Anisotropic vortex flux behavior in grain-oriented YBa2Cu3O7

Journal of Alloys and Compounds 375 (2004) 34–38

Anisotropic vortex flux behavior in grain-oriented YBa2 Cu3O7 M.K. Hasan Qaseer Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan Received 18 August 2003; received in revised form 14 November 2003; accepted 20 November 2003

Abstract Magnetization vector measurements M from field cooled (FC) and zero field cooled (ZFC) states were performed on a grain-oriented YBa2 Cu3 O7 rotated in fixed magnetic field H initially applied along the c-axis at 4.2 K. Our results show that for the low field regime (H = 0.5 kOe), the vortex flux density B stays close to the ab-plane over a wide range of the rotational angle θ, and associated with a frictional behavior of B relative to the sample rotation in this range of θ. Also, B increases very slowly in this range of θ which means that the initial vortices along the c-axis are strongly pinned inhibiting the creation of more vortices along the ab-plane. For the high field regime, B increases with θ up to 70◦ and then decreases above this angle. The orientation θ B of B relative to H shows two peaks at H = 3 kOe and another peak for H > 4 kOe. These peaks shift toward 90◦ as H is increased. Moreover, as θ exceeds 70◦ in the range of 70◦ < θ < 110◦ , new types of vortices are formed and B is aligned close to the ab-plane. The torque density τ experienced by the vortices increases almost linearly with θ for the different fields up to 70◦ , and as θ exceeds 70◦ it changes to a higher slope before reversing its sign abruptly around 90◦ . This behavior of τ confirms the formation of new type of vortices for 70◦ < θ < 110◦ . © 2003 Elsevier B.V. All rights reserved. PACS: 74.72.Bk; 74.25.Ha; 74.25.Qt Keywords: Rare earth compounds; Superconductors; Magnetic measurements; Anisotropy

1. Introduction The crystallographic asymmetry of the layered superconductors is manifested in strong anisotropies of their physical properties. These include various anisotropic magnetic properties of the mixed state. Most studies of intrinsic anisotropy properties were restricted to directions along the principal crystallographic axes whether along the c-axis or along the ab-plane, or at a specified direction with respect to these orientations. The full angular dependence remains not fully probed. Most of the studies were done by measuring the component of magnetization along the field direction [1]. The manufacturing of long tapes of layered superconductors make the angular dependence of critical currents very important. Such tapes are fabricated by inclined substrate deposition. The critical currents show strong angular dependence in the mixed state [2–4]. This results from the effect of crystal anisotropy on the magnetic properties of the mixed state [5–9]. Also, there is an interest in the anisotropy

E-mail address: [email protected] (M.K. Hasan Qaseer). 0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.11.048

enhanced by the defects produced by the ion-irradiation [10,11]. The angular studies of such experiments give a detailed description of the vortex pinning anisotropy [11,12]. Moreover, the full angular study is used as a powerful technique to distinguish between the crystal anisotropy and the extended defects produced by irradiation [12]. On the other hand, the magnetic torque measurements which depend on the angular variations are also used as a direct method of investigating the anisotropy of vortex pinning and the dimensional cross-over of the vortices with their associated phases [13–15]. In fact, the net torque is produced by the existence of non-zero average of the vortices with respect to the magnetic field. Therefore, the angular dependence technique is a very powerful tool of investigating the vortex behavior. In this work, we will study the effect of the crystal anisotropy on the vortex flux pinning using the angular variations of the magnetization vector M with the applied magnetic field H. The sample under investigation is grain-oriented YBa2 Cu3 O7 of Tc ∼ 92 K. The sample has a specified collective c-axis while the other two axes are randomly oriented. The rotational method we apply here

M.K. Hasan Qaseer / Journal of Alloys and Compounds 375 (2004) 34–38

allow the vortices to cross through the superconductor layers. What is also significance in this work is that the magnetic state is well specified by measuring the vector magnetization. This will allow us to calculate the pinning torque per vortex which is the fundamental quantity rather than the total torque exerted on the sample.

θ

ab-plane

θB

MT

Fig. 1. Schematic vector diagram showing the M L and M T relative to H. The c-axis, the ab-plane, and the angle of rotation (θ).

gives the following relations: Hc = H cos(θ) − Dc M c and Hab = H sin(θ) − Dab M ab , M c = M L cos(θ) − M T sin(θ), M ab = M L sin(θ) + M T cos(θ). Starting with the FC-state for an applied field H = 0.5 kOe, we plot in Fig. 2a the calculated vortex flux density B as function of the rotational angle θ. The figure shows that B increases fast for small values of θ up to 30◦ then it increases more slowly for 30◦ < θ < 70◦ . As θ exceeds 70◦ , B increasing fast and goes through a maximum around 120◦ before it starts to decrease as θ becomes greater than 120◦ . The slow increase of B for 30◦ < θ < 70◦ means that the initial vortices are strongly pinned along the c-axis inhibiting the magnetic field from the subsequent production of vortices along the ab-plane. This is a vortex-cross 2.5 H =0.5 kOe H // c FC - state

B(kG)

2 1.5 1 0.5 0

0

30

60

90

120

150

180

θ (deg.)

(a)

150 120

Β

Our grain-oriented YBCO sample was a circular disk of 5 mm diameter and 1mm thickness where small crystallites of YBa2 Cu3 O7 in an epoxy matrix are field oriented such that their c-axes are co-aligned while the other two axes are randomly oriented [16]. The c-axis lies in the disk plane at which the magnetic field was initially applied. The magnetization measurements were done using a vibrating-sample magnetometer (VSM) where the two components of the magnetization vector M can be measured simultaneously during the rotational process. The two components of M are M L , the longitudinal component which is parallel to the applied field H, and M T , the transverse component perpendicular to H. For low field measurement, the field cooled state (FC) is established by applying the magnetic field H parallel to c-axis and then lowering the temperature of the sample from above Tc to 4.2 K. For the high field case, the zero field cooled (ZFC) measurements were done by lowering the temperature of the sample to 4.2 K. Then the magnetic field is raised from zero to H along the c-axis before rotating the sample. After establishing the magnetic state the sample is rotated from 0 to 180◦ . The two components (M L and M T ) of magnetization vector M are measured simultaneously as function of θ. The θ = 0◦ reference angle corresponds to the direction of the c-axis before rotating the sample. The data are corrected to take into account the demagnetization effects. These corrections will not obscure the main results of our work. The demagnetization factors measured from the initial slopes of M versus H hysteresis loop along c-axis and along ab-plane were found to be Dc = 5.86 along the c-axis and Dab = 3.36 along the ab-plane, where we assumed the crystallites have identical spheriodal shapes. We are interested here in the response of the vortices to the magnetic field during the rotational process while these vortices cross the superconducting CuO2 layers. Initially the vortices are directed along the c-axis and they are perpendicular to the CuO2 layers. To calculate the vortex flux density B we use B=H i +4πM, where Hi is the internal field. We decompose the magnetic flux B into two orthogonal components, Bc the vortex flux density along the c-axis and Bab the vortex flux density along the ab-plane (or B = Bc + Bab ). The two components of B can be calculated using the following expressions: Bc = Hc + 4πM c and Bab = Hab + 4πM ab , where Hc and Hab are the internal fields along the c-axis and the ab-plane respectively, and M c and M ab are the components of M along these directions. The vector diagram of Fig. 1

H ,M L B

c-axis

θ (deg.)

2. Results and discussion

35

90 H = 0.5 kOe H // c FC

60 30 0

(b)

0

30

60

90

120

150

180

θ (deg.)

Fig. 2. (a) Vortex flux density B vs. the rotational angle θ. At θ = 0◦ , H is parallel to the c-axis. (b) θ B the orientation of B relative to applied field H as function of θ.

M.K. Hasan Qaseer / Journal of Alloys and Compounds 375 (2004) 34–38

12

B( kG)

9 3 kOe 5 kOe 10 kOe

6

3

0

0

30

60

90

120

150

180

θ (deg.)

(a)

60 3 kOe 5 kOe 10 kOe

50 40 30

B

flux effect where the initial vortices along the c-axis act as pinning agents [19]. To better understand this behavior we plot in Fig. 2b the orientation θ B of vortex flux density B relative to the applied field H versus the rotational angle θ. The figure shows that as θ exceeds 30◦ the vortices prefer to stay close to the ab-plane direction. This behavior of B is maintained for 30◦ < θ < 70◦ where a complete alignment along the ab-plane occurs around 30◦ . In this range of θ the vortices exhibit a frictional behavior relative to the sample rotation and this can be seen from the nearly constant value of θ B in this range of θ. The vortices jump from one pinning site to another by unpinning–repinning processes. As θ exceeds 70◦ and for 70◦ < θ < 130◦ , more vortices are entering the sample and the frictional behavior disappears. In this range of θ the ab-plane is closer to H. Beyond θ = 130◦ the vortices are exiting the sample and B more closer to the ab-plane and also the frictional behavior reappears. This situation remains until θ reaches 180◦ . The vortex entry to the sample as the ab-plane approaches the direction of H and its exiting as the ab-plane moves away from H demonstrates the weakness of the pinning forces along the ab-plane. The reason for establishment of the FC-state at low fields is because the vortices were formed from above Tc by lowering the temperature. When this field was taken off we measured a sizable remnant magnetization. This means that the sample was in the mixed state. In the high field regime where the sample is fully penetrated by the vortices we perform the ZFC-state measurements. The high fields advantage comes from the applicability of the bean critical state model where the critical state is established and the magnetization is directly proportional to the critical currents [17,18]. In Fig. 3a we plot the vortex flux density B versus the rotational angle θ at different applied fields. The figure shows that B increases slowly from θ = 0◦ to 70◦ with a shallow maximum near 70◦ and then decreases in this same manner. For H = 3 kOe the peak for B occurs at 90◦ .Therefore, the subsequent production of the vortices is inhibited above this angle up to 180◦ . To explain this behavior we plot in Fig. 3b θ B the orientation of B versus θ. For H = 3 kOe the figure shows two peak values for θ B for θ ∼ 30◦ and for θ ∼ 120◦ . The value of θ B at 120◦ is greater than at 30◦ . This again explains the vortex flux effect which take place at the beginning of the rotation. Also, B stays closer to the ab-plane for 30◦ < θ < 110◦ and shows a complete alignment with ab-plane around θ = 60◦ . The behavior of θ B for H = 5 kOe is almost linear with only one peak at θ ∼ 110◦ . In fact, for H > 4 kOe only one peak is seen and it is shifted toward θ = 90◦ with increasing H. As the field becomes strong enough and for H = 10 kOe, B stays close to the direction of the external field H and shows a complete alignment along ab-plane at θ = 85◦ . Therefore, at this field B is less influenced by the crystal anisotropy. The range of θ in which the vortices become very close to ab-plane is within 70◦ < θ < 110◦ except for H = 3 kOe. As H gets bigger this range of θ becomes narrow and moves toward

θ (deg.)

36

20 10 0 (b)

0

30

60

90

θ (deg.)

120

150

180

Fig. 3. (a) Vortex flux density B vs. the rotational angle θ at different fields. (b) θ B the orientation of B relative to applied field H as function of θ.

90◦ from both directions. Therefore, this suggests that a new form of the vortices exists in this range of angles whenever the ab-plane is close to the magnetic field. It is worth mentioning that for H = 3 kOe and above, the direction of internal field is almost near the direction of the applied field. For the whole spectrum of fields from H = 0.5 kOe up to the H = 10 kOe, the results suggest that a new formation of the vortices exist just above θ = 70◦ . This new type of vortices persists for 70◦ < θ < 110◦ and this angular range becomes narrower with increasing H and becomes centered around 90◦ . For the high field regime, the field is inhibited by the production of new vortices for θ > 70◦ . The vortex flux density B in this range of θ is closer to the ab-plane. Another approach which confirms the above result is the variation of the magnetic torque in the high field regime as function of θ and H. Since the detailed magnetic state is known, we can calculate the average magnetic torque per volume τ experienced by the vortices during the rotational process. The torque density is given by τ = M × H i . Here Hi is the internal field which vortices respond to. We plot in Fig. 4 the variations of τ versus the rotational angle θ. The figure shows that τ increases almost linearly with θ up 70◦ then it starts to change to bigger slope for 70◦ ≤ θ < 90◦ . As θ exceeds 90◦ τ reverse the sign and the same sort of

M.K. Hasan Qaseer / Journal of Alloys and Compounds 375 (2004) 34–38

3

/H (dyne-cm/Oe cm )

4 kOe 5 kOe 6 kOe 10 koe

1 0 -1

-3

max

-2

250

200

150

τ

-6

300

2

3

τ X 10 (dyne-cm/cm )

3

37

0

30

60

90

120

150

180

θ (deg.)

100 2

4

6

8

10

H (kOe)

Fig. 4. The magnetic torque density τ m vs. θ at different fields.

Fig. 6. The quantity τ max /H vs. the H.

behavior exists above this angle. For 70◦ < θ < 110◦ the vortices are closer to the ab-plane. Therefore, the change of τ above 70◦ indicates a new vortex mechanism appears as the vortices becomes very close to the ab-plane. This behavior may be attributed to dimensional cross-over in the vortex behavior with respect to H. Probably a canting vortex type is formed at this stage. The figure also shows that τ does not go to zero at θ = 180◦ . This behavior can be attributed to the vortex flux effect as we discussed before and also due to the effect of the grain boundaries acting as pinning agents. The maximum values of τ occurring at different fields represent the maximum magnetic torque experienced by the vortices. These maximum torques are balanced by the pinning torques. Taking these maximum values of τ which occur around 90◦ for each field we can deduce the variations of the maximum torque with magnetic field H. In fact, we took the average of the values of these maxima at which τ reveres the sign and represented it by τ max . Fig. 5 shows the variation of τ max versus H. The figure shows that τ max increases rapidly at the beginning then slowly at the higher fields. However, the fundamental quantity is the maximum torque per vortex. Therefore, we divide τ max by H and we plot in Fig. 6 this quantity of τ max /H versus H where we approximate the number of vortices by H. This approximation is valid for the high field regime. The figure shows

τ

max

3

x (dyne-cm/cm )

2.5 2 1.5 1 0.5 0

2

4

6

8

10

H (kOe) Fig. 5. The maximum torque density τ max vs. H.

that τ max /H increases with H and goes through a maximum around H = 7 kOe. This maximum value represents the maximum torque experienced by a single vortex and it is equivalent to the maximum pinning force acting on the vortex. The decrease in τ max /H for H above 7 kOe indicates that a collective sharing of pinning sites is dominates and this will reduce the effective pinning force per vortex. It should be mentioned that these maximal torques occur when the applied field H is directed along the ab-plane. Therefore, during the rotational process and while the vortices crossing the ab-plane the crystal anisotropy has more influence on the vortex flux density B at low and moderate fields while at high fields it becomes of less important.

3. Conclusions The magnetization measurements presented here show two regimes in which the vortices respond to the magnetic field. The low field behavior shows a crossing flux effect and a more anisotropic behavior of B. The vortices show frictional behavior when they become close to the ab-plane. For the high field regime, B tends to stay closer to the ab-plane when the field becomes closer to this orientation. As θ exceeds 70◦ , a new vortex type appears for 70◦ < θ < 110◦ , and the field production of these new vortices is inhibited for θ > 70◦ . The behavior of magnetic torque density with the rotational angle confirms the appearance of a new vortex form as θ exceeds 70◦ . This is seen from the increase of the slope of τ versus θ for 70◦ < θ ≤ 90◦ . The dependence of τ on the applied field H can be represented by τ max /H which increases with increasing H and goes through a maximum before diminishing slowly. The decrease in τ max /H is attributed to the collective sharing of pinning forces. The maximum value of τ max /H is equivalent to the maximum pinning forces and occurs around 7 kOe. Comparing the low field and high field behavior of B, the angular dependence is more influenced by the vortex flux effect in the low field case. Both regimes show that new vortex formation appears as θ exceeds 70◦ . The vortex

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entering and exiting the sample around ab-plane demonstrates the weakness of the pinning forces along this plane. The crystal anisotropy has a more influence on the behavior of B at low and moderate magnetic fields than at high fields. Acknowledgements I would like to acknowledge Professor N.Y. Ayoub from the Department of Physics, Yarmouk University, Irbid Jordan for the useful discussions. References [1] U. Yaron, I. Felner, Y. Yeshun, Phys. Rev. B 44 (1991) 12531. [2] T. Kiss, M. Inoue, S. Nishimura, T. Kuga, T. Mastsushita, Y. Iijima, K. Kakimoto, T. Saitoh, S. Awaji, K. Watanabe, Y. Shiohara, Physica C 378 (2002) 1113. [3] Y. Sato, S. Honjo, Y. Takahashi, K. Muranaka, K. Funjino, T. Taneda, K. Ohmastsu, H. Takei, Physica C 378 (2002) 1118. [4] A. Casaca, G. Bonfait, V. Galindo, J.P. Senateur, D. Feinberg, Physica B 284 (2000) 601.

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