with an amplitude of 1.5 mm at a frequency of 55 Hz. The dc ®eld was swept at the rate of 0.02 T/min, while recording the magnetization hysteresis loops at 4.5 K. All the measurements were carried out by cooling the sample to 4.5 K in zero ®eld (ZFC mode) and then applying the magnetic ®eld parallel to the cube edge. Fig. 1(a) shows a portion of the magnetization hysteresis loop, comprising the M vs: H curves in the increasing (forward) and decreasing (reverse) ®eld cycles. According to the CSM, the hysteresis in magnetization, DM H M H" M H#, provides a measure of the critical current density (Jc / DM) [27]. Thus, an anomalous increase in the width of the hysteresis loop is a distinct indicator of the occurrence of the PE. We identify Hpl as the onset ®eld of the PE on the forward leg, where M begins to decrease sharply (see Fig. 1(a)). The onset ®eld for the PE on the reverse leg is marked as Hpl , which is less than Hpl . The ®eld value where the magnetization hysteresis bubble is the widest identi®es the peak ®eld Hp , and the collapse of the hysteresis loop locates the irreversibility ®eld Hirr , above which the critical current density falls below the measurable limit of the present data. Fig. 1(a) and (b) also show the MHLs initiated from dierent ®elds within the PE region lying on the forward and reverse legs. As per the CSM, all the MHLs should lie within the envelope curve and saturate by overlapping with the envelope curve. However, it can be seen from Fig. 1(a) that the MHLs starting from points, Hpl < H < Hp , on the forward cycle saturate without meeting the reverse envelope curve, although they remain well
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
61
reverse curve overshoot the forward envelope curve. These observations cannot be understood within the CSM and indicate that Jc is magnetic history dependent across the PE region [11]. Moreover, they also imply that the critical current density in the forward cycle (Jcfor ) is less than the critical current density in the reverse cycle (Jcrev ). Using the saturation points of the MHLs, in principle the magnetization hysteresis loops corresponding to Jcfor and Jcrev can be generated. Jcfor H and Jcrev H can then be obtained [10] from the width of the hysteresis loops (see for instance Fig. 2). In the top panel of Fig. 3, we show the MHLs obtained by repeatedly cycling the ®eld starting from a point in the PE region on the forward leg. The cycling amplitude DH is chosen such that it is above the threshold ®eld required to reverse the direction of shielding currents throughout the sample. From Fig. 3(a), it is clear that the MHLs show expansion with ®eld cycling and after few
Fig. 1. Magnetization hysteresis data across the PE region in a single crystal of CeRu2 (H parallel to the cube edge) at 4.5 K. Panel (a) shows the MHLs starting from the forward leg and panel (b) shows MHLs starting from the reverse leg. The ®eld at which the PE commences on the forward leg and terminates on the reverse leg have been marked as Hpl and Hpl , respectively. The peak ®eld (Hp ) of the PE and the irreversiblity ®eld (Hirr ) have also been indicated in panel (a).
within the envelope curve. On the other hand, the MHLs starting from points, Hpl < H < Hp , on the
Fig. 2. Critical current densities Jcfor and Jcrev in the increasing and decreasing ®eld cases respectively (continuous lines) at 4.5 K in CeRu2 . Dotted line shows the stable state critical current density Jcst (cf. Fig. 4).
62
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
Fig. 3. The top panel (a) shows the MHLs obtained by repeatedly cycling the ®eld starting from a point in the PE region on the forward leg. The outer most MHL corresponds to the stable state. The bottom panel (b) shows the outcome of the same procedure when the starting point lies on the reverse leg.
®eld cycles, the MHLs retrace each other indicating that Jc does not change further more with ®eld cycling. We, therefore, conclude that the vortex state attains a stable con®guration. On the reverse cycle, the MHLs starting within the PE region show shrinkage with ®eld cycling, and ®nally the MHLs retrace each other indicating the approach to the stable vortex state, as shown in the bottom panel of Fig. 3. From Fig. 3 it is also clear that the stable state magnetization value does not depend on whether the starting point is on the forward or on the reverse leg. This rearms the basic assumption of the phenomenological model [5] that there exists a unique stable state, independent of the initial vortex con®guration. Fig. 4 shows the construction of the stable magnetization hysteresis loop obtained from the saturated values of the
Fig. 4. The stable magnetization hysteresis loop corresponding to the saturated magnetization values as determined via repeated ®eld cyclings (cf. Fig. 3) at 4.5 K. The dotted curve represents the forward and reverse legs of the usual envelope hysteresis loop as shown in Fig. 1.
stable MHLs as depicted in Fig. 3. The critical current density in the stable state (Jcst ) can be obtained from the width of the stable state hysteresis loop. Jcst H across the PE region along with the Jc values in the forward and reverse cycles are shown in Fig. 2. It can be noted that they follow the relation: Jcrev > Jcst > Jcfor . The equilibrium magnetization (Meq ) can be obtained from the stable state magnetization hysteresis loop using the relation, Meq M st H" M st H#=2 (see Fig. 5). It can be seen that Meq shows a sharp increase above the onset position of the PE region (cf. Meq H and Jcst H data in Figs. 2 and 5 respectively), implying the occurrence of a ®rst order phase transition from an ordered vortex phase to a disordered phase. The DMeq value of 0.75 Oe obtained in the present case compares favourably with the values reported in the literature for the ¯ux line lattice (FLL) melting transition in cuprate superconductors [28] and for the
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
63
Acknowledgements We thank Dr. G. Ravikumar for sharing insights on the principles of his phenomenological model. We also gratefully acknowledge Prof. S. Bhattacharya and other members of the vortex state studies group at TIFR/BARC, Mumbai for numerous discussions. This work was presented at The Joint Vortex-Physics and ESF-Vortex Matter Workshop held at Lunteren, The Netherlands, 27 August to 1 September, 2000.
References
Fig. 5. The dotted curve shows the stable state hysteresis loop across the PE region at 4.5 K. The solid line corresponds to the equilibrium magnetization, which shows a step change DMeq just above the onset position Hpl of the PE phenomenon along the forward leg (cf. Fig. 1).
amorphization transition across the PE in weakly pinned single crystals of 2H-NbSe2 [14,29] and Nb [4].
4. Conclusions In this paper, we have studied dierent metastable vortex con®gurations in the PE region of a weakly pinned single crystal of the superconductor CeRu2 . These states have been characterized by dierent values of critical current densities, which were obtained by dc magnetization measurements. Our new data con®rms the existence of a stable state across the PE region and reveals the occurrence of a step change in the equilibrium magnetization near the onset position of the PE. The results in CeRu2 thus rearm the notion of the stable state evident in the magnetic [14] and transport [30, Fig. 3(a)] experiments performed on 2H-NbSe2 and the structural studies carried out in Nb [4], and thereby establish the generic nature of this feature in weakly pinned systems exhibiting PE phenomenon.
[1] M.J. Higgins, S. Bhattacharya, Physica C 257 (1996) 232. [2] S.S. Banerjee, N.G. Patil, S. Saha, S. Ramakrishnan, A.K. Grover, S. Bhattacharya, G. Ravikumar, P.K. Mishra, T.V.C. Rao, V.C. Sahni, M.J. Higgins, E. Yamamoto, Y. Haga, M. Hedo, Y. Inada, Y. Onuki, Phys. Rev. B 58 (1998) 995. [3] P.L. Gammel, U. Yaron, A.P. Ramirez, D.J. Bishop, A.M. Chang, R. Ruel, L.N. Pfeier, E. Bucher, Phys. Rev. Lett. 80 (1998) 833. [4] X.S. Ling, S.R. Park, B.A. McClain, S.M. Choi, D.C. Dender, J.W. Lynn, cond-mat/0008353. [5] G. Ravikumar, K.V. Bhagwat, V.C. Sahni, A.K. Grover, S. Ramakrishnan, S. Bhattacharya, Phys. Rev. B 61 (2000) R6479. [6] M. Steingart, A.G. Putz, E.J. Kramer, J. Appl. Phys. 44 (1973) 5580. [7] R. Wordenweber, P.H. Kes, C.C. Tsuei, Phys. Rev. B 33 (1986) 3172. [8] W. Henderson, E.Y. Andrei, M.J. Higgins, S. Bhattacharya, Phys. Rev. Lett. 77 (1996) 2077. [9] W. Henderson, E.Y. Andrei, M.J. Higgins, S. Bhattacharya, Phys. Rev. Lett. 80 (1998) 381. [10] S.S. Banerjee, S. Ramakrishnan, A.K. Grover, G. Ravikumar, P.K. Mishra, V.C. Sahni, C.V. Tomy, G. Balakrishnan, D.Mck. Paul, M.J. Higgins, S. Bhattacharya, Physica C 332 (2000) 135. [11] G. Ravikumar, P.K. Mishra, V.C. Sahni, S.S. Banerjee, A.K. Grover, S. Ramakrishnan, P.L. Gammel, D.J. Bishop, E. B ucher, M.J. Higgins, S. Bhattacharya, Phys. Rev. B 61 (2000) 12490. [12] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [13] C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. [14] G. Ravikumar, V.C. Sahani, A.K. Grover, S. Ramakrishnan, P.L. Gammel, D.J. Bishop, E. B ucher, M.J. Higgins, S. Bhattacharya, cond-mat/0007436. [15] S.B. Roy, P. Chaddah, J. Phys.: Condens. Matter 9 (1997) L625. [16] S.B. Roy, P. Chaddah, S. Chaudhary, J. Phys.: Condens. Matter 10 (1998) 4885.
64
A.A. Tulapurkar et al. / Physica C 355 (2001) 59±64
[17] S.B. Roy, P. Chaddah, S. Chaudhary, J. Phys.: Condens. Matter 10 (1998) 8327. [18] R. Modler, P. Gegenwart, M. Deppe, M. Weiden, T. Luhmann, C. Geibel, F. Steglich, C. Paulsen, J.L. Tholence, N. Sato, T. Komatsubara, Y. Onuki, M. Tachiki, S. Takahashi, Phys. Rev. Lett. 76 (1996) 1292. [19] F. Steglich, R. Modler, P. Gegenwart, M. Deppe, M. Weiden, M. Lang, C. Geibel, T. Luhmann, C. Paulsen, J.L. Tholence, Y. Onuki, M. Tachiki, S. Takahashi, Physica C 263 (1996) 498. [20] A. Yamashita, K. Ishii, T. Yokoo, J. Akimitsu, M. Hedo, Y. Inada, Y. Onuki, E. Yamamoto, Y. Haga, R. Kadono, Phys. Rev. Lett. 79 (1997) 3771. [21] M. Tachiki, S. Takahashi, P. Genenwart, M. Weiden, C. Geibel, F. Steglich, R. Modler, C. Paulsen, Y. Onuki, Z. Phys. B 100 (1996) 369. [22] K. Kadowaki, H. Takeya, K. Hirata, Phys. Rev. B 54 (1996) 462.
[23] N.R. Dilley, M.B. Maple, Physica C 278 (1997) 207. [24] R. Modler, Czech. J. Phys. 46 (1996) 3123. [25] A.D. Huxley, C. Paulsen, O. Laborde, J.L. Tholence, D. Sanchez, A. Junod, R. Calemczuk, J. Phys.: Condens. Matter 5 (1993) 7709. [26] K. Tenya, S. Yasunami, T. Tayama, H. Amitsuka, T. Sakakibara, M. Hedo, Y. Inada, E. Yamamoto, Y. Haga, Y. Onuki, J. Phys. Soc. Jpn. 68 (1999) 224. [27] W.A. Fietz, W.W. Webb, Phys. Rev. 178 (1969) 657. [28] M.J.W. Dodgson, V.B. Geshkenbein, H. Nordborg, G. Blatter, Phys. Rev. Lett. 80 (1998) 837. [29] G. Ravikumar, P.K. Mishra, V.C. Sahni, S.S. Banerjee, S. Ramakrishnan, A.K. Grover, P.L. Gammel, D.J. Bishop, E. B ucher, M.J. Higgins, S. Bhattacharya, Physica C 322 (1999) 145. [30] Z.L. Xiao, E.Y. Andrei, P. Shuk, M. Greenblatt, condmat/0006197.