Temperature dependences of the first critical field and critical current in the untwinned TmBa2Cu3Ox superconducting single crystals

PhysicaC 166 (1990) 185-190 North-Holland

TEMPERATURE

DEPENDENCES

CURRENT IN THE UNTWINNED V.V. MOSHCHALKOV,

OF THE FIRST CRITICAL FIELD AND CRITICAL TmBa2Cu30, SUPERCONDUCTING

A.A. ZHUKOV,

D.K. PETROV, V.I. VORONKOVA

SINGLE CRYSTALS

and V.K. YANOVSIUI

Laboratoryof High-T, Superconductivity,PhysicsDepartment.MoscowState University,Moscow117234, USSR Received 12 April 1989 Revised manuscript received 20 December 1989

The critical field H,, of the monodomain TmBa2Cus0, superconducting single crystals are measured along all three crystallographic axes. These data determine, in the logarithmic approximation, the ratio of the penetration depths 1.:&,:1,= 1:1. 7: 4.4 for T> 10 K the dependence of H,, on the temperature is a linear function with a slope of about 22 Oe/K for Hllc and 3.1 Oe/K for HIJo.Angular dependences of the Meissner magnetic susceptibility and H,, in the (bc)-plane were studied. The expression derived in the ellipsoid approximation shows good agreement with these data. Temperature dependences of the critical current j,( T) are also measured. Different types of single crystals are used, including the monodomain crystal. For all samples the jJ T) curves follow the exponential dependence j,( T)=j,(O)exp( -T/T,) with a j,(O) value of about (2-3)

M/H =f( H) data given in fig. 1 (a, b) illustrate this difficulty. For example, from fig. lb one may see that in low magnetic field the scatter of data is large and it is not clear at all what is the proper H,, value. To avoid this obstacle we used a different method for the Hcl measurements. It is known that the H,, critical field corresponds to the beginning of the Abrikosov vortices penetration into a superconductor [ 11. If sweeping the magnetic field on, up to a certain value and then off, the H,, may be registered as the magnetic field which, for the first time, gives a nonzero trapped flux after switching the field on and off. Figure 2 shows the trapped moment versus field up to which the sweeping on is done. In this case it is easier to find the H,, value because we have to measure the appearance of the nonzero signal which may be made with better error bars than in the case when one looks for the point where the M(H) curve 0921-4534/90/$03.50 0 Elsevier Science Publishers B.V. ( North-Holland )

I/: V. Moshchalkov

186

et al. / Untwlnned

M. 1Ci5ernlJ

++

1

+

800 -

+ +

+

40:. 0

400

1200

800 H. Oe

M/H, 16%mU/Oe

0

400

single crystuls

starts to deviate from the linear dependence. The H,, temperature dependences determined in this way for H(lc and Hlla for the sample Tm4 (see table I) are shown in fig. 3. For T> 10 K the H,, ( T) curves are almost linear. For Hj\c the slope is about 22 Oe/K. This is in agreement with the earlier observations on EuBazCu30, single crystals [ 21. For Hlja we obtained dH,, /dT= - 3.1 Oe/K. The H,, anisotropy for the a-, b- and c-directions was studied. For the Tm4 sample at T= 10 K the values 250, 300 and 1700 Oe were obtained for the a-. b- and c-axes, respectively. Using the correlation lengths <, = 51 nm and <,,=3.1 nm [ 31 the penetration depth values A,=58nm, IIb= 70 nm and II,= 400 nm were calculated. The latter is close to the penetration depth anisotropy found for YBazCu30, single crystals from the muon spin rotation experiment [ 41. The Meissner phase and the first critical field angular dependences in the (bc)-plane were studied. It may be shown that the Meissner susceptibility for an ellipsoid in the magnetic field direction (the component measured in experiment) is determined by the expression:

1200

800

XH=-(n*cos2p+sin2q0)/(1-NNI),

H. Oe Fig. 1. Field dependences of magnetization M (a) and susceptibility x=M/H (b) for the TmBa,Cu,O, single crystal.

ov5emU

q

n q

-I 800

(1)

wheren=(l-N,)/(l-N,,),N,,andN, arethedemagnetization factors for the parallel and perpendicular magnetic field’s orientations with respect to the c-axis. The angle qr is measured between H and c-axis directions. The experimental results for the Tm4 sample and the calculated curve are shown in fig. 4. There is a good correspondence between theoretical and experimental curves for the rectangular sample. Moreover, the obtained value n= 10.0 is nearly the same as that calculated for the inscribed ellipsoid: n = 9.84. The H,, angular dependence for anisotropic superconductors was calculated in [ 5 ] _Taking into account the demagnetization effect we found for the ellipsoid the following relation: H~,(~)=H~1(0)/(cos2yl+~-2*~~sin2~)1’2,

(2)

1200

H. Oe Fig. 2. The magnetic field dependence the TmBaZCu,O, single crystal.

TmBaZCu,O,

of the trapped

moment

for

where p = m,/ ma& is the effective mass anisotropy, Hz, is the external field which destroys the Meissner phase. The experimental results for the Tm4 sample and the calculated curve with m,/mb=24 are also

l! K Moshchalkov

Table I

1750LH 1500

’ . 0: .

1250

0 0

1000 -

. 0

750 -

. O-lb5

500 -

I

0

m-2

0

.

250 OO

. 20 /

LO I

T,K 60 /

a

o*

I 80

Fig. 3. The H,, temperature dependences for the Tm4 sample ( 1 - hi/a, 2 - Hllc).

0.25

0

Fig. 4. The angular dependences of the Meissner susceptibility component in the field direction ( 1) and the external field HE,, which destroys the Meissner phase (2).

given in fig. 4. Their correspondence is also quite good. The H,, values reported in the present communication are larger than those found before on ceramic and single crystalline samples [ 2,6,7]. But in previous studies only polydomain superconducting single crystals were used and therefore the penetration of the Abrikosov vortices between different domains was possible. The penetration would take place then in magnetic fields H-C&~. This assumption is confirmed by our H,, results obtained on a 100% single domain single crystal (sample Tm7, see table I): H~,(O)=1800~100Oe, H:,(0)=410f70oe and HP, (0) = 720 & 70 Oe. These values are noticeably larger than those found for the Tm4 sample containing a smaller area belonging to the single domain. The H,, (0) data determine, in the logarithmic approximation, the ratio of the penetration depths 1,:1,:1,= 1: 1.7: 4.4. It is worth discussing here the H,, value scatter in available data on H,,. Besides the effect of the twin

188

V.V. Moshchalkov et al. / Untwinned TmBa2Cu,0X single cr.vstais

boundaries mentioned above, this scatter may also be associated with the existence of the Bean-Livingstone barrier [ 81 and with a larger demagnetization factor in the vicinity of sample corners and sharp edges. If the Bean-Livingstone barrier really exists, then in our experiments we registered only vortices passing through the barrier in magnetic fields H> Hb and could not detect the exponentially weak vortices penetration in fields H,,
3. Critical currents Critical currents were measured in four samples obtained in the same experimental run. These samples have domains of a different size and density. Sample Tm3 (see table I) is a polydomain one with a typical domain size less than 1 pm. Sample Tm2 consists of large domains up to 100 urn in size, whereas samples Tm4 and Tm7 are single domain ones with the domain area 80% and 100% from the total sample area, respectively. For all samples the superconducting transition temperature determined as the onset of a diamagnetic response is T, = 9 I93 K. Temperature dependences of the critical currents are determined with the help of Bean’s model [ 91 from the magnetization measurements: A41 V=j,R/3

(2)

where V is volume and R is the sample radius. This formula was obtained for a cylinder but it may be shown that the same expression is also valid for a disc or a square if inserting into eq. (2) L/2 instead of R. Here L denotes the side of a square. Temperature dependences of the critical current j,( T) for H=O are given in fig. 4. At temperatures

below 50 K these data are well fitted by the following relation: j,(T)=j,(O)exp(-T/To).

(3)

The parameters j,( 0) and To for different single crystalline samples, including the monodomain sample, are listed in table I. The exponential dependence (3) was found earlier by Guillot et al. [ lo] and by Schneemeyer et al. [ 111. It is of interest to emphasize here that for all single crystalline samples we obtained close j, (0 ) parameters of about (2-3 ) x 1O6A/cm* coinciding, probably, within the error bars of these measurements. At the same time quite a large difference in T,, values (see table I ) is observed between polydomain and single domain samples. Therefore, at least at low temperatures T< 50 K, the difference both in domain size (a factor of 10 3) and in density of the domain walls (up to 106) does not noticeably affect the critical current. This observation shows that domain boundaries are not effective pinning centers. Due to the small value of the coherence length, critical current is probably determined by characteristics of the intrinsic pinning centers such as oxygen vacancies, for example. Kupfer et al. reported the variation of j, with the sample size for the samples with weak intergrain or interdomain links [ 12 1. The effect is caused by the destruction of the weak links by the magnetic field. In this case the magnetization is produced by currents in strong coupled regions and according to (2 ) it is dependent on the size of such regions but not on the sample. Thus, the j, calculation using sample size in relation (2) gives the dependence on sample size. In order to check this assumption we took the sample Tm2 (the 0.8 x0.7 mm2 size) and broke it into two parts. Both parts showed the same j,( T) behaviour as the Tm2 sample. The j,(T) curve for the larger part (0.5 x 0.3 mm*) is given in fig. 5 together with data for the whole Tm2 sample. The close similarity between the J;( T) dependences for two samples with different dimensions indicates that the J, value is not effected by the sample size, if the sample does not contain weak links destroyed by the magnetic field.

V. V. Moshchalkov et al. / Untwinned TmBa,Cu,O,

single crystals

189

Acknowledgements

, A/cm2 107

The authors would like to thank A.A. Abrikosov, A.I. Buzdin, F. Steglich, H. Kupfer and H. Pie1 for useful discussions. This work is supported by Grants 10 and 11 of the USSR State Program on High-T, Superconductivity.

IO6

IO5

,,44 0

20

++

q

A 0

40

60 T, K

Fig. 5. Temperature dependences of the critical current j,( T) for TmBalCu,Ox single crystals. The logarithmic scale is used for j=. Open squares, diamonds, crosses and triangles are for samples m2, m4, m3 and m7 (the monodomain sample), respectively.

5.61

T. K Fig. 6. Temperature dependences of the critical current j,( T) in the logarithmic scale for the whole sample m2 (open squares) and for its part (crosses).

4. Conclusions Measurements of critical fields and critical current on single domain TmBa2Cus0, single crystals are reported. The first critical field is determined for a, b, c crystallographic axes separately. The penetration depths along these axes are found. From the H,, angular dependences the anisotropy of the effective masses is determined: m,/mb=25. The temperature dependence of the critical current is described by the empirical exponential dependence.

Note added. After this paper was submitted new results appeared which confirm our data. Using the standard H,, determination method for YBa2Cu@_-6, T. Ishii and T. Yamada [ 131 obtained for T> 40 K linear H, ( T) dependence with (EW,,/dT)=--2OOe/KforHllcand -4.4Oe/Kfor HI c. These data correspond well with ours. The upward deviation from linearity at low temperatures seems to be caused by pinning. A. Umezawa et al. [ 141 using the H,, determination method similar to that described in this paper and high quality single crystal YBa&u307_a obtained the linear H,,(T) dependence in a wide temperature range with (Cw,, / dT) = -2.4 Oe/K for HIc. For untwinned YBaZCu@_6 crystals prepared with the help of uniaxial pressure, the upper critical field measurements [ 15 ] give the value mc/rnab z 3 1 with low anisotropy mb/m.% 1.3. At the same time we must emphasize here that a disagreement there exists between the linear H,, ( T) temperature dependence and almost temperature independent penetration depth 1 found in high frequency measurements (see, e.g. [ 16 ] ). The origin of this discrepancy is not clear yet and it is the subject of further investigations.

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