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Magnetic and electrical properties of rare earth dicarbides and their solid solutions
Journal of the Less-Common
Metals,
81 (1981)
91
91 - 102
MAGNETIC AND ELECTRICAL PROPERTIES OF RARE EARTH DICARBIDES AND THEIR SOLID SOLUTIONS
TETSUO
SAKAI,
GIN-YA
ADACHI,
TAKESHI
YOSHIDA
and JIRO SHIOKAWA
Department of Applied Chemistry, Faculty of Engineering, Yamadakami, Suita-Shi, Osaka-Fu 565 (Japan) (Received
March
Osaka
University,
24,198l)
summary The magnetic and electrical properties of the CaCs-type rare earth dicarbides are reported. The Ndel temperatures and magnetic resistivities of heavy rare earth dicarbides are discussed in the light of the RudermanKittel-Kasuya-Yosida theory. The magnetic resistivities of the solid solutions Ce,La, -XCz are discussed on the basis of the p, components of Ce3+. The influence of the change in the crystal structure (b.c.t. + f.c.c.) on the superconducting transition temperatures is examined for the solid solutions La,Y, _%C,.
1. Introduction Rare earth carbides [l] are expected to form as a result of nuclear fission of uranium or thorium carbide fuels. Their thermodynamic properties at high temperatures have received remarkable attention owing to their importance in nuclear reactor technology. However, their magnetic and electrical properties at low temperature have been investigated by only a few workers [2 - 41. A CaCs-type rare earth dicarbide (RCs) is composed of a rare earth ion ( R3+), an acetylide ion (Cs2- ) and one electron per formula unit [ 51, and it has metallic conductivity. Earlier work [4] using neutron diffraction techniques has revealed that the RC2 compounds (R = Ce, Pr, Nd, Tb, Dy, Ho, Er) are antiferromagnetic at low temperatures. Since they are isostructural throughout the rare earth series, the rare earth dicarbides are convenient for the magnetic study of 4f electrons which interact via conduction electrons. Firstly, in this paper we describe the values of the NCel temperatures and magnetic resistivities of the RC2 compounds and their mixed dicarbides in terms of the Ruderman-Kittel-Kasuya-Yosida (RKKY) theory [6] . Secondly, the effect of the crystal field on the electrical resistivity is exam0022-5088/81/0000-0000/$02.50
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92
ined for the binary system CeCs-La&. Thirdly, the influence of the change in the crystal structure (b.c.t. + f.c.c.) on the superconductivity is investigated for the solid solutions Y,Lal .+Cs, which have an f.c.c. phase for compositions of about 50 mol.% La& [ 71.
2. Experimental procedure Rare earth oxides of 99.9% or 99.99% purity (Shin-e&m Chemical Corp.) and spectroscopic electrode grade graphite powder of 300 mesh (Nippon Carbon Corp.) were thoroughly mixed in an agate mortar and then pressed into pellets at 200 kgf cm -2. In all cases a 5 at.% excess of graphite was used to ensure removal of oxide. The pellets were placed in a molybdenum container and heated at 1700 “C by an induction furnace under a vacuum of 10e4 mmHg. The metallic impurities in the starting oxides for the superconducting dicarbides YCs and La& were as follows: CeOs, less than 0.003%; PrsO1l, less than 0.003%; NdsOs, less than 5 ppm in LasOs; DyaOs, less than 5 ppm; HoaOs, less than 5 ppm; ErsOs, less than 5 ppm; iron, less than 5 ppm; copper, less than 1 ppm in YsOs. The samples were kept immersed in CCL4and handled in an argon dry-box in order to prevent hydrolysis. Powder X-ray diffraction data were obtained with a Rigaku-Denki Rota-flex dif~actome~r, using nickel-fil~red Cu Ka radiation and silicon (99.999%) as an internal standard. Chemical analyses indicated that the weight percentages of free carbon were 1.0% - 1.5% and gave a met&bound carbon atomic ratio of 1:2 for all the carbides. The atomic ratios (R:R’) in the solid solutions R,R’, -xCZ were determined by means of the X-ray fluorescence method using a Rigaku-Denki X-ray fluorescence spectrometer. Magnetic susceptibility data in the temperature range 3 - 300 K were obtained with a Curie-Chenevea magnetic balance equipped with a low temperature apparatus. The samples for the magnetic measurements were mixed with Apiezon L grease (Apiezon Products Ltd.) to protect them from moist air. Electrical conductivity measurements were carried out in the temperature range 1.5 - 300 K with strip samples cut from the polycrystalline sintered pellets. Resistivities were determined by a four-probe d-c. potentiometric technique using a current of 10 - 50 mA. Copper wires which were lightly spot welded to the sample were used for the current and potential leads. The temperature of the specimen was measured with a chromel-(Au-O.O7at.%Fe) thermocouple in the temperature range 4 - 300 K and with a calibrated carbon resistance the~ome~r in the ~mpera~re range 1.5 - 20 K. Since the superconducting transition temperatures ‘I’, of the solid solutions La,Y, _%Ca depend on the measuring current I because of the self-heating effect, the values of T, were determined by extrapolation of the T,-I plots to the intercepts,
93
3. Results and discussion 3.1. Rare earth dicarbides and their mixed dicarbides AU the dicarbides and their solid solutions obtained here possessed a bodycentred tetragonal structure (D4h17, ~~/mrnrn). The lattice constants and magnetic properties of the RCa compounds and their solid solutions are summarized in Tables 1 and 2 and the electrical properties are tabulated in Table 3. The magnetic and electrical data of the light rare earth dicarbides, which were reported previously [ 113, are omitted from this paper. Figure 1 shows a plot of the c/a ratios of the lattice constants uersus the ionic radii of the R3+ ions. The values for GdCa and PrCa deviate from the smooth line. The thermal dependences of the magnetic susceptibility xm and of the electrical resistivity p for RCa compounds are shown in Fig. 2 and Fig. 3 respectively. The su~eptib~ity obeys a Curie-Weiss law in the paramagnetic region. The values of the paramagnetic moments observed are in agreement with the calculated values for R3+ ions. The RCa compounds (R = Gd, Tb, Dy, Ho, Er) are antiferromagnetic and each has a rapid decrease in resistivity below its NCel temperature TN. The values of TN reported by Atoji [ 41 using neutron diffraction techniques in the zero field are compared with the transition temperatures Tt on the resistivity uersus T curves in ‘Table 3. The reported vahzes for TbCa, DyCa and HOC, are in good agreement with the values obtained here but the Neel temperature of ErCr (16 K) is inconsistent with our value, TN = 8 K. This TN value (8 K) for ErCa is compatible with the second Neel point (TN1 = 10 + 3 K) reported by Atoji [ 41. TbCa has two transition temperatures, at 67 K and at 20 K on the p-2’ or the xM-T curve. These temperatures of TbCe can be attributed to the coexistence of the type TABLE 1 Crystallographic and magnetic date for the RC2 compounds Compound
Lattice constant (‘Q
c/a ratio
Magnetic properties
GdCz
a = 3.722 c = 6.295
1.691
42
-53
7.68
TbCz
a = 3.687 c = 6.205
1.683
67 20
-150
DyC2
a = 3.675 c = 6.179
1.681
61
HoCz
a = 3.659 c = 6.154
1.682
ErC2
a = 3.618 c = 6.096
1.685
de Gennes fat top
Reference
7.94
15.75
8
10.88
9.72
10.50
-89
10.20
10.63
7.08
25
-36
10.75
10.58
4.50
8
-17
9.43
9.59
2.55
TN W
BThe de Gennes factor is (g - 1)2J(J + 1).
8, W
Bert
l-&al
(@FIB)
(C(B)
8
94
TABLE 2 Crystallographic and magnetic properties of the solid solutions R,Dy1-& Compound
Lattice
Ce,,5gDyo&& Pro&IyO.& Ndo.54Dyo/&z Smo.~oDyo.Jg Gd,,51Dyo.4&2 Tbo.50Dyo.WC2 H~o.~Dyo.~,,Cg Ero_50Dyo.&2 Y0.56Dy0.44C2
3.772 3.757 3.744 3.714 3.693 3.683 3.668 3.650 3.671
constant
de Gennes fat tora
Magnetic properties
28
6.330 6.309 6.280 6.244 6.221 6.194 6.169 6.140 6.178
-39
40 27 50,33 68 43 30 29
-28 -8 -46 -57 -121 -46 -19 -40
ILeff
Ihal
@B)
@B)
6.91 7.92 7.46 8.09 9.55 10.91 10.98 9.82 7.35
7.59 7.93 7.68 7.54 9.32 10.19 10.62 10.12 7.05
3.49 3.94
4.25 5.77 11.50 8.79 5.79 4.82 3.12
Reference
9
8
10
=The de Gennes factor is (g - 1)2J(J + 1).
TABLE 3 Electrical resistivities of the RCg compounds Compound
GdC2 TbC2 DyC2
Hoc2 ErC2
Transition temperature (K)
P273 K
(cca cm)
PES tI.Ifi cm)
Pm (cc0 cm)
dPldT (/AI cm K-l)
43 67,18 (66)a 60 (59)a 24 ( 26)8 8 (16)a
55.3 48.5 52.5 80.3 98.3
8.0 10.6 13.0 23.2 39.4
15.2 9.1 5.8 4.1 0.6
0.14 0.13 0.17 0.25 0.24
aValue reported by Atoji [ 41, using neutron diffraction techniques.
1.70. Er
g .ti ? ”
Gd
HoDyTb d
Tm @_I-,-8./:\sm LU/’ -
Nd BY...
“\,i;‘-_. 02 Pf
La
1.65. aa5
a90
0.95 Ionic
radii
‘if))
Fig. 1. The relationship between the c/a ratios of the lattice constants and the ionic radii of the R 3+ ions: x , data taken from ref. 1; 0, data taken from ref. 4;A, this work.
95
T(K)
Fig. 2. Reciprocal magnetic susceptibility xrnM1VS.temperature T curves in a field of 6.85 kOe for TbC2, Ho& and ErC2.
Fig. 3. Electrical resistivity us. temperature curves for GdC2, TbC2, DyC2, HoC2, ErC2 and YC2.
I (TN = 67 K) and the type II spin alignment processes with the type I process below 33 K, as described previously [4]. The electrical resistivity can be analysed as the sum of the residual resistivity pres, the lattice resistivity Pph due to phonons and the magnetic resistivity pm [ 61. Assuming that the contribution of Pph to the total p for the heavy rare earth dicarbides is identical with that for YC2, the pm values for the RC2 compounds were estimated approximately by subtracting the p - presvalues of YC2 from the p - presvalues of RCs as shown in Table 3. By the RKKY theory [6] for free electrons, the f-f indirect exchange interaction can be written as He, = -2r2
c F(Zk,R)S,$,, n#??l
(1)
96
where S, is the 4f spin localized on the atom 12,R is the distance from the magnetic ion of the reference site, I’ is the s-f exchange integral and F(2kF R) = { 2kvR cos( 2kvR) - sin( 2&R)) ( 2kFR)-4. In terms of the molecular field theory the paramagnetic Curie temperature eP or the N&e1temperature TN is given by B =_ P
3~z2~*r2~~(2~~R)
(g-l)v(J+
2h2kF2 kB
1)
(2)
where z is the number of conduction electrons per atom and (g - 1)2J(J + 1) is the de Gennes factor G. Similarly, the magnetic resistivity pm is given by fikF (m*r)2 Pm
(g -- l)Q(J
= -4nz(eRa)a
+ 1)
(3)
If the crystal structure, the band structure and the number of the conduction electrons are constant throughout the rare earth dicarbide series, the values of both TN(ep) and ,cm are expected to vary linearly with the quantity (g - 1)2J(J + 1). The effect of the variation in G on the Neel temperatures was examined in the binary system RC2-DyC2 (as shown in Table 2). The detailed results for the solid solutions Ce,Dy1_,C2 [ 91, Gd,Dy, _XC2 [ 8] and Y,Dy, _XC2 [ 101 were reported in previous papers. The values of TN for the RCs compounds and the solid solutions R 0.5Dy0~,C!2(R = Er, Ho, Tb) are plotted against the values of G in Fig. 4. The TN values for the light rare earth dicarbides from CeCa to SmC2 vary widely with the G values whereas those of the heavy rare earth dicarbides and their solid solutions vary continuously, although they indicate a gradual departure from the theoretical expectation. GdCs has a significantly lower NCel temperature than that expected from the TN-G plot for other dicarbides. I
Fig. 4. Nkel temperatures (left-hand s&e) and magnetic resistivities (right-hand scale) us. the de Gennes factor (g - 1)2J(J+ 1) for the rare earth dicarbides: point 1, Ero_5Dyo.5C2; point 2, Ho0_5Dy~,5C2;point 3,Tbg.5DyO.5C2;@,$ TN;@,P~;---, theoretical curve.
97
The pm values of the heavy rare earth dicarbides are plotted linearly against the G values in Fig. 4, obeying eqn. (3). For elucidation of the difference between the TN-G and the pm-G relations for RC2 we can propose the following two models. (1) Equation (2) for TN contains the RKKY function ZF(Bk&) which is very sensitive to the crystal structure, whereas eqn. (3) for pm is independent of the structure. Since GdC, has the largest c/a ratio in the RC2 compounds, the small TN value for GdCs can be attributed to a deviation in the value of the function EF(Bk&). For PrC2 which has the smallest c/a ratio, the magnetic exchange interaction is not antiferromagnetic but ferromagnetic [ll]. (2) Earlier work [ 121 has revealed that the TN values of the sesquicarbides R&s can be expressed by the equation TN = A(g - l)J(J + 1) + B where A represents the RKKY exchange interaction and B represents the anisotropy energy. Since the anisotropy energy and the crystal field effects in GdC2 are expected to be smallest in the RC2 series owing to the S state of the Gd3+ ion, the fact that the TN value of GdCz is smaller than those of the other dicarbides can be explained reasonably in terms of the small value of the second term B. However, the ordering temperatures of gadolinium metal and its alloys are not exceptional in the heavy rare earth metal series. This difference between the magnetic behaviours of GdC2 and gadolinium metal may be ascribed to the nature of the conduction electrons, i.e. the d character for RC2 and the s character for R metal. This d character of the conduction band is well known for causing an anisotropy in the RKKY interaction [ 131. Both the large c/a ratio and the S state of the Gd3+ ion for GdC2 csnnot be related to each other here. 3.2. The binary system Ce, La1 --x C2 The magnetic [ 91 and electrical [ 111 properties of CeC, have been reported in previous papers. The temperature dependence of the electrical resistivity is unusual and reasonably well understood in terms of strong crystal field effects, whilst the TN value of CeCz (30 K) is considerably greater than those for other cerium-non-magnetic element compounds or that expected from the TN-G plots of other dicsrbides. These two phenomena were explained as follows. Since the spatial spread of the 4f orbitals of the Ce3+ ion is the largest among the R3+ ions, these 4f orbitals may overlap significantly with the C22- valency orbitals. Consequently, the effect of the crystal field on the Ce3+ ions will be strong and a superexchange interaction between the 4f orbit& via the C22- orbitals will occur as an additional magnetic interaction. In this work we have investigated the influence of the replacement of the Ce3+ ions with the non-magnetic La3+ ions on the magnetic susceptibility and the electrical resistivity. Crystallographic, magnetic and electrical data on the solid solutions Ce,Lai _XC2 are summarized in Table 4. The lattice parameters obeyed Vegard’s law over the entire composition range. The magnetic susceptibilities have a similar temperature dependence to that of
98
TABLE4 Crystallographic, magneticand electricalpropertiesof the solidsolutionsCe,Lar-,Cs x
1.0
Lattice constant (‘Q
Magnetic properties
a= 3.878
Electrical resistivities
b WI
Peff
Pcal
(PB)
(PB)
30
+12
2.40
2.54
82.1
1.3
34
21
+11
2.00
2.34
86.9
18.4
22
16 c = 6.522 a = 3.908 8 c = 6.535 a=3.926 <3 c = 6.544
+9
1.85
2.63
64.2
2.8
+6
1.65
1.80
58.4
3.0
9.6
0
1.28
1.34
57.0
8.0
4.6
c = 6.488 0.85
a =3.881 c = 6.493
0.64
a= 3.901
0.50 0.28
15
CeC2 [9] and obey a Curie-Weiss law in the range 100 - 300 K with effective magnetic moments that are in agreement with the free-ion value of Ce3+. The Nobel temperatures TN and paramagnetic Curie temperatures eP decrease rapidly with decreasing cerium ion concentration as shown in Fig. 5. As previously reported [lo], the values of TN and 8 P of the solid solutions Y,Dyr -%C2 have decreased linearly with decreasing dysprosium ion concentration. The different behaviours of these two binary systems can be interpreted as follows. Since the Ce-C2 2--Ce superexchange interaction exists dominantly between the nearest Ce3+ neighbours, the dilution of the cerium ions with the lanthanum ions rapidly weakens this magnetic exchange. Electrical resistivities of the solid solutions show similar temperature dependences to that of CeC2 [ 111 and have small humps at their Ndel temperatures. Their magnetic resistivities pm were estimated by subtracting the p - pres of LaC, from the p - pres of the solid solutions as shown in Fig. 6. The values of pm are dependent on the temperature, as has been observed for CeC2, suggesting a strong influence of the crystal field. Since the cubic crystal field removes the sixfold degenerate ground state (J = 2) of the Ce3+ ion into a r7 (doublet) state and a Ps (quartet) state, the magnetic resistivities, particularly at low temperature, behave differently according to which state, r7 or rs, is the lower lying. We have analysed the pm-T curve of CeCz [ 111 in terms of the theoretical treatment of Rao and Wallace [ 141, assuming that in our zeroth approximation the tetragonal crystal field of RC2 can be represented by a cubic NaCl-type crystal field. The theoretical pm-T curve for the I7 state with a crystal field separation E = 170 K exhibits good agreement with the experimental curve for CeC2. In a manner similar to that described, the pm-T curves observed for the solid solutions Ce,La, -%C2 are compared with the theoretical curves for the r7 state (E = 170 K) in Fig. 6. These two pm-T curves are approximately consistent with each other, confirming that
99
Fig. 5. The composition dependence of the magnetic resistivities pm” (0) at 273 K, the Nobeltemperatures TN (0) and the paramagnetic Curie temperatures 8, (*).
Fig. 6. The temperature dependences of the magnetic resistivities of the solid solutions Ce,La,-&: ---, theoretical values in the I’7 ground state of Ce3+ with E = 170 K; 0, experimental values.
the strength of the crystal field is constant over the entire composition range. The experimental values of pm at 273 K are plotted against the mole fraction of the cerium ion in Fig. 5, showing a similar behaviour to that of TN. 3.3. The superconducting dicarbide system La, Yl _-yC2 It is well known that the superconducting transition temperatures T, of d transition elements such as niobium, molybdenum, tantalum and tungsten are increased considerably by the formation of NaCl-type carbides. Yttrium and lutetium dicarbides become superconductors with T, values of 3.75 K [ 151 (or 3.88 K [ 161) and 3.33 K [ 161 respectively, though their metals [ 171
100
are not superconducting down to 0.006 K and 0.022 K respectively, whereas LaCs has rrlower T, value (1.44 K [ 181 or 1.60 K [ 161) than its metal (f.c.c.; T, = 5.91 [ 1’71). The sesquicarbides Y&Z, [19] and La&, 1201 have the highest T, values (about 11 K) among the rare earth compounds except for the solid solutions Y,Thl_xC1.5 (T, = 17 K [20]). The T, values of the yttrium carbides increase in the sequence yttrium, YCs, Y&s, whereas those of the lanthanum carbides increase in the sequence La&, lanthanum, La&s. This different superconduct~g behaviour between yttrium and lanthanum is very interesting. Earlier researchers [17] have proposed that lanthanum metal has a conduction band of 4f character distinguished from the d transition metals such as yttrium and that this 4f character might cause the comparatively high T, value of lanthanum metal. In the light of this idea we can explain the sequence of the T, values La&, l~~~urn, La&s. Since the nearest La-La distances d decrease in the order L&s (d = 3.93 A), La(f.c.c.) (d = 3.73 A), La&s (d = 3.63 A), the superconducting transition temperatures will increase in this order with the increasing overlap between 4f orbit&. In this paper the influence of the decrease in the nearest La-La distance and of the change in the crystal structure (b.c.t. --, f.c.c.) on the T, value has been examined for the solid solutions La,Y, _XCz. The appearance of the f.c.c. phase at a composition of about 50 mol.% LaCz has been illustrated by earlier researchers [ 71 by the increase in strain energy in the crystal produced by the large difference in ionic radii. The lattice constants of the b.c.t. and the f.c.c, dicarbides and the electrical data are listed in Table 5. The electrical resistivities p a,s x and pres of TABLE 5 Crystallographic and electrical properties of the solid solutions La,Y,-,Cg X
Lattice constant
Phase
P273K
(NJ
4
PXCZS (clfi -1
T,” W
A+
3.9
0.1
WI
@I 0 PC,)
0.28 0.45 0.52 0.57 0.58 0.80 1.0 (LaC2)
a = 3.669
c a c a a a
= = = = = =
a = a =
c = a =
c =
6.177 3.690 6.268 5.682 5.709 5.720 5.736 3.908 6.417 3.939 6.579
B.c.t.
32.0
7.6
B.c.t.
108
70
3.2
0.2
F.&C. F&C. F.c.c. F.c.c. B.c.t.
233 245 275 244 142
177 185 200 189 97
2.8 3.3 3.3 3.4 2.2
0.4 1.1 0.6 0.3 0.4
1.6
0.1
B.c.t.
51.4
4.8
aThe superconducting transition temperature was defined as the temperature at which the sample resistivity became 50% of the residual value. bTemperature span.
101
the f.c.c. phases are higher than those of the b.c.t. phases, indicating that the compounds become strained or inhomogeneous. The superconducting transition ~mpera~res, which are defined as the temperatures at which the total resistivities become 50% of the residual value preS, are shown by the symbols in Fig. 7. The vertical bars indicate the difference between 10% and 90% of the pres values, i.e. the temperature span. The T, values of YCa and La& are in good agreement with values from the literature [ 15,161. The T, values of the b.c.t, dicarbides vary linearly with composition, whereas the T, values of the f.c.c. dicarbides are a little higher than those expected from the b.c.t. values. This result is inconsistent with the previous model in which the increase in the nearest La-La distances lowers the T, values because the R-R distances for the f.c.c. phases are longer than those for the b.c.t. phases. Using a magnetic balance, the critical fields H,, at 2 K were observed for the solid solutions La,Y, -XCz (X = 0, x: = 0.28 and x = 0.45). The values of H,, become approximately 1 kOe for YCa, 1.8 kOe for LaezsY0,72Cz and 4.6 kOe for La0.45Y,,C2 and increase with increasing residual resistivities, verifying the usual concept that the magnetic flux is trapped in the inhomogeneous regions of the crystal, i.e. pinning.
Fig. 7. Superconducting transition temperatures Ts of the solid solutions La,Y1_.&2: 0, b.c.t. phase; a, f.c.c. phase. (The vertical bars indicate the temperature span.)
Acknowledgments This work was supported by a Grant in Aid for Scientific Research for G. Adachi from the Ministry of Education, Japan. We are grateful to Professor M. Date and Dr. K. Okuda for their helpful guidance in the magnetic measurements and for many kind suggestions. References 1 K. A. Gschneidner, Jr., Rare Earth Alloys, Van Nostrand, New York, 1961, p. 134. 2 R. Lallement and J. J. Veyssie, in L. Eyring (ed.), Progress in the Science and Technology of the Rare Earths, Vol. 3, Pergamon, Oxford, 1968, p. 284.
102 3 M. Atoji, J. Chem. Phys., 46 (1967) 4148; 54 (1971) 3504; 55 (1971) 3510. 4 M. Atoji, J. Chem. Phys., 46 (1967) 1891;48 (1968) 3384; 52 (1970) 6430,643l; 57 (1972) 2410. 5 M. Atoji, J. Phys. Sot. Jpn., Suppl., 17 (1962) 395. 6 B. Coqblin, The Electronic Structure of Rare-earth Metals and Alloys: the Magnetic Heavy Rare-earths, Academic Press, New York, 1977. 7 G. Adachi, T. Nishihata and J. Shiokawa, J. Less-Common Met., 32 (1973) 301. 8 T. Sakai, G. Adachi and J. Shiokawa, J. Appl. Phys., 60 (1979) 3592. 9 T. Sakai, G. Adachi and J. Shiokawa, Mater. Res. Bull., 15 (1980) 1001. 10 T. Sakai, G. Adachi and J. Shiokawa, Mater. Res. Bull., 14 (1979) 791. 11 T. Sakai, G. Adachi, T. Yoshida and J. Shiokawa, J. Chem. Phys., in the press. 12 M. Atoji, J. Solid State Chem., 26 (1978) 61. 13 N. I. Haung Liu, K. J. Ling and R. Orbach, Phys. Rev. B, 14 (1976) 4087. 14 V. U. S. Rao and W. E. Wallace,Phys. Rev. B, 2 (1970) 4613. 15 A. L. Giorgi, E. G. Szklarz, M. C. Krupka, T. C. Wallace and N. H. Krikorian, J. LessCommon Met., I4 (1968) 247. 16 R. W. Green, E. 0. Thorland, J. Croat and S. Legvold, J. Appt. Phys., 40 (1969) 3161. 17 C. Probst and J. Wittig, in K. A. Gschneidner, Jr., and L. Eyring (eds.), Handbook on the Physics and Chemistry of Rare Earths, North-Holland, New York, 1978, p. 749. 18 A. L. Bowman and N. H. Krikorian, in N. B. Hannay (ed.), Treatise on Solid State Chemistry, Vol. 3, Plenum, New York, 1976, p. 253. 19 A. L. Giorgi, E. G. Szklarz, M. C. Krupka and N. H. Krikorian, J. Less-Common Met., 17 (1969) 121. 20 M. C. Krupka, A. L. Giorgi, N. H. Krikorian and E. G. Szklarz, J. Less-Common Met., 17(1969)91;19(1969)113.
Metals,
81 (1981)
91
91 - 102
MAGNETIC AND ELECTRICAL PROPERTIES OF RARE EARTH DICARBIDES AND THEIR SOLID SOLUTIONS
TETSUO
SAKAI,
GIN-YA
ADACHI,
TAKESHI
YOSHIDA
and JIRO SHIOKAWA
Department of Applied Chemistry, Faculty of Engineering, Yamadakami, Suita-Shi, Osaka-Fu 565 (Japan) (Received
March
Osaka
University,
24,198l)
summary The magnetic and electrical properties of the CaCs-type rare earth dicarbides are reported. The Ndel temperatures and magnetic resistivities of heavy rare earth dicarbides are discussed in the light of the RudermanKittel-Kasuya-Yosida theory. The magnetic resistivities of the solid solutions Ce,La, -XCz are discussed on the basis of the p, components of Ce3+. The influence of the change in the crystal structure (b.c.t. + f.c.c.) on the superconducting transition temperatures is examined for the solid solutions La,Y, _%C,.
1. Introduction Rare earth carbides [l] are expected to form as a result of nuclear fission of uranium or thorium carbide fuels. Their thermodynamic properties at high temperatures have received remarkable attention owing to their importance in nuclear reactor technology. However, their magnetic and electrical properties at low temperature have been investigated by only a few workers [2 - 41. A CaCs-type rare earth dicarbide (RCs) is composed of a rare earth ion ( R3+), an acetylide ion (Cs2- ) and one electron per formula unit [ 51, and it has metallic conductivity. Earlier work [4] using neutron diffraction techniques has revealed that the RC2 compounds (R = Ce, Pr, Nd, Tb, Dy, Ho, Er) are antiferromagnetic at low temperatures. Since they are isostructural throughout the rare earth series, the rare earth dicarbides are convenient for the magnetic study of 4f electrons which interact via conduction electrons. Firstly, in this paper we describe the values of the NCel temperatures and magnetic resistivities of the RC2 compounds and their mixed dicarbides in terms of the Ruderman-Kittel-Kasuya-Yosida (RKKY) theory [6] . Secondly, the effect of the crystal field on the electrical resistivity is exam0022-5088/81/0000-0000/$02.50
@ Elsevier Sequoia/Printed
in The Netherlands
92
ined for the binary system CeCs-La&. Thirdly, the influence of the change in the crystal structure (b.c.t. + f.c.c.) on the superconductivity is investigated for the solid solutions Y,Lal .+Cs, which have an f.c.c. phase for compositions of about 50 mol.% La& [ 71.
2. Experimental procedure Rare earth oxides of 99.9% or 99.99% purity (Shin-e&m Chemical Corp.) and spectroscopic electrode grade graphite powder of 300 mesh (Nippon Carbon Corp.) were thoroughly mixed in an agate mortar and then pressed into pellets at 200 kgf cm -2. In all cases a 5 at.% excess of graphite was used to ensure removal of oxide. The pellets were placed in a molybdenum container and heated at 1700 “C by an induction furnace under a vacuum of 10e4 mmHg. The metallic impurities in the starting oxides for the superconducting dicarbides YCs and La& were as follows: CeOs, less than 0.003%; PrsO1l, less than 0.003%; NdsOs, less than 5 ppm in LasOs; DyaOs, less than 5 ppm; HoaOs, less than 5 ppm; ErsOs, less than 5 ppm; iron, less than 5 ppm; copper, less than 1 ppm in YsOs. The samples were kept immersed in CCL4and handled in an argon dry-box in order to prevent hydrolysis. Powder X-ray diffraction data were obtained with a Rigaku-Denki Rota-flex dif~actome~r, using nickel-fil~red Cu Ka radiation and silicon (99.999%) as an internal standard. Chemical analyses indicated that the weight percentages of free carbon were 1.0% - 1.5% and gave a met&bound carbon atomic ratio of 1:2 for all the carbides. The atomic ratios (R:R’) in the solid solutions R,R’, -xCZ were determined by means of the X-ray fluorescence method using a Rigaku-Denki X-ray fluorescence spectrometer. Magnetic susceptibility data in the temperature range 3 - 300 K were obtained with a Curie-Chenevea magnetic balance equipped with a low temperature apparatus. The samples for the magnetic measurements were mixed with Apiezon L grease (Apiezon Products Ltd.) to protect them from moist air. Electrical conductivity measurements were carried out in the temperature range 1.5 - 300 K with strip samples cut from the polycrystalline sintered pellets. Resistivities were determined by a four-probe d-c. potentiometric technique using a current of 10 - 50 mA. Copper wires which were lightly spot welded to the sample were used for the current and potential leads. The temperature of the specimen was measured with a chromel-(Au-O.O7at.%Fe) thermocouple in the temperature range 4 - 300 K and with a calibrated carbon resistance the~ome~r in the ~mpera~re range 1.5 - 20 K. Since the superconducting transition temperatures ‘I’, of the solid solutions La,Y, _%Ca depend on the measuring current I because of the self-heating effect, the values of T, were determined by extrapolation of the T,-I plots to the intercepts,
93
3. Results and discussion 3.1. Rare earth dicarbides and their mixed dicarbides AU the dicarbides and their solid solutions obtained here possessed a bodycentred tetragonal structure (D4h17, ~~/mrnrn). The lattice constants and magnetic properties of the RCa compounds and their solid solutions are summarized in Tables 1 and 2 and the electrical properties are tabulated in Table 3. The magnetic and electrical data of the light rare earth dicarbides, which were reported previously [ 113, are omitted from this paper. Figure 1 shows a plot of the c/a ratios of the lattice constants uersus the ionic radii of the R3+ ions. The values for GdCa and PrCa deviate from the smooth line. The thermal dependences of the magnetic susceptibility xm and of the electrical resistivity p for RCa compounds are shown in Fig. 2 and Fig. 3 respectively. The su~eptib~ity obeys a Curie-Weiss law in the paramagnetic region. The values of the paramagnetic moments observed are in agreement with the calculated values for R3+ ions. The RCa compounds (R = Gd, Tb, Dy, Ho, Er) are antiferromagnetic and each has a rapid decrease in resistivity below its NCel temperature TN. The values of TN reported by Atoji [ 41 using neutron diffraction techniques in the zero field are compared with the transition temperatures Tt on the resistivity uersus T curves in ‘Table 3. The reported vahzes for TbCa, DyCa and HOC, are in good agreement with the values obtained here but the Neel temperature of ErCr (16 K) is inconsistent with our value, TN = 8 K. This TN value (8 K) for ErCa is compatible with the second Neel point (TN1 = 10 + 3 K) reported by Atoji [ 41. TbCa has two transition temperatures, at 67 K and at 20 K on the p-2’ or the xM-T curve. These temperatures of TbCe can be attributed to the coexistence of the type TABLE 1 Crystallographic and magnetic date for the RC2 compounds Compound
Lattice constant (‘Q
c/a ratio
Magnetic properties
GdCz
a = 3.722 c = 6.295
1.691
42
-53
7.68
TbCz
a = 3.687 c = 6.205
1.683
67 20
-150
DyC2
a = 3.675 c = 6.179
1.681
61
HoCz
a = 3.659 c = 6.154
1.682
ErC2
a = 3.618 c = 6.096
1.685
de Gennes fat top
Reference
7.94
15.75
8
10.88
9.72
10.50
-89
10.20
10.63
7.08
25
-36
10.75
10.58
4.50
8
-17
9.43
9.59
2.55
TN W
BThe de Gennes factor is (g - 1)2J(J + 1).
8, W
Bert
l-&al
(@FIB)
(C(B)
8
94
TABLE 2 Crystallographic and magnetic properties of the solid solutions R,Dy1-& Compound
Lattice
Ce,,5gDyo&& Pro&IyO.& Ndo.54Dyo/&z Smo.~oDyo.Jg Gd,,51Dyo.4&2 Tbo.50Dyo.WC2 H~o.~Dyo.~,,Cg Ero_50Dyo.&2 Y0.56Dy0.44C2
3.772 3.757 3.744 3.714 3.693 3.683 3.668 3.650 3.671
constant
de Gennes fat tora
Magnetic properties
28
6.330 6.309 6.280 6.244 6.221 6.194 6.169 6.140 6.178
-39
40 27 50,33 68 43 30 29
-28 -8 -46 -57 -121 -46 -19 -40
ILeff
Ihal
@B)
@B)
6.91 7.92 7.46 8.09 9.55 10.91 10.98 9.82 7.35
7.59 7.93 7.68 7.54 9.32 10.19 10.62 10.12 7.05
3.49 3.94
4.25 5.77 11.50 8.79 5.79 4.82 3.12
Reference
9
8
10
=The de Gennes factor is (g - 1)2J(J + 1).
TABLE 3 Electrical resistivities of the RCg compounds Compound
GdC2 TbC2 DyC2
Hoc2 ErC2
Transition temperature (K)
P273 K
(cca cm)
PES tI.Ifi cm)
Pm (cc0 cm)
dPldT (/AI cm K-l)
43 67,18 (66)a 60 (59)a 24 ( 26)8 8 (16)a
55.3 48.5 52.5 80.3 98.3
8.0 10.6 13.0 23.2 39.4
15.2 9.1 5.8 4.1 0.6
0.14 0.13 0.17 0.25 0.24
aValue reported by Atoji [ 41, using neutron diffraction techniques.
1.70. Er
g .ti ? ”
Gd
HoDyTb d
Tm @_I-,-8./:\sm LU/’ -
Nd BY...
“\,i;‘-_. 02 Pf
La
1.65. aa5
a90
0.95 Ionic
radii
‘if))
Fig. 1. The relationship between the c/a ratios of the lattice constants and the ionic radii of the R 3+ ions: x , data taken from ref. 1; 0, data taken from ref. 4;A, this work.
95
T(K)
Fig. 2. Reciprocal magnetic susceptibility xrnM1VS.temperature T curves in a field of 6.85 kOe for TbC2, Ho& and ErC2.
Fig. 3. Electrical resistivity us. temperature curves for GdC2, TbC2, DyC2, HoC2, ErC2 and YC2.
I (TN = 67 K) and the type II spin alignment processes with the type I process below 33 K, as described previously [4]. The electrical resistivity can be analysed as the sum of the residual resistivity pres, the lattice resistivity Pph due to phonons and the magnetic resistivity pm [ 61. Assuming that the contribution of Pph to the total p for the heavy rare earth dicarbides is identical with that for YC2, the pm values for the RC2 compounds were estimated approximately by subtracting the p - presvalues of YC2 from the p - presvalues of RCs as shown in Table 3. By the RKKY theory [6] for free electrons, the f-f indirect exchange interaction can be written as He, = -2r2
c F(Zk,R)S,$,, n#??l
(1)
96
where S, is the 4f spin localized on the atom 12,R is the distance from the magnetic ion of the reference site, I’ is the s-f exchange integral and F(2kF R) = { 2kvR cos( 2kvR) - sin( 2&R)) ( 2kFR)-4. In terms of the molecular field theory the paramagnetic Curie temperature eP or the N&e1temperature TN is given by B =_ P
3~z2~*r2~~(2~~R)
(g-l)v(J+
2h2kF2 kB
1)
(2)
where z is the number of conduction electrons per atom and (g - 1)2J(J + 1) is the de Gennes factor G. Similarly, the magnetic resistivity pm is given by fikF (m*r)2 Pm
(g -- l)Q(J
= -4nz(eRa)a
+ 1)
(3)
If the crystal structure, the band structure and the number of the conduction electrons are constant throughout the rare earth dicarbide series, the values of both TN(ep) and ,cm are expected to vary linearly with the quantity (g - 1)2J(J + 1). The effect of the variation in G on the Neel temperatures was examined in the binary system RC2-DyC2 (as shown in Table 2). The detailed results for the solid solutions Ce,Dy1_,C2 [ 91, Gd,Dy, _XC2 [ 8] and Y,Dy, _XC2 [ 101 were reported in previous papers. The values of TN for the RCs compounds and the solid solutions R 0.5Dy0~,C!2(R = Er, Ho, Tb) are plotted against the values of G in Fig. 4. The TN values for the light rare earth dicarbides from CeCa to SmC2 vary widely with the G values whereas those of the heavy rare earth dicarbides and their solid solutions vary continuously, although they indicate a gradual departure from the theoretical expectation. GdCs has a significantly lower NCel temperature than that expected from the TN-G plot for other dicarbides. I
Fig. 4. Nkel temperatures (left-hand s&e) and magnetic resistivities (right-hand scale) us. the de Gennes factor (g - 1)2J(J+ 1) for the rare earth dicarbides: point 1, Ero_5Dyo.5C2; point 2, Ho0_5Dy~,5C2;point 3,Tbg.5DyO.5C2;@,$ TN;@,P~;---, theoretical curve.
97
The pm values of the heavy rare earth dicarbides are plotted linearly against the G values in Fig. 4, obeying eqn. (3). For elucidation of the difference between the TN-G and the pm-G relations for RC2 we can propose the following two models. (1) Equation (2) for TN contains the RKKY function ZF(Bk&) which is very sensitive to the crystal structure, whereas eqn. (3) for pm is independent of the structure. Since GdC, has the largest c/a ratio in the RC2 compounds, the small TN value for GdCs can be attributed to a deviation in the value of the function EF(Bk&). For PrC2 which has the smallest c/a ratio, the magnetic exchange interaction is not antiferromagnetic but ferromagnetic [ll]. (2) Earlier work [ 121 has revealed that the TN values of the sesquicarbides R&s can be expressed by the equation TN = A(g - l)J(J + 1) + B where A represents the RKKY exchange interaction and B represents the anisotropy energy. Since the anisotropy energy and the crystal field effects in GdC2 are expected to be smallest in the RC2 series owing to the S state of the Gd3+ ion, the fact that the TN value of GdCz is smaller than those of the other dicarbides can be explained reasonably in terms of the small value of the second term B. However, the ordering temperatures of gadolinium metal and its alloys are not exceptional in the heavy rare earth metal series. This difference between the magnetic behaviours of GdC2 and gadolinium metal may be ascribed to the nature of the conduction electrons, i.e. the d character for RC2 and the s character for R metal. This d character of the conduction band is well known for causing an anisotropy in the RKKY interaction [ 131. Both the large c/a ratio and the S state of the Gd3+ ion for GdC2 csnnot be related to each other here. 3.2. The binary system Ce, La1 --x C2 The magnetic [ 91 and electrical [ 111 properties of CeC, have been reported in previous papers. The temperature dependence of the electrical resistivity is unusual and reasonably well understood in terms of strong crystal field effects, whilst the TN value of CeCz (30 K) is considerably greater than those for other cerium-non-magnetic element compounds or that expected from the TN-G plots of other dicsrbides. These two phenomena were explained as follows. Since the spatial spread of the 4f orbitals of the Ce3+ ion is the largest among the R3+ ions, these 4f orbitals may overlap significantly with the C22- valency orbitals. Consequently, the effect of the crystal field on the Ce3+ ions will be strong and a superexchange interaction between the 4f orbit& via the C22- orbitals will occur as an additional magnetic interaction. In this work we have investigated the influence of the replacement of the Ce3+ ions with the non-magnetic La3+ ions on the magnetic susceptibility and the electrical resistivity. Crystallographic, magnetic and electrical data on the solid solutions Ce,Lai _XC2 are summarized in Table 4. The lattice parameters obeyed Vegard’s law over the entire composition range. The magnetic susceptibilities have a similar temperature dependence to that of
98
TABLE4 Crystallographic, magneticand electricalpropertiesof the solidsolutionsCe,Lar-,Cs x
1.0
Lattice constant (‘Q
Magnetic properties
a= 3.878
Electrical resistivities
b WI
Peff
Pcal
(PB)
(PB)
30
+12
2.40
2.54
82.1
1.3
34
21
+11
2.00
2.34
86.9
18.4
22
16 c = 6.522 a = 3.908 8 c = 6.535 a=3.926 <3 c = 6.544
+9
1.85
2.63
64.2
2.8
+6
1.65
1.80
58.4
3.0
9.6
0
1.28
1.34
57.0
8.0
4.6
c = 6.488 0.85
a =3.881 c = 6.493
0.64
a= 3.901
0.50 0.28
15
CeC2 [9] and obey a Curie-Weiss law in the range 100 - 300 K with effective magnetic moments that are in agreement with the free-ion value of Ce3+. The Nobel temperatures TN and paramagnetic Curie temperatures eP decrease rapidly with decreasing cerium ion concentration as shown in Fig. 5. As previously reported [lo], the values of TN and 8 P of the solid solutions Y,Dyr -%C2 have decreased linearly with decreasing dysprosium ion concentration. The different behaviours of these two binary systems can be interpreted as follows. Since the Ce-C2 2--Ce superexchange interaction exists dominantly between the nearest Ce3+ neighbours, the dilution of the cerium ions with the lanthanum ions rapidly weakens this magnetic exchange. Electrical resistivities of the solid solutions show similar temperature dependences to that of CeC2 [ 111 and have small humps at their Ndel temperatures. Their magnetic resistivities pm were estimated by subtracting the p - pres of LaC, from the p - pres of the solid solutions as shown in Fig. 6. The values of pm are dependent on the temperature, as has been observed for CeC2, suggesting a strong influence of the crystal field. Since the cubic crystal field removes the sixfold degenerate ground state (J = 2) of the Ce3+ ion into a r7 (doublet) state and a Ps (quartet) state, the magnetic resistivities, particularly at low temperature, behave differently according to which state, r7 or rs, is the lower lying. We have analysed the pm-T curve of CeCz [ 111 in terms of the theoretical treatment of Rao and Wallace [ 141, assuming that in our zeroth approximation the tetragonal crystal field of RC2 can be represented by a cubic NaCl-type crystal field. The theoretical pm-T curve for the I7 state with a crystal field separation E = 170 K exhibits good agreement with the experimental curve for CeC2. In a manner similar to that described, the pm-T curves observed for the solid solutions Ce,La, -%C2 are compared with the theoretical curves for the r7 state (E = 170 K) in Fig. 6. These two pm-T curves are approximately consistent with each other, confirming that
99
Fig. 5. The composition dependence of the magnetic resistivities pm” (0) at 273 K, the Nobeltemperatures TN (0) and the paramagnetic Curie temperatures 8, (*).
Fig. 6. The temperature dependences of the magnetic resistivities of the solid solutions Ce,La,-&: ---, theoretical values in the I’7 ground state of Ce3+ with E = 170 K; 0, experimental values.
the strength of the crystal field is constant over the entire composition range. The experimental values of pm at 273 K are plotted against the mole fraction of the cerium ion in Fig. 5, showing a similar behaviour to that of TN. 3.3. The superconducting dicarbide system La, Yl _-yC2 It is well known that the superconducting transition temperatures T, of d transition elements such as niobium, molybdenum, tantalum and tungsten are increased considerably by the formation of NaCl-type carbides. Yttrium and lutetium dicarbides become superconductors with T, values of 3.75 K [ 151 (or 3.88 K [ 161) and 3.33 K [ 161 respectively, though their metals [ 171
100
are not superconducting down to 0.006 K and 0.022 K respectively, whereas LaCs has rrlower T, value (1.44 K [ 181 or 1.60 K [ 161) than its metal (f.c.c.; T, = 5.91 [ 1’71). The sesquicarbides Y&Z, [19] and La&, 1201 have the highest T, values (about 11 K) among the rare earth compounds except for the solid solutions Y,Thl_xC1.5 (T, = 17 K [20]). The T, values of the yttrium carbides increase in the sequence yttrium, YCs, Y&s, whereas those of the lanthanum carbides increase in the sequence La&, lanthanum, La&s. This different superconduct~g behaviour between yttrium and lanthanum is very interesting. Earlier researchers [17] have proposed that lanthanum metal has a conduction band of 4f character distinguished from the d transition metals such as yttrium and that this 4f character might cause the comparatively high T, value of lanthanum metal. In the light of this idea we can explain the sequence of the T, values La&, l~~~urn, La&s. Since the nearest La-La distances d decrease in the order L&s (d = 3.93 A), La(f.c.c.) (d = 3.73 A), La&s (d = 3.63 A), the superconducting transition temperatures will increase in this order with the increasing overlap between 4f orbit&. In this paper the influence of the decrease in the nearest La-La distance and of the change in the crystal structure (b.c.t. --, f.c.c.) on the T, value has been examined for the solid solutions La,Y, _XCz. The appearance of the f.c.c. phase at a composition of about 50 mol.% LaCz has been illustrated by earlier researchers [ 71 by the increase in strain energy in the crystal produced by the large difference in ionic radii. The lattice constants of the b.c.t. and the f.c.c, dicarbides and the electrical data are listed in Table 5. The electrical resistivities p a,s x and pres of TABLE 5 Crystallographic and electrical properties of the solid solutions La,Y,-,Cg X
Lattice constant
Phase
P273K
(NJ
4
PXCZS (clfi -1
T,” W
A+
3.9
0.1
WI
@I 0 PC,)
0.28 0.45 0.52 0.57 0.58 0.80 1.0 (LaC2)
a = 3.669
c a c a a a
= = = = = =
a = a =
c = a =
c =
6.177 3.690 6.268 5.682 5.709 5.720 5.736 3.908 6.417 3.939 6.579
B.c.t.
32.0
7.6
B.c.t.
108
70
3.2
0.2
F.&C. F&C. F.c.c. F.c.c. B.c.t.
233 245 275 244 142
177 185 200 189 97
2.8 3.3 3.3 3.4 2.2
0.4 1.1 0.6 0.3 0.4
1.6
0.1
B.c.t.
51.4
4.8
aThe superconducting transition temperature was defined as the temperature at which the sample resistivity became 50% of the residual value. bTemperature span.
101
the f.c.c. phases are higher than those of the b.c.t. phases, indicating that the compounds become strained or inhomogeneous. The superconducting transition ~mpera~res, which are defined as the temperatures at which the total resistivities become 50% of the residual value preS, are shown by the symbols in Fig. 7. The vertical bars indicate the difference between 10% and 90% of the pres values, i.e. the temperature span. The T, values of YCa and La& are in good agreement with values from the literature [ 15,161. The T, values of the b.c.t, dicarbides vary linearly with composition, whereas the T, values of the f.c.c. dicarbides are a little higher than those expected from the b.c.t. values. This result is inconsistent with the previous model in which the increase in the nearest La-La distances lowers the T, values because the R-R distances for the f.c.c. phases are longer than those for the b.c.t. phases. Using a magnetic balance, the critical fields H,, at 2 K were observed for the solid solutions La,Y, -XCz (X = 0, x: = 0.28 and x = 0.45). The values of H,, become approximately 1 kOe for YCa, 1.8 kOe for LaezsY0,72Cz and 4.6 kOe for La0.45Y,,C2 and increase with increasing residual resistivities, verifying the usual concept that the magnetic flux is trapped in the inhomogeneous regions of the crystal, i.e. pinning.
Fig. 7. Superconducting transition temperatures Ts of the solid solutions La,Y1_.&2: 0, b.c.t. phase; a, f.c.c. phase. (The vertical bars indicate the temperature span.)
Acknowledgments This work was supported by a Grant in Aid for Scientific Research for G. Adachi from the Ministry of Education, Japan. We are grateful to Professor M. Date and Dr. K. Okuda for their helpful guidance in the magnetic measurements and for many kind suggestions. References 1 K. A. Gschneidner, Jr., Rare Earth Alloys, Van Nostrand, New York, 1961, p. 134. 2 R. Lallement and J. J. Veyssie, in L. Eyring (ed.), Progress in the Science and Technology of the Rare Earths, Vol. 3, Pergamon, Oxford, 1968, p. 284.
102 3 M. Atoji, J. Chem. Phys., 46 (1967) 4148; 54 (1971) 3504; 55 (1971) 3510. 4 M. Atoji, J. Chem. Phys., 46 (1967) 1891;48 (1968) 3384; 52 (1970) 6430,643l; 57 (1972) 2410. 5 M. Atoji, J. Phys. Sot. Jpn., Suppl., 17 (1962) 395. 6 B. Coqblin, The Electronic Structure of Rare-earth Metals and Alloys: the Magnetic Heavy Rare-earths, Academic Press, New York, 1977. 7 G. Adachi, T. Nishihata and J. Shiokawa, J. Less-Common Met., 32 (1973) 301. 8 T. Sakai, G. Adachi and J. Shiokawa, J. Appl. Phys., 60 (1979) 3592. 9 T. Sakai, G. Adachi and J. Shiokawa, Mater. Res. Bull., 15 (1980) 1001. 10 T. Sakai, G. Adachi and J. Shiokawa, Mater. Res. Bull., 14 (1979) 791. 11 T. Sakai, G. Adachi, T. Yoshida and J. Shiokawa, J. Chem. Phys., in the press. 12 M. Atoji, J. Solid State Chem., 26 (1978) 61. 13 N. I. Haung Liu, K. J. Ling and R. Orbach, Phys. Rev. B, 14 (1976) 4087. 14 V. U. S. Rao and W. E. Wallace,Phys. Rev. B, 2 (1970) 4613. 15 A. L. Giorgi, E. G. Szklarz, M. C. Krupka, T. C. Wallace and N. H. Krikorian, J. LessCommon Met., I4 (1968) 247. 16 R. W. Green, E. 0. Thorland, J. Croat and S. Legvold, J. Appt. Phys., 40 (1969) 3161. 17 C. Probst and J. Wittig, in K. A. Gschneidner, Jr., and L. Eyring (eds.), Handbook on the Physics and Chemistry of Rare Earths, North-Holland, New York, 1978, p. 749. 18 A. L. Bowman and N. H. Krikorian, in N. B. Hannay (ed.), Treatise on Solid State Chemistry, Vol. 3, Plenum, New York, 1976, p. 253. 19 A. L. Giorgi, E. G. Szklarz, M. C. Krupka and N. H. Krikorian, J. Less-Common Met., 17 (1969) 121. 20 M. C. Krupka, A. L. Giorgi, N. H. Krikorian and E. G. Szklarz, J. Less-Common Met., 17(1969)91;19(1969)113.