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Parallel and perpendicular magnetization on YBaCuO single crystals in the irreversible regime
Physica C 160 (1989) 185-188 North-Holland, Amsterdam
PARALLEL AND P E R P E N D I C U L A R MAGNETIZATION ON YBaCuO SINGLE CRYSTALS IN T H E IRREVERSIBLE R E G I M E
L. FRUCHTER, C. AGUILLON, S. SENOUSSI and I.A. CAMPBELL Laboratoire de Physique des Solides, 91405 Orsay C~dex, France
Received 12 May 1989
The magneticbehaviour of YBaCuOoriented crystalsis studied in the irreversible regimeusingcombined results of torque and magnetometry. Strongtransverse magnetization componentsare observed;the data show that the irreversible magnetization is essentially parallel to the c direction whateverthe field orientation except for anglesvery closeto the ab plane.
The anisotropic magnetic properties of the high Tc layered compounds have been studied recently in the reversible regime using torque measurements. It was shown in ref. [ 1 ] that for temperatures close to the transition temperature and for fields sufficiently large, irreversibility in both the magnitude and the orientation of the magnetization could be neglected. Moreover, the torque properties of YBaCuO could be described by standard phenomenological laws for uniaxial superconductors, with an effective mass ratio y2~25 to 35 between the directions perpendicular and parallel to the CuO planes. More recently, some aspects of the irreversible regime were investigated using the same technique [ 2] and magnetization measurements [3]. As well as the expected pinning effects, additional anisotropy was found and ascribed to anisotropic Bean mechanisms. Here, we present data in this regime, using both standard magnetization and torque techniques. This allows us to determine the orientation as well as the magnitude of the magnetization in the sample. The sample studied here was the same as that used in a previous publication [2 ]. It consists of a diluted dispersion (~0.5%) of approximately 10 IxM YBaCuO single crystal grains in epoxy resin. A 9 T magnetic field was used to orient the powder at room temperature, so that the c-axis in each crystal points toward the same reference direction of the sample to better than one degree. Torque signals using rotating fields lower than the first critical fields Hc~ indicate an average grain dimension along the ab planes about
twice greater than that along the c-axis. In the rest of the work to be reported here, demagnetizing factors are neglected, as high fields were used so magnetization magnitudes were always small compared to B or H. All the experiments were done at 4.2 K. We first registered torque curves using the following procedure. The field direction was set at a fixed angle 0 with respect to the c-axis (see fig. 1 for conventions used in the rest of the text). Then the field was increased from 0 to 3 T and back down to zero. This was done repeatedly for fixed 0 until the torque signal, as a function of the applied field, no longer evolved with further cycling (this could in fact be achieved by the second run). For all values of 0, except exactly for 0 ° and 90 °, the sign of the torque for increasing field is such that B is inclined towards the ab plane with respect to H. The torque signal obtained for decreasing fields was generally very different from the one for increasing fields. The raw resuits of fig. 2 show that there are two distinct regimes as a function of 0: for 0 less than about 80 ° (i.e. for
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
'C
A.B I-
Fig. 1. Notations used for the angles in the text.
L. Fruchter et al. / Magnetic behaviour of YBaCuO oriented crystals
186
and H as the applied field all in c.g.s, units. We obtain, using the notations of fig. 1:
2 _
/
t
t
/
f
-
OL.~----~-~ . . . . . .
f10
~
~
----'~301H
(kG)
~86"
Fig. 2. Torque energy for field swept up and back to zero along different directions 0.
most directions except those close to the ab plane) the torque signal changes sign when the field is swept down towards zero, which means that the major part of the transverse magnetization is irreversible as in the parallel magnetization described below. For a small range of directions near the ab plane, the torque signal is close to reversible, so the transverse magnetization does not change sign as the field is swept down. The transverse magnetization is still very strong at 86 ° and only drops sharply for angles still closer to ab (remaining essentially reversible). In independent experiments magnetization curves were obtained using a vibrating sample magnetometer (VSM). The field was applied for the same set of specified 0 directions and reversed at the same maximum 3 T field. The first magnetization cycle (sample cooled in zero field) and the second magnetization cycle (following a complete field cycle) were equivalent for fields greater than about 0.1 T. We restricted our analysis to fields greater than this value. These experiments give the component of the magnetization parallel to the applied field, while the torque gives the component perpendicular to the field. We then derived from the torque and the magnetization curves the information on the magnitude and orientation of the magnetization and induction vectors during the field cycle. We denote 3~t and/~ as the measured algebraic values of the magnetization parallel to the field and the torque per unit volume, M and B as the magnetization and induction moduli,
tan ~o= F / ( H h ~ t ) ,
(1)
M = - ~ t / c o s ~0,
(2)
B = [ H 2 + ( 4 n M ) 2 + 8nH37I] 1/2,
(3)
sin fl= - 4 m r / ( H B ) .
(4)
We first focus our attention on the components of the magnetization along the crystallographic directions (Me and Mab) for fields applied along two directions 0, one relatively close to the c-axis and the other close to the ab plane (fig. 3). The magnetization measured by the VSM is related to these components as M = M c c o s O+Mab sin 0. For fields along the c-axis the application of Bean's model to the VSM data gives critical currents of the order 3 × 105 A / c m 2, and about one order less in the 0= 90 ° direction, once the anisotropy of the grain dimensions has been taken into account. We also notice that the curves are fairly symmetric upon reversal of the field sweep, indicating a predominant irreversible component. The consideration of the projections of the total magnetization onto the crystallographic axes show up the different components of the magnetization
Mc
_ f
>
E o
e :30 °
E
i 10 30 H (kG)
Fig. 3. Components of the magnetization along the crystallographic direction c and ab (Me and Mab, respectively) for field applied close to the c-axis ( 0 = 3 0 ° ) or close to the planes (0=86°).
L. Fruchter et al. / Magnetic behaviour of YBaCuO oriented crystals
taking into account the information from the torque. For 0= 30 °, Mab is weaker than M~ and the measured parallel magnetization is almost equivalent to the total magnetization or to the Mc component. For 0= 86 °, close to the ab plane, the error in positioning the sample in the VSM is no longer negligible and the incertitude o n Mab increases strongly. We nevertheless can estimate that Mab contributes to the total magnetization for less than ten percent. Mc, which is more easily obtained due to a better determination of the sample position for the torque technique, is strong and almost reversible. From the crystallographic components of the magnetization such as those plotted in fig. 3, we can derive the angle ~obetween the magnetization and the field as a function of H for given 0 (fig. 4). We first considered fields swept upwards. In a general way, ¢ decreases with increasing fields down to an asymptotic value q%o;the set of values {0oo(0) have been plotted in fig. 5. We can compare with the orientation calculated for the reversible regime. The dependence of ~0on angle 0 at fields well above the first critical fields for a uniaxial superconductor at the thermodynamic equilibrium is given by [3]: ~Orev= t a n - ' [ ½~'2sin 20/(sin 20+ 72 cos2 0) ].
(5)
The comparison between ~0rev and the asymptotic
210 170 130
9-8O 6O 40 2O
-
I 101 H
, 20[ (kG)
1 3om
Fig. 4. Angle between the magnetization and the applied field for various directions of the swept field.
_80
187
•
z m
0 0
201
401 601 80 I e (,:leg.)
Fig. 5. Angle between the magnetization and the c-axis as a function of the cycling direction for H = 3 T. Curve calculated from the reversible theory.
value {0oois displayed in fig. 5 and shows that the irreversible magnetization differs notably from the calculated reversible behaviour. Two regimes are nevertheless observed. For most 0 smaller than 80 °, the magnetization lies closer to the applied field than the calculated value for the reversible regime. Keeping in mind that M<< H and M<< B for the field considered here, simple geometric arguments show that a small rotation of the induction toward the c-axis with respect to its equilibrium position can account for this. For fields applied close to the planes, the situation is reversed and the induction lies closer to the ab plane than in the reversible case. In the second part of the cycle, when the field is reduced, qualitatively different behaviour is observed for fields close to the ab direction (0> 80 ° ) and for field orientations further from the ab direction ( 0 < 8 0 ° ) (fig. 4). In the former case, ~ remain less than 180 °. This can be expressed by saying that for the whole cycle, B remains between H and the ab plane. Alternatively, the c component of M (which is much stronger than the ab component for this range of 0) shows mainly reversible behaviour and does not change sign during the field cycle (fig. 3). For fields at angle 0 further from the ab plane, (p becomes larger than 180 ° when the field is reduced. This indicates that the induction crosses the field direction toward the c-axis. This is also shown by the raw results of fig. 2 where the torque signal changes sign upon reversal of the field sweep for 0 smaller than about 80 ° . The discrepancy between the observed magneti-
188
L. Fruchter et al. /Magnetic behaviour of YBaCuO oriented crystals
zation behaviour at 4.2 K and the reversible theory describing the thermodynamic equilibrium is not unexpected [ 3 ] because of the irreversibility shielding current effects. The Bean critical model relates the magnetization to the critical current for fields cycled along a symmetry direction; when the field is cycled along a nonsymmetry direction, the Bean magnetization will not be along the field because of the anisotropy of the critical currents. It is well established that the critical current in the ab plane is much stronger than the effective critical current for the directions perpendicular to the plane [ 4 ]. We can as a first approximation consider that screening currents run in the ab plane only whatever the direction of the field. Then, if we have for H along the c direction a hysteresis curve Mc=M(H), we may expect for H at angle 0 a similar curve M c = M ( H cos 0). At all angles except very close to the ab plane the magnetization along c will on this assumption dominate the magnetization along ab, which agrees with what we observe. Starting from H = 0 , the curve M ( H ) along the caxis has an initial semi-reversible branch for low fields and then links onto the strongly irreversible hysteresis loop. The field at which the two curves join is about H* ~ 0.24 T in our sample. For cycling to fields H at angles 0 such that the product H cos 0 is never greater than H*, Mc(H cos 0) will follow the semi-reversible branch. We expect then that the Mc curves at angle 0 will remain semi-reversible when cycled up to high fields if 0 is near 90 °. This is in agreement with the curve of fig. 3 for 0= 86 °. In reality the assumption that screening currents are entirely in the ab plane is too extreme, as to account fully for the data we need a small but nonzero
M~a component. In fig. 5, if Mab was zero the experimental points would lie along the diagonal ~0= 0. The data suggest that rather unexpectedly the deviations from the diagonal are strongest for intermediate values of 0, so that for 0~45 ° the M a b ( H ) is stronger than for 0= 86 °, i.e. when H is almost along the ab plane. As a conclusion, let us summarize the principal results that arise from our data. We have investigated the parallel and the transverse components of the magnetization for a system of oriented YBaCuO grains in the irreversible regime at 4.2 K. A magnetic field is applied at a direction 0 with respect to the axis and is cycled up to 3 T and back. Except when the field lies along a symmetry direction (c-axis or the ab plane), the magnetization has always a strong transverse component with respect to the applied field. For 0 near to but not exactly along the ab direction, the transverse magnetization can be ten times stronger than the parallel magnetization. In the second half of the cycle when the field is swept down again, both parallel and perpendicular components of M change sign except for a small range of 0 close to 90 °. The results suggest that the screening currents flow essentially in the ab plane whatever the direction of the field. References [ 1 ] D.E. Farrell, C.M. Williams, S.A. Wolf, N.P. Bansal and V.G. Kogan, Phys. Rev. Lett. 61 (1988) 2805. [ 2 ] L. Fruchter and I.A. Campbell, to be published. [ 3 ] S. Senoussi and C. Aguillon, to be published. [4] V.G. Kogan, M.M. Fang and S. Mitra, Phys. Rev. B 38 ( 1988 ) 11958. [ 5 ] S. Senoussi, M. Oussrna, G. Collin and I.A. Campbell, Phys. Rev. B 37 (1988) 9792.
PARALLEL AND P E R P E N D I C U L A R MAGNETIZATION ON YBaCuO SINGLE CRYSTALS IN T H E IRREVERSIBLE R E G I M E
L. FRUCHTER, C. AGUILLON, S. SENOUSSI and I.A. CAMPBELL Laboratoire de Physique des Solides, 91405 Orsay C~dex, France
Received 12 May 1989
The magneticbehaviour of YBaCuOoriented crystalsis studied in the irreversible regimeusingcombined results of torque and magnetometry. Strongtransverse magnetization componentsare observed;the data show that the irreversible magnetization is essentially parallel to the c direction whateverthe field orientation except for anglesvery closeto the ab plane.
The anisotropic magnetic properties of the high Tc layered compounds have been studied recently in the reversible regime using torque measurements. It was shown in ref. [ 1 ] that for temperatures close to the transition temperature and for fields sufficiently large, irreversibility in both the magnitude and the orientation of the magnetization could be neglected. Moreover, the torque properties of YBaCuO could be described by standard phenomenological laws for uniaxial superconductors, with an effective mass ratio y2~25 to 35 between the directions perpendicular and parallel to the CuO planes. More recently, some aspects of the irreversible regime were investigated using the same technique [ 2] and magnetization measurements [3]. As well as the expected pinning effects, additional anisotropy was found and ascribed to anisotropic Bean mechanisms. Here, we present data in this regime, using both standard magnetization and torque techniques. This allows us to determine the orientation as well as the magnitude of the magnetization in the sample. The sample studied here was the same as that used in a previous publication [2 ]. It consists of a diluted dispersion (~0.5%) of approximately 10 IxM YBaCuO single crystal grains in epoxy resin. A 9 T magnetic field was used to orient the powder at room temperature, so that the c-axis in each crystal points toward the same reference direction of the sample to better than one degree. Torque signals using rotating fields lower than the first critical fields Hc~ indicate an average grain dimension along the ab planes about
twice greater than that along the c-axis. In the rest of the work to be reported here, demagnetizing factors are neglected, as high fields were used so magnetization magnitudes were always small compared to B or H. All the experiments were done at 4.2 K. We first registered torque curves using the following procedure. The field direction was set at a fixed angle 0 with respect to the c-axis (see fig. 1 for conventions used in the rest of the text). Then the field was increased from 0 to 3 T and back down to zero. This was done repeatedly for fixed 0 until the torque signal, as a function of the applied field, no longer evolved with further cycling (this could in fact be achieved by the second run). For all values of 0, except exactly for 0 ° and 90 °, the sign of the torque for increasing field is such that B is inclined towards the ab plane with respect to H. The torque signal obtained for decreasing fields was generally very different from the one for increasing fields. The raw resuits of fig. 2 show that there are two distinct regimes as a function of 0: for 0 less than about 80 ° (i.e. for
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
'C
A.B I-
Fig. 1. Notations used for the angles in the text.
L. Fruchter et al. / Magnetic behaviour of YBaCuO oriented crystals
186
and H as the applied field all in c.g.s, units. We obtain, using the notations of fig. 1:
2 _
/
t
t
/
f
-
OL.~----~-~ . . . . . .
f10
~
~
----'~301H
(kG)
~86"
Fig. 2. Torque energy for field swept up and back to zero along different directions 0.
most directions except those close to the ab plane) the torque signal changes sign when the field is swept down towards zero, which means that the major part of the transverse magnetization is irreversible as in the parallel magnetization described below. For a small range of directions near the ab plane, the torque signal is close to reversible, so the transverse magnetization does not change sign as the field is swept down. The transverse magnetization is still very strong at 86 ° and only drops sharply for angles still closer to ab (remaining essentially reversible). In independent experiments magnetization curves were obtained using a vibrating sample magnetometer (VSM). The field was applied for the same set of specified 0 directions and reversed at the same maximum 3 T field. The first magnetization cycle (sample cooled in zero field) and the second magnetization cycle (following a complete field cycle) were equivalent for fields greater than about 0.1 T. We restricted our analysis to fields greater than this value. These experiments give the component of the magnetization parallel to the applied field, while the torque gives the component perpendicular to the field. We then derived from the torque and the magnetization curves the information on the magnitude and orientation of the magnetization and induction vectors during the field cycle. We denote 3~t and/~ as the measured algebraic values of the magnetization parallel to the field and the torque per unit volume, M and B as the magnetization and induction moduli,
tan ~o= F / ( H h ~ t ) ,
(1)
M = - ~ t / c o s ~0,
(2)
B = [ H 2 + ( 4 n M ) 2 + 8nH37I] 1/2,
(3)
sin fl= - 4 m r / ( H B ) .
(4)
We first focus our attention on the components of the magnetization along the crystallographic directions (Me and Mab) for fields applied along two directions 0, one relatively close to the c-axis and the other close to the ab plane (fig. 3). The magnetization measured by the VSM is related to these components as M = M c c o s O+Mab sin 0. For fields along the c-axis the application of Bean's model to the VSM data gives critical currents of the order 3 × 105 A / c m 2, and about one order less in the 0= 90 ° direction, once the anisotropy of the grain dimensions has been taken into account. We also notice that the curves are fairly symmetric upon reversal of the field sweep, indicating a predominant irreversible component. The consideration of the projections of the total magnetization onto the crystallographic axes show up the different components of the magnetization
Mc
_ f
>
E o
e :30 °
E
i 10 30 H (kG)
Fig. 3. Components of the magnetization along the crystallographic direction c and ab (Me and Mab, respectively) for field applied close to the c-axis ( 0 = 3 0 ° ) or close to the planes (0=86°).
L. Fruchter et al. / Magnetic behaviour of YBaCuO oriented crystals
taking into account the information from the torque. For 0= 30 °, Mab is weaker than M~ and the measured parallel magnetization is almost equivalent to the total magnetization or to the Mc component. For 0= 86 °, close to the ab plane, the error in positioning the sample in the VSM is no longer negligible and the incertitude o n Mab increases strongly. We nevertheless can estimate that Mab contributes to the total magnetization for less than ten percent. Mc, which is more easily obtained due to a better determination of the sample position for the torque technique, is strong and almost reversible. From the crystallographic components of the magnetization such as those plotted in fig. 3, we can derive the angle ~obetween the magnetization and the field as a function of H for given 0 (fig. 4). We first considered fields swept upwards. In a general way, ¢ decreases with increasing fields down to an asymptotic value q%o;the set of values {0oo(0) have been plotted in fig. 5. We can compare with the orientation calculated for the reversible regime. The dependence of ~0on angle 0 at fields well above the first critical fields for a uniaxial superconductor at the thermodynamic equilibrium is given by [3]: ~Orev= t a n - ' [ ½~'2sin 20/(sin 20+ 72 cos2 0) ].
(5)
The comparison between ~0rev and the asymptotic
210 170 130
9-8O 6O 40 2O
-
I 101 H
, 20[ (kG)
1 3om
Fig. 4. Angle between the magnetization and the applied field for various directions of the swept field.
_80
187
•
z m
0 0
201
401 601 80 I e (,:leg.)
Fig. 5. Angle between the magnetization and the c-axis as a function of the cycling direction for H = 3 T. Curve calculated from the reversible theory.
value {0oois displayed in fig. 5 and shows that the irreversible magnetization differs notably from the calculated reversible behaviour. Two regimes are nevertheless observed. For most 0 smaller than 80 °, the magnetization lies closer to the applied field than the calculated value for the reversible regime. Keeping in mind that M<< H and M<< B for the field considered here, simple geometric arguments show that a small rotation of the induction toward the c-axis with respect to its equilibrium position can account for this. For fields applied close to the planes, the situation is reversed and the induction lies closer to the ab plane than in the reversible case. In the second part of the cycle, when the field is reduced, qualitatively different behaviour is observed for fields close to the ab direction (0> 80 ° ) and for field orientations further from the ab direction ( 0 < 8 0 ° ) (fig. 4). In the former case, ~ remain less than 180 °. This can be expressed by saying that for the whole cycle, B remains between H and the ab plane. Alternatively, the c component of M (which is much stronger than the ab component for this range of 0) shows mainly reversible behaviour and does not change sign during the field cycle (fig. 3). For fields at angle 0 further from the ab plane, (p becomes larger than 180 ° when the field is reduced. This indicates that the induction crosses the field direction toward the c-axis. This is also shown by the raw results of fig. 2 where the torque signal changes sign upon reversal of the field sweep for 0 smaller than about 80 ° . The discrepancy between the observed magneti-
188
L. Fruchter et al. /Magnetic behaviour of YBaCuO oriented crystals
zation behaviour at 4.2 K and the reversible theory describing the thermodynamic equilibrium is not unexpected [ 3 ] because of the irreversibility shielding current effects. The Bean critical model relates the magnetization to the critical current for fields cycled along a symmetry direction; when the field is cycled along a nonsymmetry direction, the Bean magnetization will not be along the field because of the anisotropy of the critical currents. It is well established that the critical current in the ab plane is much stronger than the effective critical current for the directions perpendicular to the plane [ 4 ]. We can as a first approximation consider that screening currents run in the ab plane only whatever the direction of the field. Then, if we have for H along the c direction a hysteresis curve Mc=M(H), we may expect for H at angle 0 a similar curve M c = M ( H cos 0). At all angles except very close to the ab plane the magnetization along c will on this assumption dominate the magnetization along ab, which agrees with what we observe. Starting from H = 0 , the curve M ( H ) along the caxis has an initial semi-reversible branch for low fields and then links onto the strongly irreversible hysteresis loop. The field at which the two curves join is about H* ~ 0.24 T in our sample. For cycling to fields H at angles 0 such that the product H cos 0 is never greater than H*, Mc(H cos 0) will follow the semi-reversible branch. We expect then that the Mc curves at angle 0 will remain semi-reversible when cycled up to high fields if 0 is near 90 °. This is in agreement with the curve of fig. 3 for 0= 86 °. In reality the assumption that screening currents are entirely in the ab plane is too extreme, as to account fully for the data we need a small but nonzero
M~a component. In fig. 5, if Mab was zero the experimental points would lie along the diagonal ~0= 0. The data suggest that rather unexpectedly the deviations from the diagonal are strongest for intermediate values of 0, so that for 0~45 ° the M a b ( H ) is stronger than for 0= 86 °, i.e. when H is almost along the ab plane. As a conclusion, let us summarize the principal results that arise from our data. We have investigated the parallel and the transverse components of the magnetization for a system of oriented YBaCuO grains in the irreversible regime at 4.2 K. A magnetic field is applied at a direction 0 with respect to the axis and is cycled up to 3 T and back. Except when the field lies along a symmetry direction (c-axis or the ab plane), the magnetization has always a strong transverse component with respect to the applied field. For 0 near to but not exactly along the ab direction, the transverse magnetization can be ten times stronger than the parallel magnetization. In the second half of the cycle when the field is swept down again, both parallel and perpendicular components of M change sign except for a small range of 0 close to 90 °. The results suggest that the screening currents flow essentially in the ab plane whatever the direction of the field. References [ 1 ] D.E. Farrell, C.M. Williams, S.A. Wolf, N.P. Bansal and V.G. Kogan, Phys. Rev. Lett. 61 (1988) 2805. [ 2 ] L. Fruchter and I.A. Campbell, to be published. [ 3 ] S. Senoussi and C. Aguillon, to be published. [4] V.G. Kogan, M.M. Fang and S. Mitra, Phys. Rev. B 38 ( 1988 ) 11958. [ 5 ] S. Senoussi, M. Oussrna, G. Collin and I.A. Campbell, Phys. Rev. B 37 (1988) 9792.