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A new anisotropy of the upper critical fields Hc2 in the Cu1.8Mo6S8 single crystal
Physica I07B (1981) 297.298 North.Hollattd Publish#lg Company
FA 4
A NEW ANISOTROPY OF THE UPPER CRITICAL FIELDS Hc2 IN THE CUl.8Mo6S 8 SINGLE CRYSTAL
Zong-Hao Lee,* Koshichi Noto, Yousuke Watanabe, and Yoshio Muto The Research Institute for Iron, Steel and Other Metals, Tohoku University, Sendai, Japan
The anisotropy of the upper critical field Hc2 near T c has been measured on single crystals of the Chevrel phase compound, CUl.8Mo6S8, with Tc~10.8 K and RRR=I0. We have observed a new type of anisotropy which reflects both a twofold symmetry and a pseudo-fourfold symmetry. This type of anisotropy is much different from the reported ones for another Chevrel phase compounds such as Snl.4Mo6Se 8. In order to analyse such an anisotropy, we propose a modified effective mass model which consists of a stack of twofold and fourfold syrmmetries. We suggest that the anisotropy of Hc2 is related to some features of the crystal structure.
The Chevrel phase superconducting compounds are well known because of their very high critical fields. It is mostly believed that the superconducting electrons of the Chevrel phase compounds are the 4d'electrons of Mo.(1) The high critical field has been thought to result from the particular Mo6X 8 cluster structure of these compounds.(1) Nearly all the ternary molybdenum chalcogenides crystallize in a hexagonal-rhombohedral structure with the rhombohedral angle & close to 90 =. According to Fischer,(1) these compounds are classified into the first kind and the second kind as regards to the size and position of the third element, M. While SnMo6Se 8 belongs to the second kind and Mo6Se 8 has no third element, CUl.sMo6S 8 belongs to the first kind. It is important to stress that the site of M atoms or the shape of interstices is not invariant among the different compounds but actually depends on the nature of the inserted M atom. In the case of PbMo6Ss, the M atom (Pb) is a big atom, while in the CUl.SMo6Ss, it (Cu) is a small atom. The size and variational behavior of the M atoms strongly affects the packing of the Mo6X8 clusters. Furthermore it is known that the M atoms do not occupy the exact site in the crystal structure. Such delocalization is particularly large for small atoms and results from their peculiar thermal motion within the large hole. Since these clusters occupy a nearly cubic lattice and since these materials have very short mean free paths, no striking anisotropy has been expected. However, Decroux et al. reported recently that the anisotropy amounting to about 20 % and 12 % was observed for Snl. 4Mo6Seg(2) and Mo6Ses(3) single crystals, respectively. Because we have firstly succeeded to find out a new type of anisotropy for the CUl.8Mo6S 8 compound, which is much different from the anisotropy reported by Decroux et al., (2,3) we present here our experimental results and propose a new model to explain the aniso0378-4363/81/0000-0000/$02.50 © North-HollandPublishingCompany
tropy appeared in Cul.sMo6S8, where the model contains both twofold and pseudo-fourfold symmeties.
Similar to Fl[ikiger et al.,(4) several single crystals of Cul.sM°6S8 compounds.were prepared from single phase powder sample in a high frequency induction furnace under a high argon pressure of about 80 kbar by using a Brldgmann technique. The crystal was cut out by a spark cutter in order to orient in the [[lOJ direction after confirming [001~ axis. Two rod-like samples were used, with the [lllj axis perpendicular to the longer direction [llOj. We confirmed that the [lllJ axis is 51 ° from the [001] axis around the [[i0[ axis. This angle is in good agreement with the expected value. Due to the processes of the sample-cutting and sample-setting in a cryostat, the orientation of the crystal axes with respect to the magnetic field was within a precision of the order of 7 °. The temperature of the sample located in an adiabatic space was regulated within a precision of i0 mK by the use of a feedback system. The upper critical field was determined by both the midpoint and the onset point of the resistive transition. The current of 5 mA was flowed in the [[10J direction. In Fig. I, Hc2 of the sample #I is shown as a function of the angle @ between the magnetic field H and the ternary axis ~lllJ in the plane containing [O01J and ~iII] axes at T=9.90 K. The results at lower temperatures down to 8 K behave quite similarly. No difference in qualitative behaviors has been observed. In Fig. 2, the result of the sample #2 is shown for T=8.37 K, which is analogous to the sample #I. In both figures, the main crystal orientations are shown by arrows for the convenience of comparison. When the field is roughly perpendicular to the
297
298
16
GJ
o,:
F i n*
i
Single
Crystal
Sample ~ I ~
'
where ~, $i, ~2, gl 2, and g22 are the parameters for fitting the experimental results. In the case of only the twofold symmetry, ie ~=90 °, Eq. (2) is reduced to Eq. (1).
Cu,.eMoeS e
.~
T- 9.9 0 K .-.-o--midpoin,
v
onisotropy
[ ~'
t
t
240 200
t
t
mo mo
t 80
t
40
18 %
[oo0
t
o
We found that the reanalysis of the Hc2 behavior of Snl.4Mo6Se8 reported by Decroux shows the trace of four-fold symmetry with ~21=~22=0.69, ~=84.6 °, BI=0 and B2=63 °.
-4
O (degree)
Angle
Single Crystal Cu,~M%Sa Sample~
2
T=8.37
K
--o-- midp0L'lt
o
×
--e-- onsetpoint
i:
--
theory
onisotropy 18%
"1-40
o
t
t
30
I
izo
I
eo
t
plo) p-] I
I
t
t
t
po,] plq I
I
LTro) I
40 o - 4 0 - e o - ~ z o - t o o Angle 0 (degree)
I
ternary axis, the Hc2 value takes a minimum and when the field is roughly parallel to the [001" axis, it takes a maximum. The anisotropy between the maximum and the minimum of Hc2 is about 18 %. This magnitude of anisotropy is comparable to 20 % for Snl.4Mo6Se 8 and to 12 % for Mo6Se 8 . Decroux et al. succeeded to explain their data for SnMo6Ses(2) and Mo6Ses(3) by the usual effective mass model HI/
(l)
Hc2(@) = (cos2@+E2sin20)i/2 ' where 62--m/M, M being the effective mass in the [III~ direction and m the one perpendicular to this direction. Decroux obtained that e2=0.69 a n d 1.25 for SnMo6Se 8 and Mo6Se 8, respectively. It is apparent that the observed anisotropy curve for CUl.8Mo6S 8 cannot be reproduced by such a simple expression as Eq. (I). Here we propose a following formula as an extension of the effective mass model, _ . j/ (l-cos2(~) Hc2(0) - " ~ 1 1 n 2 ( 6 + B l ) + C l _ 2 C O S 2 ( 0 + ~ l ] i / 2
+
In the further measurements of Hc2 anisotropy between different axes and the magnetic field, that is, in the plane containing ~001) and (TI~, iii0 and ~10j, and ~TI0) and (I12!, we also found a component of four-fold sy,~etry. We conclude, therefore, the anisotropy of Hc2 for CUl.8Mo6S 8 contains a component of four-fold syrmnetry which reflects strongly the characteristics in its crystal structure. We would like to thank Prof. T. Komatsubara for kind a c c o ~ o n d a t i o n of the high pressure induction furnace and Mr. Morohashi for the sample preparation. This work was partially supported by the Grant-in-Aid for Scientific Research (Energy and relating problem, 504505) from the Ministry of Education of Japan.
0 u
P'IZl
By using Eq. (2), we can reproduce rather well our experimental results with ~21=s22=1.48, ~= 48 ° , BI=0 and B2=63 ° as shown in Fig. i (solid lines). Almost the same fitting was found with ~21=1.37, g22=1.64, ~=50 °, BI=0 and B2=63 °. It is very important to note that ~2=63 ° is in agreement with the angle of rotation of the Mo6S 8 cluster unit.(3)
c°s20' "--- ~-L 1(2) [sin2 . . . . .(20+B2) . +c2-2cos2 (20+82) ]1/2f
References (i) ~. Fischer, Appl. Phys. 16, 1-28 (1978). (2) M. Decroux, ~. Fischer, R. Fl~kiger, B. Seeber, R. Delesclefs and M. Sergent, Sol. State. Commun. 25, 393 (1978). (3) K. Yvon, Current Topics in Materials Science, Vol. 3 (1978). On leave from the Research Institute of Metals, Scientific Academia of China, Shen Yang, China.
FA 4
A NEW ANISOTROPY OF THE UPPER CRITICAL FIELDS Hc2 IN THE CUl.8Mo6S 8 SINGLE CRYSTAL
Zong-Hao Lee,* Koshichi Noto, Yousuke Watanabe, and Yoshio Muto The Research Institute for Iron, Steel and Other Metals, Tohoku University, Sendai, Japan
The anisotropy of the upper critical field Hc2 near T c has been measured on single crystals of the Chevrel phase compound, CUl.8Mo6S8, with Tc~10.8 K and RRR=I0. We have observed a new type of anisotropy which reflects both a twofold symmetry and a pseudo-fourfold symmetry. This type of anisotropy is much different from the reported ones for another Chevrel phase compounds such as Snl.4Mo6Se 8. In order to analyse such an anisotropy, we propose a modified effective mass model which consists of a stack of twofold and fourfold syrmmetries. We suggest that the anisotropy of Hc2 is related to some features of the crystal structure.
The Chevrel phase superconducting compounds are well known because of their very high critical fields. It is mostly believed that the superconducting electrons of the Chevrel phase compounds are the 4d'electrons of Mo.(1) The high critical field has been thought to result from the particular Mo6X 8 cluster structure of these compounds.(1) Nearly all the ternary molybdenum chalcogenides crystallize in a hexagonal-rhombohedral structure with the rhombohedral angle & close to 90 =. According to Fischer,(1) these compounds are classified into the first kind and the second kind as regards to the size and position of the third element, M. While SnMo6Se 8 belongs to the second kind and Mo6Se 8 has no third element, CUl.sMo6S 8 belongs to the first kind. It is important to stress that the site of M atoms or the shape of interstices is not invariant among the different compounds but actually depends on the nature of the inserted M atom. In the case of PbMo6Ss, the M atom (Pb) is a big atom, while in the CUl.SMo6Ss, it (Cu) is a small atom. The size and variational behavior of the M atoms strongly affects the packing of the Mo6X8 clusters. Furthermore it is known that the M atoms do not occupy the exact site in the crystal structure. Such delocalization is particularly large for small atoms and results from their peculiar thermal motion within the large hole. Since these clusters occupy a nearly cubic lattice and since these materials have very short mean free paths, no striking anisotropy has been expected. However, Decroux et al. reported recently that the anisotropy amounting to about 20 % and 12 % was observed for Snl. 4Mo6Seg(2) and Mo6Ses(3) single crystals, respectively. Because we have firstly succeeded to find out a new type of anisotropy for the CUl.8Mo6S 8 compound, which is much different from the anisotropy reported by Decroux et al., (2,3) we present here our experimental results and propose a new model to explain the aniso0378-4363/81/0000-0000/$02.50 © North-HollandPublishingCompany
tropy appeared in Cul.sMo6S8, where the model contains both twofold and pseudo-fourfold symmeties.
Similar to Fl[ikiger et al.,(4) several single crystals of Cul.sM°6S8 compounds.were prepared from single phase powder sample in a high frequency induction furnace under a high argon pressure of about 80 kbar by using a Brldgmann technique. The crystal was cut out by a spark cutter in order to orient in the [[lOJ direction after confirming [001~ axis. Two rod-like samples were used, with the [lllj axis perpendicular to the longer direction [llOj. We confirmed that the [lllJ axis is 51 ° from the [001] axis around the [[i0[ axis. This angle is in good agreement with the expected value. Due to the processes of the sample-cutting and sample-setting in a cryostat, the orientation of the crystal axes with respect to the magnetic field was within a precision of the order of 7 °. The temperature of the sample located in an adiabatic space was regulated within a precision of i0 mK by the use of a feedback system. The upper critical field was determined by both the midpoint and the onset point of the resistive transition. The current of 5 mA was flowed in the [[10J direction. In Fig. I, Hc2 of the sample #I is shown as a function of the angle @ between the magnetic field H and the ternary axis ~lllJ in the plane containing [O01J and ~iII] axes at T=9.90 K. The results at lower temperatures down to 8 K behave quite similarly. No difference in qualitative behaviors has been observed. In Fig. 2, the result of the sample #2 is shown for T=8.37 K, which is analogous to the sample #I. In both figures, the main crystal orientations are shown by arrows for the convenience of comparison. When the field is roughly perpendicular to the
297
298
16
GJ
o,:
F i n*
i
Single
Crystal
Sample ~ I ~
'
where ~, $i, ~2, gl 2, and g22 are the parameters for fitting the experimental results. In the case of only the twofold symmetry, ie ~=90 °, Eq. (2) is reduced to Eq. (1).
Cu,.eMoeS e
.~
T- 9.9 0 K .-.-o--midpoin,
v
onisotropy
[ ~'
t
t
240 200
t
t
mo mo
t 80
t
40
18 %
[oo0
t
o
We found that the reanalysis of the Hc2 behavior of Snl.4Mo6Se8 reported by Decroux shows the trace of four-fold symmetry with ~21=~22=0.69, ~=84.6 °, BI=0 and B2=63 °.
-4
O (degree)
Angle
Single Crystal Cu,~M%Sa Sample~
2
T=8.37
K
--o-- midp0L'lt
o
×
--e-- onsetpoint
i:
--
theory
onisotropy 18%
"1-40
o
t
t
30
I
izo
I
eo
t
plo) p-] I
I
t
t
t
po,] plq I
I
LTro) I
40 o - 4 0 - e o - ~ z o - t o o Angle 0 (degree)
I
ternary axis, the Hc2 value takes a minimum and when the field is roughly parallel to the [001" axis, it takes a maximum. The anisotropy between the maximum and the minimum of Hc2 is about 18 %. This magnitude of anisotropy is comparable to 20 % for Snl.4Mo6Se 8 and to 12 % for Mo6Se 8 . Decroux et al. succeeded to explain their data for SnMo6Ses(2) and Mo6Ses(3) by the usual effective mass model HI/
(l)
Hc2(@) = (cos2@+E2sin20)i/2 ' where 62--m/M, M being the effective mass in the [III~ direction and m the one perpendicular to this direction. Decroux obtained that e2=0.69 a n d 1.25 for SnMo6Se 8 and Mo6Se 8, respectively. It is apparent that the observed anisotropy curve for CUl.8Mo6S 8 cannot be reproduced by such a simple expression as Eq. (I). Here we propose a following formula as an extension of the effective mass model, _ . j/ (l-cos2(~) Hc2(0) - " ~ 1 1 n 2 ( 6 + B l ) + C l _ 2 C O S 2 ( 0 + ~ l ] i / 2
+
In the further measurements of Hc2 anisotropy between different axes and the magnetic field, that is, in the plane containing ~001) and (TI~, iii0 and ~10j, and ~TI0) and (I12!, we also found a component of four-fold sy,~etry. We conclude, therefore, the anisotropy of Hc2 for CUl.8Mo6S 8 contains a component of four-fold syrmnetry which reflects strongly the characteristics in its crystal structure. We would like to thank Prof. T. Komatsubara for kind a c c o ~ o n d a t i o n of the high pressure induction furnace and Mr. Morohashi for the sample preparation. This work was partially supported by the Grant-in-Aid for Scientific Research (Energy and relating problem, 504505) from the Ministry of Education of Japan.
0 u
P'IZl
By using Eq. (2), we can reproduce rather well our experimental results with ~21=s22=1.48, ~= 48 ° , BI=0 and B2=63 ° as shown in Fig. i (solid lines). Almost the same fitting was found with ~21=1.37, g22=1.64, ~=50 °, BI=0 and B2=63 °. It is very important to note that ~2=63 ° is in agreement with the angle of rotation of the Mo6S 8 cluster unit.(3)
c°s20' "--- ~-L 1(2) [sin2 . . . . .(20+B2) . +c2-2cos2 (20+82) ]1/2f
References (i) ~. Fischer, Appl. Phys. 16, 1-28 (1978). (2) M. Decroux, ~. Fischer, R. Fl~kiger, B. Seeber, R. Delesclefs and M. Sergent, Sol. State. Commun. 25, 393 (1978). (3) K. Yvon, Current Topics in Materials Science, Vol. 3 (1978). On leave from the Research Institute of Metals, Scientific Academia of China, Shen Yang, China.