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Direct observation of collective pinning in a deformed type-II superconductor Nb-Mo
Physica B 165&166 (1990) 1179-1180 North-Holland
DIRECT OBSERVATION SUPERCX)Nl){JCIDR Nb-Mo Irina V.
OF
OOllECTlVE
PINNING
IN A DEFORMED TIPE- I I
GRlGOR\~A
Insti tute of Solid State Physics, USSR Academy of Sciences, Chernogo10vka, Moscow district, USSR
142432,
A technique of decorating a superconductor with small ferromagnetic particles has been used to observe the flux line lattice (FLL) interaction with randomly distributed dislocations in deformed single crystals NhMo. The interaction results in the break of long-range order in the FLL and its splitting into disoriented domains, the effect predicted by the collective pinning theory. The domain dimensions determine the critical current value in the crystals studied in agreement with the theory. A sharp decrease of the average domain size and a change of distortion character in the FLL have been found upon decreasing the magnetic induction inside the sample from 120 to 14 G.
1. INTRODUCTION A lossless current-carrying capacity of type -II superconductors is determined by the flux line lattice (FLL) interaction with crystal defects (by pinning). In order to calculate a volume pinning force and critical current it is necessary to know not only elementary pinning forces f from individual defects but also a summation law for these forces. Considerable progress in solving the summation problem has been achieved due to the collective pinning theory (CP)-ref.(l).The key statement of the theory is that weak randomly distributed pinning centers disturb the long-range order in the flux line positions and make the FLL split into correlation regions (CR) with regular vortex lattice inside. The CR dimensions (correlation volume V ) determine the critical current j and pinning C force density F (1): C F
C
Vc '"
R~(~) C
P
=
= ( wlv)
j B 1/2 pee ow -:3/2 1/2 2 1/2 0 " G~6 C44 rp
; R
c-
W
w = n 1
66
Here R is the transversal correlation size,C66 and C4 : are the shear and tilt modulus of the FLL calculated in detail in ref. (2), W is the characterization of the pin density n and their elementary force f .. So, a direct confirmation of the idea would 'be given by visualization of correlation regions in the FLL in different magnetic fields (i.e. upon changing the FLL elasticity (1,3)). Another interesting aspect of the FLL interaction with weak pins is the character of vortex lattice deformation: in ref.(l) the elastic vortex displacements were considered only while in ref.(4) an important role of screw disloca-
0921-4526/90/$03.50
© 1990 -
tions in the FLL was evidenced by the crossover from 2D- to 3D-collective pinning. Here we present the results of direct observations of the FLL affected by randomly distributed dislocations, in the magnetic fields from 14 to 120 G. 2. SAMPLES AND EXPERIMENTAL TECHNIQUE Samples under investigation were weakly deformed Nb-5%UO single cryst~~s ~2ntaining low density of dislocations - ~10 cm (characteristic separation of dislocations 0,5gm). Vortex lattice patterns were observed using the technique of decorating a superconductor with dispersed ferromagnetic particles (5). A distribution of iron particles on sample's surface, which replicates the vortex distribution, was examined in the scanning electron microscope. The vortex patterns in different magnetic fields Were studied on the same sample (the sample was washed up each time after the decoration and the experiment repeated). 3. EXPERIMENTAL RESULTS AND DISCUSSION Fig.1 and 2 demonstrate typical vortex patterns in the fields 120 and 40 G (bright points are vortices). In both cases the FLL is obviously seen to consist of disoriented domains with regular vortex arrangement inside. One of the domains is displayed in Fig. 1. Assuming that the observed domains are cross sections of the correlation volumes and their average dimension is R ,we found a corresponding F value (see expr~ssions in the INIRODUCTION) :Pfj>r B =~O G the pinning force density is 4.10 dyn/cm. It proved to be in good agreement with F est~mat ed 3 from j (H) measurements:F =(1,0-1,5~.10 dyn/ em and f~om the magnetic d~.duction gradients at the edge 3of the 3 sample: F =l/41!.B. dB/dx= (3,2-4,8).10 dyn/cm (for detail~ see ref.(6)).
Elsevier Science Publishers B.V. (North-Holland)
1180
FIGURE 1 The flux line lattice in the magnetic field 120G. A dotted line shows the boundary of of the domains in the FLL, solid lines show directions of close packed vortex rows their change at the domain boundaries.
I. V. Grigoryeva
B
=
one the and
most, places for vortex row bending (Fig. 1). Parts of the boundaries are formed by edge dislocations in the FLL but their relative length is small. Similar patterns are observed for B = 100 G but vortex row bending and edge dislocations in the FLL are equiprobable. In the field .8=40 G (Fig.2) the CR boundaries become more extended: there observed "vortex liquid" islands sized up to several vortex spacings between the regions of regular FLL as well as aggregations of vacancies in the FLL (one of the latter is marked by arrows in Fig.2). Individual edge dislocations can be also displayed. In the lowest magnetic field used, B = 14 G, the FLL is almost completely destroyed and hexagonal correlations can be found only for the nearest neighbors and not everywhere. Thus, upon decreasing the magnetic field we have observed a sharp decrease of the correlation radius followed by a change of the FLL de-formation from mostly elastic to the plastic one A dependence of the average correlation radius R on the reduced magnetic field b=BIH is shown i~ Fig.3 together with the dependence cgalculated following the collective pinning theory (1) ~./o.
, , ,, I
50
I
I I
1
4D
Ii
3D
20
Il
I
I
FIGURE 3 D.D1
,"
,
I
I
I
I
I
/"" 0.02
0.03
-81 IlOlt fHc,z
(the dashed line). The experimental dependence proved to be slower than the theory predicts. We believe that the discrepancy is related to the fact that the experimentally observed complicated structure of the CR boundaries (dislocations, vortex liquid islands, vacancies in the FLL) had not been taken into account in the CP. REFERENCES
(1)
FIGURE 2 The flux line lattice in the magnetic field B 40G.
=
This confirms directly the idea of CR formation whose dimensions determine the pinning force (critical current) value. On decreasing the magnetic field the FLL becomes less ordered in the whole that is followed by a change of the CR boundary structure. In the field 120 G the CR boundaries are, in the
(2) (3) (4) (5) (6)
A.I.Larkin and Yu.N.Ovchinnikov II J. Low Temp.Phys., 1979. 34, No.3/4. 409 E.H.Brandt II Phys. Stat.Solidi (b), 1976, v.77, 551; J.Low-Temp.Phys. ,1977, v.26, No.5/6,735. E.H.Brandt II J.Low-Temp.Phys., 1986,v.64, No.5/6,375. R.Wondenweber and P.H.Kes II Phys.Rev.B, 1986, v.34,No.1,494 U.Essmann and H.Trauble II Phys.Letters, 1967, A24, 526 I.V.Grigoryeva, L.Ya.Vinnikov II J.Low Temp.Phys., 1989, v.1/2, 89.
DIRECT OBSERVATION SUPERCX)Nl){JCIDR Nb-Mo Irina V.
OF
OOllECTlVE
PINNING
IN A DEFORMED TIPE- I I
GRlGOR\~A
Insti tute of Solid State Physics, USSR Academy of Sciences, Chernogo10vka, Moscow district, USSR
142432,
A technique of decorating a superconductor with small ferromagnetic particles has been used to observe the flux line lattice (FLL) interaction with randomly distributed dislocations in deformed single crystals NhMo. The interaction results in the break of long-range order in the FLL and its splitting into disoriented domains, the effect predicted by the collective pinning theory. The domain dimensions determine the critical current value in the crystals studied in agreement with the theory. A sharp decrease of the average domain size and a change of distortion character in the FLL have been found upon decreasing the magnetic induction inside the sample from 120 to 14 G.
1. INTRODUCTION A lossless current-carrying capacity of type -II superconductors is determined by the flux line lattice (FLL) interaction with crystal defects (by pinning). In order to calculate a volume pinning force and critical current it is necessary to know not only elementary pinning forces f from individual defects but also a summation law for these forces. Considerable progress in solving the summation problem has been achieved due to the collective pinning theory (CP)-ref.(l).The key statement of the theory is that weak randomly distributed pinning centers disturb the long-range order in the flux line positions and make the FLL split into correlation regions (CR) with regular vortex lattice inside. The CR dimensions (correlation volume V ) determine the critical current j and pinning C force density F (1): C F
C
Vc '"
R~(~) C
P
=
= ( wlv)
j B 1/2 pee ow -:3/2 1/2 2 1/2 0 " G~6 C44 rp
; R
c-
W
w = n
66
Here R is the transversal correlation size,C66 and C4 : are the shear and tilt modulus of the FLL calculated in detail in ref. (2), W is the characterization of the pin density n and their elementary force f .. So, a direct confirmation of the idea would 'be given by visualization of correlation regions in the FLL in different magnetic fields (i.e. upon changing the FLL elasticity (1,3)). Another interesting aspect of the FLL interaction with weak pins is the character of vortex lattice deformation: in ref.(l) the elastic vortex displacements were considered only while in ref.(4) an important role of screw disloca-
0921-4526/90/$03.50
© 1990 -
tions in the FLL was evidenced by the crossover from 2D- to 3D-collective pinning. Here we present the results of direct observations of the FLL affected by randomly distributed dislocations, in the magnetic fields from 14 to 120 G. 2. SAMPLES AND EXPERIMENTAL TECHNIQUE Samples under investigation were weakly deformed Nb-5%UO single cryst~~s ~2ntaining low density of dislocations - ~10 cm (characteristic separation of dislocations 0,5gm). Vortex lattice patterns were observed using the technique of decorating a superconductor with dispersed ferromagnetic particles (5). A distribution of iron particles on sample's surface, which replicates the vortex distribution, was examined in the scanning electron microscope. The vortex patterns in different magnetic fields Were studied on the same sample (the sample was washed up each time after the decoration and the experiment repeated). 3. EXPERIMENTAL RESULTS AND DISCUSSION Fig.1 and 2 demonstrate typical vortex patterns in the fields 120 and 40 G (bright points are vortices). In both cases the FLL is obviously seen to consist of disoriented domains with regular vortex arrangement inside. One of the domains is displayed in Fig. 1. Assuming that the observed domains are cross sections of the correlation volumes and their average dimension is R ,we found a corresponding F value (see expr~ssions in the INIRODUCTION) :Pfj>r B =~O G the pinning force density is 4.10 dyn/cm. It proved to be in good agreement with F est~mat ed 3 from j (H) measurements:F =(1,0-1,5~.10 dyn/ em and f~om the magnetic d~.duction gradients at the edge 3of the 3 sample: F =l/41!.B. dB/dx= (3,2-4,8).10 dyn/cm (for detail~ see ref.(6)).
Elsevier Science Publishers B.V. (North-Holland)
1180
FIGURE 1 The flux line lattice in the magnetic field 120G. A dotted line shows the boundary of of the domains in the FLL, solid lines show directions of close packed vortex rows their change at the domain boundaries.
I. V. Grigoryeva
B
=
one the and
most, places for vortex row bending (Fig. 1). Parts of the boundaries are formed by edge dislocations in the FLL but their relative length is small. Similar patterns are observed for B = 100 G but vortex row bending and edge dislocations in the FLL are equiprobable. In the field .8=40 G (Fig.2) the CR boundaries become more extended: there observed "vortex liquid" islands sized up to several vortex spacings between the regions of regular FLL as well as aggregations of vacancies in the FLL (one of the latter is marked by arrows in Fig.2). Individual edge dislocations can be also displayed. In the lowest magnetic field used, B = 14 G, the FLL is almost completely destroyed and hexagonal correlations can be found only for the nearest neighbors and not everywhere. Thus, upon decreasing the magnetic field we have observed a sharp decrease of the correlation radius followed by a change of the FLL de-formation from mostly elastic to the plastic one A dependence of the average correlation radius R on the reduced magnetic field b=BIH is shown i~ Fig.3 together with the dependence cgalculated following the collective pinning theory (1) ~./o.
, , ,, I
50
I
I I
1
4D
Ii
3D
20
Il
I
I
FIGURE 3 D.D1
,"
,
I
I
I
I
I
/"" 0.02
0.03
-81 IlOlt fHc,z
(the dashed line). The experimental dependence proved to be slower than the theory predicts. We believe that the discrepancy is related to the fact that the experimentally observed complicated structure of the CR boundaries (dislocations, vortex liquid islands, vacancies in the FLL) had not been taken into account in the CP. REFERENCES
(1)
FIGURE 2 The flux line lattice in the magnetic field B 40G.
=
This confirms directly the idea of CR formation whose dimensions determine the pinning force (critical current) value. On decreasing the magnetic field the FLL becomes less ordered in the whole that is followed by a change of the CR boundary structure. In the field 120 G the CR boundaries are, in the
(2) (3) (4) (5) (6)
A.I.Larkin and Yu.N.Ovchinnikov II J. Low Temp.Phys., 1979. 34, No.3/4. 409 E.H.Brandt II Phys. Stat.Solidi (b), 1976, v.77, 551; J.Low-Temp.Phys. ,1977, v.26, No.5/6,735. E.H.Brandt II J.Low-Temp.Phys., 1986,v.64, No.5/6,375. R.Wondenweber and P.H.Kes II Phys.Rev.B, 1986, v.34,No.1,494 U.Essmann and H.Trauble II Phys.Letters, 1967, A24, 526 I.V.Grigoryeva, L.Ya.Vinnikov II J.Low Temp.Phys., 1989, v.1/2, 89.