Observation of unusual metastable magnetization in the superconducting state of nearly single-phased YNi2B2C and ErNi2B2C

N

PHYSICA

ELSEVIER

Physica C 256 (1996) 39-50

Observation of unusual metastable magnetization in the superconducting state of nearly single-phased YNi2 B 2C and ErNizB2C N.X. Phuc 1, M. Batanda *, A. Bajorek, A.W. Pacyna, W. Witek The H. Niewodniczafiski Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Krakdw, Poland

Received 10 January 1995; revised manuscript received 27 July 1995

Abstract We report an unusual magnetization behavior observed by DC susceptibility measurements in the superconducting state of YNi2BzC and ErNi~BEC compounds after relatively fast cooling in zero or in magnet-remanent field. The magnetization of both substances exhibited an incomplete flux expulsion and evolved with time towards a stronger diamagnetic state, The time needed to reach a saturated value increased with the field and for H = 1 kOe the relaxation process lasted over decades of minutes. The saturated susceptibility value differed from that of the full shielding and the discrepancy increased with the field. The susceptibility observed was composed of a stable nondissipative diamagnetic part and of a decaying contribution of a positive sign, A simple thermal procedure could destroy the positive moment. This unusual magnetization behavior may be attributed to the enhanced magnetic granularity coming from a small amount of nonsuperconducting secondary phase present in the samples or to the glassy state of spontaneous orbital moments connected with "rr junctions.

1. I n t r o d u c t i o n Since the discovery of high-Tc superconductors, the report at the very beginning by Miiller, Takashige and Bednorz (MTB) [1] has initiated a special interest in the spin-glass-like [2] properties of those superconductors. The research developed in two main directions. A t first, the relaxation studies were conducted under the zero-field cooling for both ceramics and single crystals of high-T~ substances and confirmed the original MTB observation that the magnetization is metastable and relaxes to a weaker dia-

* Corresponding author. tOn leave from Institute of Materials Science, Nghia do, Hanoi, Vietnam.

magnetic state via a nonexponential time dependence. Several flux-creep based models have been developed to describe the observed relaxation of Z F C magnetization (for review, see Ref. [3]). The second research direction deals with the behavior of FC magnetization at small and very small external fields [4-8]. For the field region of 2 0 e < H < Hol, considerable incompleteness in flux expulsion has been observed for various samples. For the region of 0.001 Oe < H < 1 Oe, even a positive magnetization has been detected for some Bi based ceramics [5,6], for Y B C O single crystal [7] and, recently, for a disk sample of niobium [8]. The effect, reviewed by Braunisch et al. [6] and Khomski [9] has been called the p a r a m a g n e t i c M e i s s n e r effect ( P M E ) or Wohlleben effect (WE).

0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0921-4534(95)00629-X

40

N.X. Phuc et a l . / Physica C 256 (1996) 3 9 - 5 0

In the opinion of a majority of the authors [6,9] spontaneous magnetic moments observed below Tc can be attributed to circular currents flowing around loops with anomalous Josephson junctions, so called "rr junctions [10a], which may originate from tunneling through magnetic impurities [10a] of from d wave pairing [10b]. The chaotically distributed circular orbital moments form the so-called orbital glass [11]. At certain concentration of -rr junctions the interaction between the moments will lead to percolating superconducting clusters and normal regions with frozen-in ordered moments, as was predicted in Ref. [12]. The time dependence of the positive FC susceptibility is still an open question: while in Ref. [6] the FC magnetization MFC in H = 0 . 1 0 e did not change over 30 min, in Ref. [13] a weak increase for H _< 1 0 e and a negative relaxation for H = 3 0 e was observed. Besides papers reporting a paramagnetic MFC there exist also some experimental observations of the metastable positive magnetization which clearly point to the glassy behavior of granular high-T~ superconductors. Namely, the work [14] on Y doped Bi(2212) reported a cooling-rate dependent positive FC magnetization which markedly decreased with time. The authors of Ref. [14] connect the positive MFC contribution with the intergranular superconducting phase present in the samples. In the paper of Wolf and Gey [15] a strong magnetic relaxation toward diamagnetism in ZFC YBCO single crystals close to T~ for field range 0 . 5 0 e < H a < 10 Oe was observed. This nonlogarithmic relaxation together with the discovered irreversibility of the MFC [15b] are reminiscent of the processes found in spin glasses. In the present paper we report a relaxation toward stronger diamagnetism, that is, the development of shielding in the presence of an external magnetic field. The shape and time dependence of the relaxation was similar to that described in Ref. [15] but it appeared in a wide field and temperature range. The effect was observed for relatively fast-cooled ceramic samples of two superconductors: YNiEBEC and ErNi2B2C, while it was not visible for isostrnctural LuNi2B2C produced in the same way as the samples under study and measured according to the same scenario. Nor the high-Tc superconductors measured [16] with the same equipment showed the relaxation of this direction. Despite the same prepa-

ration method the Y and Er samples contained a small amount of nonsuperconducting secondary phases while the Lu sample was a single phase. Therefore, we incline to ascribe the untypical behavior to the non-single-phase character of our samples. To our knowledge, this is a first report on a ZFC magnetization metastability of this kind. Measurements of a DC susceptibility time dependence were performed by means of a Faraday balance. The ZFC susceptibility values registered for the as-cooled samples showed a suppressed diamagnetism. The state with an incomplete flux expulsion was metastable and relaxed to a stronger diamagnetic state. In a weak field, for example H = 40 Oe, the saturation was obtained in a short time (about 3 min) but it took a much longer time for stronger fields. In the latter case the reached susceptibility values were still a part of the maximum possible value but that could be obtained by a simple thermal treatment. In the paper, characterization of the observed relaxation process and its dependence both on magnetic field and temperature is also presented. By means of the intermittent-time measurement regime the development of two fragmentary processes with opposite directions of the magnetic response is demonstrated. The rare-earth nickel borides showing the co-existence of antiferromagnetism and superconductivity have been classified [17] as conventional, s wave pairing, type-II superconductors. Nevertheless, some questions related to magnetic behavior are not yet resolved. For the layered tetragonal ThCr2Si2-type structure [18] one should expect anisotropic features of the superconducting state while it is not distinctly seen on the HcE(T) dependence [19,20]. From the other side, for YNi2BEC lower critical field Hcl anisotropy was found [20] but there is a big spread of literature data on He1(0), i.e. from 80 to 800 Oe [21,19,22]. For YNi2B2C some universal behavior of the MzF c relaxation was noticed [21] and for ErNi2 B2C either negative [23] or positive [24] values for MFC at 30 Oe were obtained. These inconsistencies together with observations presented by us are reminiscent of the results on paramagnetic FC magnetization which were obtained only for some of the tested Bi2212 samples. The answer of the question what is specific for the samples showing PME is not clear. On the one hand a special microstructure with good contacts between the plate-like crystallites

41

N.X. Phuc et al. / Physica C 256 (1996) 3 9 - 5 0

seems to be [9] the most favorable for the effect but on the other the PME has been found [25] in isolated 1 Ixm grains, giving evidence for the intrinsic nature of spontaneous currents. One may expect that PME and our findings bear a common origin. The reason for these untypical effects may be a specific and definite current pattern in the given material.

M Ct

Hm

2. Experimental details M The ingots of YNi2B2C, ErNi2B2C and of the isostructural LuNi2BaC which did not show any unusual relaxation were prepared by high-frequency induction melting, as reported in Refs. [26] and [23]. The Lu sample was a single phase, while for Y and Er samples the impurity of secondary phases was less than 5%, as shown by X-ray diffraction analysis. The superconducting transition temperatures are 15.2 K, 10 K and 15.5 K for yttrium, erbium samples and lutetium samples, respectively. For magnetization measurements the following samples were prepared. The powder YNi z B 2C ( ~ 1) and ErNizB2C (#2) samples, each of mass of ca. 50 mg were prepared by grinding (by hand) the corresponding ingots. The granules of diameter of about 5 - 1 0 Ixm, were put into a sample holder and covered by a screw. Apart from powder samples the measurements were carried out also for a bulk erbium sample (#3), prepared from the ingot of the same batch as sample #2. The sample piece of almost cubic shape with mass of ca. 170 mg was placed in the open thin wail copper vessel and hung on the balance. Such an arrangement was aimed to exclude the delay of heat exchange and to provide a comparison of bulk versus powder behavior. The LuNiaBaC bulk sample of mass of ca. 150 mg was measured also in the open container. The X-ray theoretical sample density is 6.08 g / c m 3 and 8.17 g / c m 3 for yttrium and erbium sample, respectively. Assuming demagnetization factors equal to D = 0.2 for powder and D = 0.3 for the bulk sample, the ideal value of the diamagnetic mass susceptibility should be X = - 0.016 e m u / g for sample #1 and X = - 0 . 1 5 e m u / g for sample #3. The magnetic susceptibility (or magnetization) was measured by a Faraday type RG Cahn elec-

Hm

l

St

oOOO . . . . .

ton

.

i

i

t im t off

Fig. 1. Two time regimes used in the experiments: Ct, Continuous (field on) time, and St, Sequence (field-on-off) time. H m is the measuring field.

trobalance, which was earlier used for study of magnetic relaxation in some high-~ superconductors [16]. The field gradient which is an intrinsic attribute of the used technique varies with field strength and equals 15 O e / m m and 7 . 5 0 e / m m for a field of 1000 Oe and 218 Oe, respectively. The fluctuation of the power supply current was checked to be less than 1.8% in the first 2 and not larger than 0.2% after that. The stabilization of the magnet field checked with a Hall probe, was better than 1% over 1 h. Two regimes of time measurements were used: the continuous field-on time (Ct) and the sequence field-on-off time (SO (see Fig. 1 for illustration of (St)). The choice of time intervals in the St regime was optional. For the results presented in this paper, t = 3 s, and toef > 30 s. The magnetic response was measured with the rate of one point per second during the ton periods with a delay time of 3 s (to avoid the field fluctuation), so that the number of points collected for each run is 30 for all the measurements presented below. The sample might be subjected to various magnetothermai treatments of the following course: RT: sample first kept at room temperature for a t w waiting time of more than one day, then zero-field cooled down to a given temperature T < T~ and relaxation measured;

42

N.X. Phuc et al./ Physica C 256 (1996) 39-50

MT: after RT procedure, sample heated from a temperature T < T~ up to the middle (60 K) temperature, kept for about 30 min, Z F C to T < Tc and relaxation measured; LT: the same as in M T but sample heated to 40 K and kept for about 5 min, then Z F C to T < T~ and relaxation measured. Zero-field cooling was performed after moving the magnet apart from the cryostat. The earth field was not screened so our Z F C means the cooling in a field smaller than 0.5 Oe. One measurement was performed for ErNi2B2C bulk sample cooled in the magnet remanent field (equal to ca. 20 Oe) and is designated as RFC. The measuring field was always larger than the cooling one. The temperature of the sample was set by hand regulating the liquid-helium flow and cooling was always attained with a rate of about 3.5 K / m i n , whereas stabilization o f the temperature was better than + 0.15 K over 1 h. W h e n the thermocouple situated close to the sample holder bottom showed the required measuring temperature, we waited 5 min more before starting the measurements.

3. Results

and

discussion

3.1. Increase o f diamagnetism with time

W e started our study of magnetic relaxation with ZFC and continuous time Ct regime. The first measurement was performed for the YNi2B2C powder sample # 1 in the measuring field of 1000 Oe and at temperature of 4.5 K. W h a t we observed was extremely surprising: the diamagnetism considerably increased over a time of observation of about 30 min. W e repeated the Ct regime measurements six times more for several temperatures in the superconducting state. Two typical curves of DC susceptibility relaxation measured with Ct regime at temperatures of 4.5 and 10 K are shown in Fig. 2. This relaxation process toward stronger diamagnetism will be referred to as the R process. In order to ascertain what part in the diamagnetic relaxation is played by the applied field we changed the time regime of our relaxation experiments into the sequence time St regime (cf. Fig. 1). This St intermittent regime of measurements appeared to be

-0.000

I

YNi2BeC powder H = 1000 Oe

(a)

~-0.001

(b) o) -0.002

-0.003

i,°. . . . . . . .

, ......... i ......... i ......... i ......... i ......... ~. . . . . . . . . 500 1000 1500 2000 2500 3000 3500

Time (s)

Fig. 2. Time dependence of ZFC magnetic susceptibility for YNi2B2C powder measured in a Ct regime at H = 1000 Oe and T = 10 K and 4.5 K, curves (a) and (b), respectively. Note: the jump at t = 1500 s originates in a short turning off of the field. able to provide valuable information about :the complex relaxation phenomena in the time window of the sequence (i.e. t = 33 s). Figs. 3(b) and (c) (brackets denote the label o f the curve) and Figs. 4 - 8 present the last points of the 30 points sets as the data for discussing the global relaxation R process. Results with all experimental points will be presented in Figs. 1 0 - 1 3 and discussed in Section 3.3. A comparison of the results obtained for sample # 1 for two different time regimes is presented in Fig. 3. As one can note from curve (a) and (b) the sequence time regime gave an increased rate of the R process. This is in agreement with the direction of the sudden -0.0015

~

YNizBeC powder H = 1000 Oe T= 4.5K -0.O020

"~-0.0025

-. -0.0030

(b)"

.

Aa

• A

•

•

•A

(¢),

• •

-0.0035

.........

A

aA

aA

.

. •mmm

, ......... [ ......... , ......... , ......... J ........ 500 1000 1500 2000 2500

Time (s)

3000

Fig. 3. ZFC susceptibility vs. time for YNi2B2C powder, measured at H = 1000 Oe and the regimes (a) RT-Ct, (b) RT-St, (c) MT-St. Points of curve (b) and (c) are last points of the measurements in the St regime (see text).

N.X. P h u c et al./ Physica C 256 (1996) 39-50

43

-0.000

T i m e (s) IBm m

500 0.000 . . . . . . . . . . '

YNi2BzC powder T = 4.5 K

(a) mlmwllmlmlmnl

i000

1500

. . . . . . . . . . . . . . . . . . .

,ooo

H

2500

' . . . . . .

' ' "

3000

. . . . . . . .

ErNizBzC b u l k H = 265 Oe T= 4.2K

oo

450 0e

"~-0.005

mmmmmmmmmmmmmmmmm m

e~

•

b

(a)

nmmnm•imm m i l m

%. (b)

-0.008

e°oo~

%,

-0.010

• m

me°~m~emmo

m o• ~

•

..

o

looo

z0oo

aooo

4000

T i m e (s)

-0.015 o

. . . . . . . .

Time

jumps observed in Ct measurements at the time of short field disconnections (Fig. 2(a)). For studying the influence of the magnet•thermal history on the susceptibility of the as-cooled samples the MT temperature treatment was used in addition to the usual RT procedure. The comparison of the effect of the RT and MT treatment is shown in Figs. 3(b) and (c). One can note a strong increase of the as-cooled diamagnetism after the MT procedure. The dependence of the susceptibility on a magnet•thermal treatment is reminiscent of a metastable behavior of spin glass.

Time 500

1000

• •••••••,

2000

2500

"•A•

l'ObO....

6 ..........

3000

(s)

Time

1000 (s)

s u r e d a t H = 265 O e a n d T = 4.2 K f o r t h r e e s e q u e n c e (a) R T , (b) M T a n d ( c ) r e p e a t e d

tempera-

MT.

The field influence on the relaxation rate of the R process for the sample # 1 is presented in Fig. 4. The relaxation rate expressed by the slope of the curve is higher for the lower field. For ErNi2B2C samples only the sequence time measurement regime was used. The results are presented in Fig. 5 for powder and in Figs. 6 - 8 for bulk erbium samples. As one can see, the described effect of increasing diamagnetism was observed again for erbium samples of both the bulk and the powder forms. In comparison with yttrium, the erbium sampies exhibit a considerably larger susceptibility change over the same observation time but the gen-

3500 0.005

(a) A••.

-0.000

(s)

1500

(elm,,,,, '

Fig. 6. Z F C - S t s u s c e p t i b i l i t y v s . t i m e f o r E r N i 2 B 2 C bulk, m e a ture treatments:

0

(b)

• mmmmmmmmmmmmmmm

5000

Fig. 4. ZFC-RT-St susceptibility vs. time curves for Y N i 2 B z C powder measured at T = 4.5 K in two fields: (a) 1000 Oe and (b) 450 Oe.

0.002

2000

. . . . . . . . .

m U m • l e a • • m e rome•mira m e •

~-0.004

-0.012

'

•

A•

ErNizBzC bulk ZFC T = 4~2 K

• A••mA

ErNizB2C p o w d e r H = 285 Oe

0-000

"

~-0.002

• (c)

v

3.4 I~

-x

•

H = 265 Oe

•

(b) o

H = g

150

0e

.~-0.005

mmmmm ~-0,004 o -0.006

mm

[.............- - . . -.. [

A

(e) ..........

t o• . . o • • • • • • • T= 3.4K

,3 -0.008

Time

~z4 0 . 0 1 0

""

A •inm•m

m

mmmm•imi

1000 (s)

Fig. 5. ZFC-St susceptibility vs. time for E r N i 2 B 2 C powder, measured at H = 1000 Oe: (a) RT, Tm = 6.9 K, (b) RT, Tm = 3.4 K. Curve (c) in inset: is the RT regime with a particularly long waiting time (equal to 50 min) at T = 3.8 K.

g

(~) ~ = 4o oe

-0.015

-0.020

.

.

.

.

.

.

.

.., ......... , ......... , ......... , ........ 200 400 600 800 1000 .

.

Time

(s)

Fig. 7. ZFC-St susceptibility vs. time for ErNi2B2C bulk, measured at T = 4.2 K for three measuring fields of 40 Oe, 150 Oe and 256 Oe, correspondingly, for (a), (b) and (c) curves.

44

N.X. Phuc et a l . / Physica C 256 (1996) 39-50 Time (s)

500

loo0

,50o

zo0o

z~0o

aooo

0.005

0.000

ErNizBzC bulk RFC H = 265 Oe T = 4.2 K

I I

•

u•

naB•

"''m...

:~-o.oo5

(a) Ilmll~llllllllBll~

I

m

2-0.O10 g

(b) m..m,•

-0.015

o' ' ' ~66 ' 'fo'oo

Time (s)

(e) mmm

6"

uni

'~66

•

' 'fo'0o

Time (s)

Fig. 8. Time dependence of susceptibility at T = 4.2 K and H = 265 Oe in a St time regime for the ErNi2B2C bulk sample cooled in the magnet-remanent field (RFC) for various temperature regimes: (a) RT, (b) LT, (c) repeated LT.

eral shape of the curves is similar to those observed for the yttrium sample. The influence of the temperature on relaxation probed for ZFC ErNi2B2C powder (Fig. 5(a)) showed that saturation of susceptibility at Tm = 6.9 K is achieved in a shorter time than for lower temperature, Tm = 3.4 K. The measured time dependences are featured by one or more inflection points and the R relaxation curves cannot be described by a single exponential function. Only the shape of " t a i l s " of the curves is common and can be fitted by an exponent. The curves inserted in Figs. 6(a) and 8(a) represent the relaxation in H = 265 Oe and T = 4.2 K for the sample cooled in zero field XZFC(t) or in remanent field of a magnet XRFC(t), respectively. The presence of external vortices pinned during the RFC process makes the shape of the relaxation curve more complex and is responsible for the difference of susceptibility saturation values equal to 0.0016 e m u / g , which corresponds to the remanent field of 3 . 5 0 e . The part of the XRFC(t) curve above the inflection point (t > 1200 s) and the XZFC(t) curve coincide and both can be fitted by the exponential function X(t) cx exp( - t/rR), where r R = 570 s. For the XRFc(t) one should not expect a depinning of vortices because the activation energy at liquidhelium temperature is very low (about 0.4 meV). As was mentioned before, the LuNi2B2C sample cooled with the same cooling rate and processed like

the yttrium and erbium samples, did not show any metastable behavior. The full and stable diamagnetic response at Tm = 4.2 K was obtained immediately after switching on the field. Susceptibility did not change with time and equaled - 0 . 0 1 9 e m u / g and - 0 . 0 1 4 e m u / g for H = 100 Oe and 500 Oe, respectively. To summarize this introductory part we conclude that after a relatively fast cooling in zero field to T < T~ the YNi2B2C and ErNi2B2C samples showed up a suppressed diamagnetism which then increased with time. The diamagnetic relaxation lasted several minutes up to decades of minutes tending to reach a saturation value. Saturation of the susceptibility was achieved more quickly in a weak field and at a higher temperature. " T a i l s " of the relaxation curves can be fitted by the exponential function.

3.2. Extreme susceptibility values It is worth considering the conditions for observing the extreme values of the as-cooled susceptibility. Magnetic response coming from the as-cooled sample depends on both the cooling and measuring fields, as well as on the measuring temperature Tm. For ErNi2B2C in some cases positive values of the susceptibility have been obtained, during the first minutes of observation (see Figs. 5(a), 7(a) and (b), and 8(a)). The results shown in Figs. 5(a) and 8(a) can be explained. The former, obtained for ZFC, Tm = 6.9 K carries the paramagnetic contribution of the Er moments (T N = 6.7 K) (compare Fig. 2 in Ref. [23]). The latter, obtained after cooling in the remanent field of the magnet has a contribution from the magnetic flux trapped in the intergranular phase of our ceramic sample (compare Fig. 13 in Ref. [24]). The positive values for ZFC, Tm = 4.2 K detected at the first seconds in H = 40 Oe and first minutes in 150 Oe shown in Figs. 7(a) and (b) and in detailed form in Figs. 13(a) and (b) are very interesting and shed a new light to the study of the behavior of superconductor shielding in a magnetic field. One should notice that for all curves with positive values of the as-cooled susceptibility the X values first increase towards a stronger paramagnetic state until they reach a maximum and then decrease via a long-time process.

N.X. Phuc et a l . / Physica C 256 (1996) 39-50

0.005

O.O00

.~-0.005

0

Temperature (K) 10 20 30 J ......... L......... i ......... ErNizB2C ( 4 0 0 e )

.........

. . . . . . . . . . . . . . . . . nn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - - ~ # n

$

s o2

(a)~ a

I::i,-0.010

D o D o

o (c)

-0.015

40

ZFC j

(b) ZFC YNizBzC ( 2 1 8

0e)

-0.020 10 Temperature

20 (K)

Fig. 9. ZFC and FC temperature dependences of the susceptibility measured at the used smallest magnetic fields: 40 Oe for the erbium (curves (a, b)) and 218 Oe for the yttrium sample (curve (c)). The upper and lower axis refers to the former and latter sample, respectively.

All detected relaxation curves tend to saturate. The time t S needed to get saturation and the reached susceptibility value Xs depend on the field, temperature and the used measurement regime (Ct or St). For the case of 40 O e (Fig. 7(a)) the stable and full diamagnetism was observed already after several minutes of measurement. One can expect no relaxation, i.e. a full shielding at t = 0 for a very weak field, let us say H = 5 Oe. The two typical ZFC and FC temperature dependences of the susceptibility, registered just after the relaxation measurement, are shown in Figs. 9(a) and (b). The two branches shown in this figure are consistent with those shown in Fig. 2(b) of Ref. [23]. Thus, it is seen that depending on sample treatment one can obtain either a positive as-cooled susceptibility (Fig. 8(a) in this work and Fig. 13 in Ref. [24]) or a strong negative FC branch (Fig. 9(a) in this work and Fig. 2(b) in Ref. [23]). The results show that the time ts and the difference between the maximum possible value and susceptibility saturation value X~ increase with the field. For the case of the yttrium sample the lowest field used was 218 Oe. The ZFC branch measured after a waiting time of 10 min at temperature T = 4.5 K is shown in Fig. 9(c). The susceptibility value obtained for the lowest temperature is comparable with the ideal value of - 1 / 4 " r r . A considerable broadening

45

of the superconducting transition region can be reduced by using a smaller measuring field. On the other hand, the relaxation in the highest used field H = 1 kOe (Ct regime) for YNi2B2C lasted t s = 1 h and the reached Xs at T = 4.5 K equaled 29% of that reported in Ref. [26]. We tried several procedures to get a maximum possible value of susceptibility. The first method was to run a ZFC with our ordinary cooling rate to the lowest temperature and wait for 50 min at this temperature before moving the magnet to the cryostat and starting the measurements. The result of this experiment is shown in the inset in Fig. 5. As one can see, the first points collected after switching on the field (points A*) show already the susceptibility values as low as those obtained after 50 min in an as-cooled measurement (region A in Fig. 5). This observation shows that phenomena responsible for the relaxation R process occur spontaneously after the cooling. Switching the field on in order to collect the data brings an obstacle to reach the fully diamagnetic equilibrium state because of freezing some metastable state of the random network of shielding loops. The other methods were thermal procedures, MT and LT, which led to a much stronger diamagnetic as-cooled state, as demonstrated in Figs. 6(b) and (c), and 8(b) and (c), respectively. We should emphasize that by use of the LT we obtained the same ZFC values as those reported elsewhere [23]. We also note that this ZFC value of the susceptibility, X = - 0 . 0 1 3 e m u / g , was stable (compare Figs. 8(b) and (c)) and in the field of 265 Oe it represented a fully saturated equilibrium response. 3.3. T h e f r a g m e n t a r y p r o c e s s e s

In Figs. 10-13 we present all collected experimental points of the susceptibility versus time for some of the measurements already discussed above. The inset in Fig. 10 shows a representative sequence. A taken from the curve measured at 4.5 K in 450 Oe for the case of the YNi2B2C sample. For the ErNi2B2C sample, four sequences taken at different relaxation stages (marked in Fig. 11) are shown in Fig. 12. The inset in Fig. 11 is provided to present a typical behavior of the case when a stable state with a full diamagnetism (already shown in Fig. 8(b)) had already been settled.

46

N.X. Phuc et a l . / Physica C 256 (1996) 39-50 T i m e (s) 1500 Z000

-0.002 YNi~BzC powder H = 450 Oe T = 4.5 K

500

0.005

~ -0.004

I000

~ftr r (a)

~-o.ooo

-0.0O8

,

,

,

I

435

,

,

,

3000

ErNieB~C H = 265 0e T = 4.2 K

A -0.0080

0.000

2500

"

r~rrrrr~,

455

B

""%'~rrr

c D "",tffr ftgrr~;;;;;;;;;;;

"~-0.005

:5c~

m

-0.008

¢-0.010

g- 0 . 0 1 0

o

. . . . . . . . .

, . . . . . . . . .

2oo

, . . . . . . . . .

, . . . . . . . . .

600

400

T i m e (s)

, . . . . . . . . .

aoo

.... :::

~ooo

(b) -0.015

0

Fig. 11. Time dependence of the RFC susceptibility for ErNi2BeC bulk sample: all points presentation of the curves (a) and (b) from Fig. 8.

These detailed results show that relaxation curves consist of two components of the magnetization each changing in the opposite direction. The first component (called process rl), corresponding to the region of a few first seconds (see the inset in Figs. 10, and 12(c) and (d)), represents the fast process of establishing the maximum diamagnetism at a given stage. For the states with incomplete diamagnetism a dis-

"-:'.2.0

tinct curvature of this relaxation curve is observed because of simultaneous appearing of the second (opposite) process. The second component (called process r2) comes from the decrease of diamagnetism and, comparing to the r~ is a slower process. The characteristic time of the process r~ varies depending on several factors

-3.0

v

r"

/I

~1.0

ErNi2B2C B

.

~;

=

T=

f

im

265

0e

4.2K

-4.0

/

(a)

.~o.%

(b) -5.0 105 1220 -5.0

85

-'--2._4.5

1240

? i

1260

(d)

(c) "~'-5. D

i000

T i m e (s)

Fig. 10. Susceptibility of YNi2B2C powder vs. time. The presentation of all 30-points sets (see text) of the curve (b) in Fig. 4. The inset shows the enlargement of the marked sequence A.

-5.5

ID ,

-~3o

,m

2050 Time (s)

-6.0 2070 2820

2840 Time (s)

2860

Fig. 12. Susceptibility of ErNi2B2C bulk vs. time. Curves (a), (b), (c) and (d) Correspond to the sequences marked as A, B, C and D in Fig. 11.

N.X. Phuc et a l . / Physica C 256 (1996) 39-50 0.004

47

0.0016 BrNieBeC bulk ZFC T = 4.2 dlB

0.000

(b)

H

=

150

K

,IP

Oe

S

.~0.0014

(c) H = 265 Oe

~--

.o~-0.004 ~0.0012

~

-0.006

m ~0.0010 o "~ - 0 . 0 1 2 .

(a)

H =

40

0e

~:~0.0008

-0.016

0

100

200

300 Time (s)

400

500

600

Fig. 13. Susceptibility of ErNi2B2C bulk vs. time; all points presentation of the corresponding (a), (b) a n d (c) curves from Fig. 7.

ErNizBzC bulk It = 2 6 5 Oe T = 6.9K 0.0006 200

400

600

800

1000

T i m e (s) Fig. 15. Time dependence of susceptibility for Z F C E r N i 2 B a C for H = 265 Oe at T = 6.9 K. Note: there is a 15 s shift between switching on the field and starting to detect points.

such as the measuring temperature, the measuring field and, also, the local stage of the evolution of the R process (see Fig. 13). The RFC measurement at 265 Oe for the erbium sample provided a regular variation of the r2 process over the whole occurrence of the R process, which might be worth of analyzing (see Figs. 1 l(a) and 12). When we assume that the process r2 develops from the maximum diamagnetism point to the last measured point (as the equilibrium state), the difference between these two points, A X, can be treated as an amplitude of the process. Its evolution over the observation time is presented in Fig. 14. In the

4.0

,, ErNiaB2C H = 265 Oe T = 4.2K o oO o

3.0

,o •

ooooo experiment ..... fit = A exp(-B't). Y 33, B = 1 / 5 4 0

k

OOo

Oo °

£,~

interval above 1200 s the decay of the amplitude of r2 process follows the exponential law

A X( t ) ¢x e x p ( - - t / r ) , with ~-= 540 s, (cf. Fig. 14). The time constant of the r2 process is more or less the same as that estimated from the corresponding R curve from Fig. 6(a), which equals 570 s. Thus, one can say that the increase of diamagnetism (process R) is gained at the expense of the decreasing magnetic moment of the positive sign. The last figure, Fig. 15, shows the behavior of the response for the ZFC erbium sample in H = 265 Oe at T = 6.9 K with the 15 s shift between switching on the field and starting to detect points. One can notice a much stronger time dependence of the r 2 process at this elevated temperature.

3.4. Discussion

\ o

2.0

o

oo o

"o ', ',,o "Qo

.,Q ,Q

1.0

0.0

........ 0

t ......... i ......... t ......... r ......... *........ , 500 1000 1500 2000 2500 3000

Time (s) Fig. 14. The evolution of the A X amplitude of the r2 relaxation process (see text) with time.

The magnetic susceptibility observed in the present work is composed of a stable, nondissipative diamagnetic part and of a decaying contribution of a positive sign. The decay of the magnetic state (Fig. 14) showing up in the increase of a shielding during the R process reminds one of the FC magnetization metastable state observed by Zhao et al. [6] for a PME sample and the diamagnetic relaxation investigated by Wolf and Gey [15] close to Tc in

48

N.X. Phuc et al. / Physica C 256 (1996) 39-50

ZFC YBCO single crystal. Although in their measurements Wolf and Gey found no indication of PME, nevertheless they explained their finding in terms of the orbital glass [11] possibly formed by a network of Josephson loops containing q-r junctions. The behavior discovered by us of ZFC susceptibility for YNi2B2C and ErNizB2C samples shows all the features characteristic for a glassy state of orbital moments associated with circular currents through negative Josephson junctions [ 11,12]: (1) coexistence of a paramagnetic state with the superconducting state, (2) metastability, (3) magnetothermal history effects, (4) a complex time dependence of the susceptibility pointing to the variety of relaxation times/rates, (5) the fact that thermal fluctuations destroy paramagnetic moments. From the other side, the field dependence of the effects observed is opposite t o that characteristic for PME, regardless the quite different field regions. In our case the difficulties in reaching the fully diamagnetic state increase with the field value. The " u n usual 'r relaxation would not be seen in the very weak field or by the AC method. The characteristics of our effect bear a resemblance to those of the resistive transition to the superconducting state in the magnetic field: a sharp temperature dependence at H = 0 and the smeared-out one at H > 0. However, thermal drift which might induce an increase of diamagnetism was fully excluded by the experimental arrangement and thermal stability was additionally proved by a stable and fully diamagnetic behavior of the LuNizB2C sample. The explanation of the non-typical properties of our YNi2B2C and ErNizB2C samples may come from the specific structure of the intergranular phase. As was mentioned before, both Y and Er samples contain a small amount of secondary phases, contrary to the Lu sample which was a single phase. Therefore, the foreign phase present in the material is probably resposible for the untypical behavior. Nevertheless, one should find a mechanism responsible for the time dependence of the magnetic shielding. It is clear that the size and the relative alignment of the grains and the type of the junctions between the grains decide about the actual current distribution in the sample and so, about the magnetic-screening

capability. In a ceramic superconductor there are two current systems, the first corresponding to high currents (J~Jc) circulating within the grains and the second system of low macroscopic currents flowing through the junctions. The critical currents of the junctions are inhomogeneous and depend strongly on H and T. Even in a single-phase superconductor the magnetic field affects the junctions and may drive them to the resistive state, leading to the, so-called magnetic granularity [27]. Magnetic granularity for the ZFC Ag sheathed BSCCO tape has recently been convincingly imaged by the magnetooptical technique [28]. It was found that laminar, high-jc magnetization current flow takes place through the colonies of well-aligned long grains while the less aligned structure of smaller grains is associated with percolative behavior and a much lower current-carrying capability. It was further shown that at higher external fields the direction of magnetization currents in some loops can be opposite to that in the high-jc layers because those paths are chosen which minimize the overall dissipation. In this situation the flux profiles are homogeneous Bean-like at low fields but become very inhomogeneous in higher fields. As a result, the flux can effectively bypass high-jc regions, accumulating in domains with reduced JeThe optical micrograph picture (enclosed in Ref. [26]) of the YNi2B2C sample taken from the same batch as our sample shows the system of well aligned grains divided by secondary-phase plates of width equal up to 2.5 Ixm. One may consider the precipitations of secondary phase playing the role of unaligned small grains associated with a low currentcarrying capability. So, a magnetic granularity model can be adapted to our problem because of microstructural non-uniformities which may be a reason of significant inhomogeneity of current distribution. The resistive character of these weak currents results in the electromagnetic instability of the system showing up in a decrease of the relevant magnetic moment. At the moment it is difficult to predict whether assuming a high enough contribution of current loops with opposite direction to that of the nondissipative shielding currents one could get an explanation of the effects observed without invoking -rr junctions as the origin of positive moments. Anyhow, the picture of randomly distributed current loops giving rise to the glassy state of orbital mo-

• N.X. P h u c et a l . / P h y s i c a C 256 (1996) 3 9 - 5 0

ments (macrovortices) is a good description of the shielding pattern in our samples. The constant external magnetic field will tend to freeze the macrovortex structure with the positive contribution proportional to the field value which will coexist with the diamagnetic shielding. Thus, the obtained equilibrium state will be like that predicted in Ref. [12] and this is what we see in the experiment. For a magnetic-granularity explanation the time dependence of the susceptibility would be connected with the resistive character of the intergranular currents giving the electromagnetic instability and a decrease of the relevant magnetic moment. In the xr junction picture a model [29] based on thermally activated flipping of spontaneous orbital magnetic moments should hold. Finally we would like to mention that it is interesting why such relaxation effects have not been observed for other superconducting samples investigated in the literature, many of which appeared not to be an ideal single phase. Probably, in the geometry with the magnetic-field gradient which is an attribute of our measurement technique the inhomogeneity of current distribution is intensified and all instability effects are more evident. In addition, the used fast cooling with only one direction of temperature change favors trapping the system in the metastable state. In conclusion, we have shown that when being treated via a rather fast cooling the YNi2B2C and ErNi 2 B2C samples exhibited an incomplete diamagnetism and that the as-cooled susceptibility relaxed towards a stronger diamagnetic state. Depending on the field value the diamagnetic relaxation lasted several minutes up to decades of minutes (for H = 1 kOe) tending to reach a saturation value. Saturation was achieved more quickly in a weak field and at a higher temperature. The susceptibility-saturation value differed from that of the full shielding and this discrepancy increased with the field. On the basis of the sequence field-on intermittent measurement regime a decaying positive contribution to the susceptibility has been investigated. A simple thermal procedure could destroy the positive moment. We ascribe the unusual behavior of our samples to the small amount of nonmagnetic nonsuperconducting secondary phase which may be a reason for the enhanced magnetic granularity [27,28] for which an inhomogeneous current distribution may lead to the

49

occurrence of intergranular current loops with opposite direction to that of the high-current shielding loops [28]. At present, it is difficult to say if a mechanism based on magnetic granularity alone can give an explanation of the effects observed or one has to invoke a 7r junction origin of the positive moments. Probably, the field gradient connected with our measuring technique and a fast cooling with only a negative temperature drift favor the observation of the instability effects like those reported above.

Acknowledgements We express many thanks to N.M. for kindly providing the samples, for correspondence and stimulating discussions. We are also indebted to G. Hilscher, J. Janik, A. Szytuta and P. Nordblad for their interest in this work and valuable discussions. We are especially grateful to J. Spatek for critical reading of the manuscript. One of the authors NXP expresses his gratitude to the Institute of Nuclear Physics in Krak6w and the International Programmes in Physical Sciences in Uppsala for the financial support.

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