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Nb Josephson junction arrays
Physica B 280 (2000) 444}445
The paramagnetic Meissner e!ect in Nb/AlO /Nb Josephson V junction arrays A.P. Nielsen *, J. Holzer, A.B. Cawthorne , C.J. Lobb , R.S. Newrock, J. Markus CSR, Physics Department, University of Maryland, College Park, Maryland, MD 20742-4111, USA Physics Department, University of Cincinnati, Cincinnati, OH 45221-0011, USA
Abstract We discuss preliminary measurements from a scanning SQUID microscope of a paramagnetic Meissner e!ect (PME) in Josephson junction arrays (JJAs). We "nd that the qualitative features of the data can roughly be replicated by a simple four-junction loop with inductance. We conclude that p-junctions are not necessary to observe a PME. 2000 Elsevier Science B.V. All rights reserved.
The paramagnetic Meissner e!ect is currently of considerable interest. The e!ect has been observed in a variety of superconductors [1}3] but it is of particular interest in the granular cuprates [4,5] where it has been attributed to the d-wave symmetry of the order parameter and the presence of p-junctions across the grain boundaries of the material [4}6]. Recently [7], from AC susceptibility measurements, indirect evidence for a paramagnetic Meissner e!ect was seen in two-dimensional unshunted SIS Josephson junction arrays. This is of
considerable interest since such arrays are well-understood, well-characterized and do not contain p-junctions. We have made "eld-cooled measurements of the magnetization of under-damped unshunted Nb/AlO /Nb V tunnel junction arrays with strong pinning (b "2p¸I /U "30). We used a scanning SQUID * microscope to determine the local magnetization over the array surface.
Fig. 1. Image of the #ux at the surface of a 30;100 Josephsonjunction array, after "eld-cooling in a 47 mG "eld.
* Corresponding author. These arrays were fabricated for us by Martin Forrester of the Northrup}Grumman Company.
Fig. 2. Flux map of a JJA produced by a scanning SQUID microscope. The gray scale indicates the relative magnitude of the #ux.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 8 3 0 - X
A.P. Nielsen et al. / Physica B 280 (2000) 444}445
Fig. 3. The magnetization (proportional to the di!erence between the total and applied #ux) as a function of the applied "eld. Both paramagnetic and diamagnetic states are observed.
Fig. 1 is a an image of the #ux at the surface of an array after cooling in a 47 mG "eld. The output voltage of the microscope (proportional to the #ux) is translated into a gray scale; darker gray represents more (positive) #ux. The underlying structure of the array is visible and the plaquette-to-plaquette variation of the magnetic "eld is easily observed. Fig. 2 shows the #ux through the array minus the external #ux; this is essentially the magnetization M"B!H. These data are for an applied #ux U / # U "4.8. The data look very similar to that taken re cently [5] on the ceramic BSCCO, which was also done with a scanning SQUID microscope. From this "gure one can see the magnetization of di!erent plaquettes in the array. The magnetization values of each plaquette can be determined and the average magnetization of the entire sample calculated. We did this for a range of applied "elds from !12U to #12U . Fig. 3 shows some of these mean values as a function of the applied "eld; one observes states that are paramagnetic and diamagnetic, that is, for certain values of the applied "eld a PME is seen. Insight into the source of the paramagnetic behavior may be gained from a simple model: the response to a magnetic "eld of a single four-junction loop with inductance, with parameters chosen so that b "30, the value * for the array. From the relationship between U ,U , and the current 2 # U "U #¸I 2 # and using the Josephson relation for the current through a junction in terms of the gauge invariant phase di!erence, one "nds that the two #uxes are related by [7]
pn pU ! 2 , U "U #¸I sin 2 # 2 2U
(1)
445
Fig. 4. In the upper portion U (from Eq. (2)) is plotted as a function of the applied "eld for various values of n. Both paramagnetic and diamagnetic states are seen. The lower portion of the "gure shows the Gibbs free energy as a function of the applied "eld.
where n"0, 1, 22 . This is plotted in the upper portion of Fig. 4. We see that for a given value of U many # values of U are possible, depending on n. We note 2 that the calculations qualitatively resemble the experimental data. The question then arises as to how the values of U and n are determined. 2 To determine this we examined the Gibbs free energy as a function of U , determined numerically from # dG"IdU and shown in the bottom portion of # Fig. 4. The minima of the free energy curves always occur for U "U , implying that !U )U ! # 2 # U )#U and that the loop can be either paramag2 netic or diamagnetic depending on the value of the applied "eld. We conclude that for certain values of an applied magnetic "eld a JJA can exhibit a paramagnetic Meissner e!ect. p-junctions are not a prerequisite for this e!ect. The four-junction loop model appears to provide a reasonable explanation of the e!ect but much physics is missing * for example, plaquette-to-plaquette coupling. We are currently doing a similar calculation for the entire array.
References [1] A.K. Geim et al., Nature 396 (1998) 144. [2] P. Kostic et al., Phys. Rev. B 53 (1996) 791. [3] D.J. Thompson, M.S.M. Minhaj, L.E. Wenger, J.T. Chen, Phys. Rev. Lett. 75 (1996) 529. [4] W. Braunsish et al., Phys. Rev. Lett. 68 (1992) 1908. [5] J.R. Kirtley, A.C. Mota, M. Sigrist, T.M. Rice, J. Phys.: Condens. Matter 10 (1998) L97. [6] J.R. Kirtley, K.A. Moler, D.J. Scalapino, Phys. Rev. B 56 (1997) 886. [7] F.M. Araujo-Moreira, P. Barbara, A.B. Cawthorne, C.J. Lobb, Phys. Rev. Lett. 78 (1997) 4625.
The paramagnetic Meissner e!ect in Nb/AlO /Nb Josephson V junction arrays A.P. Nielsen *, J. Holzer, A.B. Cawthorne , C.J. Lobb , R.S. Newrock, J. Markus CSR, Physics Department, University of Maryland, College Park, Maryland, MD 20742-4111, USA Physics Department, University of Cincinnati, Cincinnati, OH 45221-0011, USA
Abstract We discuss preliminary measurements from a scanning SQUID microscope of a paramagnetic Meissner e!ect (PME) in Josephson junction arrays (JJAs). We "nd that the qualitative features of the data can roughly be replicated by a simple four-junction loop with inductance. We conclude that p-junctions are not necessary to observe a PME. 2000 Elsevier Science B.V. All rights reserved.
The paramagnetic Meissner e!ect is currently of considerable interest. The e!ect has been observed in a variety of superconductors [1}3] but it is of particular interest in the granular cuprates [4,5] where it has been attributed to the d-wave symmetry of the order parameter and the presence of p-junctions across the grain boundaries of the material [4}6]. Recently [7], from AC susceptibility measurements, indirect evidence for a paramagnetic Meissner e!ect was seen in two-dimensional unshunted SIS Josephson junction arrays. This is of
considerable interest since such arrays are well-understood, well-characterized and do not contain p-junctions. We have made "eld-cooled measurements of the magnetization of under-damped unshunted Nb/AlO /Nb V tunnel junction arrays with strong pinning (b "2p¸I /U "30). We used a scanning SQUID * microscope to determine the local magnetization over the array surface.
Fig. 1. Image of the #ux at the surface of a 30;100 Josephsonjunction array, after "eld-cooling in a 47 mG "eld.
* Corresponding author. These arrays were fabricated for us by Martin Forrester of the Northrup}Grumman Company.
Fig. 2. Flux map of a JJA produced by a scanning SQUID microscope. The gray scale indicates the relative magnitude of the #ux.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 8 3 0 - X
A.P. Nielsen et al. / Physica B 280 (2000) 444}445
Fig. 3. The magnetization (proportional to the di!erence between the total and applied #ux) as a function of the applied "eld. Both paramagnetic and diamagnetic states are observed.
Fig. 1 is a an image of the #ux at the surface of an array after cooling in a 47 mG "eld. The output voltage of the microscope (proportional to the #ux) is translated into a gray scale; darker gray represents more (positive) #ux. The underlying structure of the array is visible and the plaquette-to-plaquette variation of the magnetic "eld is easily observed. Fig. 2 shows the #ux through the array minus the external #ux; this is essentially the magnetization M"B!H. These data are for an applied #ux U / # U "4.8. The data look very similar to that taken re cently [5] on the ceramic BSCCO, which was also done with a scanning SQUID microscope. From this "gure one can see the magnetization of di!erent plaquettes in the array. The magnetization values of each plaquette can be determined and the average magnetization of the entire sample calculated. We did this for a range of applied "elds from !12U to #12U . Fig. 3 shows some of these mean values as a function of the applied "eld; one observes states that are paramagnetic and diamagnetic, that is, for certain values of the applied "eld a PME is seen. Insight into the source of the paramagnetic behavior may be gained from a simple model: the response to a magnetic "eld of a single four-junction loop with inductance, with parameters chosen so that b "30, the value * for the array. From the relationship between U ,U , and the current 2 # U "U #¸I 2 # and using the Josephson relation for the current through a junction in terms of the gauge invariant phase di!erence, one "nds that the two #uxes are related by [7]
pn pU ! 2 , U "U #¸I sin 2 # 2 2U
(1)
445
Fig. 4. In the upper portion U (from Eq. (2)) is plotted as a function of the applied "eld for various values of n. Both paramagnetic and diamagnetic states are seen. The lower portion of the "gure shows the Gibbs free energy as a function of the applied "eld.
where n"0, 1, 22 . This is plotted in the upper portion of Fig. 4. We see that for a given value of U many # values of U are possible, depending on n. We note 2 that the calculations qualitatively resemble the experimental data. The question then arises as to how the values of U and n are determined. 2 To determine this we examined the Gibbs free energy as a function of U , determined numerically from # dG"IdU and shown in the bottom portion of # Fig. 4. The minima of the free energy curves always occur for U "U , implying that !U )U ! # 2 # U )#U and that the loop can be either paramag2 netic or diamagnetic depending on the value of the applied "eld. We conclude that for certain values of an applied magnetic "eld a JJA can exhibit a paramagnetic Meissner e!ect. p-junctions are not a prerequisite for this e!ect. The four-junction loop model appears to provide a reasonable explanation of the e!ect but much physics is missing * for example, plaquette-to-plaquette coupling. We are currently doing a similar calculation for the entire array.
References [1] A.K. Geim et al., Nature 396 (1998) 144. [2] P. Kostic et al., Phys. Rev. B 53 (1996) 791. [3] D.J. Thompson, M.S.M. Minhaj, L.E. Wenger, J.T. Chen, Phys. Rev. Lett. 75 (1996) 529. [4] W. Braunsish et al., Phys. Rev. Lett. 68 (1992) 1908. [5] J.R. Kirtley, A.C. Mota, M. Sigrist, T.M. Rice, J. Phys.: Condens. Matter 10 (1998) L97. [6] J.R. Kirtley, K.A. Moler, D.J. Scalapino, Phys. Rev. B 56 (1997) 886. [7] F.M. Araujo-Moreira, P. Barbara, A.B. Cawthorne, C.J. Lobb, Phys. Rev. Lett. 78 (1997) 4625.