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Lock-in transition of flux-lines in layered superconductors
Physica C 185-189 (1991) 2345-2346 North-Holland
Lock-in transition of flux-lines in layered superconductors A.J. Vermeer, D.G. de Groot, N.J. Koeman, R. Gfiesse.~n, and C. van H~sendonck Free University, Faculty of Physics and Astronomy, De Boelelaan 1081,1081 HV Amsterdam, The Netherlands In an attempt to prove the existence of a lock-in transition of flux-lines in layered superconductors, we have synthesised Nb/Cu multilayers by means of evaporation under ultra-high vacuum conditions. Magnetic moment measurements by means of a hiLqh-sensitivity torque magnetometer show a series of maxima at fields B n = 1.01 4- 0.13 x 10 -15 (n2/D-2) , with B n in Tesla and the tota/thickness D in nm. Maxima upton = 7 have been observed in several NblCu multilayers with different single layer thickness (varying from 4 to 20 nm). The effect disappears when the angle between B and the plane of the multilayer is larger than ~5 °. This is in good agreement with the critical angle predicted for lock-in of flux-lines in the layer plane. To our knowledge, this is the first experimental evidence for a lock-in transition and enhanced pinning in a layered superconductor with a coherence length ~ comparable to the single layer thickness.
1. Introduction Several authors have recently predicted that flux vortices in a layered superconductor are more strongly pinned if the vortex lattice is locked-in by a multilayer structure. 1"5 This effect is expected to be visible only within a narrow range of field directions, almost parallel to the layers. So far, these predictions could not be confirmed experimentally in high-Tc superconductors. As B ~
_
|
0
+,_ L t_
2 lal
4B~ 0
I 01
these predictions are not bound to high-Tc superconductors, but only to layered superconductors with a coherence length comparable to the thickness of individual layers, we have studied these effects in multilayer structures. We present experimental evidence for a lock-in transition and enhanced pinning in Nb/Cu muRilayers.
2. Experiments We have grown niobium / copper multilayers on sapphire substrates at ambient temperatures, using a two electron gun bHV evaporation system. Modulation periods range from 8.4 nm to 60 nm: and totai thicknesses from 164 to 620 rim. Top and base layers are a~ways copper in order to avoid surface superconductivity. The samples were characterised with X- ray diffraction {82¢), showing a modulated Nb(110)/Cu(111) growth. Tile magnetic moment of the multilayers is measured with a capacitance torque magnetometer, at temperatures between 1.5 K and Tc and fields up to 1.5 Tesla. The measured torque is proportional to the critica0 current and, consequently, to the pinning force on the flux vortices.
19B 1 --[ 02
I 03
0.4
P.oH (T) Figure 1 : Torque magnetic moment measurement in nearly parallel field, i.e. with an angle ® = 1.0 ° between the field and the plane of the multilayer. The arrows indicate local maxima in the torque hysteresis, which correspond to maxima in the pinning of vortices. The fields at which maxima occur, scale as 1:4:9, and are therefore labelled with integer numbers, i.e. Bn with n = 1, 2, and 3. T = 4.2 K, Tc = 6.9 K. The sample has a total thickness D = 186 nm, with single layers of 12.5 rim.
0921-4534/97 '$03.50 © 1991 - Elsevier Science Publishers B.V.
& Results Figure 1 shows a typical torque measurement i~ nearly parallel field. The arrows indicate Boca1maxima of the torque (and hence of pinning force) at some specific field strengths. We measured six different muitilayers, which all showed similar maxima, albeit at different fie!d strengths. A detailed investigation of these maxima revealed the following remarkable properties. (s) The vortex pinning maxima are only visible when the field is nearly parallel to the layers, and disappear at field am gles ® > 5 °. (h) Each sample has maxima at field All rights reserve&
A,J. Vermeer et aL / Lock-in transition of flux-lines in layered superconductors
2346
strengths B n = n2 B 1 (n = 1,2, 3...). Therefore, we may assign an integer number n to each maximum. In a multilayer with a total thickness of 620 nm, maxima up to n = 7 could be detected. (i#) The value B 1 depends on the total thickness D of the samples, irrespective of the thickness d of individual single layers. (iv) The maxima in all six samples obey (see figure 2) the universal relation: 2 B n = 1.01 +0.13x10-19(D) where D is in meters and B n in Tesla. (v) We have also noticed that the layered structure is essential for this effect. The maxima were not found in unmodulated niobium films with thicknesses of 90 and 390 nm. 4. Discussion Ivlev eta/. 4 have argued that in layered superconductors intrinsic pinning will occur due to the variation of the condensation energy when the vortex core crosses a layer. This intrinsic interlayer pinning will be predominant if the vortex lattice is commensurate with the interlayer spacing. In the case of weak intrinsic pinning (i.e. when Hcl<
TOTALA ~64nmTHICKNESS(D) / V
200
186 nm 317nm X 390 nm [ ] 488 am + 620 am
)¢X
+-~+
/
E 150 CC
/ "100
50
/
P
The field strengths B n where this matching occurs, depend on multiples of the multilayer spacing d or on D/n, and on the superconducting anisotropy ~///P~.: Bn = o 4 ~ / / ( 5 )
= 1x10-15(D)2
for n = 1, 2, 3 .... as long as D / n >> d. The anisotropy P,///P~. is obtained from upper critical fields measurements, and is typically Pw//P,±= 1.8 for our samples. This result is in good agreement with our measurements. The preference of the flux lines to be locked-in parallel to the layers occurs only for a small range of field orientations. Feinberg et al. 5 have pointed out that this trapping of flux lines will happen for nearly parallel field orientations, Le. for ® < ®c. Using equation 11 from reference (5) we find for fields of the order of 10 Hcl, £. :=1.8 and ix1 = 0.5 a critical angle Oc = 6°. This value is indicative for the small region of (internal) field orientations for which flux lines are locked-in. Experimentally we find that the pinning maxima disappear when the external field is turned over 5 ° away from the parallel orientation. The observed matching of the vortex lattice to the layered structure does not imply that vortex tines are perfectly (on their full length) locked-in parallel to the layers, as described in reference (5). In our torque experiments large critical currents Jcare flowing in the plane of the sample, producing magnetic moments many orders of magnitude larger than the magnetization due to the equilibrium properties studied by Feinberg et aL 5 In this situation, even in (almost) parallel fields, the nucleation of kinks across the layers should occur due to extrinsic pinning (see also reference 2). Hence, we expect in nearly parallel fields undulating flux lines of which large portions are locked-in parallel to the layers, whereas for larger field angles this trapping of the flux lines does no longer exist. Our work is supported by the Stichting Fundamenteel Onderzoek der Materie (FOM) in The Netherlands. References
2
I
I
I
4
6
8
(,~o H )-V2 ( T ) J/2
Figure 2: The fields Bn where maxima in pinning force occur plotted against the total thickness of the sample divided by the index (see text and figure 1) of the maximum. These results were obtained from six different multilayer samples, with different thicknesses and number of layers. T = 4.2 K.
(198 °) 291 . 2. M. Tachiki and S. Takahashi, Sol. State Comm. 72 (1989)1083. 3. S. Takahashi and M. Tachiki, Phys. Rev. E} 83 (1986) 4620. 4. B,I. Ivlev and N,B. Kopnin, Phys. Rev. Letters8#, (1990), 1828. 5. D. Feinberg and C, VilIard, Phys. Rev. Letters 85 (1990) 919.
Lock-in transition of flux-lines in layered superconductors A.J. Vermeer, D.G. de Groot, N.J. Koeman, R. Gfiesse.~n, and C. van H~sendonck Free University, Faculty of Physics and Astronomy, De Boelelaan 1081,1081 HV Amsterdam, The Netherlands In an attempt to prove the existence of a lock-in transition of flux-lines in layered superconductors, we have synthesised Nb/Cu multilayers by means of evaporation under ultra-high vacuum conditions. Magnetic moment measurements by means of a hiLqh-sensitivity torque magnetometer show a series of maxima at fields B n = 1.01 4- 0.13 x 10 -15 (n2/D-2) , with B n in Tesla and the tota/thickness D in nm. Maxima upton = 7 have been observed in several NblCu multilayers with different single layer thickness (varying from 4 to 20 nm). The effect disappears when the angle between B and the plane of the multilayer is larger than ~5 °. This is in good agreement with the critical angle predicted for lock-in of flux-lines in the layer plane. To our knowledge, this is the first experimental evidence for a lock-in transition and enhanced pinning in a layered superconductor with a coherence length ~ comparable to the single layer thickness.
1. Introduction Several authors have recently predicted that flux vortices in a layered superconductor are more strongly pinned if the vortex lattice is locked-in by a multilayer structure. 1"5 This effect is expected to be visible only within a narrow range of field directions, almost parallel to the layers. So far, these predictions could not be confirmed experimentally in high-Tc superconductors. As B ~
_
|
0
+,_ L t_
2 lal
4B~ 0
I 01
these predictions are not bound to high-Tc superconductors, but only to layered superconductors with a coherence length comparable to the thickness of individual layers, we have studied these effects in multilayer structures. We present experimental evidence for a lock-in transition and enhanced pinning in Nb/Cu muRilayers.
2. Experiments We have grown niobium / copper multilayers on sapphire substrates at ambient temperatures, using a two electron gun bHV evaporation system. Modulation periods range from 8.4 nm to 60 nm: and totai thicknesses from 164 to 620 rim. Top and base layers are a~ways copper in order to avoid surface superconductivity. The samples were characterised with X- ray diffraction {82¢), showing a modulated Nb(110)/Cu(111) growth. Tile magnetic moment of the multilayers is measured with a capacitance torque magnetometer, at temperatures between 1.5 K and Tc and fields up to 1.5 Tesla. The measured torque is proportional to the critica0 current and, consequently, to the pinning force on the flux vortices.
19B 1 --[ 02
I 03
0.4
P.oH (T) Figure 1 : Torque magnetic moment measurement in nearly parallel field, i.e. with an angle ® = 1.0 ° between the field and the plane of the multilayer. The arrows indicate local maxima in the torque hysteresis, which correspond to maxima in the pinning of vortices. The fields at which maxima occur, scale as 1:4:9, and are therefore labelled with integer numbers, i.e. Bn with n = 1, 2, and 3. T = 4.2 K, Tc = 6.9 K. The sample has a total thickness D = 186 nm, with single layers of 12.5 rim.
0921-4534/97 '$03.50 © 1991 - Elsevier Science Publishers B.V.
& Results Figure 1 shows a typical torque measurement i~ nearly parallel field. The arrows indicate Boca1maxima of the torque (and hence of pinning force) at some specific field strengths. We measured six different muitilayers, which all showed similar maxima, albeit at different fie!d strengths. A detailed investigation of these maxima revealed the following remarkable properties. (s) The vortex pinning maxima are only visible when the field is nearly parallel to the layers, and disappear at field am gles ® > 5 °. (h) Each sample has maxima at field All rights reserve&
A,J. Vermeer et aL / Lock-in transition of flux-lines in layered superconductors
2346
strengths B n = n2 B 1 (n = 1,2, 3...). Therefore, we may assign an integer number n to each maximum. In a multilayer with a total thickness of 620 nm, maxima up to n = 7 could be detected. (i#) The value B 1 depends on the total thickness D of the samples, irrespective of the thickness d of individual single layers. (iv) The maxima in all six samples obey (see figure 2) the universal relation: 2 B n = 1.01 +0.13x10-19(D) where D is in meters and B n in Tesla. (v) We have also noticed that the layered structure is essential for this effect. The maxima were not found in unmodulated niobium films with thicknesses of 90 and 390 nm. 4. Discussion Ivlev eta/. 4 have argued that in layered superconductors intrinsic pinning will occur due to the variation of the condensation energy when the vortex core crosses a layer. This intrinsic interlayer pinning will be predominant if the vortex lattice is commensurate with the interlayer spacing. In the case of weak intrinsic pinning (i.e. when Hcl<
TOTALA ~64nmTHICKNESS(D) / V
200
186 nm 317nm X 390 nm [ ] 488 am + 620 am
)¢X
+-~+
/
E 150 CC
/ "100
50
/
P
The field strengths B n where this matching occurs, depend on multiples of the multilayer spacing d or on D/n, and on the superconducting anisotropy ~///P~.: Bn = o 4 ~ / / ( 5 )
= 1x10-15(D)2
for n = 1, 2, 3 .... as long as D / n >> d. The anisotropy P,///P~. is obtained from upper critical fields measurements, and is typically Pw//P,±= 1.8 for our samples. This result is in good agreement with our measurements. The preference of the flux lines to be locked-in parallel to the layers occurs only for a small range of field orientations. Feinberg et al. 5 have pointed out that this trapping of flux lines will happen for nearly parallel field orientations, Le. for ® < ®c. Using equation 11 from reference (5) we find for fields of the order of 10 Hcl, £. :=1.8 and ix1 = 0.5 a critical angle Oc = 6°. This value is indicative for the small region of (internal) field orientations for which flux lines are locked-in. Experimentally we find that the pinning maxima disappear when the external field is turned over 5 ° away from the parallel orientation. The observed matching of the vortex lattice to the layered structure does not imply that vortex tines are perfectly (on their full length) locked-in parallel to the layers, as described in reference (5). In our torque experiments large critical currents Jcare flowing in the plane of the sample, producing magnetic moments many orders of magnitude larger than the magnetization due to the equilibrium properties studied by Feinberg et aL 5 In this situation, even in (almost) parallel fields, the nucleation of kinks across the layers should occur due to extrinsic pinning (see also reference 2). Hence, we expect in nearly parallel fields undulating flux lines of which large portions are locked-in parallel to the layers, whereas for larger field angles this trapping of the flux lines does no longer exist. Our work is supported by the Stichting Fundamenteel Onderzoek der Materie (FOM) in The Netherlands. References
2
I
I
I
4
6
8
(,~o H )-V2 ( T ) J/2
Figure 2: The fields Bn where maxima in pinning force occur plotted against the total thickness of the sample divided by the index (see text and figure 1) of the maximum. These results were obtained from six different multilayer samples, with different thicknesses and number of layers. T = 4.2 K.
(198 °) 291 . 2. M. Tachiki and S. Takahashi, Sol. State Comm. 72 (1989)1083. 3. S. Takahashi and M. Tachiki, Phys. Rev. E} 83 (1986) 4620. 4. B,I. Ivlev and N,B. Kopnin, Phys. Rev. Letters8#, (1990), 1828. 5. D. Feinberg and C, VilIard, Phys. Rev. Letters 85 (1990) 919.