Magnetization hysteresis loops of the granular high-Tc superconductors in the AC measurements

PHYSICA 8 ELSEVIER

Physica C 279 (1997) 233-240

Magnetization hysteresis loops of the granular high-q superconductors in the AC measurements Z.M. Ji a, J.F. Geng b, W.M. Chen b, H.X. Yu b, A.M. Sun ‘, Q.H. Chen a, S.Z. Yang a, X. Jin bl* a Department b Department

of Electronic

Science and Engineering,

of Physics and Nationul Laboratory

’ Structure Research

Laboratory,

Nanjing University, Nanjing 210093,

of Solid State Microstructure,

University of Science and Technology

Received 6 January

Chinu

Nanjing University, Nanjing 210093, of China, Hefei 230026,

China

Chinu

1997

Abstract In this paper, with some improvements to the conventional AC response technique, we report experimentally on the hysteresis loops at different temperatures and frequencies when applying an AC field H = h,sin(wt) to the granular Two kinds of hysteresis loops are found with different shapes in different AC field superconductor of YBa,Cu,O,,.

M-H

frequencies. Based on the simple Bean model and the extended Bean model, considering the influence of the intergranular lower critical field, we derived the expressions of the magnetization in the AC case, which are in good agreement with the M-H curves measured by our experiments. 0 1997 Elsevier Science B.V.

1. Introduction There have been numerous studies of the real and imaginary parts of the AC susceptibility x = x’ + ix” of high-T, superconductors [l-4]. It is generally agreed that the imaginary x” represents total hysteresis losses per volume of the sample through a cycle of the magnetization curve [1,2,51: xtr=

--

1 rrh; #

M.dH

where h, is the applied AC field amplitude. If one plots the hysteresis loop of M against H, the total

Corresponding author. Fax: + 86 25 3609458; e-mail: [email protected]. ??

area enclosed by the contour will be proportional to the AC susceptibility imaginary part x’ [5]. In fact, the M-H curves can give more information such as the penetration depth [6,7], the lower critical field h,, of the sample [6], etc. M-H curves are useful in studying the effective pinning potential of the high-T, superconductors which will be done in our further work. But, experimentally, we did not find any previous reports that studied the M-H loops in detail, with the presence of an AC background field H = h,sin(wr). In this paper, with some improvements on the magnetization measuring apparatus, we report on the various hysteresis loops recorded at different temperatures and AC field frequencies. In our experiment, the AC field amplitude pOhO is up to 60 X 10e4 T (the coupling h, is 4.8 X 10’ A/m), which is higher than usual [2]. But the lower field

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Z.M. Ji et al./ Physica C 279 (1997) 233-240

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h,, of the granular high-T, superconductor that is needed for the flux to penetrate between the grains is about 1 X 10m4 T [2], and the intragranular lower critical field needed for the flux to penetrate the grain is of the order of 100-200 X 10d4 T. Therefore, in this paper we mainly deal with the intergranular properties of the granular superconductors in the present AC field amplitude range. Since the criticalstate model has been used successfully to describe many properties in high-T, superconductors, we will use the Bean model [8] and the extended Bean model, considering the influence of the intergranular lower critical field h,, [6] to explain the two kinds of M-H curves with different shapes in high and low AC field frequencies, respectively. Based on experimental results, it is shown that the higher the frequency of the applied AC field, the closer the M-H curve is to the hysteresis loop in the critical state.

2. Experiments

and results

The experimental diagram, which is shown in Fig. 1, is similar to the circuit that measures the magnetization using the integral method by Fietz [9]. B is the coil that generates the background field. E is the AC current source. The phase shifter shifts the phase of V,,, and V, is the voltage of the standard resistor of 10 fl which measures the background field. The windings 1 and 2 form a mutual-inductance coil set balanced to zero output voltage in the absence of the sample, and the winding 3 is for measuring the real flux density by the equation Ha = V,/( p. osN),

E

I

1

Fig. I. Schematic ing system.

diagram of the magnetic hysteresis

loop measur-

Frequency (Hz) Fig. 2. Frequency response of the transformer circuit at both room temperature and nitrogen temperature without placing the sample.

where V, is the output voltage of the winding 3, w is the AC current source frequency, s is the section of the winding 3, and N is the turns of the coil. To generate a background field that is strong enough at a frequency of 10 kHz, we make a 1000 turns electromagnet by ferrite of permeability p = 1000. The power of this electromagnet is less than 100 W and the area for placing the sample is about 1 cm’. For running experiments, both the specimen and the magnet are in the low temperature range. The frequency characteristic of the system shows good linearity either at room temperature or liquid nitrogen temperature. In Fig. 2, the characteristic curve of the ratio of the secondary winding current to the primary winding current versus the frequency is shown. The magnetization in high frequency is measured as follows. When the sample is placed in the winding 1, the relation V,, = k(dM/dt), where k is a constant, is valid. If the magnetic field is sinusoid type [H(t) = h,sin(wt)], the magnetization will be expressed by M(t) = M,sin( wr + 01 when the harmonic wave is neglected, where 8 is the phase lag. So V,, is kWMOsin( wt + 0 + 7r/2), shifting a 77/2 phase comparing with the M(t). Using a 7r/2 phase-shifter to M(t), M(r) will be V,/(kw), where V, is the output voltage of the phase shifter. Thus, connecting the V, and V, to the x-axis and y-axis of the oscillograph respectively, the hysteresis loop will be shown dynamically in the fluorescent screen.

Z.M. Ji et al./Physica

(a)

235

C 279 (1997) 233-240

0.60 7

-0.20

-1vvmnm 80.0 82.0

84.0

88.0

86.0

90.0

9.

T(K) lb)

Fig, 3. (a) The imaginary with the frequency temperatures of YBa,Cu,O,,. vertical

f=

part of the AC susceptibility,

x”.

as a function

IO4 Hz for a plateau sample of YBa,Cu,O,,,.

from the oscilloscope 7he temperatures

axis is 5 mV/div.

with the AC field amplitude correspondin, u to (A)-(E)

of temperature

(b) (A)-(E)

at the AC field amplitude

are the M vs. H hysteresis

pOhO = 60 X 1O-4 T, and the frequency

f’=

/.+,/I~ = 60 X lO--4 T,

loops measured at different IO4 Hz for a plateau sample

are 86.4, 87.4, 88.2, 89.0 and 89.4 K, respectively.

The sensitivity

of the

Z.M. Ji et al./ Physica C 279 (1997) 233-240

236

-0.40

1,,,,,,,1,,,,,,,,1,1,,,,,,,,,,,~,,,,~,,,,,,,,,~,,,,,,,,,,,, 80.0 82.0 84.0 86.0

r

88.0

90.0

9: 2. 0

-w

Fig. 4. (a) The imaginary part of the AC susceptibility, x”, as a function of temperature at the AC field amplitude p,,h, = 60 X IO- 4 T, with the frequency f= 2COO Hz for a plateau sample of YBa,Cu,O, 4. (b) (A)-(E) are the M vs. H hysteresis loops measured at different temperatures from the oscilloscope with the AC field amplitude poh, = 60 X 10m4 T, and the frequency f= 2ooO Hz for a plateau sample of YBazCu306,4. The temperatures correspondin, 0 to (A)-(E) are 84.1, 86.3, 87.0, 88.5 and 88.8 K, respectively. The sensitivity of the vertical axis is 0.5 mV/div.

Z.M. Ji et al./ Physica C 279 (1997) 233-240

The high-T, superconductor used in our experiment is a disk ceramic sample of YBa,Cu,O,,, attained in our lab. Shown in Fig. 3a is the temperature dependence of the AC susceptibility imaginary ,$’ at the AC field h, = 4.8 X lo3 A/m, f= lo4 Hz without the presence of a DC bias field for the sample. When recording the XI’ vs. T plot, the photos of the hysteresis loops on the oscillograph are taken simultaneously at different temperatures, which is shown in Fig. 3b. In fact, Fig. 3a is derived from Fig. 3b by an integral according to Eq. (I) as pointed out previously. When the temperature is far below the temperature of the peak TP of the AC susceptibility imaginary part, the applied field does not penetrate the sample and the screening is complete, and the M-H plot is almost a straight line. When partially penetrated with the temperature increasing, the M-H plot becomes lenticular [ 1I. In this case, if we assume that the penetration depth is A, the shielding current density J will be J = h,/A [6,7,10-121. The area enclosed by the M-H curve will reach the maximum when the flux front reaches the centre of the sample. At this time the temperature is TP and the shielding current density is J = 2/2,/d, where d is the thickness of the slab sample. When the temper-

237

ature is higher than TP, the sample is fully penetrated and the total area enclosed by the M-H curve decreases. This is the first category of M vs. H graphs with lenticular shapes. The second category of M vs. H graphs with different shapes is shown in Fig. 4b. The only difference between Fig. 3 and Fig. 4 is that the applied AC field frequency is lo4 Hz in the former case and 2000 Hz in the latter. In Fig. 4b, the asymmetry of the hysteresis loops mainly results from the irregular shape of the sample. One of the important characteristics of this kind of hysteresis loop is that the middle of the loop is thinner than the other parts. Fig. 5 shows the hysteresis loops at different frequencies at a constant temperature. Taking care of the y-axis sensitivity, it is found that the total area enclosed by the M-H curve at higher frequencies is larger than that at lower frequencies.

3. Models and discussion 3.1. Field-sweep

rate

When using the conventional magnetization measurements (e.g. VSM) to plot the hysteresis loops,

Fig. 5. The plot of M vs. H hysteresis loops from the oscilloscope at different applied AC field frequencies with the temperature T being about 87.0 K, and /I, = 4.8 X IO’ A/m. y-axis = 0.5 mV/div,

(a) f’= 200 Hz, y-axis = 0.05 mV/div;

(d) f’= 5000 Hz, y-axis = 2 mV/div;

(e) f=

(b) f’=

loo0 Hz, y-axis = 0.2 mV/div;

IO4 Hz, y-axis = 5 mV/dlv.

(c) f’= 2000 Hz,

238

Z.M. Ji er al./Physica

we always come across the field-sweep rate H, typically 200 Gs/s [1,2]. This time scale is large enough to show the influence of magnetization relaxation. Because the magnetization relaxation decays with time from the critical state [5], there is always a deviation from the value of magnetization of the critical state when measuring it [5]. Obviously, the magnetization measured at certain external fields is smaller than the value of the critical state. On the contrary, if we apply an AC field H = hOemiw’to the sample [for example, h, = 4.8 X lo3 A/m, f= lo4 Hz (w = 27rf)], then the mean sweep field rate (H) is about lo7 Gs/s. This means that one gauss sweeping needs low7 s. The field-sweep rate in this case is far bigger than that in the conventional one. The magnetic relaxation is not complete in the time scale of 10m7 s. Hence, the magnetization hysteresis loops measured are approaching the value of the critical state. If we increase the frequency of the AC field applied on the sample, the value of the magnetization of the hysteresis loops will be closer to the value of

Fig. 6. The theoretical HZ.

C 279 (1997) 233-240

the critical state. This is the reason why the total area enclosed by the M-H curve at high frequencies is larger than that at lower frequencies. Discussions above are in agreement with that shown in Fig. 5. 3.2. Bean model To interpret the shape of the magnetization loops at a higher frequency f= lo4 Hz (w = 2rf), we invoke the Bean critical state model [8]. For brief and simplicity, we assume that the sample is a slab with thickness d, and the applied AC field H = h,e- iot is parallel to the slab. Following Ref. [6,7], Fig. 6 is easily obtained. The critical temperature of the sample T, is 89.7 K, and the temperature Tp corresponding to the peak of the x” is 88.0 K from Fig. 3a. The shielding current density J,(T) is described by 113,141: J,(T)

=J,(O)(l

M vs. H plots based on the Bean critical state model. (A)-(E)

-T/T*)’

are at different temperatures

(2)

at a frequency

of IO4

Z.M. Ji et al./Physica

where J,(O) is the critical current density at zero Kelvin, /3 is the characteristic constant for a certain superconducting material, and T * is the temperature corresponding to the irreversibility line. Here, we substitute T, for T *. When T = Tp, the shielding current density J, = 2&/d, where d, the thickness of the sample, is about 1 cm. J,(O) is about 3.4 X lo8 A/m2. In the partially field-penetrated state below Tp, the magnetization - (M) in Fig. 6A,B corresponds to the variation of AC field from h, to --ha as expressed by -(M)

=

(h;-$J2 _$ c

+h.

(3)

c

Fig. 6C,D shows the fully field-penetrated state above Tp, with the magnetization - (M) from ho to ho tic being

Fig. 7. The theoretical frequency of 2000 Hz.

A4 vs. H plots based on the extended

C 279 (1997) 233-240

-(M)=

(h2-$J2 c

and -(M) -(M)=

239

+ (h;h”) c

from ho-d/,

+:

(4)

to -ho is

-+.

(5)

Comparing Fig. 6 with Fig. 3b, we find that they are in excellent agreement. 3.3. Extended Bean model considering h,, When the frequency is lower, e.g. f = 2000 Hz, the shape of the hysteresis loops is not lenticular. But, when considering the intergranular lower critical field h,,, we may get a reasonable explanation [6]. In this case, similar to Section 3.2, if Tp is taken as 87.0 K and T, is 90.0 K, J,(O) is 1.4 X 10’ A/m2. However, we select the intergranular lower

Bean model considering

h,,. (A)-(E)

are at different

temperatures

a~ a

Z.M. Ji et al./ Physics

240

critical field h,, to be about 0.4 X lo3 A/m (5 Gauss). In Fig. 7A,B, the sample being partially penetrated by the applied AC field below Tp, the magnetization -(M) that corresponds to the AC field decrement from h, to h,, is

The AC field decrement from -h,, _(M)=

_

to -ho is

Who+2M2+h 2&c

+

h* + hz, - 2h,( h + 2h,,)

4. Conclusion In this paper, we report on the hysteresis loops at different temperatures and at different AC field frequencies using a new measurement technique. Based on two different models, we explain the two kinds of M-H curves with different shapes. In fact, from this paper, it is proven experimentally that the imaginary part of the susceptibility x” is proportional to the areas enclosed by the hysteresis loops, and the higher the frequency of the applied AC field, the closer the M-H curves are to the hysteresis loop in the critical state. Further work on these hysteresis loops is being done.

(7)

d/,

and, from h,, to - h,, the AC field decrement is constant. When the h is equal to -h,, , the - ( M > decreases by the value of 2h,, . As shown in Fig. 7A,B, the central part of the M-H curve becomes thinner, similar to the shape of the M-H curve in Fig. 4b(A,B) as derived from the experiment. In Fig. 7C,D, the fully field-penetrated state above Tp, the equations that describe the M-H curve are almost the same as that in Fig. 6C,D, except for two corners. The equation that describes the comer corresponding to the variation of the AC field from - h,, to -h,, - d1,/2 represents a straight line: . h,, - 4.

(8) The shapes of the M-H

C 279 (19971233-240

loops in Fig. 7, derived from the calculations, and in Fig. 4b, from the experiment, are in such good agreement that one has to assume that although the intergranular lower critical field, h,,, is very small, it is not negligible [6].

References 113T. El L.

Ishida, R.B. Goldfarb, Phys. Rev. B 41 (1990) 8937. Ji, R.H. Sohn, G.C. Spalding, C.J. Lobb, M. Tit&ham, Phys. Rev. B 40 (1989) 10936. [31 R.B. Flippen, Phys. Rev. B 45 (1992) 12498. [41 G. Shaw, SD. Murphy, Z.-Y. Li, A.M. Stewart, SM. Bhagat, IEEE Trans. Magn. 25 (1989) 3512. [51 G. Blatter, M.V. Feigelman, V.B. Keskenbein, M. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66 (4) (1994) 1125. [61 S. Lofland, M.X. Huang, S.M. Bhagat, Physica C 203 (1992) 271. [71 S.D. Murphy, K. Renouard, R. Crittemdem, SM. Bhagat, Solid State Commun. 69 (1989) 367. 181 C.P. Bean, Phys. Rev. Lett. 8 (1962) 250; C.P. Bean, J.D. Livingston, Phys. Rev. Lett. 12 (1964) 14; C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. 191 W.A. Fietz, Rev. Sci. Instr. 36 (1965) 1621. [lOI G.P. Meisner, J. Appl. Phys. 66(11) (1989). [I 11 F. GiimBry, P. Lobotka, Solid State Commun. 66 (1988) 645. 1121 Y. Rui, H.L. Ji, X.N. Xu, H.M. Shao, M.J. Qin, X.X. Yao, X.S. Rong, B. Ying, Z.X. Zhao, Phys. Rev. B 51 (1995). [I31 Y. YeshuNn, A.P. Malozemoff, F. Holtzberg. J. Appl. Phys. 64 (1988) 5797. L.G. Turner, E.L. Hall, J. Appl. Phys. [I41 A. Mogro-Campero, 65 (1989) 4951.