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Angular magnetoresistance provides texture information on high-Tc conductors
PhysicaC 195 (1992) North-Holland
PHYSICA B
93-102
Angular magnetoresistance conductors
provides texture information on high-T,
P. Berdahl, X.L. Mao, R.P. Reade, M.D. Rubin, R.E. Russo and E. Yin Lawrence Berkeley Laboratory, Berkeley, CA 94720. USA Received 7 November 199 I Revised manuscript received 3 1 January
1992
Angular magnetoresistance measurements are performed by rotating a superconductor to an angle 13in a fixed magnetic field, while monitoring the resistance R. It is argued theoretically that for fields well above the lower critical field, H> H,,, the bulk resistivity of the conductor is independent of 0 if the crystallites of which it is composed are randomly oriented. Non-random orientation (a key aspect of texture) is revealed, therefore, by variations of R with 0. Dips in R indicate that the lield is parallel to the copper oxide planes in a significant fraction of the current-carrying crystallites. C-axis, a-axis, and other textured film conductors are used to illustrate the technique. The angular magnetoresistance is found to be an important supplement to conventional texture determinations by microscopy and X-ray diffraction.
1. Introduction The high-T, cuprate superconductors are laminar in nature, due to the presence of copper oxide sheets. Normal conductivity and superconductivity are due primarily to charge carriers (holes) which move on these sheets. The free energy of a single crystallite of superconductor is quite anisotropic in the presence of a magnetic field, as is revealed in measurements of the upper critical field Hc2 (19) [ l-3 1. The free energy of the superconducting state is raised most markedly (and the superconducting state, destabilized) when the applied field is perpendicular to the copper oxide layers. For fields parallel to the sheets the free energy is less affected; in fact for artificially isolated layers, fields of a few tesla have little effect [ 4 1. Due to the destabilizing effect of a magnetic field on the superconducting state, then, sufficiently close to the normal state, there is electrical resistance which depends on the angle of an applied magnetic field. Physically, this resistance is due to the motion of quantized flux vortices. It exhibits a minimum when the field becomes parallel to the copper oxide planes. This anisotropic magnetoresistance of individual crystallites permits the extraction of texture information on polycrystalline samples. 0921~4534/92/$05.00
0 1992 Elsevier Science Publishers
A precise quantitative connection between angular magnetoresistance and texture is not presently available. One would need to have an effective medium theory from which to compute the resistance of an aggregate of crystallites based on their orientations in the magnetic field, taking into account the effects of the resistance at grain boundaries, the viscosity of the vortex “fluid”, and the effects of flux pinning at defects. Obviously, such a theory would be complex; transport processes are not yet understood very well even in single crystals and epitaxial films. It is necessary for the present to rely on thermodynamic considerations, such as the dependence of free energy on the field orientation already mentioned, and heuristic considerations. (This approach may be particularly useful for high-current conductors because the desired strong flux pinning is limited by the available superconducting free energy relative to the normal state.) This situation is in contrast with texture determination by X-ray diffraction, for which a quantitative theory is available. Nevertheless, the data we present illustrate that it is a simple matter to extract texture information. For example one can readily determine whether a conductor is “unoriented,” or has a preferred orientation for the Cu02 planes.
B.V. All rights reserved.
94
P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates
The information obtainable from angular magnetoresistance measurements is particularly useful under circumstances in which alternative techniques fail. For example X-ray diffraction may not work well due to a coating on a sample or due to a sample size which is too small. Further, the coincidence of diffraction peaks may render results ambiguous. Each of these limitations may be sometimes mitigated by angular magnetoresistance measurements. Although the point of this paper is that angular magnetoresistance is useful for the determination of conductor texture, the same measurements are useful for the technical characterization of magneticfield-induced losses. The relationship between texture and angular magnetoresistance also suggests that optimization of conductor properties for applications will in general involve manipulation of texture. For example, a tape conductor may have its critical current in a perpendicular field enhanced by the intentional introduction of u-axis grains. Some authors prefer to focus on the critical current density rather than resistivity as a key variable. This information is of course equivalent to resistivity if sufficient information on the current-voltage characteristics is available. We favor the resistivity because ( 1) it simplifies the use of the effective medium theory for composite media, (2) the resistivity is directly related to energy dissipation, and ( 3 ) the critical current density becomes rather ill-defined under conditions, frequently encountered, in which the resistivity does not vanish abruptly at the superconducting transition.
2. Conductors with randomly oriented grains As an idealized special case, we consider conductors composed of randomly oriented grains. Even though each individual crystallite may be quite anisotropic, on the average there is no preferred direction in space. Furthermore, we assume that the applied field freely penetrates the conductor. This conduction requires that Hs H,,. If the superconductor is in an irreversible regime, it is also required that H xwJ,d, where d is the grain or filament size, so that pre-existing circulating current in the con-
ductor are “erased” by the applied field. (Altematively, the field may be applied before cooling below Tc.) Other conditions under which full field penetration of a granular sample may occur that the field exceeds the intergranular H,, and the grain size is smaller than the London penetration depth. In any case, when the field freely penetrates the sample, the local field inside the sample is approximately equal to the applied field. In particular, demagnetizing effects are unimportant. The conductor exhibits magnetoresistance near T, but cannot exhibit angular magnetoresistance due to local isotropy. The local current density introduces a definite direction into the physical problem, and hence the absence of angular magnetoresistance strictly holds only for rotations such that the angle between the current density and applied field is fixed. For example, a cylindrical conductor rotated about its axis should display no angular magnetoresistance. However, in many physical situations it is found that the angle between current and field is quite unimportant; it has in fact been difficult even to demonstrate the sensitivity required by the mechanism of flux creep under the (JX B) Lorentz force. For example, Iye et al. [ 51 have shown that for c-axis thin films of BiZSrZCaCu208+,,, the resistivity depends only on the field direction relative to the c-axis, not on that relative to the transport current. The same situation often prevails for YBa2Cu307 [ 61. The lack of dependence of the resistance on the angle between field and current is a definite advantage for texture determinations because it allows data at all field angles to be analyzed in a similar way. In most angular magnetoresistance measurements R is a single-valued (reversible) function of 8. However, hysteresis is sometimes observed. That is, as the conductor is initially rotated, the resistance changes, as circulating currents are induced in the grains of which the conductor is composed. Hysteresis loops can be obtained by rotating the sample in one direction, and then in the other (see fig. 2(b), below). What happens physically is that the changing magnetic field induces local circulating currents in grains of the sample, currents which interact with the transport currents used to monitor the resistance. This can happen, for example, if the magnetic field induced by the circulating currents modulates the Josephson transport currents tunneling between
P. Berdahl et al. /
Anguhr magnetoresistance ofhigh-TC cup-ales
grains [ 7 1. In practice, resistance hysteresis is most readily observed in heterogeneous (granular) samples at temperatures well below T,. What is ensured by the symmetry of the situation for a conductor without texture is that continued rotation in one direction should eventually lead to a stable resistance, provided that the field is strong enough to penetrate to the interior of the conductor. (Otherwise the conductor can “remember” a preferred orientation due to pre-existing circulating currents [ 7 1. ) Under conditions in which the R versus 13dependence is nonhysteretic (i.e., reversible), symmetry requires that R must be independent of 8. An important effect which depends on conductor shape, and which could introduce angular magnetoresistance even in the absence of bulk texture, is the phenomenon of surface superconductivity [ 8,9]. Even for random orientation of crystal grains, a minimum in resistance can be expected when a smooth conductor surface is aligned nearly parallel to the applied magnetic field, for fields somewhat above the upper critical field H,,. While bulk superconductivity is unstable in these strong fields, a surface layer can remain superconducting, as Saint James and de Gennes showed directly from the Ginzburg-Landau equations [ 8 1. The thickness of the surface layer is on the order of the Ginzburg-Landau coherence length, and is consequently only a few angstroms in the cuprate superconductors, except very near T,. To observe resistance anisotropy due to surface superconductivity in an otherwise isotropic sample, several conditions must be met. (1) The surface must not be covered by a metal. (2) The surface should be sufficiently smooth to permit the surface superconductivity to provide a continuous current path (surfaces orthogonal to the field do not display surface superconductivity. (3) The applied magnetic field should be above the bulk upper critical field, Hc2 < H< 1.7H,*, which occurs only over a narrow temperature range near T,, except for very high magnetic fields. (4) The measuring current must be small compared to the critical current which can be carried through the small cross section near the sample surface. If these conditions are satisfied, and surface superconductivity is present, clearly all current will flow on the surface and no information about bulk texture can be obtained. If surface superconductivity is sus-
95
petted, then measurements over a range of temperatures, fields, and current densities can be used to clarify the situation. However, due to the various conditions which must be satisfied, it appears unlikely that the phenomenon of surface superconductivity will present serious obstacles to the use of angular magnetoresistance to determine texture in a given experiment.
3. Observations of angular magnetoresistance thin-film conductors of YBa#&O,
in
Angular magnetoresistance data from a variety of thin film samples have been examined. Results for Bi2Sr2CaCu208 films on YSZ-buffered alloy substrates have been reported earlier [ lo]. Briefly, the films examined so far show c-axis texture and an R versus 8 pattern similar to that of films deposited on single-crystal substrates. Here, we report on the more varied patterns obtained in YBazCu30, films. The deposition processes employed include both magnetron sputtering and pulsed laser deposition; substrates include the usual single-crystal materials and metal alloys coated with buffer layers. Further details on the processing methods may be found in refs. [ 1I-141. The resistance measurements were performed with the usual four-probe technique, using a 37 Hz AC current. A lock-in amplifier was used to determine the voltage drop. The geometry of the measurement is shown in fig. 1. The angle of the applied magnetic field, 0, is taken as zero when the field is perpendicular to the film. The first example of angular magnetoresistance data has been chosen to illustrate a number of the general features which are observed. Figure 2 displays R versus 6 data for a film which showed a relatively small variation of resistance with field direction, on the order of 10% for the data shown. This film has a broad resistive transition, with measurable resistance well below T, even at low current density; R(300 K)/R( 100 K)=1.2. The maximum resistance ratio as a function of angle (2.7 : 1, data not shown) occurred at 80 K. At 75 K (fig. 2(a) ) the weak maximum at 8= 0 (field orthogonal to the film) and minima at 8= 90” (field parallel to film) is evidence for weak c-axis texture. At the lower temperature of 59 K (fig. 2(b)), the curve has developed
P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates 0012,
Geometry for measurement of voltage drop vs magnetic field direction
/
/
I
T=75K I = 0.5 mA B =0.4 T
: 0.010
cc
, c !
-\
1._._/’
.’
E
0.008
‘“\*, ./*
l\
\
l
.-._A
offset zero 0.006
’ I
I I
/ /
l decreasing 0 increasmg
.0012
/ /
6 B
T = 59.1 K I= 5mA B =0.4 T
Fig. 1. Geometry for the R versus fl measurements for a laminar conductor such as a thin film on a flat substrate. The four point probe is aligned along the direction of the transport current.
a new minimum near &O and has bifurcated into two curves; the measured resistance depends upon the direction of rotation in the field. According to our thesis, the new minimum at 0= 0 is evidence for some u-axis grains (or, more precisely, grains which have the CuOz planes perpendicular to the film), which have enhanced conductivity when the field is perpendicular to the film. The hysteretic behavior is associated with an R versus 6’pattern which becomes asymmetric. This behavior is most readily observed in granular films at lower temperatures, and as noted above, is believed to be due to persistent currents within grains which “remember” the magnetic field history and which interact with the transport current. The X-ray diffraction data for this film (fig. 3 ) shows evidence for both c-axis grains ( (005 ), (007 ) peaks) and a-axis grains ((200) peak). The remaining peaks give evidence for still further orientations. The diffraction data differ from that of a powder diffraction pattern, as is expected for any film grown on a single-crystal substrate; however, the Xray data certainly show that the film has no dominant orientation, in agreement with the angular magnetoresistance measurements. Figure 4 presents angular magnetoresistance data for a high-quality c-axis oriented film fabricated by pulsed laser deposition. The supporting diffraction
i
(b)
offset zero / -90
90
0 0 (degrees)
Fig. 2. Normalized resistance as a plied magnetic field for a granular 75 K and (b) at 59 K. The normal is 2.6 R. Curves are guides for the
function of the angle of an apYBCO film on SrTiOs (a) at state resistance R, (at 100 K) eye.
t (/1
z
F Z / t i10
20
40
30
50
60
70
28cdegrees) Fig. 3. X-ray diffraction
data for the film of fig. 2.
I
P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates
0 800
1=0.5 T=91 B=O.4
mA 6 K T
0.600
c q
0 400
14: 0 200
0 000
.? I.i5
-90
0
-45
45
135
90
(degrees)
t?
Fig. 4. Angular magnetoresistance pattern for a high-quality, highly textured c-axis YBa2Cu307 film, deposited on (100) SrTi03. Resistance minima correspond to a field parallel to the film.
Here A and Care fitted constants, which depend upon temperature and the magnetic field strength, and the ratio ml/m3 is the mass ratio which determines the angular dependence of the upper critical field in the anisotropic Ginzburg-Landau theory. For the tits in figs. 4 and 6, mJm,=49, a parameter with a large uncertainty but which falls in the expected range. The simple phenomenological function of eq. ( 1) often seems to be useful for fitting data from c-axis epitaxial films of various cuprate superconductors. For the more highly two-dimensional materials, such as the bismuth cuprate superconductors, we find that better fits are produced when eq. (2) is replaced by the Tinkham’s implicit formula [ 161 for H,,(e), valid when the Ginzburg-Landau coherence length is small compared to the unit cell dimension in the c-axis direction:
in o x
00)SrTt03
Y&IO/(;
+
t z
Z
m n
P Z _
:
x
1
E
b
10
/
B
-A
4
20
v) 0; 8
E
A\--/ 40
30
50
60
70
i
ZB(degrees) Fig. 5. X-ray diffraction
data for the film of fig. 4.
data (fig. 5) show the expected pattern for a highly textured c-axis film. Electrical parameters for this film were R(300 K)/R( 100 K)=3.2, T,,,,,=90 K. The angular resistance variation is about 10: 1 (increasing with decreasing temperature), and the dips occurring at 90” are distinctly sharper than the broad maximum near 0” (field perpendicular to film). Similar, much more detailed, data for epitaxial films may be found elsewhere [ 15 1. The scatter in the data is caused by temperature drifts of about 0.02 K, due to the sharpness of the resistive transition. The curve through the data is a simple phenomenological fit of the form R=Aexp[
-C&(8)]
97
,
(1)
[kfc2(e) c0s(e)iHc2(90~)12=1 .
(3)
The recent paper by Fastampa et al. [ 17 ] discusses the interesting crossover from eq. (3 ) to eq. (2) in bismuth compound films, which occurs as the temperature approaches T, from below, due to the divergence in the coherence length. Figure 6 shows angular magnetoresistance data for a c-axis film of lower quality (laser deposited, R (300 K)/R( 100 K)= 1.6, T,,,,,=78 K). There is a slight asymmetry in this data; the broad maximum is distorted, indicating the presence of a small amount of hysteresis. Despite the film properties being quite
00001 -135
-90
-45
45 0
90
135
(de0grees)
where Hc2(6)=HcZ(0)[cos2B+
(ml/m3)
sin20]-‘I’.
(2)
Fig. 6. Angular magnetoresistance highly oriented c-axis YBa2Cu307
data for a “low-quality” film on ( 100) SrTiOl.
but
P, Berdahl et al. /Angular magnetoresistance of high-T, cuprates
98
different from the film of fig. 4, the shape of the data is still well fit by eqs. ( 1) and (2). The X-ray diffraction (fig. 7) indicates some minor deviations from the simple (001) pattern of fig. 5. Evidently, the few misoriented grains carry little of the transport current, and therefore have little impact on the angular magnetoresistance measurement. R versus 8 data for a more complex (multilayered) thin-film conductor are shown in fig. 8. This film was deposited by magnetron sputtering on a nickel alloy substrate (Hastelloy X), using a buffer layer of yttria stabilized zirconia. The buffer layer is about 200 nm thick, the superconducting layer about 250 nm. Because the substrate is polycrystalline, the superconducting film is also polycrystalline, but it nevertheless exhibits c-axis texture in the angular magnetoresistance pattern. There is a broad maximum at 19~0, and there are sharper mimima when
the magnetic field is parallel to the film. A few other electrical parameters of this film are J,=7,000 A cm-* at 16 K, 0 T ( 1 uV/cm criterion); R( 300 K)/R( 100 K)= 1.4; TC( 10e3R,)=75 K. The X-ray diffraction data (fig. 9) show the usual series of (001) peaks, confirming the c-axis texture. Angular magnetoresistance data for a sputtered epitaxial u-axis film is shown in fig. 10, for three different temperatures. The corresponding diffraction data appear in fig. 11. This film was patterned into a bridge 0.4 mm wide, which increased its resistance about a factor of ten from the initial unpatterned film. The electrical parameters were J,, roughly 10’ Acm-2 (16K,OT);R(300K)/R(100K)=1.3; I-,,,,,=81 K. The angular dependence of the resistance is completely different from the pattern for c-axis films. The mimimum resistance now occurs when the magnetic
“//
"BCO,':l00)Sr'103
21 I!
T
Epi,~,,//,i,I\,! J
10 10
20
30
40
50
60
70
I
30
Fig. 7. X-ray diffraction data for the film of fig. 6. The shoulder labeled (200) and the peak labeled (1 IO), (013), (103) indicate that a few grains are not c-axis oriented.
I=22mA T=16.4 K
40
50
60
..*A 70
80
28 (degrees)
80
ZO(degrees)
200E-4-
/ 20
Fig. 9. X-ray diffraction data for the film of fig. 8. The peaks labeled S are due to the alloy substrate.
100
/
0 10
;==“;; n
2
-225-180-135 000
:I
:!‘:!E
-225-180-135
I:‘t::ii
-90
-45 0 45 B (degrees)
!“!.:I:
90
135
180
Fig. 8. Angular magnetoresistance data for a c-axis oriented deposited on a buffered metal substrate.
225
film
-90
-45
0
45
90
135
180
225
0 (degrees)
Fig. 10. Angular magnetoresistance data (I= 1 mA, B=0.4 T) for an a-axis oriented film deposited on ( 100) SrTiOs, at three temperatures.
P. Berdahl et al. /Angular magnetoresistance ofhigh-T, cuprates
r tt
YSCO/(i
00)SrT103
4
io
20
40
30
50
60
70
80
_
28(degrees)
Fig. 11. X-ray diffraction
0.015
data for the film of fig. IO.
I=lmA T=40.45 K B=O.4 T R,=4.4 n
YBCO/SrT103/SS
I
0010 L % 0.005
0.000
+
2: !5-180-135
I -90
-45
0
45
90
135
180
225
0 (degrees)
Fig. 12. Angular magnetoresistance for an a-axis oriented deposited on a metal alloy with a buffer layer of SrTiOs.
film
field is perpendicular to the film (8= 0). As before, however, the dip corresponds to the magnetic field being parallel to the copper oxide sheets, which are now normal to the film. At all temperatures shown, there is a strong resistance anisotropy, which increases with decreasing temperature. The presence of a few grains of c-axis oriented material in this film is evident from the small (005 ) diffraction peak in fig. 11. However, the strong (200) peak confirms that the dominant texture is a-axis. An example of u-axis texture in a non-epitaxial film on a coated metal substrate is shown in fig. 12. The resistance anisotropy shows clearly that the CuOz planes are perpendicular to the film. This film was deposited on stainless steel by pulsed laser deposition, using a buffer layer of SrTi03. T,( 10m3R,) = 70 K, and R (300 K) /R ( 100 K) = 1.08. .I, for this film was roughly lo3 A cmV2 at low temperatures, and was reduced by a factor of only 2 in perpendicular fields of 0.4 T. The reduction factor was 2.4 for the parallel
99
field orientation. Although these values for J, are not very high, it is interesting to note that they are not very sensitive to applied magnetic fields, as would be expected if the resistance were dominated by “weak links.” At higher temperatures ( > 40 K) J, was reduced by more than an order of magnitude and exhibited 10: 1anisotropy. J, is of course larger for field perpendicular to the film. X-ray diffraction data (not shown) confirm the u-axis texture by the presence of the (200) peak and the absence of the (005) and (007) peaks. A final, and particularly interesting, angular magnetoresistance plot is shown in fig. 13. There are dips at both 0 and 90 degrees, indicating that there are two preferred orientations for the conductor crystallites. The film and its YSZ buffer layer were deposited on an alloy substrate (Haynes alloy # 230) by pulsed laser deposition [ 141. The film has a T, of 86 K, R(300 K)/R( 100 K)= 1.6. The X-ray diffraction in fig. 14 indicates primarily c-axis orientation; however, a small peak indexed as ( 1 lo), ( 103), (013) occurs as well. The resistance dip at 90” is clearly due to the c-axis grains, but there is no evidence for a-axis grains which might explain the pronounced resistance dip at 0”. However, the ( 110) orientation does have the Cu02 planes oriented normal to the substrate, and can therefore explain the 0” dip. The (103) and (013) orientations can be ruled out because they have Cu02 planes at a 45” angle relative to the substrate. This example shows how angular magnetoresistance can complement X-
0.30 tmA 80. 0.4
K T
0.25
2
rpr75 0.15 -90
0
90
e (degrees)
Fig. 13. Angular magnetoresistance data for a laser deposited film on a buffered metal substrate [ 141. The dip due to c-axis grains at 90” is much less pronounced than the dip at 0”.
100
P. Berdahl et al. /Angular magnetoresistance ofhigh-T, cuprates
b
rpr75
Fig. 14. X-ray diffraction data for the film of fig. 13. The (001) series shows c-axis texture, the 0” dip shown in fig. 13. No (200) peak is present.
ray diffraction, in this case identifying which of the three orientations is present in the film. Also of interest is that a small quantity of misoriented grains has a dramatic effect on the R versus 8 pattern.
4. Discussion The data we have presented shows that basic texture information can be obtained by angular magnetoresistance measurements; the information on the orientation of CuOz planes consistently agrees with X-ray diffraction and can be used to complement this information. In all cases which have been examined here, a dip in the R versus 0 curve indicates that the magnetic field is parallel to the Cu02 planes in a significant fraction of the crystallites in the conductor. The presence of a dip can have other origins. For example, a sharp dip is seen in some measurements on single crystals of YBa2Cu30,, for rotations in which the field is maintained parallel to the CuOz planes, due to flux pinning on twin boundaries [ 18 1. The data are quite unambiguous because untwinned single crystals show no such dips. Twin boundary dips may be regarded as being due to a particular type of conductor texture. They are very narrow in angular width, as the pinning is most effective when the flux line is accurately parallel to the twin boundary. Another type of resistivity dip has been demonstrated
but the
( 110) orientation
is responsible
for
recently by Iye et al. [ 191. An unusual non-monotonic R versus 6’dependence is seen, which is of unknown origin but occurs only at higher current densities ( lo’-lo6 A cm-*). This phenomenon can be avoided in angular magnetoresistance measurements by making measurements at lower current densities (below lo4 A cm-‘). A recent paper by Christen et al. (201 showed R versus 8 data for YBCO films grown on strontium titanate substrates cut at small angles with respect to the (00 1) lattice planes. The films grew epitaxially on the substrate, with the (00 1) axis of the film parallel to the (00 1) axis of the substrate. The characteristic resistance minima were observed when the field was misaligned from the film by the precise angles by which the substrates were misaligned (2.5”) 6” ), thus demonstrating that the dip occurs when the field is parallel to the Cu02 planes. Roas et al. [ 2 1] show data for (primarily) c-axis oriented films which exhibit J, peaks when the field is both parallel and perpendicular to the film. Of course, peaks in J, correspond to dips in R. The “extra” peak appeared to depend “on microstructural features of the samples, as defect concentration, twinboundary distance, etc.” Iye et al. [ 191 also show analogous minor resistance dips for a field parallel to the film in c-axis oriented films, dips which are ascribed to flux pinning on twin boundaries. Likewise, measurements by Ekin et al. [ 22 ] on the crit-
P. Berdahl et al. /Angular magnetoresistance oshigh-T, cuprates
ical current of oriented-grained bulk YBazCu30, material show secondary peaks in J, when the magnetic field is at right angles to the direction of highest J,. Selvamanickam et al. [ 23 ] have presented some evidence that twin boundaries may cause the “extra” J, peak. However, the experimental case is not very conclusive; it is primarily theoretical expectations which are used to argue for twin boundary pinning. From the present perspective, it is natural to interpret these “extra” minima in the R versus 13patterns as being due to a few crystal grains which have CuOz planes which lie perpendicular to the predominant orientation. In the case of c-axis films, this behavior is most likely due to a small number of a-axis grains which may be present. Such grains have been observed with high resolution electron microscopy of films [24]. To further develop the thesis that the extra resistance dip seen in some magnetoresistance measurements is due to a few misoriented grains, it is of interest to estimate the volume fraction of misoriented grains using effective medium theory [ 25 1. For the sake of a simple rough estimate, we may assume that there are a few superconducting inclusions (the 90” misoriented grains) in a resistive matrix. Then the change in resistance due to the inclusions is given by: ZiR/R= -C/X,
(4)
where C is the volume fraction of inclusions and X is a geometrical factor of order unity, equal to ) for spheres. X is less than f if the inclusions are elongated in the direction of current flow. The data of Iye et al. [ 191 show a maximum value of 6R/R of roughly 10%. Thus eq. (4) shows that in this case a volume fraction of 3% misoriented material would be sufficient to explain the electrical measurements. This example illustrates the point that a small quantity of misoriented material can be quite evident in R versus 13measurements.
5. Conclusions The idea that resistivity dips occur when a magnetic field is aligned parallel to the copper oxide planes in cuprate superconductors is quite useful for providing texture information. While there are exceptions to this rule, it is nevertheless quite useful
101
for characterizing complex conductor structures. One obtains information specific to the part of the conductor through which the current flows, which should be helpful in the study of heterogeneous materials. The angular magnetoresistance technique is at present a qualitative technique. However, as experience is gained by measurements on conductors of various types, and as the effective medium theory is developed for at least simple textures, we anticipate that it will assume a more quantitative stature in the future.
Acknowledgements We acknowledge the technical assistance of J. McMillan, M. Nichols and A. Mesa. This work was supported by the Assistant Secretary for Conservation and Renewable Energy, Office of Energy Management, Division of Advanced Utility Concepts of the U.S. Department of Energy, under Contract No. DE-AC03-76SF00098.
References [ 1] W.J. Gallagher, T.K. Worthington,
T.R. Diner, F. Holtzberg, D.L. Kaiser and R.L. Sanstrom, Physica 148 B (1987) 228. [2] Y. Iye, T. Tamegai, H. Takeya and H. Takei, Jpn. J. Appl. Phys. 26 (1987) L1850. [ 31 T.T.M. Palstra, B. Batlogg, L.F. Schneemeyer, R.B. van Dover and J.V. Waszczak, Phys. Rev. 38 ( 1988). [4] J.M. Triscone, 0. Fisher, 0. Brunner, L. Antognazza, A.D. Kent and M.G. Karkut, Phys. Rev. Lett. 64 ( 1990) 804. [ 5 ] Y. Iye, S. Nakamura and T. Tamegai, Physica C 159 ( 1989) 433. [6] For example, see Y. Iye, T. Tamegai, H. Takeya and H. Takei, Jpn. J. Appl. Phys. 26 (1987) L1057. [ 71 J.E. Evetts and B.A. Glowacki, Cryogenics 28 (1988) 641. [8] D. Saint-James and P.G. de Gennes, Phys. Lett. 7 (1963) 306. [ 91 M. Tit&ham, Introduction to Superconductivity (Kreiger, Malabar, FL, 1980) p. 130. [lo] X.L. Mao, P. Berdahl, R.E. Russo, H.B. Liu and J.C. Ho, PhysicaC 183 (1991) 167. [ 111 M. Rubin, LG. Brown, E. Yin and D. Wruck, J. Appl. Phys. 66 (1989) 3940. [ 12 ] M. Balooch, D.R. Olander and R.E. Russo, Appl. Phys. Lett. 55 (1989) 197. [ 13 ] R.E. Russo, R.P. Reade, J.M. McMillan and B.L. Olsen, J. Appl. Phys. 68 ( 1990) 1354.
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P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates
[ 141 R.P. Reade, X.L. Maoand R.E. Russo, Appl. Phys. Lett. 59 (1991) 739. [ 15 ] Y. Iye, S. Nakamura, T. Tamegai, T. Terashima, K. Yamamoto and Y. Bando, Physica C 166 ( 1990) 62. [ 161 M. Tinkham, Phys. Rev. 129 (1963) 2413; F.E. Harper and M. Tinkham, Phys. Rev. 172 ( 1968). Note that in these references the definition of 6 is different from that used here. [ 171 R. Fastampa, M. Giura, R. Marcon and E. Silva, Phys. Rev. Lett. 67 (1991) 1795. [ 181 W.K. Kwok, U. Welp, S. Fleshier, K.G. Vandervoort, H. Claus, Y. Fang, G.W. Crabtree and J.Z. Liu, in: Superconductivity and Its Applications, AIP Conf. Proc. 2 19, eds. Y. Kao, P. Coppens and H. Kwok ( 199 1) 111. [ 191 Y. Iye, T. Terashima and Y. Bando, Physica C 177 ( 1991) 393. [ 201 D.K. Christen, C.E. Klabunde, R. Feenstra, D.H. Lowndes, D.P. Norton, J.D. Budai, H.R. Kerchner, J.R. Thompson, S. Zhu and A.D. Marwick, in: Superconductivity and Its
Applications, AIP Conf. Proc. 2 19, eds. Y. Kao, P. Coppens and H. Kwok (1991) 336. [ 211 B. Roas, L. Schultz and G. Saemann-Ischenko, Phys. Rev. Lett. 64 (1990) 479. [22] J.W. Ekin, K. Salama and V. Selvamanickam, Appl. Phys. Lett. 59 ( 1991) 360. [23] V. Selvamanickam, K. Forster and K. Salama, Physica C 178 (1991) 147. [ 241 R. Ramesh, C.C. Chang, T.S. Ravi, D.M. Hwang, A. Inam, X.X. Xi, Q. Li, X.D. Wu and T. Venkatesan, Appl. Phys. Lett. 57 (1990) 1064; C.C. Chang, X.D. Wu, X.X. Xi, T.S. Ravi, T. Venkatesan, D.M. Hwang, R.E. Muenchausen, S. Foltyn and N.S. Nogar, Appl. Phys. Lett. 57 (1990) 1814; R. Ramesh, A. Inam, D.M. Hwang, T.D. Sands, C.C. Chang andD.L. Hart, Appl. Phys. Lett. 58 (1991) 1557. [25] A. Davidson and M. Tinkham, Phys. Rev. B 13 ( 1976) 3261.
PHYSICA B
93-102
Angular magnetoresistance conductors
provides texture information on high-T,
P. Berdahl, X.L. Mao, R.P. Reade, M.D. Rubin, R.E. Russo and E. Yin Lawrence Berkeley Laboratory, Berkeley, CA 94720. USA Received 7 November 199 I Revised manuscript received 3 1 January
1992
Angular magnetoresistance measurements are performed by rotating a superconductor to an angle 13in a fixed magnetic field, while monitoring the resistance R. It is argued theoretically that for fields well above the lower critical field, H> H,,, the bulk resistivity of the conductor is independent of 0 if the crystallites of which it is composed are randomly oriented. Non-random orientation (a key aspect of texture) is revealed, therefore, by variations of R with 0. Dips in R indicate that the lield is parallel to the copper oxide planes in a significant fraction of the current-carrying crystallites. C-axis, a-axis, and other textured film conductors are used to illustrate the technique. The angular magnetoresistance is found to be an important supplement to conventional texture determinations by microscopy and X-ray diffraction.
1. Introduction The high-T, cuprate superconductors are laminar in nature, due to the presence of copper oxide sheets. Normal conductivity and superconductivity are due primarily to charge carriers (holes) which move on these sheets. The free energy of a single crystallite of superconductor is quite anisotropic in the presence of a magnetic field, as is revealed in measurements of the upper critical field Hc2 (19) [ l-3 1. The free energy of the superconducting state is raised most markedly (and the superconducting state, destabilized) when the applied field is perpendicular to the copper oxide layers. For fields parallel to the sheets the free energy is less affected; in fact for artificially isolated layers, fields of a few tesla have little effect [ 4 1. Due to the destabilizing effect of a magnetic field on the superconducting state, then, sufficiently close to the normal state, there is electrical resistance which depends on the angle of an applied magnetic field. Physically, this resistance is due to the motion of quantized flux vortices. It exhibits a minimum when the field becomes parallel to the copper oxide planes. This anisotropic magnetoresistance of individual crystallites permits the extraction of texture information on polycrystalline samples. 0921~4534/92/$05.00
0 1992 Elsevier Science Publishers
A precise quantitative connection between angular magnetoresistance and texture is not presently available. One would need to have an effective medium theory from which to compute the resistance of an aggregate of crystallites based on their orientations in the magnetic field, taking into account the effects of the resistance at grain boundaries, the viscosity of the vortex “fluid”, and the effects of flux pinning at defects. Obviously, such a theory would be complex; transport processes are not yet understood very well even in single crystals and epitaxial films. It is necessary for the present to rely on thermodynamic considerations, such as the dependence of free energy on the field orientation already mentioned, and heuristic considerations. (This approach may be particularly useful for high-current conductors because the desired strong flux pinning is limited by the available superconducting free energy relative to the normal state.) This situation is in contrast with texture determination by X-ray diffraction, for which a quantitative theory is available. Nevertheless, the data we present illustrate that it is a simple matter to extract texture information. For example one can readily determine whether a conductor is “unoriented,” or has a preferred orientation for the Cu02 planes.
B.V. All rights reserved.
94
P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates
The information obtainable from angular magnetoresistance measurements is particularly useful under circumstances in which alternative techniques fail. For example X-ray diffraction may not work well due to a coating on a sample or due to a sample size which is too small. Further, the coincidence of diffraction peaks may render results ambiguous. Each of these limitations may be sometimes mitigated by angular magnetoresistance measurements. Although the point of this paper is that angular magnetoresistance is useful for the determination of conductor texture, the same measurements are useful for the technical characterization of magneticfield-induced losses. The relationship between texture and angular magnetoresistance also suggests that optimization of conductor properties for applications will in general involve manipulation of texture. For example, a tape conductor may have its critical current in a perpendicular field enhanced by the intentional introduction of u-axis grains. Some authors prefer to focus on the critical current density rather than resistivity as a key variable. This information is of course equivalent to resistivity if sufficient information on the current-voltage characteristics is available. We favor the resistivity because ( 1) it simplifies the use of the effective medium theory for composite media, (2) the resistivity is directly related to energy dissipation, and ( 3 ) the critical current density becomes rather ill-defined under conditions, frequently encountered, in which the resistivity does not vanish abruptly at the superconducting transition.
2. Conductors with randomly oriented grains As an idealized special case, we consider conductors composed of randomly oriented grains. Even though each individual crystallite may be quite anisotropic, on the average there is no preferred direction in space. Furthermore, we assume that the applied field freely penetrates the conductor. This conduction requires that Hs H,,. If the superconductor is in an irreversible regime, it is also required that H xwJ,d, where d is the grain or filament size, so that pre-existing circulating current in the con-
ductor are “erased” by the applied field. (Altematively, the field may be applied before cooling below Tc.) Other conditions under which full field penetration of a granular sample may occur that the field exceeds the intergranular H,, and the grain size is smaller than the London penetration depth. In any case, when the field freely penetrates the sample, the local field inside the sample is approximately equal to the applied field. In particular, demagnetizing effects are unimportant. The conductor exhibits magnetoresistance near T, but cannot exhibit angular magnetoresistance due to local isotropy. The local current density introduces a definite direction into the physical problem, and hence the absence of angular magnetoresistance strictly holds only for rotations such that the angle between the current density and applied field is fixed. For example, a cylindrical conductor rotated about its axis should display no angular magnetoresistance. However, in many physical situations it is found that the angle between current and field is quite unimportant; it has in fact been difficult even to demonstrate the sensitivity required by the mechanism of flux creep under the (JX B) Lorentz force. For example, Iye et al. [ 51 have shown that for c-axis thin films of BiZSrZCaCu208+,,, the resistivity depends only on the field direction relative to the c-axis, not on that relative to the transport current. The same situation often prevails for YBa2Cu307 [ 61. The lack of dependence of the resistance on the angle between field and current is a definite advantage for texture determinations because it allows data at all field angles to be analyzed in a similar way. In most angular magnetoresistance measurements R is a single-valued (reversible) function of 8. However, hysteresis is sometimes observed. That is, as the conductor is initially rotated, the resistance changes, as circulating currents are induced in the grains of which the conductor is composed. Hysteresis loops can be obtained by rotating the sample in one direction, and then in the other (see fig. 2(b), below). What happens physically is that the changing magnetic field induces local circulating currents in grains of the sample, currents which interact with the transport currents used to monitor the resistance. This can happen, for example, if the magnetic field induced by the circulating currents modulates the Josephson transport currents tunneling between
P. Berdahl et al. /
Anguhr magnetoresistance ofhigh-TC cup-ales
grains [ 7 1. In practice, resistance hysteresis is most readily observed in heterogeneous (granular) samples at temperatures well below T,. What is ensured by the symmetry of the situation for a conductor without texture is that continued rotation in one direction should eventually lead to a stable resistance, provided that the field is strong enough to penetrate to the interior of the conductor. (Otherwise the conductor can “remember” a preferred orientation due to pre-existing circulating currents [ 7 1. ) Under conditions in which the R versus 13dependence is nonhysteretic (i.e., reversible), symmetry requires that R must be independent of 8. An important effect which depends on conductor shape, and which could introduce angular magnetoresistance even in the absence of bulk texture, is the phenomenon of surface superconductivity [ 8,9]. Even for random orientation of crystal grains, a minimum in resistance can be expected when a smooth conductor surface is aligned nearly parallel to the applied magnetic field, for fields somewhat above the upper critical field H,,. While bulk superconductivity is unstable in these strong fields, a surface layer can remain superconducting, as Saint James and de Gennes showed directly from the Ginzburg-Landau equations [ 8 1. The thickness of the surface layer is on the order of the Ginzburg-Landau coherence length, and is consequently only a few angstroms in the cuprate superconductors, except very near T,. To observe resistance anisotropy due to surface superconductivity in an otherwise isotropic sample, several conditions must be met. (1) The surface must not be covered by a metal. (2) The surface should be sufficiently smooth to permit the surface superconductivity to provide a continuous current path (surfaces orthogonal to the field do not display surface superconductivity. (3) The applied magnetic field should be above the bulk upper critical field, Hc2 < H< 1.7H,*, which occurs only over a narrow temperature range near T,, except for very high magnetic fields. (4) The measuring current must be small compared to the critical current which can be carried through the small cross section near the sample surface. If these conditions are satisfied, and surface superconductivity is present, clearly all current will flow on the surface and no information about bulk texture can be obtained. If surface superconductivity is sus-
95
petted, then measurements over a range of temperatures, fields, and current densities can be used to clarify the situation. However, due to the various conditions which must be satisfied, it appears unlikely that the phenomenon of surface superconductivity will present serious obstacles to the use of angular magnetoresistance to determine texture in a given experiment.
3. Observations of angular magnetoresistance thin-film conductors of YBa#&O,
in
Angular magnetoresistance data from a variety of thin film samples have been examined. Results for Bi2Sr2CaCu208 films on YSZ-buffered alloy substrates have been reported earlier [ lo]. Briefly, the films examined so far show c-axis texture and an R versus 8 pattern similar to that of films deposited on single-crystal substrates. Here, we report on the more varied patterns obtained in YBazCu30, films. The deposition processes employed include both magnetron sputtering and pulsed laser deposition; substrates include the usual single-crystal materials and metal alloys coated with buffer layers. Further details on the processing methods may be found in refs. [ 1I-141. The resistance measurements were performed with the usual four-probe technique, using a 37 Hz AC current. A lock-in amplifier was used to determine the voltage drop. The geometry of the measurement is shown in fig. 1. The angle of the applied magnetic field, 0, is taken as zero when the field is perpendicular to the film. The first example of angular magnetoresistance data has been chosen to illustrate a number of the general features which are observed. Figure 2 displays R versus 6 data for a film which showed a relatively small variation of resistance with field direction, on the order of 10% for the data shown. This film has a broad resistive transition, with measurable resistance well below T, even at low current density; R(300 K)/R( 100 K)=1.2. The maximum resistance ratio as a function of angle (2.7 : 1, data not shown) occurred at 80 K. At 75 K (fig. 2(a) ) the weak maximum at 8= 0 (field orthogonal to the film) and minima at 8= 90” (field parallel to film) is evidence for weak c-axis texture. At the lower temperature of 59 K (fig. 2(b)), the curve has developed
P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates 0012,
Geometry for measurement of voltage drop vs magnetic field direction
/
/
I
T=75K I = 0.5 mA B =0.4 T
: 0.010
cc
, c !
-\
1._._/’
.’
E
0.008
‘“\*, ./*
l\
\
l
.-._A
offset zero 0.006
’ I
I I
/ /
l decreasing 0 increasmg
.0012
/ /
6 B
T = 59.1 K I= 5mA B =0.4 T
Fig. 1. Geometry for the R versus fl measurements for a laminar conductor such as a thin film on a flat substrate. The four point probe is aligned along the direction of the transport current.
a new minimum near &O and has bifurcated into two curves; the measured resistance depends upon the direction of rotation in the field. According to our thesis, the new minimum at 0= 0 is evidence for some u-axis grains (or, more precisely, grains which have the CuOz planes perpendicular to the film), which have enhanced conductivity when the field is perpendicular to the film. The hysteretic behavior is associated with an R versus 6’pattern which becomes asymmetric. This behavior is most readily observed in granular films at lower temperatures, and as noted above, is believed to be due to persistent currents within grains which “remember” the magnetic field history and which interact with the transport current. The X-ray diffraction data for this film (fig. 3 ) shows evidence for both c-axis grains ( (005 ), (007 ) peaks) and a-axis grains ((200) peak). The remaining peaks give evidence for still further orientations. The diffraction data differ from that of a powder diffraction pattern, as is expected for any film grown on a single-crystal substrate; however, the Xray data certainly show that the film has no dominant orientation, in agreement with the angular magnetoresistance measurements. Figure 4 presents angular magnetoresistance data for a high-quality c-axis oriented film fabricated by pulsed laser deposition. The supporting diffraction
i
(b)
offset zero / -90
90
0 0 (degrees)
Fig. 2. Normalized resistance as a plied magnetic field for a granular 75 K and (b) at 59 K. The normal is 2.6 R. Curves are guides for the
function of the angle of an apYBCO film on SrTiOs (a) at state resistance R, (at 100 K) eye.
t (/1
z
F Z / t i10
20
40
30
50
60
70
28cdegrees) Fig. 3. X-ray diffraction
data for the film of fig. 2.
I
P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates
0 800
1=0.5 T=91 B=O.4
mA 6 K T
0.600
c q
0 400
14: 0 200
0 000
.? I.i5
-90
0
-45
45
135
90
(degrees)
t?
Fig. 4. Angular magnetoresistance pattern for a high-quality, highly textured c-axis YBa2Cu307 film, deposited on (100) SrTi03. Resistance minima correspond to a field parallel to the film.
Here A and Care fitted constants, which depend upon temperature and the magnetic field strength, and the ratio ml/m3 is the mass ratio which determines the angular dependence of the upper critical field in the anisotropic Ginzburg-Landau theory. For the tits in figs. 4 and 6, mJm,=49, a parameter with a large uncertainty but which falls in the expected range. The simple phenomenological function of eq. ( 1) often seems to be useful for fitting data from c-axis epitaxial films of various cuprate superconductors. For the more highly two-dimensional materials, such as the bismuth cuprate superconductors, we find that better fits are produced when eq. (2) is replaced by the Tinkham’s implicit formula [ 161 for H,,(e), valid when the Ginzburg-Landau coherence length is small compared to the unit cell dimension in the c-axis direction:
in o x
00)SrTt03
Y&IO/(;
+
t z
Z
m n
P Z _
:
x
1
E
b
10
/
B
-A
4
20
v) 0; 8
E
A\--/ 40
30
50
60
70
i
ZB(degrees) Fig. 5. X-ray diffraction
data for the film of fig. 4.
data (fig. 5) show the expected pattern for a highly textured c-axis film. Electrical parameters for this film were R(300 K)/R( 100 K)=3.2, T,,,,,=90 K. The angular resistance variation is about 10: 1 (increasing with decreasing temperature), and the dips occurring at 90” are distinctly sharper than the broad maximum near 0” (field perpendicular to film). Similar, much more detailed, data for epitaxial films may be found elsewhere [ 15 1. The scatter in the data is caused by temperature drifts of about 0.02 K, due to the sharpness of the resistive transition. The curve through the data is a simple phenomenological fit of the form R=Aexp[
-C&(8)]
97
,
(1)
[kfc2(e) c0s(e)iHc2(90~)12=1 .
(3)
The recent paper by Fastampa et al. [ 17 ] discusses the interesting crossover from eq. (3 ) to eq. (2) in bismuth compound films, which occurs as the temperature approaches T, from below, due to the divergence in the coherence length. Figure 6 shows angular magnetoresistance data for a c-axis film of lower quality (laser deposited, R (300 K)/R( 100 K)= 1.6, T,,,,,=78 K). There is a slight asymmetry in this data; the broad maximum is distorted, indicating the presence of a small amount of hysteresis. Despite the film properties being quite
00001 -135
-90
-45
45 0
90
135
(de0grees)
where Hc2(6)=HcZ(0)[cos2B+
(ml/m3)
sin20]-‘I’.
(2)
Fig. 6. Angular magnetoresistance highly oriented c-axis YBa2Cu307
data for a “low-quality” film on ( 100) SrTiOl.
but
P, Berdahl et al. /Angular magnetoresistance of high-T, cuprates
98
different from the film of fig. 4, the shape of the data is still well fit by eqs. ( 1) and (2). The X-ray diffraction (fig. 7) indicates some minor deviations from the simple (001) pattern of fig. 5. Evidently, the few misoriented grains carry little of the transport current, and therefore have little impact on the angular magnetoresistance measurement. R versus 8 data for a more complex (multilayered) thin-film conductor are shown in fig. 8. This film was deposited by magnetron sputtering on a nickel alloy substrate (Hastelloy X), using a buffer layer of yttria stabilized zirconia. The buffer layer is about 200 nm thick, the superconducting layer about 250 nm. Because the substrate is polycrystalline, the superconducting film is also polycrystalline, but it nevertheless exhibits c-axis texture in the angular magnetoresistance pattern. There is a broad maximum at 19~0, and there are sharper mimima when
the magnetic field is parallel to the film. A few other electrical parameters of this film are J,=7,000 A cm-* at 16 K, 0 T ( 1 uV/cm criterion); R( 300 K)/R( 100 K)= 1.4; TC( 10e3R,)=75 K. The X-ray diffraction data (fig. 9) show the usual series of (001) peaks, confirming the c-axis texture. Angular magnetoresistance data for a sputtered epitaxial u-axis film is shown in fig. 10, for three different temperatures. The corresponding diffraction data appear in fig. 11. This film was patterned into a bridge 0.4 mm wide, which increased its resistance about a factor of ten from the initial unpatterned film. The electrical parameters were J,, roughly 10’ Acm-2 (16K,OT);R(300K)/R(100K)=1.3; I-,,,,,=81 K. The angular dependence of the resistance is completely different from the pattern for c-axis films. The mimimum resistance now occurs when the magnetic
“//
"BCO,':l00)Sr'103
21 I!
T
Epi,~,,//,i,I\,! J
10 10
20
30
40
50
60
70
I
30
Fig. 7. X-ray diffraction data for the film of fig. 6. The shoulder labeled (200) and the peak labeled (1 IO), (013), (103) indicate that a few grains are not c-axis oriented.
I=22mA T=16.4 K
40
50
60
..*A 70
80
28 (degrees)
80
ZO(degrees)
200E-4-
/ 20
Fig. 9. X-ray diffraction data for the film of fig. 8. The peaks labeled S are due to the alloy substrate.
100
/
0 10
;==“;; n
2
-225-180-135 000
:I
:!‘:!E
-225-180-135
I:‘t::ii
-90
-45 0 45 B (degrees)
!“!.:I:
90
135
180
Fig. 8. Angular magnetoresistance data for a c-axis oriented deposited on a buffered metal substrate.
225
film
-90
-45
0
45
90
135
180
225
0 (degrees)
Fig. 10. Angular magnetoresistance data (I= 1 mA, B=0.4 T) for an a-axis oriented film deposited on ( 100) SrTiOs, at three temperatures.
P. Berdahl et al. /Angular magnetoresistance ofhigh-T, cuprates
r tt
YSCO/(i
00)SrT103
4
io
20
40
30
50
60
70
80
_
28(degrees)
Fig. 11. X-ray diffraction
0.015
data for the film of fig. IO.
I=lmA T=40.45 K B=O.4 T R,=4.4 n
YBCO/SrT103/SS
I
0010 L % 0.005
0.000
+
2: !5-180-135
I -90
-45
0
45
90
135
180
225
0 (degrees)
Fig. 12. Angular magnetoresistance for an a-axis oriented deposited on a metal alloy with a buffer layer of SrTiOs.
film
field is perpendicular to the film (8= 0). As before, however, the dip corresponds to the magnetic field being parallel to the copper oxide sheets, which are now normal to the film. At all temperatures shown, there is a strong resistance anisotropy, which increases with decreasing temperature. The presence of a few grains of c-axis oriented material in this film is evident from the small (005 ) diffraction peak in fig. 11. However, the strong (200) peak confirms that the dominant texture is a-axis. An example of u-axis texture in a non-epitaxial film on a coated metal substrate is shown in fig. 12. The resistance anisotropy shows clearly that the CuOz planes are perpendicular to the film. This film was deposited on stainless steel by pulsed laser deposition, using a buffer layer of SrTi03. T,( 10m3R,) = 70 K, and R (300 K) /R ( 100 K) = 1.08. .I, for this film was roughly lo3 A cmV2 at low temperatures, and was reduced by a factor of only 2 in perpendicular fields of 0.4 T. The reduction factor was 2.4 for the parallel
99
field orientation. Although these values for J, are not very high, it is interesting to note that they are not very sensitive to applied magnetic fields, as would be expected if the resistance were dominated by “weak links.” At higher temperatures ( > 40 K) J, was reduced by more than an order of magnitude and exhibited 10: 1anisotropy. J, is of course larger for field perpendicular to the film. X-ray diffraction data (not shown) confirm the u-axis texture by the presence of the (200) peak and the absence of the (005) and (007) peaks. A final, and particularly interesting, angular magnetoresistance plot is shown in fig. 13. There are dips at both 0 and 90 degrees, indicating that there are two preferred orientations for the conductor crystallites. The film and its YSZ buffer layer were deposited on an alloy substrate (Haynes alloy # 230) by pulsed laser deposition [ 141. The film has a T, of 86 K, R(300 K)/R( 100 K)= 1.6. The X-ray diffraction in fig. 14 indicates primarily c-axis orientation; however, a small peak indexed as ( 1 lo), ( 103), (013) occurs as well. The resistance dip at 90” is clearly due to the c-axis grains, but there is no evidence for a-axis grains which might explain the pronounced resistance dip at 0”. However, the ( 110) orientation does have the Cu02 planes oriented normal to the substrate, and can therefore explain the 0” dip. The (103) and (013) orientations can be ruled out because they have Cu02 planes at a 45” angle relative to the substrate. This example shows how angular magnetoresistance can complement X-
0.30 tmA 80. 0.4
K T
0.25
2
rpr75 0.15 -90
0
90
e (degrees)
Fig. 13. Angular magnetoresistance data for a laser deposited film on a buffered metal substrate [ 141. The dip due to c-axis grains at 90” is much less pronounced than the dip at 0”.
100
P. Berdahl et al. /Angular magnetoresistance ofhigh-T, cuprates
b
rpr75
Fig. 14. X-ray diffraction data for the film of fig. 13. The (001) series shows c-axis texture, the 0” dip shown in fig. 13. No (200) peak is present.
ray diffraction, in this case identifying which of the three orientations is present in the film. Also of interest is that a small quantity of misoriented grains has a dramatic effect on the R versus 8 pattern.
4. Discussion The data we have presented shows that basic texture information can be obtained by angular magnetoresistance measurements; the information on the orientation of CuOz planes consistently agrees with X-ray diffraction and can be used to complement this information. In all cases which have been examined here, a dip in the R versus 0 curve indicates that the magnetic field is parallel to the Cu02 planes in a significant fraction of the crystallites in the conductor. The presence of a dip can have other origins. For example, a sharp dip is seen in some measurements on single crystals of YBa2Cu30,, for rotations in which the field is maintained parallel to the CuOz planes, due to flux pinning on twin boundaries [ 18 1. The data are quite unambiguous because untwinned single crystals show no such dips. Twin boundary dips may be regarded as being due to a particular type of conductor texture. They are very narrow in angular width, as the pinning is most effective when the flux line is accurately parallel to the twin boundary. Another type of resistivity dip has been demonstrated
but the
( 110) orientation
is responsible
for
recently by Iye et al. [ 191. An unusual non-monotonic R versus 6’dependence is seen, which is of unknown origin but occurs only at higher current densities ( lo’-lo6 A cm-*). This phenomenon can be avoided in angular magnetoresistance measurements by making measurements at lower current densities (below lo4 A cm-‘). A recent paper by Christen et al. (201 showed R versus 8 data for YBCO films grown on strontium titanate substrates cut at small angles with respect to the (00 1) lattice planes. The films grew epitaxially on the substrate, with the (00 1) axis of the film parallel to the (00 1) axis of the substrate. The characteristic resistance minima were observed when the field was misaligned from the film by the precise angles by which the substrates were misaligned (2.5”) 6” ), thus demonstrating that the dip occurs when the field is parallel to the Cu02 planes. Roas et al. [ 2 1] show data for (primarily) c-axis oriented films which exhibit J, peaks when the field is both parallel and perpendicular to the film. Of course, peaks in J, correspond to dips in R. The “extra” peak appeared to depend “on microstructural features of the samples, as defect concentration, twinboundary distance, etc.” Iye et al. [ 191 also show analogous minor resistance dips for a field parallel to the film in c-axis oriented films, dips which are ascribed to flux pinning on twin boundaries. Likewise, measurements by Ekin et al. [ 22 ] on the crit-
P. Berdahl et al. /Angular magnetoresistance oshigh-T, cuprates
ical current of oriented-grained bulk YBazCu30, material show secondary peaks in J, when the magnetic field is at right angles to the direction of highest J,. Selvamanickam et al. [ 23 ] have presented some evidence that twin boundaries may cause the “extra” J, peak. However, the experimental case is not very conclusive; it is primarily theoretical expectations which are used to argue for twin boundary pinning. From the present perspective, it is natural to interpret these “extra” minima in the R versus 13patterns as being due to a few crystal grains which have CuOz planes which lie perpendicular to the predominant orientation. In the case of c-axis films, this behavior is most likely due to a small number of a-axis grains which may be present. Such grains have been observed with high resolution electron microscopy of films [24]. To further develop the thesis that the extra resistance dip seen in some magnetoresistance measurements is due to a few misoriented grains, it is of interest to estimate the volume fraction of misoriented grains using effective medium theory [ 25 1. For the sake of a simple rough estimate, we may assume that there are a few superconducting inclusions (the 90” misoriented grains) in a resistive matrix. Then the change in resistance due to the inclusions is given by: ZiR/R= -C/X,
(4)
where C is the volume fraction of inclusions and X is a geometrical factor of order unity, equal to ) for spheres. X is less than f if the inclusions are elongated in the direction of current flow. The data of Iye et al. [ 191 show a maximum value of 6R/R of roughly 10%. Thus eq. (4) shows that in this case a volume fraction of 3% misoriented material would be sufficient to explain the electrical measurements. This example illustrates the point that a small quantity of misoriented material can be quite evident in R versus 13measurements.
5. Conclusions The idea that resistivity dips occur when a magnetic field is aligned parallel to the copper oxide planes in cuprate superconductors is quite useful for providing texture information. While there are exceptions to this rule, it is nevertheless quite useful
101
for characterizing complex conductor structures. One obtains information specific to the part of the conductor through which the current flows, which should be helpful in the study of heterogeneous materials. The angular magnetoresistance technique is at present a qualitative technique. However, as experience is gained by measurements on conductors of various types, and as the effective medium theory is developed for at least simple textures, we anticipate that it will assume a more quantitative stature in the future.
Acknowledgements We acknowledge the technical assistance of J. McMillan, M. Nichols and A. Mesa. This work was supported by the Assistant Secretary for Conservation and Renewable Energy, Office of Energy Management, Division of Advanced Utility Concepts of the U.S. Department of Energy, under Contract No. DE-AC03-76SF00098.
References [ 1] W.J. Gallagher, T.K. Worthington,
T.R. Diner, F. Holtzberg, D.L. Kaiser and R.L. Sanstrom, Physica 148 B (1987) 228. [2] Y. Iye, T. Tamegai, H. Takeya and H. Takei, Jpn. J. Appl. Phys. 26 (1987) L1850. [ 31 T.T.M. Palstra, B. Batlogg, L.F. Schneemeyer, R.B. van Dover and J.V. Waszczak, Phys. Rev. 38 ( 1988). [4] J.M. Triscone, 0. Fisher, 0. Brunner, L. Antognazza, A.D. Kent and M.G. Karkut, Phys. Rev. Lett. 64 ( 1990) 804. [ 5 ] Y. Iye, S. Nakamura and T. Tamegai, Physica C 159 ( 1989) 433. [6] For example, see Y. Iye, T. Tamegai, H. Takeya and H. Takei, Jpn. J. Appl. Phys. 26 (1987) L1057. [ 71 J.E. Evetts and B.A. Glowacki, Cryogenics 28 (1988) 641. [8] D. Saint-James and P.G. de Gennes, Phys. Lett. 7 (1963) 306. [ 91 M. Tit&ham, Introduction to Superconductivity (Kreiger, Malabar, FL, 1980) p. 130. [lo] X.L. Mao, P. Berdahl, R.E. Russo, H.B. Liu and J.C. Ho, PhysicaC 183 (1991) 167. [ 111 M. Rubin, LG. Brown, E. Yin and D. Wruck, J. Appl. Phys. 66 (1989) 3940. [ 12 ] M. Balooch, D.R. Olander and R.E. Russo, Appl. Phys. Lett. 55 (1989) 197. [ 13 ] R.E. Russo, R.P. Reade, J.M. McMillan and B.L. Olsen, J. Appl. Phys. 68 ( 1990) 1354.
102
P. Berdahl et al. /Angular magnetoresistance of high-T, cuprates
[ 141 R.P. Reade, X.L. Maoand R.E. Russo, Appl. Phys. Lett. 59 (1991) 739. [ 15 ] Y. Iye, S. Nakamura, T. Tamegai, T. Terashima, K. Yamamoto and Y. Bando, Physica C 166 ( 1990) 62. [ 161 M. Tinkham, Phys. Rev. 129 (1963) 2413; F.E. Harper and M. Tinkham, Phys. Rev. 172 ( 1968). Note that in these references the definition of 6 is different from that used here. [ 171 R. Fastampa, M. Giura, R. Marcon and E. Silva, Phys. Rev. Lett. 67 (1991) 1795. [ 181 W.K. Kwok, U. Welp, S. Fleshier, K.G. Vandervoort, H. Claus, Y. Fang, G.W. Crabtree and J.Z. Liu, in: Superconductivity and Its Applications, AIP Conf. Proc. 2 19, eds. Y. Kao, P. Coppens and H. Kwok ( 199 1) 111. [ 191 Y. Iye, T. Terashima and Y. Bando, Physica C 177 ( 1991) 393. [ 201 D.K. Christen, C.E. Klabunde, R. Feenstra, D.H. Lowndes, D.P. Norton, J.D. Budai, H.R. Kerchner, J.R. Thompson, S. Zhu and A.D. Marwick, in: Superconductivity and Its
Applications, AIP Conf. Proc. 2 19, eds. Y. Kao, P. Coppens and H. Kwok (1991) 336. [ 211 B. Roas, L. Schultz and G. Saemann-Ischenko, Phys. Rev. Lett. 64 (1990) 479. [22] J.W. Ekin, K. Salama and V. Selvamanickam, Appl. Phys. Lett. 59 ( 1991) 360. [23] V. Selvamanickam, K. Forster and K. Salama, Physica C 178 (1991) 147. [ 241 R. Ramesh, C.C. Chang, T.S. Ravi, D.M. Hwang, A. Inam, X.X. Xi, Q. Li, X.D. Wu and T. Venkatesan, Appl. Phys. Lett. 57 (1990) 1064; C.C. Chang, X.D. Wu, X.X. Xi, T.S. Ravi, T. Venkatesan, D.M. Hwang, R.E. Muenchausen, S. Foltyn and N.S. Nogar, Appl. Phys. Lett. 57 (1990) 1814; R. Ramesh, A. Inam, D.M. Hwang, T.D. Sands, C.C. Chang andD.L. Hart, Appl. Phys. Lett. 58 (1991) 1557. [25] A. Davidson and M. Tinkham, Phys. Rev. B 13 ( 1976) 3261.