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Influence of plastic deformation of the flux line lattice on the 2D pinning
Physica B 165&166 (1990) 1171-1172 North-Holland
INFLUENCE OF PLASTIC DEFORMATION OF 'ffiE FLUX LINE LATIICE ON lHE 2D PINNI1\'G
v.G.pnOl\HOROV, G.G.KAMINSKY, C.G.TRETIATCHENKO, V.M.PAN Institute of Metal Physics, 252142 Kiev, U.S.S.R.
The field and temperature dependences of the volume pinning Nb Ge fi lms. The resul ts are discussed in the frameworks of J pinning theory. A discrepancy in the high field range is deformation of the flux line lattice due to shear modulus
1. INTRODUGfION The two-dimensional collective pinning has been observed experimentally for example in amorphous Nb Ge, Nb Si, and M0 Si films (e.g. 3 3 3 see (1». In all cases the experimental F (b) dependences showed a smooth increase wifh a sharp peak near b 1. In spite of a rather good agreement in the weak field range the volume pinning force behavior near H is not clear yet. At least there are twoC~easons which could result in an inconsistency of theoretical and experimental F (b) dependences. For the first, a sharp ihcrease of the volume pinning force can be due to a dimensional cross-over from two-dimensional to three-dimensional collective pinning (2DCP 3DCP) (1) at which the correlation length gets to be smaller than a sample thickness, L 0.5d. For the second, the effect can be due tg a topology disordering of the flux line lattice because of dislocation penetration (3). In the last case an essential contradiction between the theory (2) and the experiments arises since the theory was developed in the frameworks of the linear elasticity and cannot adequatly describe a plastic deformation of the flux line lattice.
=
2. EXPERIMENTAL PROCEDURE The amorphous Nb Ge films were prepared by 3 the electron beam vacuum codeposi tion. The Nb deposition rate was about 1.5 nm/s and the Ge deposition rate was adjusted to reach the stoichiometry. The sapphire substrate temperature was ranged from 100 to 400 K. The films were 0.325 mm width, 2 - 4 mm length, and 70 200 nm thickness (i.e. much thinner than that used in (1». The superconducting transition temperature was 3.2 - 3.8 K.
0921.4526/90/$03.50
© 1990 -
force were investiget.ed far amorphous Lal'kin - Ovchinnikov' s coll ecti ve flttributed to t.he strong pl.astic reduction near the cl'i tical field.
3. RESULTS AND DISCUSSION The experimental dependences of the volume pinning force on the reduced magnetic field at different temperatures are shown in Fig.1 for the perpendicular applied field and in Fig.2 for the parallel filed. It is seen that at low enough temperatures there are peaks in the high field range. It should be noted that for the parallel orientation the shape of the pinning cUI've is extremely unsual beacuse it has the second iritermediate peak. The longitudinal correlalation length was estimated to be about 10 fim (i.e. much more than the film thickness). Therefore, it is clear the two - dimensional collective pinning is the case for the perpendicular applied filed at the whole filed range. The theory for this case predicts a monotonous volume pinning force increase up to the highest fields. Nevertheless, the experimental data show that starting from a certain field value the volume pinning force rises much more rapidly. The calculated from the experimental data c constant, which was used in the theory (2) tg characterize the elementary pinning force, is shown in the insert in Fig.! versus reduced magnetic field to make discrepancies more clear. The c (b) dependence fairly shows field ranges wherePthe theory does not describe the experimental data. It is seen that at high temperatures the c constancy range is rather wide. As th~ t.emperature decreases it becomes more narrow. The c value inclines at high as well as at low fields~ Dashed lines show calculated F (b) dependences for the mean c value. PTh~ inclination at low field seems to ~ due to a transition to the quasi-single vortex pinning. Indeed at low enough field a distance between vortices gets to be comparable with the mean
Elsevier Science Publishers B.V. (North-Holland)
V.G. Prokhorov, G.G. Kaminsky, e.G. Tretiatchenko, V.M. Pan
1172
120
100
.......
"'~ BO
~
~ C 60
.....
~
40
20
2.0
B (T)
2.5
3.0
3.5
4.0
FIGURE 1 Volume pinning force vs reduced magnetic field at different temperatures ... - TIT 0.85, G c 0.69, !i - 0.46.
=
distance between pins which is in contradiction with basis of the theory because deformations in this case cannot be considered as small. 35
30
6
"'.......25
~ ~20
4. CONCLUSION As magnetic increases the strong plastic strains arise within FLL resulting in volume is as well usual pimling for'c8 rise that conventional fOl' superconductors wi th quasi-single vortex pinning.
..,
C
.....
~
15
0
b
10
b FIGURE 2 Volume pinning force vs applied = 0.46. 0 parallel field, D field. Insert: TIT = 0.85. c
TIT
A nature of the F (b) inclination at the high field range is le~s obvious. It cannot be explained by 2DCP - 3DCP dimensional cross-over similarly (1) because at the whole field range the longitudinal correlation length is much greater than the film thickness. An alternative suggestion is that the shear modulus c rapidly 66 decreases near H resulting in FLL instability. c2 Such instability can be considered as penetration of dislocations into FLL. Supposing dislocattiog bei~ generated by Frank Reed source, 10 Nlm force is need. This value is the same order of magnitude as the volume pinning force. Thus, the Lorentz force can induce generation of dislocations in FLL transfOl'ming it from 'clast ic to plastic strained state. Supposing the correlation volume is restricted by edge dislocations (4) the volume pilming force can be computed. The dashed line in Fig. 1 shows computed curve for reduced temperature t=0.46. This curve well agrees with the experimental data at high applied fileds. The origin of three peaks for the parallel applied field is not completely clear. Nevertheless, we consider the first peak is due to the dominant quasi-single vortex pinning. the last one is well described in the frameworks of elasticity theory for the 3D case in non-local approach, and the intermediate one is due to the dislocation generation because it position is the same as for the perpendicular orientation.
field at normal
REFERENCES (I) P. H. Kes and R. Wordenweber, J . Low. Temp. Phys . 67 (1987) 1. (2) A.I.Lal'kin and Yu.N.Ovchinnikov. J.Low.Temp. Phys. 34 (1979) 409. (3) E.H.Brandt and U.Essmann, Phys.Stat.Sol. 144 (1987) 13. (4) S.J.Mullock and J.E.Evetts, J.Appl.P~ys. 57 (1985) 2588.
INFLUENCE OF PLASTIC DEFORMATION OF 'ffiE FLUX LINE LATIICE ON lHE 2D PINNI1\'G
v.G.pnOl\HOROV, G.G.KAMINSKY, C.G.TRETIATCHENKO, V.M.PAN Institute of Metal Physics, 252142 Kiev, U.S.S.R.
The field and temperature dependences of the volume pinning Nb Ge fi lms. The resul ts are discussed in the frameworks of J pinning theory. A discrepancy in the high field range is deformation of the flux line lattice due to shear modulus
1. INTRODUGfION The two-dimensional collective pinning has been observed experimentally for example in amorphous Nb Ge, Nb Si, and M0 Si films (e.g. 3 3 3 see (1». In all cases the experimental F (b) dependences showed a smooth increase wifh a sharp peak near b 1. In spite of a rather good agreement in the weak field range the volume pinning force behavior near H is not clear yet. At least there are twoC~easons which could result in an inconsistency of theoretical and experimental F (b) dependences. For the first, a sharp ihcrease of the volume pinning force can be due to a dimensional cross-over from two-dimensional to three-dimensional collective pinning (2DCP 3DCP) (1) at which the correlation length gets to be smaller than a sample thickness, L 0.5d. For the second, the effect can be due tg a topology disordering of the flux line lattice because of dislocation penetration (3). In the last case an essential contradiction between the theory (2) and the experiments arises since the theory was developed in the frameworks of the linear elasticity and cannot adequatly describe a plastic deformation of the flux line lattice.
=
2. EXPERIMENTAL PROCEDURE The amorphous Nb Ge films were prepared by 3 the electron beam vacuum codeposi tion. The Nb deposition rate was about 1.5 nm/s and the Ge deposition rate was adjusted to reach the stoichiometry. The sapphire substrate temperature was ranged from 100 to 400 K. The films were 0.325 mm width, 2 - 4 mm length, and 70 200 nm thickness (i.e. much thinner than that used in (1». The superconducting transition temperature was 3.2 - 3.8 K.
0921.4526/90/$03.50
© 1990 -
force were investiget.ed far amorphous Lal'kin - Ovchinnikov' s coll ecti ve flttributed to t.he strong pl.astic reduction near the cl'i tical field.
3. RESULTS AND DISCUSSION The experimental dependences of the volume pinning force on the reduced magnetic field at different temperatures are shown in Fig.1 for the perpendicular applied field and in Fig.2 for the parallel filed. It is seen that at low enough temperatures there are peaks in the high field range. It should be noted that for the parallel orientation the shape of the pinning cUI've is extremely unsual beacuse it has the second iritermediate peak. The longitudinal correlalation length was estimated to be about 10 fim (i.e. much more than the film thickness). Therefore, it is clear the two - dimensional collective pinning is the case for the perpendicular applied filed at the whole filed range. The theory for this case predicts a monotonous volume pinning force increase up to the highest fields. Nevertheless, the experimental data show that starting from a certain field value the volume pinning force rises much more rapidly. The calculated from the experimental data c constant, which was used in the theory (2) tg characterize the elementary pinning force, is shown in the insert in Fig.! versus reduced magnetic field to make discrepancies more clear. The c (b) dependence fairly shows field ranges wherePthe theory does not describe the experimental data. It is seen that at high temperatures the c constancy range is rather wide. As th~ t.emperature decreases it becomes more narrow. The c value inclines at high as well as at low fields~ Dashed lines show calculated F (b) dependences for the mean c value. PTh~ inclination at low field seems to ~ due to a transition to the quasi-single vortex pinning. Indeed at low enough field a distance between vortices gets to be comparable with the mean
Elsevier Science Publishers B.V. (North-Holland)
V.G. Prokhorov, G.G. Kaminsky, e.G. Tretiatchenko, V.M. Pan
1172
120
100
.......
"'~ BO
~
~ C 60
.....
~
40
20
2.0
B (T)
2.5
3.0
3.5
4.0
FIGURE 1 Volume pinning force vs reduced magnetic field at different temperatures ... - TIT 0.85, G c 0.69, !i - 0.46.
=
distance between pins which is in contradiction with basis of the theory because deformations in this case cannot be considered as small. 35
30
6
"'.......25
~ ~20
4. CONCLUSION As magnetic increases the strong plastic strains arise within FLL resulting in volume is as well usual pimling for'c8 rise that conventional fOl' superconductors wi th quasi-single vortex pinning.
..,
C
.....
~
15
0
b
10
b FIGURE 2 Volume pinning force vs applied = 0.46. 0 parallel field, D field. Insert: TIT = 0.85. c
TIT
A nature of the F (b) inclination at the high field range is le~s obvious. It cannot be explained by 2DCP - 3DCP dimensional cross-over similarly (1) because at the whole field range the longitudinal correlation length is much greater than the film thickness. An alternative suggestion is that the shear modulus c rapidly 66 decreases near H resulting in FLL instability. c2 Such instability can be considered as penetration of dislocations into FLL. Supposing dislocattiog bei~ generated by Frank Reed source, 10 Nlm force is need. This value is the same order of magnitude as the volume pinning force. Thus, the Lorentz force can induce generation of dislocations in FLL transfOl'ming it from 'clast ic to plastic strained state. Supposing the correlation volume is restricted by edge dislocations (4) the volume pilming force can be computed. The dashed line in Fig. 1 shows computed curve for reduced temperature t=0.46. This curve well agrees with the experimental data at high applied fileds. The origin of three peaks for the parallel applied field is not completely clear. Nevertheless, we consider the first peak is due to the dominant quasi-single vortex pinning. the last one is well described in the frameworks of elasticity theory for the 3D case in non-local approach, and the intermediate one is due to the dislocation generation because it position is the same as for the perpendicular orientation.
field at normal
REFERENCES (I) P. H. Kes and R. Wordenweber, J . Low. Temp. Phys . 67 (1987) 1. (2) A.I.Lal'kin and Yu.N.Ovchinnikov. J.Low.Temp. Phys. 34 (1979) 409. (3) E.H.Brandt and U.Essmann, Phys.Stat.Sol. 144 (1987) 13. (4) S.J.Mullock and J.E.Evetts, J.Appl.P~ys. 57 (1985) 2588.