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Influence of composition on some physical properties of the narrow band material CeSn3
Journal of Magnetism and Magnetic North-Holland, Amsterdam
INVITED
Materials
47&48
PAPER
INFLUENCE OF COMPOSITION BAND MATERIAL CeSn, K.A. GSCHNEIDNER, and O.D.
(1985) 51-56
ON SOME
Jr., S.K. DHAR,
PHYSICAL
R.J. STIERMAN
PROPERTIES
*, T.-W.E.
TSANG
OF THE NARROW
**
McMASTERS
Ames Laboratory
*** and Department
of Materrals Science and Engineering,
Iowa State University, Ames, IA 50011, USA
The results of low temperature (1.5 to 20 K) high magnetic field (0 to 10 T) heat capacity, magnetic susceptibility (1.5 to 300 K). electrical resistivity ratio and optical metallographic analysis of a series of alloys near the CeSn,, composition are to CeSn, as. The electronic reported here. We have found that CeSn,, ,, exists over a solid solution region from CeSn,,,, specific heat constant, the resistance ratio, the magnetic susceptibility at T = 0 K, and the quenching of spin fluctuations vary from large values for the Ce-rich alloys to small values for Sn-rich alloys.
1. Introduction Several years ago Ikeda and Gschneidner [l] found that the spin fluctuations could be quenched in CeSn,. They measured the low temperature (l-20 K) heat capacity as a function of magnetic field (0 to 10 T), and found that the electronic specific heat constant, y, was reduced by 26.9% at 10 T from the zero field value. This reduction was attributed to the quenching of spin fluctuations by the high magnetic fields. They also found that the coefficient /? to the T3 (or lattice contribution) term of the normal heat capacity increased with increasing magnetic field until it saturated between 5 and 7 T. This increase was thought to be due to an induced magnetic moment on the Ce atoms by the applied field. This magnetic contribution initially goes as T’, reaches a maximum at = 5 K, falls off rapidly and goes to zero at = 6 K. Although these authors thought these effects were intrinsic to CeSn,, they noted that their sample contained = 175 ppm atomic Fe. They believed that the only effect that the Fe impurity had on the heat capacity was a short upturn below = 1.8 K which became more pronounced with increasing magnetic field. * Present address:
Semiconductor Group, Texas Instruments. Dallas, TX 75265, USA. ** Present address: Mechanical Engineering Department, University of South Alabama, Mobile, AL 36688, USA. *** Operated for the U.S. Department of Energy by Iowa State University contract no. W-7405-ENG-82. This work was supported by the Office of Basic Energy Sciences. 0304-8853/85/$03.30
(North-Holland
0 Elsevier
Physics Publishing
Science
Publishers
Division)
B.V.
Because of the possibility that the observed effects might be due to Fe impurities, we thought that purer samples, at least with respect to Fe, should be examined to verify the reported quenching of spin fluctuation behavior. Furthermore, Gschneidner and Ikeda [2] reported four different types of spin fluctuation quenching behaviors, which has recently been extended to six types by Gschneidner and Dhar [3]. Thus, we decided to see if CeSn, existed over a composition range and, if it did, to see if more than one type of behavior could be found in a single substance. Some of the results of this study, which is still in progress, are reported here.
2. Experimental The samples were prepared by arc-melting a total of 20-30 g of 99.9 at% pure Ce and 99.99 at% pure Sn in the proper portions to give the desired compositions, which varied from CeSn,,,, to CeSn,,, for those alloys near the 1 : 3 stoichiometry and CezSn, the next Ce-rich phase. Weight losses after arc-melting were generally about 0.1 g, indicating an uncertainty of +0.02 in the Sn to Ce ratio, i.e. an alloy prepared with the nominal CeSn, oo composition could have a true composition between CeSn 2.98 (if all the loss was Sn) and CeSn,,,, (if all the loss was Ce). Although the true composition may not be known exactly, the relative Sn to Ce ratios in the various samples are probably maintained as prepared, i.e. a CeSn,,, sample is richer in Ce than CeSn,,,. The samples were heat treated for 330 h at 1100°C
K.A. Gschneidner et ul. / Physical propertres of C&n< + ,
52
ceS”z,ga 0
0.00T
. A . x
2.50T 5.39 T 7.62 T 9.96 T
Li., , , , , , , , , , , , I
0
4
6
12
16
20
8
(,
, , 26
32
,( 36
T2(K2)
Fig. 2. Low temperature five magnetic fields. 0
4
8
12
16
20
24
26
32
36
heat capacity
of a CeSn,,,
of a CeSn, O5 alloy at
40
T2(K21
Fig. 1. Low temperature five magnetic fields.
heat capacity
alloy at
and then furnace cooled. After heat treatment they were examined metallographically to see if they were single phase. Alloys containing more Ce than CeSn,,a, contained second phase Ce,Sn, which orders magnetically at 2.9 K. The presence of Ce,Sn, was also clearly evident in the heat capacity measurements of the alloys because of the CeSn 2.98 (see fig. 1) and CeSn,,,, extra contribution to the heat capacity due to the magnetic ordering of Ce,Sn, (the peak in the zero field measurements). The CeSn3.a5 alloy contained a slight amount of the second phase (pure Sn) in the grain boundaries. The data indicate that CeSn, exists over a solid solution range from CeSn,,,, to CeSn,,,,. The CeSn, single crystals were grown by using a Bridgman technique, melting the sample in a tungsten crucible. The samples were all examined by spark source mass spectrometry to determine the impurity concentrations, especially that of iron. The experimental equipment and procedures used for making the heat capacity measurements from 1 to 20 K in fields from 0 to 10 T and the magnetic susceptibility measurements from 1 to 300 K at fields which varied from 0.9 to 1.8 T are described by Ikeda and co-workers [1,4] and Stierman et al. [5], respectively.
the CeSn, a5 sample. From a cursory inspection it would appear that the heat capacities at the five fields are essentially the same. An in-depth analysis, however, shows that this is due to the fact that the field dependence of the various contributions tend to cancel each other. The applied field lowers the electronic contribuI
I
I
I
,_---__c . .
I
0
I
CeSn2.99
A QS”3.00 0
CeSnJD2
-J CeSn3.05
I
I
I
I
I
I
0
2
4
6
8
IO
I
H(T)
3. Experimental results A typical heat capacity plot for the various CeSn, solid solution alloys at five fields is shown in fig. 2 for
Fig. 3. Field dependence of y and p for four CeSn, samples. The solid points were obtained from a three parameter least squares fit of the experimental data to eq. (I), while the open circles were derived from a two parameter fit of eq. (2).
53
K.A. Gschneidner ef al. / Physical properries of CeSn, k y
tion (y) and raises the lattice (/3) contribution, see fig. 3. Since the T3 In T term is a negative contribution below T, (see below - eq. (1) and definition of terms), and since the applied field suppresses this contribution, this causes an increase in the heat capacity. These data are similar in general to the results reported earlier by Ikeda and Gschneidner [l] for a polycrystalline CeSn, sample and Tsang et al. (61 for a CeSn, single crystal. The major differences are the higher y values and large field dependencies of y for the samples reported in the literature. The low temperature upturn ((1.8 K) reported for the polycrystalline sample and thought to be due to Fe impurities is definitely absent in our sample, as well as in the single crystal samples studied by Tsang et al. [6]. The weak T31n T spin fluctuation term is also present in all samples studied at fields up to 2.5 T, but disappears for fields greater than 5 T in agreement with the previously reported data. Because of this the low field data were fitted to the expression C/T=
A + BT2 + DT2
In T,
(1)
where A = y (the experimental electronic specific heat constant), B = p - (qo/Ts2 In T,), D = qo/Ts2. /3 is the coefficient of the lattice contribution to the heat capacity, T, is the spin fluctuation temperature, ye is the electronic specific heat constant calculated from the bare density of states and (Y is proportional to S(1 S-‘)2 with S being the Stoner enhancement factor. The heat capacity data taken at fields greater than 5 T were fitted to the normal heat capacity expression C/T=
1
y + pT2,
(2)
where y and p are the same as defined above. The various coefficients were obtained by a least squares
1
I I I I 3.04 3.06 3.00 3.02 x Fig. 4. The compositional dependence of the resistance ratio, y, for CeSn, r 4,2, and the electronic specific heat constant, alloys. 601 2.94
I 2.96
I 2.98
fitting of the data to eqs. (1) or (2), and these are shown in fig. 3, where y and /3 are plotted as a function of the applied field. The zero field fl value is calculated from the 8, derived from inelastic neutron scattering [7]. The field dependence of /3 seems to be essentially the same for all four samples and also about the same as for the
Table 1 Some physical properties of CeSn, samples r 4.2
Sample
CeSn z 99 C&n,,,-1 CeSn NO-II CeSn 3.02 CeSn,,s Published
Y (mJ/g
at.K’)
- AY/Y(O) at 10T
AP/‘B(O) at 10 T
(S)
(W)
Aspin
xx104 (at 0 K) (emu/g-at)
s
T, (K)
Fe content
Ref.
(ppm at)
16.26 16.30 16.42
14.1 _ 8.2 8.3 10.3
77 _ 75 70 74
4.82 _ 4.36 4.38 4.42
6.0 5.4
_ 17 _ _ 15
5.1 3.9 4.1 4.4
12 16 20 2 3
_ _ _ _ _
18.15 18.75 18.75
26.9 15.4 21.1
113 65 120
5.07 5.67 5.67
7.2 8.0 10.0
20 22 28
5.6 5.6 5.8
175 6 6
VI [61
_ 144 127 82 77
17.49
236 -
results
C&n,,, CeSn,,O [loo] CeSn,, [llO]
161
K.A. Gschnetdner et al. / Physil XII properties of CeSn .I + ,
54
zero field heat capacity at = 2.9 K (8.2 K2) for these two samples we know the composition must have a Sn content greater than CeSn2,98 (see fig. 1). The magnetic susceptibility of three of our samples, plus that of the Ikeda-Gschneidner heat capacity samples (which we measured) are plotted as a function of temperature from 1.7 to 300 K in fig. 5 along with the data reported in literature by other investigators. The general shape of all the curves is the same - a maximum at = 150 K, a minimum which varies from 25 to 90 K, and a rapid rise in x as T* 0, but which varies considerably in slope and in the maximum value of x at T = 0 K. As noted earlier the CeSn,,,, sample contains a considerable amount of Ce,Sn, which orders magnetically at 2.9 K. see fig. 1. However. the x vs. T curve does not give any evidence for the presence of this second phase - see fig. 6a. But if one plots dx/dT vs. T (fig. 6b) it is quite evident that a small part of the sample is magnetically ordering at 3.1 K.
data reported for two other CeSn, samples (see table 1). The field dependence of y for the Ce-rich sample is larger than that for the three Sn-rich samples. The reported results for the depression of y for the other two CeSn, samples is comparable or even greater than for the CeSn,,, alloy (see table 1). The variation of the resistance ratio, r,,, = and of y as a function of composition is R WI/R 4.23 shown in fig. 4, where it is seen that both quantities seem to rise rapidly as the composition changes from Sn-rich to Ce-rich. The magnetic susceptibility at 0 K, x(O), seems to show the same type of compositional dependence as r,,, and y, but at the present time we have less data available to support this statement. The magnitude of the y, r,,, and x(O), see table 1, suggest that both the polycrystalline sample of Ikeda and Gschneidner [l] and the single crystal sample of Tsang et al. [6] have a composition between CeSn,,,, and Because of the absence of any bump in the CeSn2.99.
-P
I
I
I
I
I
x
\
P
CeSn2.95
3.0
---.-
XXI03 (emu /mole )
2.5
1
I
\\
s B \ 0v
0 CeSn3.05 A CeSn3.00
SERENI TSUCHIDA and WALLACE STASSIS et 01.
x MALIK ------
I
50
I 100
IKEDA
and VIJAYARAGHAVAN and GSCHNEIDNER (Cp)
I 150
T(K) Fig. 5. The magnetic susceptibility of eight different CeSn, samples.
I 200
I 250
K.A. Gschneidner et al. /
Physical properties
On the basis of our measurements on the three CeSn, samples we can draw the following conclusions. The presence of second phase Ce,Sn, tends to “wipe out” the minimum and if enough of it were present the susceptibility would exhibit Curie-Weiss-like behavior.
of CeSn, + ,
5s
The deeper the minimum and the lower its temperature the purer the sample, at least with respect to second phase Ce,Sn, and possibly excess Ce (but still dissolved in CeSn,). This is consistent with the similar behavior observed in pure SC - the purer the sample the sharper the maximum and minimum, and the larger the slope (in a negative sense) as T+ 0 K [S].
4. Discussion
I 2O
I
I
I
I
5
IO
15
20
25
T(K)
-
CeSn2.95
b
-
-
4.0
-
3.0
? f f 01 0
I I
I 2
I 3
I 5
I 4
I 6
I 7
I 8
I 9
TiKl
Fig. 6. The magnetic K.
susceptibility
of CeSn2,95 from 1.7 to 23
1.0 IO
Our studies to date show that CeSn, exists over a solid solution range from CeSn,,,, to CeSn,,as. Thus a small fraction of the larger Ce atoms (radius = 1.846 A) can substitute for by the smaller Sn atoms (radius = 1.580 A), which are located on the face-centered sites of the AuCu, structure, to give substoichiometric CeSn,_,. When an excess Ce atom is placed on a Sn face-centered site it forms a pentad with 4 Ce-Ce contacts at a distance of 0.707a, where a is the lattice parameter (the normal Ce-Ce distance is a in the perfectly ordered, fully stoichiometric CeSn3.00). Thus one finds that for CeSn 2.99 there is one Ce-Ce contact per 100 atoms assuming perfect ordering except for the excess atoms which must be located on a wrong site. This number of Ce-Ce contacts drops to zero at CeSn,., and remains at that value for excess Sn atoms if the material is perfectly ordered for the given composition. This may explain the shape of the r,,, and y vs. composition (x) curve (fig. 4). This would seem a logical explanation as far as y is concerned - an increase in y as the number of Ce-Ce contacts increases. But one would generally expect the resistance ratio to drop as imperfections and the number of Ce-Ce contacts increases. Apparently the presence of Ce-Ce contacts raises the room temperature resistivity more rapidly than the 4.2 K resistivity, however, this needs to be studied in more detail. The other remarkable fact is that r,,, is extremely large for any intermetallic compound, even at the Sn-richest compositions, by about one order to magnitude. If one takes into account disorder then one can even get a larger number of Ce-Ce contacts. For each Ce-Sn interchange a tetrad is formed with three Ce-Ce contacts at 0.707~. The standard x-ray and neutron diffraction techniques for determining the relative order in CeSn, will not work because the atomic scattering factors and the scattering amplitudes (even if the most favorable isotopes were readily available) of Ce and Sn are too similar to one another. Thus one must use more indirect techniques to estimate the perfection in such crystals. Magnetic susceptibility measurements offer some promise, if one can find a field dependence in the
56
K.A. Gschneidner et al. / Physical properties of CeSn, + ,
1000
-
600
-
E(eVl
34
-
4.9
50
51
E(eV)
Fig. 7. Schematic representation of the density of states of CeSn,. The inset shows what might be derived from band structure calculations. See text for further details and discussion.
magnetic susceptibility at low temperatures below 4 K, assuming that the Ce-Ce contacts act as ferromagnetic impurities. Tsang et al. [6] report that the field dependence of their single crystal CeSn, sample suggested = 18 Ce-Ce contacts per 10’ atoms. A similar analysis of our CeSn,,,, alloys suggests = 1 Ce-Ce contact per lo5 atoms. Both of these numbers are much smaller (by a factor of lo’, to 103) than the number of Ce-Ce contacts in CeSn,,,, just due to non-stoichiometry. Additional measurements such as these are needed to see if they can shed some meaningful light on the nature of non-stoichiometry and sample perfection. An analysis of the excess magnetic contribution due to the induced moment lead Ikeda and Gschneidner [l] to conclude that = 1 electron per 1000 Ce atoms is responsible for the observed effects. Analysis of our alloys indicates that this number is consistent with the excess magnetic contribution calculated for our alloys. One possible model which explains the observed behaviors is that there is an extremely high density of states ( = 1000 states per ev per atom per spin) associated with a small part of the Fermi surface of CeSn, (fig. 7). A schematic representation of a band structure that might be calculated using the best computational techniques currently available is shown in the inset of fig. 7. An
enlargement of the density of state curve around the Fermi energy is shown in the main part of fig. 7, where an extremely narrow partially filled band is superimposed on the calculated curve. The narrow band would never be calculated using the standard techniques. The application of a large magnetic field would “wipe-out” the part of the Fermi surface responsible for the narrow peak and thus this would lower y as the applied field increases. This narrow partially filled band would also be extremely sensitive to impurities which would lower or raise the electron concentration. Changing the alloy composition from CeSn,,,, to CeSn,, increases the electron concentration by 0.04 electrons per atom if Ce is trivalent and Sn is tetravalent. This might account for the drop in the lowering of y [i.e. Ay/y(O)] by = 20% for the substoichiometric alloys to = 10% for the stoichiometric and hyperstoichiometric compositions, but it does not explain why quenching of spin fluctuations are still observed in the CeSn 3 + ~ alloys ( y > 0, i.e. stoichiometric and hyperstoichiom&ric alloys) since presumably the narrow band will have filled before the CeSn,, composition is reached. Clearly more experimental work is necessary to completely describe the behavior of the CeSn, alloys. The experimental results reported here indicate that the theory of spin fluctuations, which is 20 years old. is inadequate and needs to be reexamined in light of these experimental studies and those on other spin fluctuation materials.
References [l] K. Ikeda and K.A. Gschneidner, [2] [3]
[4] [5]
[6] [7]
Jr., Phys. Rev. B25 (1982) 4623. K.A. Gschneidner, Jr. and K. Ikeda, J. Magn. Magn. Mat. 31-34 (1983) 265. K.A. Gschneidner, Jr. and SK. Dhar, Magnetic Excitations and Fluctuations, eds. SW. Lovesey, U. Balucani, F. Borsa and V. Tognetti (Springer-Verlag, Berlin, 1984) p. 177. K. Ikeda, K.A. Gschneidner, Jr., B.J. Beaudry and U. Atzmony, Phys. Rev. B25 (1982) 4604. R.J. Stierman, K.A. Gschneidner, Jr., T.-W.E. Tsang, F.A. Schmidt, P. Klavins, R.N. Shelton, J. Queen and S. Legvold, J. Magn. Magn. Mat. 36 (1983) 249. T.-W. E. Tsang, K.A. Gschneidner, Jr., O.D. McMasters, R.J. St&man and S.K. Dhar, Phys. Rev. B29 (1984) 4185. C. Stassis, C.-K. Loong, J. Zarestky, O.D. McMasters and R.M. Nicklow, Phys. Rev. 823 (1981) 5128.
INVITED
Materials
47&48
PAPER
INFLUENCE OF COMPOSITION BAND MATERIAL CeSn, K.A. GSCHNEIDNER, and O.D.
(1985) 51-56
ON SOME
Jr., S.K. DHAR,
PHYSICAL
R.J. STIERMAN
PROPERTIES
*, T.-W.E.
TSANG
OF THE NARROW
**
McMASTERS
Ames Laboratory
*** and Department
of Materrals Science and Engineering,
Iowa State University, Ames, IA 50011, USA
The results of low temperature (1.5 to 20 K) high magnetic field (0 to 10 T) heat capacity, magnetic susceptibility (1.5 to 300 K). electrical resistivity ratio and optical metallographic analysis of a series of alloys near the CeSn,, composition are to CeSn, as. The electronic reported here. We have found that CeSn,, ,, exists over a solid solution region from CeSn,,,, specific heat constant, the resistance ratio, the magnetic susceptibility at T = 0 K, and the quenching of spin fluctuations vary from large values for the Ce-rich alloys to small values for Sn-rich alloys.
1. Introduction Several years ago Ikeda and Gschneidner [l] found that the spin fluctuations could be quenched in CeSn,. They measured the low temperature (l-20 K) heat capacity as a function of magnetic field (0 to 10 T), and found that the electronic specific heat constant, y, was reduced by 26.9% at 10 T from the zero field value. This reduction was attributed to the quenching of spin fluctuations by the high magnetic fields. They also found that the coefficient /? to the T3 (or lattice contribution) term of the normal heat capacity increased with increasing magnetic field until it saturated between 5 and 7 T. This increase was thought to be due to an induced magnetic moment on the Ce atoms by the applied field. This magnetic contribution initially goes as T’, reaches a maximum at = 5 K, falls off rapidly and goes to zero at = 6 K. Although these authors thought these effects were intrinsic to CeSn,, they noted that their sample contained = 175 ppm atomic Fe. They believed that the only effect that the Fe impurity had on the heat capacity was a short upturn below = 1.8 K which became more pronounced with increasing magnetic field. * Present address:
Semiconductor Group, Texas Instruments. Dallas, TX 75265, USA. ** Present address: Mechanical Engineering Department, University of South Alabama, Mobile, AL 36688, USA. *** Operated for the U.S. Department of Energy by Iowa State University contract no. W-7405-ENG-82. This work was supported by the Office of Basic Energy Sciences. 0304-8853/85/$03.30
(North-Holland
0 Elsevier
Physics Publishing
Science
Publishers
Division)
B.V.
Because of the possibility that the observed effects might be due to Fe impurities, we thought that purer samples, at least with respect to Fe, should be examined to verify the reported quenching of spin fluctuation behavior. Furthermore, Gschneidner and Ikeda [2] reported four different types of spin fluctuation quenching behaviors, which has recently been extended to six types by Gschneidner and Dhar [3]. Thus, we decided to see if CeSn, existed over a composition range and, if it did, to see if more than one type of behavior could be found in a single substance. Some of the results of this study, which is still in progress, are reported here.
2. Experimental The samples were prepared by arc-melting a total of 20-30 g of 99.9 at% pure Ce and 99.99 at% pure Sn in the proper portions to give the desired compositions, which varied from CeSn,,,, to CeSn,,, for those alloys near the 1 : 3 stoichiometry and CezSn, the next Ce-rich phase. Weight losses after arc-melting were generally about 0.1 g, indicating an uncertainty of +0.02 in the Sn to Ce ratio, i.e. an alloy prepared with the nominal CeSn, oo composition could have a true composition between CeSn 2.98 (if all the loss was Sn) and CeSn,,,, (if all the loss was Ce). Although the true composition may not be known exactly, the relative Sn to Ce ratios in the various samples are probably maintained as prepared, i.e. a CeSn,,, sample is richer in Ce than CeSn,,,. The samples were heat treated for 330 h at 1100°C
K.A. Gschneidner et ul. / Physical propertres of C&n< + ,
52
ceS”z,ga 0
0.00T
. A . x
2.50T 5.39 T 7.62 T 9.96 T
Li., , , , , , , , , , , , I
0
4
6
12
16
20
8
(,
, , 26
32
,( 36
T2(K2)
Fig. 2. Low temperature five magnetic fields. 0
4
8
12
16
20
24
26
32
36
heat capacity
of a CeSn,,,
of a CeSn, O5 alloy at
40
T2(K21
Fig. 1. Low temperature five magnetic fields.
heat capacity
alloy at
and then furnace cooled. After heat treatment they were examined metallographically to see if they were single phase. Alloys containing more Ce than CeSn,,a, contained second phase Ce,Sn, which orders magnetically at 2.9 K. The presence of Ce,Sn, was also clearly evident in the heat capacity measurements of the alloys because of the CeSn 2.98 (see fig. 1) and CeSn,,,, extra contribution to the heat capacity due to the magnetic ordering of Ce,Sn, (the peak in the zero field measurements). The CeSn3.a5 alloy contained a slight amount of the second phase (pure Sn) in the grain boundaries. The data indicate that CeSn, exists over a solid solution range from CeSn,,,, to CeSn,,,,. The CeSn, single crystals were grown by using a Bridgman technique, melting the sample in a tungsten crucible. The samples were all examined by spark source mass spectrometry to determine the impurity concentrations, especially that of iron. The experimental equipment and procedures used for making the heat capacity measurements from 1 to 20 K in fields from 0 to 10 T and the magnetic susceptibility measurements from 1 to 300 K at fields which varied from 0.9 to 1.8 T are described by Ikeda and co-workers [1,4] and Stierman et al. [5], respectively.
the CeSn, a5 sample. From a cursory inspection it would appear that the heat capacities at the five fields are essentially the same. An in-depth analysis, however, shows that this is due to the fact that the field dependence of the various contributions tend to cancel each other. The applied field lowers the electronic contribuI
I
I
I
,_---__c . .
I
0
I
CeSn2.99
A QS”3.00 0
CeSnJD2
-J CeSn3.05
I
I
I
I
I
I
0
2
4
6
8
IO
I
H(T)
3. Experimental results A typical heat capacity plot for the various CeSn, solid solution alloys at five fields is shown in fig. 2 for
Fig. 3. Field dependence of y and p for four CeSn, samples. The solid points were obtained from a three parameter least squares fit of the experimental data to eq. (I), while the open circles were derived from a two parameter fit of eq. (2).
53
K.A. Gschneidner ef al. / Physical properries of CeSn, k y
tion (y) and raises the lattice (/3) contribution, see fig. 3. Since the T3 In T term is a negative contribution below T, (see below - eq. (1) and definition of terms), and since the applied field suppresses this contribution, this causes an increase in the heat capacity. These data are similar in general to the results reported earlier by Ikeda and Gschneidner [l] for a polycrystalline CeSn, sample and Tsang et al. (61 for a CeSn, single crystal. The major differences are the higher y values and large field dependencies of y for the samples reported in the literature. The low temperature upturn ((1.8 K) reported for the polycrystalline sample and thought to be due to Fe impurities is definitely absent in our sample, as well as in the single crystal samples studied by Tsang et al. [6]. The weak T31n T spin fluctuation term is also present in all samples studied at fields up to 2.5 T, but disappears for fields greater than 5 T in agreement with the previously reported data. Because of this the low field data were fitted to the expression C/T=
A + BT2 + DT2
In T,
(1)
where A = y (the experimental electronic specific heat constant), B = p - (qo/Ts2 In T,), D = qo/Ts2. /3 is the coefficient of the lattice contribution to the heat capacity, T, is the spin fluctuation temperature, ye is the electronic specific heat constant calculated from the bare density of states and (Y is proportional to S(1 S-‘)2 with S being the Stoner enhancement factor. The heat capacity data taken at fields greater than 5 T were fitted to the normal heat capacity expression C/T=
1
y + pT2,
(2)
where y and p are the same as defined above. The various coefficients were obtained by a least squares
1
I I I I 3.04 3.06 3.00 3.02 x Fig. 4. The compositional dependence of the resistance ratio, y, for CeSn, r 4,2, and the electronic specific heat constant, alloys. 601 2.94
I 2.96
I 2.98
fitting of the data to eqs. (1) or (2), and these are shown in fig. 3, where y and /3 are plotted as a function of the applied field. The zero field fl value is calculated from the 8, derived from inelastic neutron scattering [7]. The field dependence of /3 seems to be essentially the same for all four samples and also about the same as for the
Table 1 Some physical properties of CeSn, samples r 4.2
Sample
CeSn z 99 C&n,,,-1 CeSn NO-II CeSn 3.02 CeSn,,s Published
Y (mJ/g
at.K’)
- AY/Y(O) at 10T
AP/‘B(O) at 10 T
(S)
(W)
Aspin
xx104 (at 0 K) (emu/g-at)
s
T, (K)
Fe content
Ref.
(ppm at)
16.26 16.30 16.42
14.1 _ 8.2 8.3 10.3
77 _ 75 70 74
4.82 _ 4.36 4.38 4.42
6.0 5.4
_ 17 _ _ 15
5.1 3.9 4.1 4.4
12 16 20 2 3
_ _ _ _ _
18.15 18.75 18.75
26.9 15.4 21.1
113 65 120
5.07 5.67 5.67
7.2 8.0 10.0
20 22 28
5.6 5.6 5.8
175 6 6
VI [61
_ 144 127 82 77
17.49
236 -
results
C&n,,, CeSn,,O [loo] CeSn,, [llO]
161
K.A. Gschnetdner et al. / Physil XII properties of CeSn .I + ,
54
zero field heat capacity at = 2.9 K (8.2 K2) for these two samples we know the composition must have a Sn content greater than CeSn2,98 (see fig. 1). The magnetic susceptibility of three of our samples, plus that of the Ikeda-Gschneidner heat capacity samples (which we measured) are plotted as a function of temperature from 1.7 to 300 K in fig. 5 along with the data reported in literature by other investigators. The general shape of all the curves is the same - a maximum at = 150 K, a minimum which varies from 25 to 90 K, and a rapid rise in x as T* 0, but which varies considerably in slope and in the maximum value of x at T = 0 K. As noted earlier the CeSn,,,, sample contains a considerable amount of Ce,Sn, which orders magnetically at 2.9 K. see fig. 1. However. the x vs. T curve does not give any evidence for the presence of this second phase - see fig. 6a. But if one plots dx/dT vs. T (fig. 6b) it is quite evident that a small part of the sample is magnetically ordering at 3.1 K.
data reported for two other CeSn, samples (see table 1). The field dependence of y for the Ce-rich sample is larger than that for the three Sn-rich samples. The reported results for the depression of y for the other two CeSn, samples is comparable or even greater than for the CeSn,,, alloy (see table 1). The variation of the resistance ratio, r,,, = and of y as a function of composition is R WI/R 4.23 shown in fig. 4, where it is seen that both quantities seem to rise rapidly as the composition changes from Sn-rich to Ce-rich. The magnetic susceptibility at 0 K, x(O), seems to show the same type of compositional dependence as r,,, and y, but at the present time we have less data available to support this statement. The magnitude of the y, r,,, and x(O), see table 1, suggest that both the polycrystalline sample of Ikeda and Gschneidner [l] and the single crystal sample of Tsang et al. [6] have a composition between CeSn,,,, and Because of the absence of any bump in the CeSn2.99.
-P
I
I
I
I
I
x
\
P
CeSn2.95
3.0
---.-
XXI03 (emu /mole )
2.5
1
I
\\
s B \ 0v
0 CeSn3.05 A CeSn3.00
SERENI TSUCHIDA and WALLACE STASSIS et 01.
x MALIK ------
I
50
I 100
IKEDA
and VIJAYARAGHAVAN and GSCHNEIDNER (Cp)
I 150
T(K) Fig. 5. The magnetic susceptibility of eight different CeSn, samples.
I 200
I 250
K.A. Gschneidner et al. /
Physical properties
On the basis of our measurements on the three CeSn, samples we can draw the following conclusions. The presence of second phase Ce,Sn, tends to “wipe out” the minimum and if enough of it were present the susceptibility would exhibit Curie-Weiss-like behavior.
of CeSn, + ,
5s
The deeper the minimum and the lower its temperature the purer the sample, at least with respect to second phase Ce,Sn, and possibly excess Ce (but still dissolved in CeSn,). This is consistent with the similar behavior observed in pure SC - the purer the sample the sharper the maximum and minimum, and the larger the slope (in a negative sense) as T+ 0 K [S].
4. Discussion
I 2O
I
I
I
I
5
IO
15
20
25
T(K)
-
CeSn2.95
b
-
-
4.0
-
3.0
? f f 01 0
I I
I 2
I 3
I 5
I 4
I 6
I 7
I 8
I 9
TiKl
Fig. 6. The magnetic K.
susceptibility
of CeSn2,95 from 1.7 to 23
1.0 IO
Our studies to date show that CeSn, exists over a solid solution range from CeSn,,,, to CeSn,,as. Thus a small fraction of the larger Ce atoms (radius = 1.846 A) can substitute for by the smaller Sn atoms (radius = 1.580 A), which are located on the face-centered sites of the AuCu, structure, to give substoichiometric CeSn,_,. When an excess Ce atom is placed on a Sn face-centered site it forms a pentad with 4 Ce-Ce contacts at a distance of 0.707a, where a is the lattice parameter (the normal Ce-Ce distance is a in the perfectly ordered, fully stoichiometric CeSn3.00). Thus one finds that for CeSn 2.99 there is one Ce-Ce contact per 100 atoms assuming perfect ordering except for the excess atoms which must be located on a wrong site. This number of Ce-Ce contacts drops to zero at CeSn,., and remains at that value for excess Sn atoms if the material is perfectly ordered for the given composition. This may explain the shape of the r,,, and y vs. composition (x) curve (fig. 4). This would seem a logical explanation as far as y is concerned - an increase in y as the number of Ce-Ce contacts increases. But one would generally expect the resistance ratio to drop as imperfections and the number of Ce-Ce contacts increases. Apparently the presence of Ce-Ce contacts raises the room temperature resistivity more rapidly than the 4.2 K resistivity, however, this needs to be studied in more detail. The other remarkable fact is that r,,, is extremely large for any intermetallic compound, even at the Sn-richest compositions, by about one order to magnitude. If one takes into account disorder then one can even get a larger number of Ce-Ce contacts. For each Ce-Sn interchange a tetrad is formed with three Ce-Ce contacts at 0.707~. The standard x-ray and neutron diffraction techniques for determining the relative order in CeSn, will not work because the atomic scattering factors and the scattering amplitudes (even if the most favorable isotopes were readily available) of Ce and Sn are too similar to one another. Thus one must use more indirect techniques to estimate the perfection in such crystals. Magnetic susceptibility measurements offer some promise, if one can find a field dependence in the
56
K.A. Gschneidner et al. / Physical properties of CeSn, + ,
1000
-
600
-
E(eVl
34
-
4.9
50
51
E(eV)
Fig. 7. Schematic representation of the density of states of CeSn,. The inset shows what might be derived from band structure calculations. See text for further details and discussion.
magnetic susceptibility at low temperatures below 4 K, assuming that the Ce-Ce contacts act as ferromagnetic impurities. Tsang et al. [6] report that the field dependence of their single crystal CeSn, sample suggested = 18 Ce-Ce contacts per 10’ atoms. A similar analysis of our CeSn,,,, alloys suggests = 1 Ce-Ce contact per lo5 atoms. Both of these numbers are much smaller (by a factor of lo’, to 103) than the number of Ce-Ce contacts in CeSn,,,, just due to non-stoichiometry. Additional measurements such as these are needed to see if they can shed some meaningful light on the nature of non-stoichiometry and sample perfection. An analysis of the excess magnetic contribution due to the induced moment lead Ikeda and Gschneidner [l] to conclude that = 1 electron per 1000 Ce atoms is responsible for the observed effects. Analysis of our alloys indicates that this number is consistent with the excess magnetic contribution calculated for our alloys. One possible model which explains the observed behaviors is that there is an extremely high density of states ( = 1000 states per ev per atom per spin) associated with a small part of the Fermi surface of CeSn, (fig. 7). A schematic representation of a band structure that might be calculated using the best computational techniques currently available is shown in the inset of fig. 7. An
enlargement of the density of state curve around the Fermi energy is shown in the main part of fig. 7, where an extremely narrow partially filled band is superimposed on the calculated curve. The narrow band would never be calculated using the standard techniques. The application of a large magnetic field would “wipe-out” the part of the Fermi surface responsible for the narrow peak and thus this would lower y as the applied field increases. This narrow partially filled band would also be extremely sensitive to impurities which would lower or raise the electron concentration. Changing the alloy composition from CeSn,,,, to CeSn,, increases the electron concentration by 0.04 electrons per atom if Ce is trivalent and Sn is tetravalent. This might account for the drop in the lowering of y [i.e. Ay/y(O)] by = 20% for the substoichiometric alloys to = 10% for the stoichiometric and hyperstoichiometric compositions, but it does not explain why quenching of spin fluctuations are still observed in the CeSn 3 + ~ alloys ( y > 0, i.e. stoichiometric and hyperstoichiom&ric alloys) since presumably the narrow band will have filled before the CeSn,, composition is reached. Clearly more experimental work is necessary to completely describe the behavior of the CeSn, alloys. The experimental results reported here indicate that the theory of spin fluctuations, which is 20 years old. is inadequate and needs to be reexamined in light of these experimental studies and those on other spin fluctuation materials.
References [l] K. Ikeda and K.A. Gschneidner, [2] [3]
[4] [5]
[6] [7]
Jr., Phys. Rev. B25 (1982) 4623. K.A. Gschneidner, Jr. and K. Ikeda, J. Magn. Magn. Mat. 31-34 (1983) 265. K.A. Gschneidner, Jr. and SK. Dhar, Magnetic Excitations and Fluctuations, eds. SW. Lovesey, U. Balucani, F. Borsa and V. Tognetti (Springer-Verlag, Berlin, 1984) p. 177. K. Ikeda, K.A. Gschneidner, Jr., B.J. Beaudry and U. Atzmony, Phys. Rev. B25 (1982) 4604. R.J. Stierman, K.A. Gschneidner, Jr., T.-W.E. Tsang, F.A. Schmidt, P. Klavins, R.N. Shelton, J. Queen and S. Legvold, J. Magn. Magn. Mat. 36 (1983) 249. T.-W. E. Tsang, K.A. Gschneidner, Jr., O.D. McMasters, R.J. St&man and S.K. Dhar, Phys. Rev. B29 (1984) 4185. C. Stassis, C.-K. Loong, J. Zarestky, O.D. McMasters and R.M. Nicklow, Phys. Rev. 823 (1981) 5128.