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A μSR determination of the penetration depth in superconducting YNi2B2C
ELSEVIER
Physica C 233 (1994) 273-280
A @R determination of the penetration depth in superconducting YNi2B2C R. Cywinski ‘,*, Z.P. Han ‘, R. Bewley a, R. Cubitt b, M.T. Wylie b, E.M. Forgan b, S.L. Lee ‘, M. Warden ‘, S.H. Kilcoyne d aJ.J. Thomson Physical Laboratory, University ofReading, Reading RG6 2AF, UK b School ofphysics and Space Research, Birmingham University, Birmingham, B15 2Ti7 UK c Physik-Institut der Universittit Zurich, CH-805 7 Zurich, Switzerland d ISIS, Rutherford Appleton Laboratory, Chilton. Oxon OXI 1 OQX, UK Received 20 July 1994; revised manuscript received 20 September 1994
Abstract Muon spin rotation (pSR) and magnetisation measurements have been used to characterise the superconducting state of YNi2B2C below r,= 15 K. A measured &(O) of 6.0( 5) T and B,, (0) of 36.9(5) mT from magnetisation measurements, together with the pSR measurements, provide a coherence length, <( 0), of 8.1 nm and a magnetic penetration depth, I(O), of 103 nm. The temperature dependence of the penetration depth deduced from the pSR measurements is consistent with the BCS model and implies conventional s wave pairing in YNi,B&. Using these results together with existing thermodynamic data we estimate a superconducting carrier density of 1.9 per formula unit and an electron-mass enhancement factor of 9.4.
1. Introduction The discovery of a new family of superconductors always arouses considerable interest. Such interest has been particularly intense in the case of the recently reported R-T-B-C quaternary compounds, where R is a rare earth or Y and T is Ni or Pd [ l-5 1. This is largely because superconductivity is observed at temperatures close to the maximum yet found for metallic alloys: a T, of 23 K is reported for Y-Pd-B-C [ 3 1. However, early claims that these quaternary compounds constitute a new class of superconductors [ 41 still require substantiation by careful characterisation of the superconducting ground state. One of the most fundamental parameters of the superconducting state is the magnetic penetration depth, * Corresponding author.
1. Its low-temperature value is directly related to the effective mass, m*, and density, n,, of the superconducting carriers through nJm*, while its temperature dependence provides information on the symmetry of the superconducting pairing mechanisms. Muon spin rotation ( ySR) is a unique tool with which to probe the microscopic internal field distribution in the bulk of a type-II superconductor (see, e.g. Ref. [ 61). A study of the details of the probability distribution of internal fields, p(B), can provide valuable information on the internal arrangement of flux vortices, and pSR has been successfully used to detect changes of the vortex structure at a microscopic level [ 71. What is of particular importance is that determination of the width of p (B), via measurement of the @R depolarisation rates in the mixed state, allows a reliable estimate to be obtained of the superconducting penetration depth L(T).
0921-4534/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIO921-4534(94)00604-O
274
R. Cywinski et al. /Physica C233 (1994) 273-280
In the present study we used uSR techniques to probe the superconducting state of a well characterised sample of YNi2B2C ( T,= 15 K) with the aim of extracting n(T). In addition we have made conventional magnetisation measurements, which yield information about the macroscopic bulk properties, from which can be extracted complementary information about the superconducting state, especially at applied fields beyond the range where it is appropriate to use pSR.
3. Results 3.1. Magnetisation measurements Fig. 1 (a) shows zero-field cooled (ZFC ) and fieldcooled (FC) magnetisation measurements on the resin-bonded YNi2B2C powder sample in a field of 20 mT. The superconducting transition temperature in this field is 14.9 K. At 5 K the initial field-dependent magnetisation of the YNi2B2C sample is linear (Fig. 1 (b) ) and consistent with a diamagnetic sus-
2. Experimental
A 12 g sample of YNi2B2C was prepared by melting together appropriate quantities of Y (99.9%), Ni (99.99%), B (99.99%) and C (99.99%) in an argon arc furnace. The resulting ingot was coarsely powdered, resulting in plate-like grains. X-ray and neutron-diffraction measurements showed the sample to be essentially single phase with the modified ThCrzSiz structure reported earlier [ 5 1. However, the diffraction patterns also show evidence of impurity phases at the level of approximately 10 vol.%. Muon spin rotation (l&R) measurements were performed at ISIS (U.K.) and PSI (Switzerland) using the MuSR [ 81 and 1tM3 spectrometers in transverse geometry i.e. spin-polarised positive muons were incident on the sample face with spin vectors perpendicular to the applied field. The uSR sample consisted of powdered YNi,B,C bonded with epoxy resin and mounted in the form of a 25 mm diameter, 4 mm thick, pellet. The resin constituted less than 4 wt.% of the total sample. The aluminium sample holder was masked with powdered, resin-bonded, Fe203; muons implanted in haematite depolarise too rapidly to contribute an unwanted background signal in the time regime of interest. Magnetisation measurements down to 4 K, and in fields of up to 12 T, were made using an Oxford Instruments Vibrating Sample Magnetometer (VSM) on a 0.26 g piece of YNi2B2C resin-bonded powder taken from the same sample used in the uSR experiments.
FC
Temperature
z-
(K)
20.0
2
z:
-25.0 0.0
5.0
10.0
Field(
15.0
20.0
103A/m)
Fig. I. (a) Temperature dependence of the zero-field cooled (ZFC) and field-cooled (FC ) magnetisation of YNi,BzC in an applied field of 20 mT. (b) Magnetisation of the YNizBJ sample in the Meissner region at a temperature of 5 K as a function of applied field. Closed and open circles represent data taken with increasing and decreasing field, respectively. The solid line corresponds to a susceptibility of x= - 1.4, while the dotted line showsx= - 1.5.
R. Cywinskiet al. / PhysicaC 233 (I 994) 273-280
ceptibility of x= - 1.4. A random alignment of the plate-like YNi2B,C grains should lead to a spherically averaged demagnetisation factor of N= f , and hence a diamagnetic susceptibility of x= - 1.5. The discrepancy between this and the measured value is attributable to the non-superconducting impurity phases in the sample. Magnetisation measurements were performed principally to map the temperature dependences of the upper and lower critical fields, Bc2 and B,,, of the YNi2B2C sample. The values obtained will subsequently be used to deduce the low-temperature values of the London penetration depth and the coherence length for comparison with the values obtained by the uSR experiments. B,, (T) was estimated by first cooling the sample in zero field and then measuring minor isothermal hysteresis loops to progressively higher magnetic fields. The field at which the loops begin to open indicates flux penetration, and hence the upper limit of the Meissner state. The resulting B,, (T) is shown in Fig. 2 taking into account the demagnetisation factor to give the true thermodynamic value. The data closely follow the conventional empirical relationship
40.0 t
with B,,(O)=37 mTand T,= 14.9 K. Bc2( T) was determined by measuring the fieldcooled magnetisation of the sample and noting the onset temperature for superconductivity in that field. The results are plotted in Fig. 3. B,, ( T) clearly does not follow the empirical quadratic temperature dependence given by Eq. ( 1). Instead a marked concave curvature is apparent as T, is approached. Such a temperature dependence of B,, ( T) is observed in a diverse range of superconducting materials, including high-T, cuprates, barium bismuthates and transition metal dichalcogenides. The phenomenon is variously attributed to magnetic impurities, to layered crystal structures (and hence to anisotropy ), to large TJphonon frequency ratios, and to multiple superconducting phases [see Ref. [ 93 and references therein]. It is too early to speculate which of these mechanisms are responsible for the form of Bc2( T) in YNi2B2C, although we believe that the last can be excluded. It should also be noted that the curvature of Bc2( T) is not only seen in the resin-bonded powder sample studied here, but also in bulk samples. The form of Bc2( T) makes extrapolation to zero temperature rather unreliable. However, below 12 K a reasonable fit of Eq. ( 1) to the measured B,,( T) can be obtained. The fit gives a somewhat reduced T, of 13.5 K and an upper critical field, Bc2( 0), of 6.0( 5) T.
6.0
1.0
0.0
t
0
215
I
’
5
10
Temperature
.a--’
F
YNi,B,C
15
(K)
Fig. 2. Temperature dependence of the lower critical field, B,, ( T) of YNi2B2C. The solid line represents a fit of the empirical relation of Eq. ( I), with T,= 14.9 K and B,, (0) = 36.9 mT.
Temperature
(K)
Fig. 3. Bc2( T) of YNi2B2C. The solid line is a fit of Eq. ( 1) with r,= 13.5 and &(O) = 6.0 T, while the dashed line is a guide to the eye.
276
R. Cywinskiet al. /Physica C 233 (1994)273-280
The magnitude and form of Bc2( T) are similar to those recently reported for YNi,B,C [ lo]. Bc2 (0) is rather low in YNizB$Z, and suggests that the upper critical field may be Pauli paramagnetic limited. Such an effect is evident in, for example, V,Si [ 111, and is perhaps to be expected in a Ni based superconductor. Working within the framework of the GinzburgLandau theory in the limit K=A/(> 1 we have [ 121 Bc2(T)=
&-!27rrz(T)
’
isation function describing the oscillating counting rate, the Fourier transform of which is the distribution of rotation frequencies which is in turn proportional to the probability distribution of internal field valuesp(B). For a genera1 type-II superconductor, the internal field variation is a function of the penetration depth, d, the coherence length,
(2)
and
(%,kZO) , (3) where t(T) is the superconducting coherence length, and n(T) is the penetration depth. Substitution of the experimentally determined upper critical field, Bc2(0) =6.0( 5) T, in Eq. (2) gives a coherencelength of ((0)=7.4(3) nm. An estimate of A(O) can then be obtained from Eq. (3 ): assuming B,, (0) = 37 ( 1) mT we find A( 0) is approximately 108 nm. For a significantly more reliable determination of 2 (0) we now turn to the uSR measurements. 3.2. ,uSR measurements Muon-spin rotation allows a direct measure to be obtained of the probability distribution of internal magnetic fields within the bulk of a type-II superconductor in the mixed state [ 6 1. Low-momentum spinpolarised muons, after coming to rest in the sample, undergo Larmor precession around the local internal field at angular frequency w= yB, where y= 2rc 135.5 x lo* rads-‘T-l, and Bis the local field. The range of internal field values thus gives rise to a range of muon-precession rates. The muon, which has an average lifetime of r=2.2 us, decays into two neutrinos and a positron, the latter being emitted preferentially along the muon-spin direction. Positron counts as a function of time and the angle to the initial spin polarisation can be described by the following relation: N(&t)=N,exp(-t/r)[l+AR(t)]+b,
(4)
where No is a normalisation constant, A is the precession amplitude or asymmetry, 8 is the initial phase and b is a constant background. R(t) is the depolar-
(5)
where B. is the mean field, b= B,/Bc2, and the sum is over all non-zero reciprocal lattice vectors, qh,k, of the flux-line lattice. In the London limit t-0, and when the applied field is well above B,, (Aq,,l > 1) the second moment of the internal field distribution can be deduced from the simplified version of Eq. ( 5 ) [ 14 ] :
The temperature dependence of ( AR2 )I/’ is thus directly proportional to the density of superelectrons. Although Eq. (6 ) is often found to be a good approximation for the case of the high-T, cuprate superconductors in applied fields Bx= Bcl, it was found to be an inappropriate oversimplification in the case of the present measurements, as will be discussed below. The standard deviation of field values (AR’ ) “’ was measured directly from the widths of the Fourier spectra obtained by the technique of maximum entropy which requires no mode1 of the form of p( B). The temperature dependence was measured at the applied field of 45 mT and the field dependence by cooling to 3 Kin a range of fields up to 550 mT. Above the superconducting transition temperature muon depolarisation was found to be negligibly small. The measured values of ( AR2 ) ‘/2 ( T) at 45 mT obtained at the different muon sources of ISIS and PSI are shown in Fig. 4 with a conventional BCS temperature dependence. Due to a very fast depolarisation of the muon spin we were unable to obtain reliable data at low temperatures with the ISIS facility. The lowtemperature value ( AB’) ‘/’ of 11.5(4) mT corresponds to a penetration depth, A( 0), of 104( 3) nm
R. Cywinskiet al. /PhysicaC 233 (1994) 273-280
217
6.0
2.0
~-
BCS
theory 0.1
0.0
0.2
O.O 0t--r-7e% Temperature
Time
0.3
0.4
0.5
0.6
0.5
0.6
(microseconds)
(K) (b)
F&4. The variation of the @R internal field variation, (AB’)“‘, with temperature for an applied field of 45 mT. The solid lines represent a conventional BCS temperature dependence in the clean limit with (AB*)‘/*(O)= 11.5(4) mT and T,= 14.2 K.
at 45 mT using the simplified proportionality relation of Eq. (6). Typical data taken above and below T, are shown in Figs. 5(a) and (b) with the muon lifetime and background ( Noexp( - t/r) + b) subtracted. Also shown are the respective probability distributions of internal fields, the Fourier transforms of which allow the lit to be compared to the data in the time domain. Above T, the lineshape is as expected, narrow and gaussian reflecting the nuclear dipole contribution to the internal field distribution. At low temperatures a broad and relatively symmetrical distribution is observed. This lineshape possibly arises from the broad distribution of demagnetising factors anticipated from the sample of randomly oriented plate-like grains. It is important to note that ( AB2 ) “’ has been extracted using a model-independent Fourier transform process and is therefore not subject to the inherent errors incurred by assuming the conventional gaussian lineshapes. From the magnetisation measurements described above it is clear that the 45 mT applied in this uSR experiment is not very much greater than the measured B,,(O) of 36.9 mT. In addition it is apparent from the value of HC2, that at moderate fields the finite flux-line core size will have a significant effect on z (AB ) “2. Eq. (6) can thus be expected to lead to a
T=3K
t.,,.1....,....1....1...,I,...l.d 0.0
0.1
0.2
Time
0.3
0.4
(microseconds)
Fig. 5. Raw data with the muon lifetime and background (No exp( -t/r) +h) subtracted. With the applied field at 45 mT the data are shown at (a) 15 K and (b) 3 K. The insets show p(B) as deduced from the maximum-entropy technique, the Fourier transforms of which, after multiplication by the factor No exp ( - t/r)A can be compared to the data.
modification of the deduced value of I (0). This effect is evident in the reduction of the low-temperature values of ( AB2 ) ‘I2 with increasing applied fields (Fig. 6). In order to account for these effects it is necessary to use the full expression given by Eq. ( 5). The sum in Eq. (5) has been evaluated for a range of internal fields using ((0) =8.1 nm and A(O) = 103 nm. The resulting theoretical dependence of ( AB2 ) ‘I2 on the internal magnetic field Bo, is plotted in Fig. 6 with the values of (AB2 ) ‘I2 and B. deduced from p(B) at different applied fields. For fields greater than 100
R. Cywinski et al. / Physica C 233 (I 994) 2 73-280
278
measurements, considering the essentially different nature of the two techniques. Finally it should be noted that in the above analysis we have assumed that YNi2B2C is an isotropic superconductor. The layered nature of the unit cell [ 5 1, in which structurally distinct R-C and B-Ni planes are evident, might lead to anisotropic features in the superconducting state. This possibility will be explored in greater detail elsewhere.
12.0
z
10.0
2
? N
8.0
:
6.0
4. Discussion and conclusions T=3K 4.0 0
100
200
Internal
300
field
400
500
600
(mT)
Fig. 6. The solid line shows the dependence of (AB’ ) ‘I2 on mean internal field, &,, calculated using Eq. (5) and assuming <( 0) = 8.1 nm and a penetration depth of A(O) = 103 nm. The data points are the measured values of ( AB * ) ‘I* derived from p(B) from the JSR measurements plotted at the internal field value deduced from the mean ofp(B).
mT the curve is a good description of the data. At lower flux densities, where the inter-vortex repulsion is reduced, the data lie above the calculated curve. This is most likely due to the enhancement of (AB2)“2 resulting from disorder of the flux-line structure in the presence of pins. This effect is well documented in high-T, materials where a broadening of p( B) is often observed at low fields [ 15 1. In considering the effects of the suggested distribution of demagnetising factors present within the sample we find that even for a relatively broad distribution neither the shape of the curve shown in Fig. 6, nor our estimate of A( 0), is significantly modified. Uncertainties in the value of n(O) from this source are within the quoted error. The values of A( 0) and t(O) determined from the uSR measurements allow an estimate of the Ginzburg-Landau parameter to be made: K=A/(= 13 ( 1). This in turn can be used to perform a simple self-consistency test to estimate B,, from Eq. (3): for /2(0)=103(3) nm we obtain &=40.1 mT compared to 36.9 mT determined directly from the magnetisation measurements. This constitutes a reasonable agreement between the uSR and magnetisation
Using the value for the penetration depth determined from our uSR measurements, together with existing thermodynamic and conductivity data we can attempt to extract values for the superconducting carrier density and the effective mass of the carriers. The London formula gives (7) where m * is the effective carrier mass, n, is the electron density and r, (=2.82x IO-i5 m) classical radius of the electron. l= is the electron free path and in the clean limit r/Z, << 1, while dirty limit c/l, Z+ 1. The Sommerfeld constant, tracted from the linear electronic contribution heat capacity can also be expressed in terms effective mass and carrier density, n,: y=
0 f
superis the mean for the y, exto the of the
2’3kirn*Q3 fi2
’
(8)
For conventional superconductors n, at T=O, is equivalent to the carrier density, n,, above T,. The reported value for y for YNi,B,C is 18 mJ/mole K* [ lo], while the resistivity just above T, is very small, typically 2 ucm [ 41. From these results a mean free path, I,, of 50 nm can be estimated, implying a dirtylimit correction of only 7%. Combining Eqs. (7) and (8 ) we estimate a carrier density of n, = 2.9 x 1022 cmw3, corresponding to 1.9 carriers per formula unit. Such a value is not entirely consistent with the supposition in Ref. [ IO] that the Ni 3d band is filled and the 4d states are responsible for the observed superconductivity in YNi2B2C. The mass enhancement factor, m*/me is calculated to be 9.4. While this value
R. Cywinski et al. / Physica C 233 (I 994) 273-280
279
Table 1 A summary of the superconducting ground state parameters of YNisBzC obtained from these pSR and magnetisation studies
Tc W)
&(O) (mT)
42(O) U)
n(O) (nm)
80) (nm)
n, (cm-))
15
36.9
6.0
103
8.1
2.9x lo**
a
??l*/m a
TF (K) a
9.4
4200
a These parameters have been estimated using values of p and y taken from Refs. [ 4 ] and [ 10 1, respectively.
is approximately twice that of the high-T, cuprate superconductors, it is much lower than that generally associated with the heavy-fermion compounds (i.e. typically > 100 ) . Table 1 summarises the parameters determined from this study of the superconducting state of YNi2B2C. Uemura [ 161 has proposed a method by which superconductors may be classified according to their critical point, T,, and Fermi temperature, T,: a plot of T, versus T, reveals a “universal curve” encompassing the more exotic superconductors, i.e. high-T, cuprates, organic superconductors, Chevrel phases, heavy fermions and ChObased compounds. All these materials are characterised by large ratios of TJT,, in the range 1 / 100 to 1/ 10, while the more conventional BCS superconductors have TJ TF less than 1/ 1000. Estimating T, for YNi2B2C using the expression: k T = ft2(37c2n,)2’3 B F
2m+
(9)
we find T,/T,= l/280. This places YNi2B2C at the very limits of Uemura’s class of exotic superconductors, and in fact, close to V$i which is also a Pauli paramagnetic limited superconductor [ Ill. Although clearly a member of an “exotic” family, in the sense that several RNi2B2C compounds support coexisting superconductivity and magnetic order [ 17 1, YNi2B2C cannot readily be classed with other unconventional systems, such as the high-T, cuprates, the fermions, or heavy the Chevrel phase superconductors.
Acknowledgements We gratefully acknowledge the Swiss National Science Foundation (NFP30 4030-32785), the Science and Engineering Research Council and the BritishSwiss Joint Research Program for financial support.
We should also like to thank W.I.F. David for his interest and advice, and G. Hilscher for a pre-print of Ref. [lo].
References
[ 11 C. Mazumdar, R. Nagarajan, C. Godart, L.C. Gupta, M. Latroche, SK. Dhar, C. Levy-Clement, B.D. Padalia and R. Vijayaraghavan, Solid State Commun. 87 ( 1993) 413. [2] R. Nagarajan, C. Mazumdar, Z. Hossain, SK. Dhar, K.V. Gopalakrishnan, L.C. Gupta, C. Godart, B.D. Padalia and R. Vijayaraghavan, Phys. Rev. Lett. 72 (1994) 274. [ 31 R.J. Cava, H. Takagi, B. Batlogg, H.W. Zandbergen, J.J. Krajewski, W.F. Peck Jr., R.B. van Dover, R.J. Felder, T. Siegrist, K. Mizuhashi, J.O. Lee, E. Eisaki, S.A. Carter and S. Uchida, Nature (London) 367 (1994) 146. [4] R.J. Cava, H. Takagi, H.W. Zandbergen, J.J. Krajewski, W.F. Peck Jr., T. Siegrist, B. Batlogg, R.B. van Dover, R.J. Felder, K. Mizuhashi, J.O. Lee, E. Eisaki and S. Uchida, Nature (London) 367 (1994) 252. [ 51 T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski and W.F. Peck Jr., Nature (London) 367 (1994) 254. [6] W.D. Wu, A. Keren, L.P. Le, B.J. Stemlieb, G.M. Luke, Y.J. Uemura, P. Dosanjh and T.M. Riseman, Phys. Rev. B 47 (1993) 8172. [ 7 ] S.L. Lee, P. Zimmerman, H. Keller, M. Warden, I.M. Savic, R. Schauwecker, D. Zech, R. Cubitt, E.M. Forgan, P.H. Kes, T.W. Li, A.A. Menovsky and Z. Tamawski, Phys. Rev. Lett. 71 (1993) 3862. [ 81 G.H. Eaton, Z. Phys. C: Particles and Fields 56 (1992) S232. [ 91 M. Affronte, J. Marcus, C. Escribe-Filippini, A. Sulpce, H. Rakoto, J.M. Broto, J.C. Ousset, S. Askenazy and A.G.M. Jansen, Phys. Rev. B 49 ( 1994) 3502. [lo] N.M. Hong, H. Michor, M. Vybomov, T. Holubar, P. Hudegger, W. Perthold, G. Hilscher and P. Rogl, Physica C 227 ( 1994) 85. [ 111 M. Schossman and E. Schachinger, Phys. Rev. B 33 ( 1986) 6123. [ 121 M. Tinkham, Introduction to Superconductivity (McGrawHill, New York, 1975). [ 131 P. Pincus, A.C. Gossard, V. Jaccarino and J. Wemick, Phys. Lett. 13 (1964) 21. [ 141 E.H. Brandt, Phys. Rev. B 37 (1988) 2349.
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[ 151 B. Pumpin, K. Keller, W. Kundig, I.M. Savic, J.W. Schneider, H. Simmler, P. Zimmermann, E. Kaldis, S. Rusiecki, C. Rossel and E.M. Forgan, J. Less Common Metals 164&165 ( 1990) 994.
[16]Y.J.Uemura,PhysicaC 185-189 (1991) 733. [ 171 R. Cywinski, Z.P. Han and B.D. Rainford, (1994), in preparation.
Physica C 233 (1994) 273-280
A @R determination of the penetration depth in superconducting YNi2B2C R. Cywinski ‘,*, Z.P. Han ‘, R. Bewley a, R. Cubitt b, M.T. Wylie b, E.M. Forgan b, S.L. Lee ‘, M. Warden ‘, S.H. Kilcoyne d aJ.J. Thomson Physical Laboratory, University ofReading, Reading RG6 2AF, UK b School ofphysics and Space Research, Birmingham University, Birmingham, B15 2Ti7 UK c Physik-Institut der Universittit Zurich, CH-805 7 Zurich, Switzerland d ISIS, Rutherford Appleton Laboratory, Chilton. Oxon OXI 1 OQX, UK Received 20 July 1994; revised manuscript received 20 September 1994
Abstract Muon spin rotation (pSR) and magnetisation measurements have been used to characterise the superconducting state of YNi2B2C below r,= 15 K. A measured &(O) of 6.0( 5) T and B,, (0) of 36.9(5) mT from magnetisation measurements, together with the pSR measurements, provide a coherence length, <( 0), of 8.1 nm and a magnetic penetration depth, I(O), of 103 nm. The temperature dependence of the penetration depth deduced from the pSR measurements is consistent with the BCS model and implies conventional s wave pairing in YNi,B&. Using these results together with existing thermodynamic data we estimate a superconducting carrier density of 1.9 per formula unit and an electron-mass enhancement factor of 9.4.
1. Introduction The discovery of a new family of superconductors always arouses considerable interest. Such interest has been particularly intense in the case of the recently reported R-T-B-C quaternary compounds, where R is a rare earth or Y and T is Ni or Pd [ l-5 1. This is largely because superconductivity is observed at temperatures close to the maximum yet found for metallic alloys: a T, of 23 K is reported for Y-Pd-B-C [ 3 1. However, early claims that these quaternary compounds constitute a new class of superconductors [ 41 still require substantiation by careful characterisation of the superconducting ground state. One of the most fundamental parameters of the superconducting state is the magnetic penetration depth, * Corresponding author.
1. Its low-temperature value is directly related to the effective mass, m*, and density, n,, of the superconducting carriers through nJm*, while its temperature dependence provides information on the symmetry of the superconducting pairing mechanisms. Muon spin rotation ( ySR) is a unique tool with which to probe the microscopic internal field distribution in the bulk of a type-II superconductor (see, e.g. Ref. [ 61). A study of the details of the probability distribution of internal fields, p(B), can provide valuable information on the internal arrangement of flux vortices, and pSR has been successfully used to detect changes of the vortex structure at a microscopic level [ 71. What is of particular importance is that determination of the width of p (B), via measurement of the @R depolarisation rates in the mixed state, allows a reliable estimate to be obtained of the superconducting penetration depth L(T).
0921-4534/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIO921-4534(94)00604-O
274
R. Cywinski et al. /Physica C233 (1994) 273-280
In the present study we used uSR techniques to probe the superconducting state of a well characterised sample of YNi2B2C ( T,= 15 K) with the aim of extracting n(T). In addition we have made conventional magnetisation measurements, which yield information about the macroscopic bulk properties, from which can be extracted complementary information about the superconducting state, especially at applied fields beyond the range where it is appropriate to use pSR.
3. Results 3.1. Magnetisation measurements Fig. 1 (a) shows zero-field cooled (ZFC ) and fieldcooled (FC) magnetisation measurements on the resin-bonded YNi2B2C powder sample in a field of 20 mT. The superconducting transition temperature in this field is 14.9 K. At 5 K the initial field-dependent magnetisation of the YNi2B2C sample is linear (Fig. 1 (b) ) and consistent with a diamagnetic sus-
2. Experimental
A 12 g sample of YNi2B2C was prepared by melting together appropriate quantities of Y (99.9%), Ni (99.99%), B (99.99%) and C (99.99%) in an argon arc furnace. The resulting ingot was coarsely powdered, resulting in plate-like grains. X-ray and neutron-diffraction measurements showed the sample to be essentially single phase with the modified ThCrzSiz structure reported earlier [ 5 1. However, the diffraction patterns also show evidence of impurity phases at the level of approximately 10 vol.%. Muon spin rotation (l&R) measurements were performed at ISIS (U.K.) and PSI (Switzerland) using the MuSR [ 81 and 1tM3 spectrometers in transverse geometry i.e. spin-polarised positive muons were incident on the sample face with spin vectors perpendicular to the applied field. The uSR sample consisted of powdered YNi,B,C bonded with epoxy resin and mounted in the form of a 25 mm diameter, 4 mm thick, pellet. The resin constituted less than 4 wt.% of the total sample. The aluminium sample holder was masked with powdered, resin-bonded, Fe203; muons implanted in haematite depolarise too rapidly to contribute an unwanted background signal in the time regime of interest. Magnetisation measurements down to 4 K, and in fields of up to 12 T, were made using an Oxford Instruments Vibrating Sample Magnetometer (VSM) on a 0.26 g piece of YNi2B2C resin-bonded powder taken from the same sample used in the uSR experiments.
FC
Temperature
z-
(K)
20.0
2
z:
-25.0 0.0
5.0
10.0
Field(
15.0
20.0
103A/m)
Fig. I. (a) Temperature dependence of the zero-field cooled (ZFC) and field-cooled (FC ) magnetisation of YNi,BzC in an applied field of 20 mT. (b) Magnetisation of the YNizBJ sample in the Meissner region at a temperature of 5 K as a function of applied field. Closed and open circles represent data taken with increasing and decreasing field, respectively. The solid line corresponds to a susceptibility of x= - 1.4, while the dotted line showsx= - 1.5.
R. Cywinskiet al. / PhysicaC 233 (I 994) 273-280
ceptibility of x= - 1.4. A random alignment of the plate-like YNi2B,C grains should lead to a spherically averaged demagnetisation factor of N= f , and hence a diamagnetic susceptibility of x= - 1.5. The discrepancy between this and the measured value is attributable to the non-superconducting impurity phases in the sample. Magnetisation measurements were performed principally to map the temperature dependences of the upper and lower critical fields, Bc2 and B,,, of the YNi2B2C sample. The values obtained will subsequently be used to deduce the low-temperature values of the London penetration depth and the coherence length for comparison with the values obtained by the uSR experiments. B,, (T) was estimated by first cooling the sample in zero field and then measuring minor isothermal hysteresis loops to progressively higher magnetic fields. The field at which the loops begin to open indicates flux penetration, and hence the upper limit of the Meissner state. The resulting B,, (T) is shown in Fig. 2 taking into account the demagnetisation factor to give the true thermodynamic value. The data closely follow the conventional empirical relationship
40.0 t
with B,,(O)=37 mTand T,= 14.9 K. Bc2( T) was determined by measuring the fieldcooled magnetisation of the sample and noting the onset temperature for superconductivity in that field. The results are plotted in Fig. 3. B,, ( T) clearly does not follow the empirical quadratic temperature dependence given by Eq. ( 1). Instead a marked concave curvature is apparent as T, is approached. Such a temperature dependence of B,, ( T) is observed in a diverse range of superconducting materials, including high-T, cuprates, barium bismuthates and transition metal dichalcogenides. The phenomenon is variously attributed to magnetic impurities, to layered crystal structures (and hence to anisotropy ), to large TJphonon frequency ratios, and to multiple superconducting phases [see Ref. [ 93 and references therein]. It is too early to speculate which of these mechanisms are responsible for the form of Bc2( T) in YNi2B2C, although we believe that the last can be excluded. It should also be noted that the curvature of Bc2( T) is not only seen in the resin-bonded powder sample studied here, but also in bulk samples. The form of Bc2( T) makes extrapolation to zero temperature rather unreliable. However, below 12 K a reasonable fit of Eq. ( 1) to the measured B,,( T) can be obtained. The fit gives a somewhat reduced T, of 13.5 K and an upper critical field, Bc2( 0), of 6.0( 5) T.
6.0
1.0
0.0
t
0
215
I
’
5
10
Temperature
.a--’
F
YNi,B,C
15
(K)
Fig. 2. Temperature dependence of the lower critical field, B,, ( T) of YNi2B2C. The solid line represents a fit of the empirical relation of Eq. ( I), with T,= 14.9 K and B,, (0) = 36.9 mT.
Temperature
(K)
Fig. 3. Bc2( T) of YNi2B2C. The solid line is a fit of Eq. ( 1) with r,= 13.5 and &(O) = 6.0 T, while the dashed line is a guide to the eye.
276
R. Cywinskiet al. /Physica C 233 (1994)273-280
The magnitude and form of Bc2( T) are similar to those recently reported for YNi,B,C [ lo]. Bc2 (0) is rather low in YNizB$Z, and suggests that the upper critical field may be Pauli paramagnetic limited. Such an effect is evident in, for example, V,Si [ 111, and is perhaps to be expected in a Ni based superconductor. Working within the framework of the GinzburgLandau theory in the limit K=A/(> 1 we have [ 121 Bc2(T)=
&-!27rrz(T)
’
isation function describing the oscillating counting rate, the Fourier transform of which is the distribution of rotation frequencies which is in turn proportional to the probability distribution of internal field valuesp(B). For a genera1 type-II superconductor, the internal field variation is a function of the penetration depth, d, the coherence length,
(2)
and
(%,kZO) , (3) where t(T) is the superconducting coherence length, and n(T) is the penetration depth. Substitution of the experimentally determined upper critical field, Bc2(0) =6.0( 5) T, in Eq. (2) gives a coherencelength of ((0)=7.4(3) nm. An estimate of A(O) can then be obtained from Eq. (3 ): assuming B,, (0) = 37 ( 1) mT we find A( 0) is approximately 108 nm. For a significantly more reliable determination of 2 (0) we now turn to the uSR measurements. 3.2. ,uSR measurements Muon-spin rotation allows a direct measure to be obtained of the probability distribution of internal magnetic fields within the bulk of a type-II superconductor in the mixed state [ 6 1. Low-momentum spinpolarised muons, after coming to rest in the sample, undergo Larmor precession around the local internal field at angular frequency w= yB, where y= 2rc 135.5 x lo* rads-‘T-l, and Bis the local field. The range of internal field values thus gives rise to a range of muon-precession rates. The muon, which has an average lifetime of r=2.2 us, decays into two neutrinos and a positron, the latter being emitted preferentially along the muon-spin direction. Positron counts as a function of time and the angle to the initial spin polarisation can be described by the following relation: N(&t)=N,exp(-t/r)[l+AR(t)]+b,
(4)
where No is a normalisation constant, A is the precession amplitude or asymmetry, 8 is the initial phase and b is a constant background. R(t) is the depolar-
(5)
where B. is the mean field, b= B,/Bc2, and the sum is over all non-zero reciprocal lattice vectors, qh,k, of the flux-line lattice. In the London limit t-0, and when the applied field is well above B,, (Aq,,l > 1) the second moment of the internal field distribution can be deduced from the simplified version of Eq. ( 5 ) [ 14 ] :
The temperature dependence of ( AR2 )I/’ is thus directly proportional to the density of superelectrons. Although Eq. (6 ) is often found to be a good approximation for the case of the high-T, cuprate superconductors in applied fields Bx= Bcl, it was found to be an inappropriate oversimplification in the case of the present measurements, as will be discussed below. The standard deviation of field values (AR’ ) “’ was measured directly from the widths of the Fourier spectra obtained by the technique of maximum entropy which requires no mode1 of the form of p( B). The temperature dependence was measured at the applied field of 45 mT and the field dependence by cooling to 3 Kin a range of fields up to 550 mT. Above the superconducting transition temperature muon depolarisation was found to be negligibly small. The measured values of ( AR2 ) ‘/2 ( T) at 45 mT obtained at the different muon sources of ISIS and PSI are shown in Fig. 4 with a conventional BCS temperature dependence. Due to a very fast depolarisation of the muon spin we were unable to obtain reliable data at low temperatures with the ISIS facility. The lowtemperature value ( AB’) ‘/’ of 11.5(4) mT corresponds to a penetration depth, A( 0), of 104( 3) nm
R. Cywinskiet al. /PhysicaC 233 (1994) 273-280
217
6.0
2.0
~-
BCS
theory 0.1
0.0
0.2
O.O 0t--r-7e% Temperature
Time
0.3
0.4
0.5
0.6
0.5
0.6
(microseconds)
(K) (b)
F&4. The variation of the @R internal field variation, (AB’)“‘, with temperature for an applied field of 45 mT. The solid lines represent a conventional BCS temperature dependence in the clean limit with (AB*)‘/*(O)= 11.5(4) mT and T,= 14.2 K.
at 45 mT using the simplified proportionality relation of Eq. (6). Typical data taken above and below T, are shown in Figs. 5(a) and (b) with the muon lifetime and background ( Noexp( - t/r) + b) subtracted. Also shown are the respective probability distributions of internal fields, the Fourier transforms of which allow the lit to be compared to the data in the time domain. Above T, the lineshape is as expected, narrow and gaussian reflecting the nuclear dipole contribution to the internal field distribution. At low temperatures a broad and relatively symmetrical distribution is observed. This lineshape possibly arises from the broad distribution of demagnetising factors anticipated from the sample of randomly oriented plate-like grains. It is important to note that ( AB2 ) “’ has been extracted using a model-independent Fourier transform process and is therefore not subject to the inherent errors incurred by assuming the conventional gaussian lineshapes. From the magnetisation measurements described above it is clear that the 45 mT applied in this uSR experiment is not very much greater than the measured B,,(O) of 36.9 mT. In addition it is apparent from the value of HC2, that at moderate fields the finite flux-line core size will have a significant effect on z (AB ) “2. Eq. (6) can thus be expected to lead to a
T=3K
t.,,.1....,....1....1...,I,...l.d 0.0
0.1
0.2
Time
0.3
0.4
(microseconds)
Fig. 5. Raw data with the muon lifetime and background (No exp( -t/r) +h) subtracted. With the applied field at 45 mT the data are shown at (a) 15 K and (b) 3 K. The insets show p(B) as deduced from the maximum-entropy technique, the Fourier transforms of which, after multiplication by the factor No exp ( - t/r)A can be compared to the data.
modification of the deduced value of I (0). This effect is evident in the reduction of the low-temperature values of ( AB2 ) ‘I2 with increasing applied fields (Fig. 6). In order to account for these effects it is necessary to use the full expression given by Eq. ( 5). The sum in Eq. (5) has been evaluated for a range of internal fields using ((0) =8.1 nm and A(O) = 103 nm. The resulting theoretical dependence of ( AB2 ) ‘I2 on the internal magnetic field Bo, is plotted in Fig. 6 with the values of (AB2 ) ‘I2 and B. deduced from p(B) at different applied fields. For fields greater than 100
R. Cywinski et al. / Physica C 233 (I 994) 2 73-280
278
measurements, considering the essentially different nature of the two techniques. Finally it should be noted that in the above analysis we have assumed that YNi2B2C is an isotropic superconductor. The layered nature of the unit cell [ 5 1, in which structurally distinct R-C and B-Ni planes are evident, might lead to anisotropic features in the superconducting state. This possibility will be explored in greater detail elsewhere.
12.0
z
10.0
2
? N
8.0
:
6.0
4. Discussion and conclusions T=3K 4.0 0
100
200
Internal
300
field
400
500
600
(mT)
Fig. 6. The solid line shows the dependence of (AB’ ) ‘I2 on mean internal field, &,, calculated using Eq. (5) and assuming <( 0) = 8.1 nm and a penetration depth of A(O) = 103 nm. The data points are the measured values of ( AB * ) ‘I* derived from p(B) from the JSR measurements plotted at the internal field value deduced from the mean ofp(B).
mT the curve is a good description of the data. At lower flux densities, where the inter-vortex repulsion is reduced, the data lie above the calculated curve. This is most likely due to the enhancement of (AB2)“2 resulting from disorder of the flux-line structure in the presence of pins. This effect is well documented in high-T, materials where a broadening of p( B) is often observed at low fields [ 15 1. In considering the effects of the suggested distribution of demagnetising factors present within the sample we find that even for a relatively broad distribution neither the shape of the curve shown in Fig. 6, nor our estimate of A( 0), is significantly modified. Uncertainties in the value of n(O) from this source are within the quoted error. The values of A( 0) and t(O) determined from the uSR measurements allow an estimate of the Ginzburg-Landau parameter to be made: K=A/(= 13 ( 1). This in turn can be used to perform a simple self-consistency test to estimate B,, from Eq. (3): for /2(0)=103(3) nm we obtain &=40.1 mT compared to 36.9 mT determined directly from the magnetisation measurements. This constitutes a reasonable agreement between the uSR and magnetisation
Using the value for the penetration depth determined from our uSR measurements, together with existing thermodynamic and conductivity data we can attempt to extract values for the superconducting carrier density and the effective mass of the carriers. The London formula gives (7) where m * is the effective carrier mass, n, is the electron density and r, (=2.82x IO-i5 m) classical radius of the electron. l= is the electron free path and in the clean limit r/Z, << 1, while dirty limit c/l, Z+ 1. The Sommerfeld constant, tracted from the linear electronic contribution heat capacity can also be expressed in terms effective mass and carrier density, n,: y=
0 f
superis the mean for the y, exto the of the
2’3kirn*Q3 fi2
’
(8)
For conventional superconductors n, at T=O, is equivalent to the carrier density, n,, above T,. The reported value for y for YNi,B,C is 18 mJ/mole K* [ lo], while the resistivity just above T, is very small, typically 2 ucm [ 41. From these results a mean free path, I,, of 50 nm can be estimated, implying a dirtylimit correction of only 7%. Combining Eqs. (7) and (8 ) we estimate a carrier density of n, = 2.9 x 1022 cmw3, corresponding to 1.9 carriers per formula unit. Such a value is not entirely consistent with the supposition in Ref. [ IO] that the Ni 3d band is filled and the 4d states are responsible for the observed superconductivity in YNi2B2C. The mass enhancement factor, m*/me is calculated to be 9.4. While this value
R. Cywinski et al. / Physica C 233 (I 994) 273-280
279
Table 1 A summary of the superconducting ground state parameters of YNisBzC obtained from these pSR and magnetisation studies
Tc W)
&(O) (mT)
42(O) U)
n(O) (nm)
80) (nm)
n, (cm-))
15
36.9
6.0
103
8.1
2.9x lo**
a
??l*/m a
TF (K) a
9.4
4200
a These parameters have been estimated using values of p and y taken from Refs. [ 4 ] and [ 10 1, respectively.
is approximately twice that of the high-T, cuprate superconductors, it is much lower than that generally associated with the heavy-fermion compounds (i.e. typically > 100 ) . Table 1 summarises the parameters determined from this study of the superconducting state of YNi2B2C. Uemura [ 161 has proposed a method by which superconductors may be classified according to their critical point, T,, and Fermi temperature, T,: a plot of T, versus T, reveals a “universal curve” encompassing the more exotic superconductors, i.e. high-T, cuprates, organic superconductors, Chevrel phases, heavy fermions and ChObased compounds. All these materials are characterised by large ratios of TJT,, in the range 1 / 100 to 1/ 10, while the more conventional BCS superconductors have TJ TF less than 1/ 1000. Estimating T, for YNi2B2C using the expression: k T = ft2(37c2n,)2’3 B F
2m+
(9)
we find T,/T,= l/280. This places YNi2B2C at the very limits of Uemura’s class of exotic superconductors, and in fact, close to V$i which is also a Pauli paramagnetic limited superconductor [ Ill. Although clearly a member of an “exotic” family, in the sense that several RNi2B2C compounds support coexisting superconductivity and magnetic order [ 17 1, YNi2B2C cannot readily be classed with other unconventional systems, such as the high-T, cuprates, the fermions, or heavy the Chevrel phase superconductors.
Acknowledgements We gratefully acknowledge the Swiss National Science Foundation (NFP30 4030-32785), the Science and Engineering Research Council and the BritishSwiss Joint Research Program for financial support.
We should also like to thank W.I.F. David for his interest and advice, and G. Hilscher for a pre-print of Ref. [lo].
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