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Effect of pressure on superconductivity in the quaternary compounds RENi2B2C (RE=Lu, Y, Tm, Er, Ho)
ELSEVIER
PhysicaC229
(1994) 315-319
Effect of pressure on superconductivity in the quaternary compounds RENi2B2C (RE=Lu, Y, Tm, Er, Ho) H. Schmidt *, H.F. Braun Physikdisches Institut, Universitiit Bayreuth. 95440 Bayreuth, Germany Received 7 May 1994; revised manuscript received 15 June 1994
Abstract The effect of hydrostatic pressure up to 15 kbar on the superconducting transition temperature T, is reported for five compounds in the quatemary system RENi,B& (RE=Y, Lu, Tm, Er, Ho). The compounds with RE=Y, Lu, Tm, Er display a modest linear variation of T, with pressure. The value of dT,/dp is ranging from - 1.78 X lo-’ K/bar up to + 1.88X 10e5 K/ bar. In contrast, for HoNi2B2C some kind of interplay between long-range magnetic order and superconductivity occurs, which is strongly modified under applied pressure.
1. Introduction In many binary and ternary intermetallic alloys, like the lanthanum compounds La& and La,Se, [ 11, the Chevrel-phases CuMo& and Pb0.92M06S7.5 [ 21 and the ternary silicides YzFe& [ 3 ] and TmzFe& [ 41 occurs a striking nonlinear variation of the superconducting transition temperature under applied pressure. Very high values dTJdp in the order of 5 x 1Op4 K/bar are observed. These compounds demonstrate how phononic and electronic quantities, modified under pressure, may affect T, in many different ways. The recent report of superconductivity in the quaternary systems LuNi2B2C [ 5 ] and YPdSB3& [ 61 with for intermetallic phases relatively high T,‘s of 16.6 K and 23.2 K and an unusual combination of states at the Fermi level [ 7 1, are a worthwhile object for a study under pressure. The structure of LuNi2B2C was determined to be a derivative of the ThCr& type (space group 14/mmm) and may be * Corresponding author.
considered a three dimensional Ni-B-C framework [ 8 1. Substituting the rare earths Tm, Er, Ho and Y for nonmagnetic Lu in RENi2B2C, the compounds retain superconductivity at some lower critical temperatures [ 5 1. This raises hope to observe interplay between superconductivity and long-range magnetic order like in the ternary RE rhodium borides RERh4B4 [ 9 1, RE molybdenum sulfides REMo& [ 9 ] and ternary iron silicide TmzFe& [ 10 1. For that reason, measurements under hydrostatic pressure for RENi2B2C RE = Lu, Y and the magnetic rare earths Tm, Er, Ho were performed.
2. Experimental details All samples in this investigation were prepared from high-purity elements (RE 99.9%, Ni 99.9%, B 99% and C 99.5%) by arc melting stoichiometric mixtures of the ingots under argon atmosphere. First, Ni, B and the rare-earth metal were melted together and then small carbon pieces were added one by one
0921-4534/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI0921-4534(94)00379-T
H. Schmidt. H.F. Braun /Physica C229 (1994) 315-319
316
to minimize losses. The resulting ingots were turned over and remelted four times after each step to promote homogeneity. Weight losses during arc melting were about 0.5 wt.O/6.After a thermal treatment of 3 days at 1100°C under argon, the samples were quenched in water. X-ray powder patterns taken on a powder diffractometer with secondary monochromator, using Cu Ku radiation, showed that the samples are nearly single phase. From the integrated diffraction intensities, the impurity phase content was estimated to less than 2%, except for one of the Ho samples, where it reached 15%. With the exception of the Tm sample, where an unknown phase is present, the impurity phase was determined to be REB&. Lattice parameters were refined by the method of least squares and are in agreement with the literature [ 81. The superconducting transition temperatures were measured using an AC susceptibility technique at 20 Hz. T, is taken as the midpoint of the lo%-90% signal. The pressure dependence was determined with a piston-cylinder-type hydrostatic pressure clamp with Pb as superconducting manometer.
3. Results and discussion 3.1. RENi2B2C (RE= Lu, X Tm, Er) The temperatures for the midpoint of the superconducting transition measured by AC susceptibility at atmospheric pressure (Table 1) are, except for TmNi2B2C, equal to or higher than the SQUID data and correspond to the resistive offset data published by Cava et al. [ 51. The highest T, is obtained for LuNiZB,C ( 16.2 K). T, decreases for RE=Y ( 15.3
K) and for the magnetic rare earths Tm ( 10.0 K) and Er ( 10.4 K). The transition widths of about 0.2 to 0.5 K are comparable to the literature data [ 5 1. The effective magnetic moment of Tm (7.56~~) is smaller than that of Er (9.58~~) and thus the associated pairbreaking effect of the 4f electrons in TmNi2B2C is expected to be weaker, resulting in a higher T, than in the Er compound. However, the critical temperature of TmNizBzC is about 0.4 K lower than that for ErNi2B2C. The reason for this behaviour might be that T, is very sensitive to the exact phase composition of these compounds. A parameter which may influence the exact value of T, is the carbon content of the sample. A detailed study of the dependence of T, on the phase composition may make clear this point and allow one to determine the maximum possible transition temperature. The critical temperatures of all four boron-carbides show a linear dependence on pressure up to 15 kbar. For the Lu sample, T, increases under external hydrostatic pressure while for all the other samples (RE=Y, Er, Tm) T, is decreased (Fig. 1). The data for each of these compounds were fitted by the method of least squares to obtain the pressure derivatives dT,/dp listed in Table 1. For all samples the effect of pressure is quite small. The absolute value of dT,/dp decreases with increasing volume of the unit cell, reaching a value of almost zero for YNi2B2C, but dT,/dp changes sign abruptly between Lu and Tm. The value of dT,/dp for YNi2B2C was confirmed within experimental error for another single phase sample with a T, of 15 K. The volume change dT,/dVresulting from the application of external pressure may affect the superconducting transition temperature via several quan-
Table 1 Pressure effect on RENiZB2C superconductors Compound
L lo%-90% AC susceptibility b Explanation see text.
transition
a
C
T,(O)
(A)
(A)
W)
(lo-’
3.462 ( 1) 3.484( 1) 3.500( 1) 3.525(l) 3.515( 1) 3.516(l)
10.629(2) 10.579(2) 10X3(2) 10.536(2) 10.518(2) 10.522(2)
16.35-15.92 10.25-9.74 10.56-10.14 15.40-15.23 b b
+1.88f0.12 - 1.78kO.22 -0.82f0.17 -0.58kO.21 b b
signal.
’
dTcl&
K/bar)
H. Schmidt.
H.F. Braun /Physica
C 229 (1994) 315-319
---=B dT, Tc dp
0
2
4
6
pressure
8
10
12
14
(kbar)
Fig. 1. Dependence of the superconducting transition temperature on hydrostatic pressure for RENi,B*C (RE=Lu, Y, Tm and Er). Filled circles indicate the midpoint of Lc transition, the bars 10% to 90% of the superconducting transition signals.
tities. Theoretical calculations incorporating resistive data indicate that LuNi2B2C is a strong-coupling superconductor [ 7 1. It is therefore possible to use the Allen-Dynes equation [ 111, where T, can be expressed as a function of the electron-phonon coupling constant 1, the Coulomb pseudopotential ,u* and averaged phonon frequencies:
317
VdT a dmph dq,, -2 T, dV =gdV’dV’dV (-
where B is the bulk modulus and g a universal function. Under the assumption that the volume dependence of the phonon terms and the bulk modulus are not changing significantly by substitution throughout the rare-earth series, dT,/dV is determined mainly through the variation of the electronic contribution to 1, namely N( EF). The change in sign of dTJdp in the lanthanide series could be explained qualitatively with the competition of electronic and phononic contributions of opposite sign. While the phononic term is expected to be negative due to lattice stiffening, the electronic contribution would be required to be positive at least for the Lu compound. Such an effect could be realized in a model where the Fermi level sweeps through a peak in the density of states. Such a peak near N(&) is predicted by band-structure calculations [ 7,12 1. Assuming that the application of pressure shifts the Fermi level to higher energies, the positive dTJdp of LuNi2B2C is consistent [ 71 with the Fermi level lying on the low-energy side of a density of state peak. In contrast, for all other compounds the Fermi level appears to lie either on the high-energy side of the peak or in a region of smaller positive slope. Application of pressure then would either force EF to increasingly lower values of the density of states or the positive electronic contribution to dTJdp would be smaller than the negative phononic contribution. 3.2. HoNi2B2C
Assuming constant
the form of the electron-phonon
coupling
A= N(J%)( V> M(w’) ’ where the numerator is a purely electronic quantity (N( EF) is the density of states at the Fermi level, ( V) the matrix element of the electron-phonon interaction) whereas the denominator is mainly a phonon term (M is the ionic mass, ( w2) the square averaged phonon frequency). Assuming that ,u* and ( V) are not pressure dependent, the pressure dependence of T, may be written as
The compound HoNi,B,C is reported as a superconductor with a resistive onset temperature of about 8 K [ 5 1. We have prepared two different samples of HoNi,B,C, sample A which is almost single phase and sample B which contains about 15% impurity phases, as seen from the powder X-ray patterns (Fig. 2). Comparing the real part of the AC susceptibility of both samples without applied pressure (Figs. 3(a) and 4 (a) ) we find a completely different behaviour. Sample A shows an onset of diamagnetism at 7.1 K. The signal drops down to a minimum at about 6.1 K and then returns to its previous value at 5.3 K. At lower temperatures, the signal drops again, showing
H. Schmidt, H.F. Braun / Physica C 229 (1994) 315-319
318
800
I
I
’
I
I
*
2
_
sample A
/---~.~,... .---+ /
4.47 kbar
2' __.---*d
”
20
30
40
50
60 2 theta
800
z
sj
E 2 0 x
I
’
I
’
I
I
’
2
/ . ....-.-**
’
sample
.e--
B-
600 -
9.31 kba
i ..._.a@-
400 -
.-..J
6
p---
Z” ,lL
20
30
40
I
12.43 kb
z "_.._ij' I .
r;. h
50
60
2 theta Fig. 2. X-ray powder pattern for two different samples of HoNi2B2C, taken with Cu Ku radiation. The indexing in the LuNi,B,C-type structure (14/mmm) is indicated.
2
0
I
I
4
I
I
temperature
(K)
Fig. 3. Real part of the AC susceptibility of HoN&B,C (sample A) for different pressure values. The curves are displaced vertically for clarity. I
I
I
..._
0 kbar
a full XAC shielding. This behaviour may be interpreted as the onset of superconductivity at 7.1 K which is destroyed at a lower temperature before the transition is complete. At an even lower temperature the compound again becomes superconducting. Considering the large free ion value of the effective magnetic moment of 10.6 1,u~ for Ho and the fact that the compound DyNi2B2C (pufr,,= 10.65~~) shows a magnetic transition [ 5 1, the large peak in the susceptibility at 5.3 K indicates that the superconducting phase is disturbed due to magnetic pairbreaking. A very similar behaviour is reported for the ternary molybdenum chalcogenide GdMo& [ 13,141, where an antiferromagnetic transition is responsible for this anomaly. In GdMo,& the resistance remains zero below the superconducting transition without applied magnetic field [ 13 1. After completion of this work, we received a preprint by Eisaki et al. [ 15 ] who find resistance anomalies in zero field below T,, compatible with our xAc data. They attribute this behaviour tentatively to antiferromagnetic order of the Ho moments. At applied hydrostatic pressure up to 15 kbar the
I
8
6
%i C c 3 4 m
/ m___.__L-.--...* ......10.03 kba
-+! /.*.......*..a 4
./" .....* .* I
I
6
8
temperature
(K)
Fig. 4. Real part of the AC susceptibility of HoNi2B2C (sample B) for different pressure values. The curves are displaced vertically for clarity.
behaviour of the AC susceptibility of sample A changes drastically (Fig. 3 (a-e) ). The susceptibility minimum at 6.1 K becomes less pronounced with increasing pressure until at about 12 kbar the first diamagnetic signal has vanished while the superconducting transition at about 4.2 K remains stable, except for a small shift to higher temperatures. Measurements performed on the powdered sample confirmed the results of the bulk sample. The magnetic interaction of these rare earth com-
H. Schmidt, H.F. Braun / Physica C 229 (1994) 315-319
pounds is mainly governed by the 4f-4f indirect RKKY exchange interaction via conduction electron spins. The interaction energy He,=
$$“r2(g_r-1)2 C JiJjF(XFIR,-RjI), F
F(x) =
x cos(x) -sin(x) x4
’
is an oscillatory function, depending significantly on the distance of the rare earth in the metal (n is the density of conduction electrons, r the exchange integral, kF the Fermi wave vector, Ji the total angular momentum of rare-earth atom i, Ri its position and gJ the Landt factor) [ 16 1. The lattice compression under hydrostatic pressure may be responsible for a drastically changed magnetic interaction between rare-earth moments which could cause increased pairbreaking. It is astonishing, however, that only the upper transition is suppressed, while T, of the lower transition increases slightly. An alternative explanation might involve a pressure-induced crystallographic transition. For sample B (Fig. 4) we find only an ordinary, but 1 K higher superconducting transition at 8 K and a very slight anomaly around 6 K. The signal remains diamagnetic below 8 K and no reentrant behaviour or additional transitions were observed down to 1.2 K. The signal for sample B also remains essentially unchanged over the whole attainable pressure range of 15 kbar. The variability of T, for single-phase samples of RENi2B2C and the slightly different lattice parameters (Table 1) of our two Ho samples indicate the existence of a homogeneity range, presumably in the carbon concentration. This could be the reason for the striking differences in the AC signal of the two samples, in which the phase composition may be different. Since bands of every atom seem to contribute to the peak in the density of states [ 71 it is possible that very small changes in phase composition can influence the electronic structure and therefore the physical properties. For further clarification of this behaviour, samples with exactly known composition in the homogeneity range of HoNi2B2C must be prepared and characterized as a function of pressure, magnetic field and
319
concentration of each atomic constituent. These investigations are in progress. Neutron diffraction under pressure and specific-heat measurements will be helpful for the determination of the exact magnetic state of the compound.
Acknowledgements We thank W. Ettig for technical support and L.F. Mattheiss, W.E. Pickett and H. Eisaki for sending preprints prior to publication.
References [ 1] R.N. Shelton, A.R. Moodenbaugh,
P.D. Denier and B.T. Matthias, Mater. Res. Bull. 10 ( 1975 ) 1111. [ 21 R.N. Shelton, A.C. Lawson and D.C. Johnston, Mater. Res. Bull. 10 (1975) 297. [ 31 C.U. Segre and H.F. Braun, in: Physics of Solids under High Pressure, eds. J.S. Schilling, R.N. Shelton (North-Holland, New York, 198 1). [4] C.B. Vining and R.N. Shelton, Solid State Commun. 54 (1985) 53. [ 51 R.J. Cava, H. Takagi, B. Batlogg, H.W. Zandbergen, J.J. Krajewski, W.F. Beck Jr., T. Siegrist, K. Mizuhashi, J.O. Lee, H. Eisaki and S. Uchida, Nature (London) 367 ( 1994) 252. [6] R.J. Cava, H. Takagi, B. Batlogg, H.W. Zandbergen, J.J. Krajewski, W.F. Beck Jr., R.B. van Dover, R.J. Felder, T. Siegrist, K. Mizuhashi, J.O. Lee, H. Eisaki, S.A. Carter and S. Uchida, Nature (London) 367 (1994) 146. [ 71 W.E. Pickett and D.J. Singh, preprint. [ 8 ] T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski and W.F. Beck Jr., Nature (London) 367 (1994) 254. [ 91 See e.g. Superconductivity in Ternary Compounds II, eds. M.B. Maple and Oy. Fischer (Springer, Berlin, 1982). [lo] CU. Segre andH.F. Braun, Phys. Lett. A 85 (1981) 372. [ 111 P.B. Allen and R.C. Dynes, Phys. Rev. B 12 (1975) 905. [ 121 L.F. Mattheiss, Phys. Rev. B, to be published. [ 131 M. Ishikawa, Oy. Fischer and J. Muller, in: Superconductivity in Ternary Compounds II, eds. M.B. Maple and Oy. Fischer (Springer, Berlin, 1982) p. 148. [ 141 M. Ishikawa, Oy. Fischer and J. Muller, J. Phys. (Paris) C 6 (1978) 1379. [ 151 H. Eisaki, H. Takagi, R.J. Cava, K. Mizuhashi, J.O. Lee, B. Batlogg, J.J. Krajewski, W.F. Beck Jr. and S. Uchida, preprint. [ 161 See e.g. D. Gignoux, in: Material Science and Technology, vol. 3a, eds. R.W. Cahn, P. Haasen and E.J. Kramer (VCH, Weinheim, 1992) p. 412.
PhysicaC229
(1994) 315-319
Effect of pressure on superconductivity in the quaternary compounds RENi2B2C (RE=Lu, Y, Tm, Er, Ho) H. Schmidt *, H.F. Braun Physikdisches Institut, Universitiit Bayreuth. 95440 Bayreuth, Germany Received 7 May 1994; revised manuscript received 15 June 1994
Abstract The effect of hydrostatic pressure up to 15 kbar on the superconducting transition temperature T, is reported for five compounds in the quatemary system RENi,B& (RE=Y, Lu, Tm, Er, Ho). The compounds with RE=Y, Lu, Tm, Er display a modest linear variation of T, with pressure. The value of dT,/dp is ranging from - 1.78 X lo-’ K/bar up to + 1.88X 10e5 K/ bar. In contrast, for HoNi2B2C some kind of interplay between long-range magnetic order and superconductivity occurs, which is strongly modified under applied pressure.
1. Introduction In many binary and ternary intermetallic alloys, like the lanthanum compounds La& and La,Se, [ 11, the Chevrel-phases CuMo& and Pb0.92M06S7.5 [ 21 and the ternary silicides YzFe& [ 3 ] and TmzFe& [ 41 occurs a striking nonlinear variation of the superconducting transition temperature under applied pressure. Very high values dTJdp in the order of 5 x 1Op4 K/bar are observed. These compounds demonstrate how phononic and electronic quantities, modified under pressure, may affect T, in many different ways. The recent report of superconductivity in the quaternary systems LuNi2B2C [ 5 ] and YPdSB3& [ 61 with for intermetallic phases relatively high T,‘s of 16.6 K and 23.2 K and an unusual combination of states at the Fermi level [ 7 1, are a worthwhile object for a study under pressure. The structure of LuNi2B2C was determined to be a derivative of the ThCr& type (space group 14/mmm) and may be * Corresponding author.
considered a three dimensional Ni-B-C framework [ 8 1. Substituting the rare earths Tm, Er, Ho and Y for nonmagnetic Lu in RENi2B2C, the compounds retain superconductivity at some lower critical temperatures [ 5 1. This raises hope to observe interplay between superconductivity and long-range magnetic order like in the ternary RE rhodium borides RERh4B4 [ 9 1, RE molybdenum sulfides REMo& [ 9 ] and ternary iron silicide TmzFe& [ 10 1. For that reason, measurements under hydrostatic pressure for RENi2B2C RE = Lu, Y and the magnetic rare earths Tm, Er, Ho were performed.
2. Experimental details All samples in this investigation were prepared from high-purity elements (RE 99.9%, Ni 99.9%, B 99% and C 99.5%) by arc melting stoichiometric mixtures of the ingots under argon atmosphere. First, Ni, B and the rare-earth metal were melted together and then small carbon pieces were added one by one
0921-4534/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI0921-4534(94)00379-T
H. Schmidt. H.F. Braun /Physica C229 (1994) 315-319
316
to minimize losses. The resulting ingots were turned over and remelted four times after each step to promote homogeneity. Weight losses during arc melting were about 0.5 wt.O/6.After a thermal treatment of 3 days at 1100°C under argon, the samples were quenched in water. X-ray powder patterns taken on a powder diffractometer with secondary monochromator, using Cu Ku radiation, showed that the samples are nearly single phase. From the integrated diffraction intensities, the impurity phase content was estimated to less than 2%, except for one of the Ho samples, where it reached 15%. With the exception of the Tm sample, where an unknown phase is present, the impurity phase was determined to be REB&. Lattice parameters were refined by the method of least squares and are in agreement with the literature [ 81. The superconducting transition temperatures were measured using an AC susceptibility technique at 20 Hz. T, is taken as the midpoint of the lo%-90% signal. The pressure dependence was determined with a piston-cylinder-type hydrostatic pressure clamp with Pb as superconducting manometer.
3. Results and discussion 3.1. RENi2B2C (RE= Lu, X Tm, Er) The temperatures for the midpoint of the superconducting transition measured by AC susceptibility at atmospheric pressure (Table 1) are, except for TmNi2B2C, equal to or higher than the SQUID data and correspond to the resistive offset data published by Cava et al. [ 51. The highest T, is obtained for LuNiZB,C ( 16.2 K). T, decreases for RE=Y ( 15.3
K) and for the magnetic rare earths Tm ( 10.0 K) and Er ( 10.4 K). The transition widths of about 0.2 to 0.5 K are comparable to the literature data [ 5 1. The effective magnetic moment of Tm (7.56~~) is smaller than that of Er (9.58~~) and thus the associated pairbreaking effect of the 4f electrons in TmNi2B2C is expected to be weaker, resulting in a higher T, than in the Er compound. However, the critical temperature of TmNizBzC is about 0.4 K lower than that for ErNi2B2C. The reason for this behaviour might be that T, is very sensitive to the exact phase composition of these compounds. A parameter which may influence the exact value of T, is the carbon content of the sample. A detailed study of the dependence of T, on the phase composition may make clear this point and allow one to determine the maximum possible transition temperature. The critical temperatures of all four boron-carbides show a linear dependence on pressure up to 15 kbar. For the Lu sample, T, increases under external hydrostatic pressure while for all the other samples (RE=Y, Er, Tm) T, is decreased (Fig. 1). The data for each of these compounds were fitted by the method of least squares to obtain the pressure derivatives dT,/dp listed in Table 1. For all samples the effect of pressure is quite small. The absolute value of dT,/dp decreases with increasing volume of the unit cell, reaching a value of almost zero for YNi2B2C, but dT,/dp changes sign abruptly between Lu and Tm. The value of dT,/dp for YNi2B2C was confirmed within experimental error for another single phase sample with a T, of 15 K. The volume change dT,/dVresulting from the application of external pressure may affect the superconducting transition temperature via several quan-
Table 1 Pressure effect on RENiZB2C superconductors Compound
L lo%-90% AC susceptibility b Explanation see text.
transition
a
C
T,(O)
(A)
(A)
W)
(lo-’
3.462 ( 1) 3.484( 1) 3.500( 1) 3.525(l) 3.515( 1) 3.516(l)
10.629(2) 10.579(2) 10X3(2) 10.536(2) 10.518(2) 10.522(2)
16.35-15.92 10.25-9.74 10.56-10.14 15.40-15.23 b b
+1.88f0.12 - 1.78kO.22 -0.82f0.17 -0.58kO.21 b b
signal.
’
dTcl&
K/bar)
H. Schmidt.
H.F. Braun /Physica
C 229 (1994) 315-319
---=B dT, Tc dp
0
2
4
6
pressure
8
10
12
14
(kbar)
Fig. 1. Dependence of the superconducting transition temperature on hydrostatic pressure for RENi,B*C (RE=Lu, Y, Tm and Er). Filled circles indicate the midpoint of Lc transition, the bars 10% to 90% of the superconducting transition signals.
tities. Theoretical calculations incorporating resistive data indicate that LuNi2B2C is a strong-coupling superconductor [ 7 1. It is therefore possible to use the Allen-Dynes equation [ 111, where T, can be expressed as a function of the electron-phonon coupling constant 1, the Coulomb pseudopotential ,u* and averaged phonon frequencies:
317
VdT a dmph dq,, -2 T, dV =gdV’dV’dV (-
where B is the bulk modulus and g a universal function. Under the assumption that the volume dependence of the phonon terms and the bulk modulus are not changing significantly by substitution throughout the rare-earth series, dT,/dV is determined mainly through the variation of the electronic contribution to 1, namely N( EF). The change in sign of dTJdp in the lanthanide series could be explained qualitatively with the competition of electronic and phononic contributions of opposite sign. While the phononic term is expected to be negative due to lattice stiffening, the electronic contribution would be required to be positive at least for the Lu compound. Such an effect could be realized in a model where the Fermi level sweeps through a peak in the density of states. Such a peak near N(&) is predicted by band-structure calculations [ 7,12 1. Assuming that the application of pressure shifts the Fermi level to higher energies, the positive dTJdp of LuNi2B2C is consistent [ 71 with the Fermi level lying on the low-energy side of a density of state peak. In contrast, for all other compounds the Fermi level appears to lie either on the high-energy side of the peak or in a region of smaller positive slope. Application of pressure then would either force EF to increasingly lower values of the density of states or the positive electronic contribution to dTJdp would be smaller than the negative phononic contribution. 3.2. HoNi2B2C
Assuming constant
the form of the electron-phonon
coupling
A= N(J%)( V> M(w’) ’ where the numerator is a purely electronic quantity (N( EF) is the density of states at the Fermi level, ( V) the matrix element of the electron-phonon interaction) whereas the denominator is mainly a phonon term (M is the ionic mass, ( w2) the square averaged phonon frequency). Assuming that ,u* and ( V) are not pressure dependent, the pressure dependence of T, may be written as
The compound HoNi,B,C is reported as a superconductor with a resistive onset temperature of about 8 K [ 5 1. We have prepared two different samples of HoNi,B,C, sample A which is almost single phase and sample B which contains about 15% impurity phases, as seen from the powder X-ray patterns (Fig. 2). Comparing the real part of the AC susceptibility of both samples without applied pressure (Figs. 3(a) and 4 (a) ) we find a completely different behaviour. Sample A shows an onset of diamagnetism at 7.1 K. The signal drops down to a minimum at about 6.1 K and then returns to its previous value at 5.3 K. At lower temperatures, the signal drops again, showing
H. Schmidt, H.F. Braun / Physica C 229 (1994) 315-319
318
800
I
I
’
I
I
*
2
_
sample A
/---~.~,... .---+ /
4.47 kbar
2' __.---*d
”
20
30
40
50
60 2 theta
800
z
sj
E 2 0 x
I
’
I
’
I
I
’
2
/ . ....-.-**
’
sample
.e--
B-
600 -
9.31 kba
i ..._.a@-
400 -
.-..J
6
p---
Z” ,lL
20
30
40
I
12.43 kb
z "_.._ij' I .
r;. h
50
60
2 theta Fig. 2. X-ray powder pattern for two different samples of HoNi2B2C, taken with Cu Ku radiation. The indexing in the LuNi,B,C-type structure (14/mmm) is indicated.
2
0
I
I
4
I
I
temperature
(K)
Fig. 3. Real part of the AC susceptibility of HoN&B,C (sample A) for different pressure values. The curves are displaced vertically for clarity. I
I
I
..._
0 kbar
a full XAC shielding. This behaviour may be interpreted as the onset of superconductivity at 7.1 K which is destroyed at a lower temperature before the transition is complete. At an even lower temperature the compound again becomes superconducting. Considering the large free ion value of the effective magnetic moment of 10.6 1,u~ for Ho and the fact that the compound DyNi2B2C (pufr,,= 10.65~~) shows a magnetic transition [ 5 1, the large peak in the susceptibility at 5.3 K indicates that the superconducting phase is disturbed due to magnetic pairbreaking. A very similar behaviour is reported for the ternary molybdenum chalcogenide GdMo& [ 13,141, where an antiferromagnetic transition is responsible for this anomaly. In GdMo,& the resistance remains zero below the superconducting transition without applied magnetic field [ 13 1. After completion of this work, we received a preprint by Eisaki et al. [ 15 ] who find resistance anomalies in zero field below T,, compatible with our xAc data. They attribute this behaviour tentatively to antiferromagnetic order of the Ho moments. At applied hydrostatic pressure up to 15 kbar the
I
8
6
%i C c 3 4 m
/ m___.__L-.--...* ......10.03 kba
-+! /.*.......*..a 4
./" .....* .* I
I
6
8
temperature
(K)
Fig. 4. Real part of the AC susceptibility of HoNi2B2C (sample B) for different pressure values. The curves are displaced vertically for clarity.
behaviour of the AC susceptibility of sample A changes drastically (Fig. 3 (a-e) ). The susceptibility minimum at 6.1 K becomes less pronounced with increasing pressure until at about 12 kbar the first diamagnetic signal has vanished while the superconducting transition at about 4.2 K remains stable, except for a small shift to higher temperatures. Measurements performed on the powdered sample confirmed the results of the bulk sample. The magnetic interaction of these rare earth com-
H. Schmidt, H.F. Braun / Physica C 229 (1994) 315-319
pounds is mainly governed by the 4f-4f indirect RKKY exchange interaction via conduction electron spins. The interaction energy He,=
$$“r2(g_r-1)2 C JiJjF(XFIR,-RjI), F
F(x) =
x cos(x) -sin(x) x4
’
is an oscillatory function, depending significantly on the distance of the rare earth in the metal (n is the density of conduction electrons, r the exchange integral, kF the Fermi wave vector, Ji the total angular momentum of rare-earth atom i, Ri its position and gJ the Landt factor) [ 16 1. The lattice compression under hydrostatic pressure may be responsible for a drastically changed magnetic interaction between rare-earth moments which could cause increased pairbreaking. It is astonishing, however, that only the upper transition is suppressed, while T, of the lower transition increases slightly. An alternative explanation might involve a pressure-induced crystallographic transition. For sample B (Fig. 4) we find only an ordinary, but 1 K higher superconducting transition at 8 K and a very slight anomaly around 6 K. The signal remains diamagnetic below 8 K and no reentrant behaviour or additional transitions were observed down to 1.2 K. The signal for sample B also remains essentially unchanged over the whole attainable pressure range of 15 kbar. The variability of T, for single-phase samples of RENi2B2C and the slightly different lattice parameters (Table 1) of our two Ho samples indicate the existence of a homogeneity range, presumably in the carbon concentration. This could be the reason for the striking differences in the AC signal of the two samples, in which the phase composition may be different. Since bands of every atom seem to contribute to the peak in the density of states [ 71 it is possible that very small changes in phase composition can influence the electronic structure and therefore the physical properties. For further clarification of this behaviour, samples with exactly known composition in the homogeneity range of HoNi2B2C must be prepared and characterized as a function of pressure, magnetic field and
319
concentration of each atomic constituent. These investigations are in progress. Neutron diffraction under pressure and specific-heat measurements will be helpful for the determination of the exact magnetic state of the compound.
Acknowledgements We thank W. Ettig for technical support and L.F. Mattheiss, W.E. Pickett and H. Eisaki for sending preprints prior to publication.
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