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Quenched superconductivity by rapid cooling down to low temperatures below Tc2 in single-crystal HoMo6S8
~
Solid State Communications, Printed in Great Britain.
QUENCHED
Vol.60,No.|O,
SUPERCONDUCTIVITY
pp.771-775,
1986.
0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.
BY RAPID COOLING DOWN TO LOW TEMPERATURES IN SINGLE-CRYSTAL HoMo6S 8
Y. Koike, T. Fukase, N. Kobayashi,
BELOW Tc2
S. Hosoya and H. Takei %
The Research
Institute for Iron, Steel and Other Metals, Tohoku University, Katahira, Sendal, 980 Japan 'The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo, 106 Japan (Received 4 September
1986 by T. TsuzukI)
Electrical resistivity of single-crystal HoMo.S 8 has been measured at low temperatures down to 0 . 0 1 K . By slow cooking, the resistivity In the re-entrant normal state below T ~ is recovered up to 98 % of its c value above T .. This suggests t H ~ there still remains a little cl superconductive region not due to Bloch walls, but rather to ferromagnetic mlcrodomains of comparatively small sizes. By rapid cooling, on the other hand, the superconductivity above T ~ has been found to be quenched at low temperatures below T 2" T~C~s quenched superconductivity, coexisting with the quenched ~odulated magnetic structure, is destroyed as a function of time and magnetic field, which seems attributed to the growth of the microdomains.
I. Introduction
the polycrystalline nature. Recently a few groups,B, 6 including our group, 7 have succeeded in preparing single-crystals of this material, though their dimensions are at most ! mm in edge-length. Detailed studies on the single-crystals have been in progress. An interesting matter with respect to the electrical resistivity of the slngle-crystals is whether the region inside Bloch walls in the ferromagnetic state becomes superconducting or not. The possible occurrence of this superconductivity has been theoretically investigated by Tachiki et al.. 8 From the experimental point of view, this has been also supported, based on the result that the resistivity below T are not fully recovered up to its value i~2 the normal state above T This result, however, has been obtained ~ ; sintered samples2, 9 and a polycrystalline sample composed of a few single-crystals, I0 which more or less include grain boundaries besides the Bloch walls. Therefore, an experiment using one single-crystal without any grain boundary is valuable to insist on the superconductivity within the Bloch walls. Another matter of interest is regarding a modulated magnetic structure quenched by fast cooling down to 0.I0 K, which was found in neutron diffraction studies by Rossat-Mignod et al..ll, 12 Although the modulated magnetic structure in the temperature range between T 2 and T is known to coexist with the s~perconduc~ivity, whether the quenched modulated magnetic state is superconducting is an unsettled matter. In this report we present the first experimental result on the electrical resistivity of a HoMo. S^ sample composed of only one single-crysta~ at low temperatures down to 0.01K. Our attention is focused on the su-
Since the discovery of ternary rareearth superconductors which achieve longrange magnetic order below their superconducting transition temperatures T _, the relationship between superconductivity and magnetism has attracted renewed attention. Many experimental and theoretical studies have been devoted to this kind of material.l For materials developing antiferromagnetic order, the superconductivity is generally known to be preserved and coexist with the magnetic order because of the absence of spatially averaged magnetic moments. For materials developing ferromagnetic order, on the other hand, the superconductivity is destroyed by the onset of the magnetic ordering at a low temperature T 2" However, a modulated magnetic structurec of a long wavelength, which appears in a narrow temperature range Just above Tc2, coexists with the superconductivity. A typical material developing ferromagnetic order is the Chevrel-phase compound HoMo. S_, whose re-entrant behavior at T ~ was discbov~ered by Ishikawa and Fischer. 2 wceZknow that HoMo.b S_ first becomes superconducting at T . ~ 1.8 K and then re-enters a normal state L aT T ~ ~ 0.6 K as the ferromagnetic ordering c 3 sets ~n. , A thermal hysteresis has been observed for the re-entrant transition at Tc2" On cooling, the superconductivity is nown to coexist with a modulated magnetic structure in a narrow temperature range between T 2 and T ~ 0.7 K, while this modulated structure ~ o e s not appear on warming. Most of experimental works on HoMo6S 8 , however, have been carried out on polycrystalline specimens with some ambiguity due to 771
Vol. 60, No. I0
LOW TEMPERATURES BELOW Tc2 IN SINGLE-CRYSTAL ltoMo6S8
772
perconductivity within the Bloch walls in the ferromagnetic state and the superconductivity in the quenched modulated magnetic state.
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HoMo6S8 #2"2
2. Experimental
40 Slngle-crystals of HoMo6S 8 were prepared in a high pressure, high temperature furnace. Details about the preparation procedure are reported in the preceding paper. ? Chemical and X-ray analyses have revealed that the composition of the single-crystals is almost stolchlometrlc. The dimension of the singlecrystal used here was 0.2 mm x 0.2 mm x 0.45 •am. The sample was placed on a large copper block thermally connected to the mixing chamber of a dilution refrigerator with a copper rod. Resistivity measurements ~~re made using a usual ac four-point probe method at a frequency of 70 Hz. The lead wires were attached to the sample with silver paste. The current in the sample was mainly as small as I0 pA to prevent self-heating. Moreover, we also made measurements using a very small current of 1 ~A to check the self-heating effect. Rapid cooling of the sample down to low temperatures below T ~ was performed as folcz lows. The sample was warmed up to a temperature above Tel by applying a large current of 5 mA to the sample itself for 2 minutes, keeping the temperature of the mixing chamber constant at a low temperature below T followed by shutting off the current. ~ this case the warming was attributed to the Joule heat due to the contact resistance between the lead wires and the sample. Whether the sample was warmed up to a temperature above T i was known by monitoring the resistivity o~ the sample with a current of 5 mA. In warming up the sample, the large copper block loaded with the sample was also warmed up a little, compared with the temperature of the mixing chamber• As soon as the current was shut off, however, it was cooled down to the temperature of the mixing chamber within I0 seconds. Although the temperature of the sample itself could not be measured, the sample was considered to be cooled down within a comparable time because of its very very small heat capacity. Magnetic fields were applied parallel to the rhombohedral [III] direction of the single-crystal, namely to the easy axis of magnetization. 3. Results and Discussion 3.1
Resistivity at Low Temperatures
Figure I displays the electrical resistivity p in the absence of magnetic field as a function of temperature. The transition temperatures T and T ~ are estimated as 1.82 K and 0 . 6 ~ K at ~ e midpoint of each transition, respectively• The transition widths ~T . and AT 2' corresponding to variaC tlons between i0 % and 90 % of the resistzvlty in the normal state, are 0.22 K and 0.055 K, respectively. Not only T . and T ~ but also 6T and &T 2 are not soC~ifferen~ L from • cl c those values o~tained for polycrystalline specimens. •
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T (K) Fig. I : Temperature dependence of the electrical resistivity in the absence of magnetic field.
As regards the thermal hysteresis at Tc_, it may be said that there are no hysteresis if the sample were cooled down at an extremely slow speed, for the hysteresis becomes as small as less than 2 mK with slowing down the cooling speed. Similarly to the ac susce~tlbillty measurement by Holtzberg et al., I~ on cooling the resistivity takes over 2 hours to reach its equilibrium value in the re-entrant transition region, while on warming it takes only a few minutes. All thermal hystereses observed in other experiments on single-crystals of HoMo. SA, including ou~ preceding ac susceptib~l~ty measurement, seem due to comparatively fast cooling• The long-time effect on cooling is considered to be related to the quenched modulated magnetic state to be discussed later• The resistivity in the re-entrant normal state below T ~ is recovered up to 98 % of its value in ~ e normal state above Tel and is kept constant at low temperatures below 0.5 K. This recovery rate of the resistivity is much larger than those for polycrystalline specimens, which are contrary to our expectation that a single-crystal with only Bloch walls without any grain boundary would be still superconductive at low temperatures below T ~ because of possible percolation of c supercon~uctlve paths formed inside the Bloch wa]Is. I~ The resistivity in the re-entrant normal state, however, increases a little Jn low magnetic f~elds up to I kOe and then it is constant up to 20 kOe, suggesting that there still remains a little superconductive region in the re-entrant normal state ~n the absence of magnetic field. From magnetization and ac susceptibility mea~ur~,ments,5,12, ~3 the grouted state of the Ho J+ magnetic moments has heen known to be a well isolated IJ =~8> doublet with strong unlaxial anisotropy z along the rhombohedral [lll ] direction, implying very narrow Bloch walJs. This is also negative to the superc,),ductivity inside the Bloch walls in lloMo S . From neutron d~ffraction studies, I!,12 onbt~e other hand, the ferrumagnetic ~;tate has b(~en
Vol. 60, No.
I0
LOW TEMPERATURES
BELOW Tc2 IN SINGLE-CRYSTAL
Quenched Cooling
Superconductivity
773
nlng up to about I0 % of the full destruction of the superconductivity. This is c l e a r l y estimated a t l ow t e m p e r a t u r e s b e l o w 0 . 3 K. The s e c o n d ~^ i s d e f i n e d a s a m a i n r e l a x a t i o n tlme in a wl~e region after the first relaxation. The third T^ is defined toward the end of the full destr~ctlon only in the temperature range between 0.5 K and 0.65 K, corresponding to the range where the re-entrant transition occurs on slow cooling as seen in Fig. i. Moreover, the time T n from the rapid cooling till the appearance o~ the resistivity is also regarded as a klnd of relaxation time. In Fig. 3 is shown the temperature dependence of these four relaxation times. At low temperatures below 0.5 K, the relaxation times increase with decreasing temperature. The temperature dependence in the low temperature region below 0.3 K is given by t 0 = T-6"5' ~1 = T-7"2' ~ = T-7"6' respectively. In ~ h ~ + quenches modulated magnetic state, the Ho- magnetic moments are known to be aligned along the rhombohedral [lll] or [III] direction with a transverse and square modulation, propagating along a direction with a wavelength A = 570 ~, as in the modulated magnetic state between T . and T .11,12 Therefore, the coexistence % ~ t h e m quenched modulated magnetic structure and superconductlvity may be reasonable. The relaxation from the quenched superconducting state to the normal stable state can be regarded as a process of growth of the microdomains from the square modulated magnetic structure. With growing microdomain, the superconductivity is considered to be destroyed
found to be composed of microdomalns of sizes of the order of i000 ~ to 1500 ~. In the ferromagnetic state, therefore, the superconductivity may be considered to still survive in regions consisting of mlcrodomalns of relatively small sizes. The resistivity below T ~ seems strongly dependent not on the Bloch w ~ i s but on the size and distribution of the ferromagnetic microdomalns. According to this argument, sample dependence of the recovery rate of the resistivity in the reentrant normal state is also well understood.
3.2
HoMo6S 8
by Rapid
We have found that the superconductivity above T ~ Is quenched by rapid cooling from a cz hlgh temperature above T , down to a low temperature below T ~.15 ~l~is Just means that c the quenched modulated magnetic structure by rapid cooling, observed in neutron diffraction studles,ll, 12 coexists with the superconductivity. This quenched superconductivity is metastable and destroyed as a function of tlme t, as shown in Flg. 2. The relaxation tlme T from the superconducting metastable state to the normal stable one can be defined as p = o={l - exp(-t/z)} , (i) where p= is a saturated value of the resistivity after a sufficiently long time at each temperature. As seen in Flg. 2, three kinds of relaxation times are obtained. The first relaxation time ~I is defined in the begin-
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Fig. 2 : Time dependence of the electrical resistivity In the metastable state caused by rapid cooling down to various temperatures. p is a saturated value of the resistivity a~ter a sufficiently long time at each temperature.
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LOW TEMPERATURESBELOWTc2 IN SINGLE-CRYSTAL HoMo6SS
Vol.
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T (K) Fig. 4 : Temperature dependence of the upper critical field in magnetic fields parallel to the rhombohedral Cl111 direction, namely to the easy axis of magnetization. Open circles are data in the usual superconducting state. Solid circles are data in the quenched superconducting state.
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dependence of the relaxFig. 3 : Temperature as the time from ation times: 0 - T defined the rapid cooling ? ill the appearance of the in the beginning resistlvlty; 7 - T1 defined of the full destruction of the superconducas a main relaxation tivity; . - T2 defined time after the first relaxation; A - T defined tovard the end of the full destru%tion of the superconductivity.
In regions consisting of microdomains of It follows that the process of large sizes. growth of the microdomains strongly depends on temperature, as given by Ts6e5, Tm7e2 or T-7.6. For the time being, these three relaxation times TV, TV and ~2, which have similar temperature dependence to each other, In the temperature cannot be told apart. range betveen 0.5 K and 0.65 K, corresponding to the range where the re-entrant transition the relaxation times occurs on slow cooling, This increase with increasing temperature. may be associated with critical slowing-dovn phenomena generally observed in phase transitions of the second order, though the reis widely believed entrant transition at T The order of the to be of the first order?. re-entrant transition should be reconsidered, taking account of no hysteresis effect at T c2 as mentioned in 3.1. The quenched superconductivity is also In Fig. 4 is destroyed by magnetic field. in magnetshown the upper critical field H direction, ic fields parallel to the clll’? namely to the easy axis of magnetization, determined by extrapolation to P = 0 of the As the linear part of the P vs H curve.
resistlvity in the quenched state is a function of time as well as magnetic field, H depends on time, namely on the sweep rate oc3 the magnetic field. The data in Fig. 4 have been obtained at the sweep rate of 2.3 Oelsec. The data in the temperature range between 0.3 K and 0.65 K are strongly affected by the time effect. The data at low temperatures below 0.3 K. on the other hand, are considered not to be affected by the time effect, for T is much longer than the sweep There H time of the gagnetic field. increases linearly with decreasing tempera% ure. The precise mechanism of the destruction of the quenched superconductivity by magnetic field is not yet clarified. It may be merely attributed to the enhancement of the growth the microdomains by magnetic field, of because it is known from neutron diffraction studies” that the modulated magnetic structure between T and T is suppressed by magnetic field %d tha? ferromagnetic order develops alternatively. On the other hand, it may be explained by a theory based on the modulated magnetic structure by analogy with antiferromagnetic superconductors.17 In Fig. 4 is also shown Hc2 in the usual superconducting state between T in magnetic fields parallel to the ?11”1;” dTf?ection. The demagnetization factor, which affects the H is not taken into accounf! value near Tc2, The anisotropy and temperature dependence of in the usual superconducting state will H bg2reported elsewhere. it may be worth while making a Finally, The ferromagnetic microdofollowing remark. main structure is just regarded as a square modulated magnetic structure of X = 2000 d to 3000 A, which is several times longer than in the real modulated one of X = 570 A. There is no essential difference between the ferromagnetic microdomain structure and the moduHowever, lated magnetic structure. it takes
Vol, 60, No. ]0
LOW TEMPERATURES BELOW Tc2 IN SINCLE-CRYSTAL HoMo6S 8
775
Acknowledgements- We w i s h to t h a n k P r o f . M. T a c h i k i and Dr. H. I w a s a k i f o r many h e l p f u l discussions. We a r e a l s o g r a t e f u l t o P r o f . Y. Muto, Mr. S. Sakatsume and t h e members o f C r y o n e n i c C e n t e r o f Tohoku U n i v e r s i t y f o r their aid in using the dilution refrigerator. T h i s work was s u p p o r t e d by t h e G r a n t - i n - A i d f o r S p e c i a l P r o j e c t R e s e a r c h on New S u p e r c o n d u c t i n g Materials No.61105001 from the Ministry of Education, Science and Culture, Japan.
long time for the modulated structure to change i n t o t h e mtcrodomain s t r u c t u r e , as o b s e r v e d a t T 2 on slow c o o l i n g and moreover as found i n t ~ e r e l a x a t i o n from t h e quenched s u p e r c o n d u c t i n g s t a t e t o t h e normal s t a t e . T h i s seems due t o t h e d i f f i c u l t y in large inversion of the magnetic moments between two ground states of IJz -+8> and IJz •-8> at low temperatures. More detailed experiments are under way to obtain a better understanding.
References 1.
2. 3. 4. 5. 6. 7.
8.
9.
I0.
For a g e n e r a l r e v i e w , s e e " S u p e r c o n d u c t i v i t y i n T e r n a r y Compounds I I " , e d s . M. B. Maple and 0. F i s c h e r , Vol. 34 o f Topics in Current Physics ( S p r i n g e r V e r l a g , B e r l i n , H e i d e l b e r g , New-York, 1982). M. I s h t k a w a and ~. F i s c h e r , S o l i d S t a t e Commun. 23, 37 (1977). L.D. Woolf, M. Tovar, H.C. Hamaker and M.B. Maple, Phys. L e t t . 71A, 137 (1979). J.W. Lynn, G. S h i r a n e , W. Thomlinson, R.N. S h e l t o n and D.E. Moneton, Phys. Rev. B24, 3817 (1981). F. H o l t z b e r g , S . J . L a P l a c a , T.R. McGuire and R.A. Webb, J . Appl. Phys. 5 5 , 2013 (1984). R. Horyn, O. Pe~a and M. S e r g e n t , J . Less-Common Met. 105, 55 (1985). S. Hosoya, H. T a k e i , Y. Koike, N. Kobayasht and Y. Muto, Jpn. J . Appl. Phys. 2 5 , 279 (1986). M. Tachiki, A. Kotanl, H. Matsumoto and H. Umezawa, Solid State Commun. 32, 599 (1979). T. FuJita, Y. Maeno and Y. Ikuta, Proc. Symposium on New Superconducting Materials, Tokyo, 1986, p. 52. J.L. Genlcon, J.P. Modon Danon, R.
i1.
12.
13. 14.
15.
16
17.
T o u r n i e r , O. Pefia, R. Horyu and M. S e r g e n t , J . P h y s i q u e L e t t . 4_55, L-1175 (1984). J . R o s s a t - M i g n o d , P. B u r l e t , S. Qu~zel, A. Beno~t, J . F l o u q u e t , R. Horyn, O. Pefla and M. S e r g e n t , J . P h y s i q u e L e t t . 46, L-373 (1985). P. B u r l e t , A. D i n i a , S. Qu~zel, J . R o s s a t - M i g n o d , J . L . G~nieon, A. B e n o t t , J . F l o u q u e t , R. T o u r n i e r , R. Horyn, O. Pe~a and M. S e r g e n t , J . Mag. Mag. Mat. 54-57, 1534 (1986). F. H o l t z b e r g , R.A. Webb, T.R. McGuire and S . J . L a P l a c a , J . Appl. Phys. 5 7 , 3121 (1985). J.L. Genlcon, B. Laaboudl, R. Tournier, R. Chevrel and M. Sergent, J. Physique 45, 1079 (1984). The same e x p e r i m e n t a l r e s u l t h a s b e e n obtained a l s o in the ease of r a p i d c o o l i n g from a temperature between Tcl and Lynn, R. J L ggazoni and J. Joffrin, J. Mag. Mag. Mat. 31-34, 493 (1983). K. Machida, K. Nokura and T. M a t s u b a r a , Phys. Rev. B22, 2307 (1980).
Solid State Communications, Printed in Great Britain.
QUENCHED
Vol.60,No.|O,
SUPERCONDUCTIVITY
pp.771-775,
1986.
0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.
BY RAPID COOLING DOWN TO LOW TEMPERATURES IN SINGLE-CRYSTAL HoMo6S 8
Y. Koike, T. Fukase, N. Kobayashi,
BELOW Tc2
S. Hosoya and H. Takei %
The Research
Institute for Iron, Steel and Other Metals, Tohoku University, Katahira, Sendal, 980 Japan 'The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo, 106 Japan (Received 4 September
1986 by T. TsuzukI)
Electrical resistivity of single-crystal HoMo.S 8 has been measured at low temperatures down to 0 . 0 1 K . By slow cooking, the resistivity In the re-entrant normal state below T ~ is recovered up to 98 % of its c value above T .. This suggests t H ~ there still remains a little cl superconductive region not due to Bloch walls, but rather to ferromagnetic mlcrodomains of comparatively small sizes. By rapid cooling, on the other hand, the superconductivity above T ~ has been found to be quenched at low temperatures below T 2" T~C~s quenched superconductivity, coexisting with the quenched ~odulated magnetic structure, is destroyed as a function of time and magnetic field, which seems attributed to the growth of the microdomains.
I. Introduction
the polycrystalline nature. Recently a few groups,B, 6 including our group, 7 have succeeded in preparing single-crystals of this material, though their dimensions are at most ! mm in edge-length. Detailed studies on the single-crystals have been in progress. An interesting matter with respect to the electrical resistivity of the slngle-crystals is whether the region inside Bloch walls in the ferromagnetic state becomes superconducting or not. The possible occurrence of this superconductivity has been theoretically investigated by Tachiki et al.. 8 From the experimental point of view, this has been also supported, based on the result that the resistivity below T are not fully recovered up to its value i~2 the normal state above T This result, however, has been obtained ~ ; sintered samples2, 9 and a polycrystalline sample composed of a few single-crystals, I0 which more or less include grain boundaries besides the Bloch walls. Therefore, an experiment using one single-crystal without any grain boundary is valuable to insist on the superconductivity within the Bloch walls. Another matter of interest is regarding a modulated magnetic structure quenched by fast cooling down to 0.I0 K, which was found in neutron diffraction studies by Rossat-Mignod et al..ll, 12 Although the modulated magnetic structure in the temperature range between T 2 and T is known to coexist with the s~perconduc~ivity, whether the quenched modulated magnetic state is superconducting is an unsettled matter. In this report we present the first experimental result on the electrical resistivity of a HoMo. S^ sample composed of only one single-crysta~ at low temperatures down to 0.01K. Our attention is focused on the su-
Since the discovery of ternary rareearth superconductors which achieve longrange magnetic order below their superconducting transition temperatures T _, the relationship between superconductivity and magnetism has attracted renewed attention. Many experimental and theoretical studies have been devoted to this kind of material.l For materials developing antiferromagnetic order, the superconductivity is generally known to be preserved and coexist with the magnetic order because of the absence of spatially averaged magnetic moments. For materials developing ferromagnetic order, on the other hand, the superconductivity is destroyed by the onset of the magnetic ordering at a low temperature T 2" However, a modulated magnetic structurec of a long wavelength, which appears in a narrow temperature range Just above Tc2, coexists with the superconductivity. A typical material developing ferromagnetic order is the Chevrel-phase compound HoMo. S_, whose re-entrant behavior at T ~ was discbov~ered by Ishikawa and Fischer. 2 wceZknow that HoMo.b S_ first becomes superconducting at T . ~ 1.8 K and then re-enters a normal state L aT T ~ ~ 0.6 K as the ferromagnetic ordering c 3 sets ~n. , A thermal hysteresis has been observed for the re-entrant transition at Tc2" On cooling, the superconductivity is nown to coexist with a modulated magnetic structure in a narrow temperature range between T 2 and T ~ 0.7 K, while this modulated structure ~ o e s not appear on warming. Most of experimental works on HoMo6S 8 , however, have been carried out on polycrystalline specimens with some ambiguity due to 771
Vol. 60, No. I0
LOW TEMPERATURES BELOW Tc2 IN SINGLE-CRYSTAL ltoMo6S8
772
perconductivity within the Bloch walls in the ferromagnetic state and the superconductivity in the quenched modulated magnetic state.
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HoMo6S8 #2"2
2. Experimental
40 Slngle-crystals of HoMo6S 8 were prepared in a high pressure, high temperature furnace. Details about the preparation procedure are reported in the preceding paper. ? Chemical and X-ray analyses have revealed that the composition of the single-crystals is almost stolchlometrlc. The dimension of the singlecrystal used here was 0.2 mm x 0.2 mm x 0.45 •am. The sample was placed on a large copper block thermally connected to the mixing chamber of a dilution refrigerator with a copper rod. Resistivity measurements ~~re made using a usual ac four-point probe method at a frequency of 70 Hz. The lead wires were attached to the sample with silver paste. The current in the sample was mainly as small as I0 pA to prevent self-heating. Moreover, we also made measurements using a very small current of 1 ~A to check the self-heating effect. Rapid cooling of the sample down to low temperatures below T ~ was performed as folcz lows. The sample was warmed up to a temperature above Tel by applying a large current of 5 mA to the sample itself for 2 minutes, keeping the temperature of the mixing chamber constant at a low temperature below T followed by shutting off the current. ~ this case the warming was attributed to the Joule heat due to the contact resistance between the lead wires and the sample. Whether the sample was warmed up to a temperature above T i was known by monitoring the resistivity o~ the sample with a current of 5 mA. In warming up the sample, the large copper block loaded with the sample was also warmed up a little, compared with the temperature of the mixing chamber• As soon as the current was shut off, however, it was cooled down to the temperature of the mixing chamber within I0 seconds. Although the temperature of the sample itself could not be measured, the sample was considered to be cooled down within a comparable time because of its very very small heat capacity. Magnetic fields were applied parallel to the rhombohedral [III] direction of the single-crystal, namely to the easy axis of magnetization. 3. Results and Discussion 3.1
Resistivity at Low Temperatures
Figure I displays the electrical resistivity p in the absence of magnetic field as a function of temperature. The transition temperatures T and T ~ are estimated as 1.82 K and 0 . 6 ~ K at ~ e midpoint of each transition, respectively• The transition widths ~T . and AT 2' corresponding to variaC tlons between i0 % and 90 % of the resistzvlty in the normal state, are 0.22 K and 0.055 K, respectively. Not only T . and T ~ but also 6T and &T 2 are not soC~ifferen~ L from • cl c those values o~tained for polycrystalline specimens. •
C l
m. o . 20
I
, , , I
. . . .
'
1
. . . .
'
. . . .
L
. . . .
2
,
. . . .
,
3
. . . .
,
. . . .
,
. . . .
4
T (K) Fig. I : Temperature dependence of the electrical resistivity in the absence of magnetic field.
As regards the thermal hysteresis at Tc_, it may be said that there are no hysteresis if the sample were cooled down at an extremely slow speed, for the hysteresis becomes as small as less than 2 mK with slowing down the cooling speed. Similarly to the ac susce~tlbillty measurement by Holtzberg et al., I~ on cooling the resistivity takes over 2 hours to reach its equilibrium value in the re-entrant transition region, while on warming it takes only a few minutes. All thermal hystereses observed in other experiments on single-crystals of HoMo. SA, including ou~ preceding ac susceptib~l~ty measurement, seem due to comparatively fast cooling• The long-time effect on cooling is considered to be related to the quenched modulated magnetic state to be discussed later• The resistivity in the re-entrant normal state below T ~ is recovered up to 98 % of its value in ~ e normal state above Tel and is kept constant at low temperatures below 0.5 K. This recovery rate of the resistivity is much larger than those for polycrystalline specimens, which are contrary to our expectation that a single-crystal with only Bloch walls without any grain boundary would be still superconductive at low temperatures below T ~ because of possible percolation of c supercon~uctlve paths formed inside the Bloch wa]Is. I~ The resistivity in the re-entrant normal state, however, increases a little Jn low magnetic f~elds up to I kOe and then it is constant up to 20 kOe, suggesting that there still remains a little superconductive region in the re-entrant normal state ~n the absence of magnetic field. From magnetization and ac susceptibility mea~ur~,ments,5,12, ~3 the grouted state of the Ho J+ magnetic moments has heen known to be a well isolated IJ =~8> doublet with strong unlaxial anisotropy z along the rhombohedral [lll ] direction, implying very narrow Bloch walJs. This is also negative to the superc,),ductivity inside the Bloch walls in lloMo S . From neutron d~ffraction studies, I!,12 onbt~e other hand, the ferrumagnetic ~;tate has b(~en
Vol. 60, No.
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LOW TEMPERATURES
BELOW Tc2 IN SINGLE-CRYSTAL
Quenched Cooling
Superconductivity
773
nlng up to about I0 % of the full destruction of the superconductivity. This is c l e a r l y estimated a t l ow t e m p e r a t u r e s b e l o w 0 . 3 K. The s e c o n d ~^ i s d e f i n e d a s a m a i n r e l a x a t i o n tlme in a wl~e region after the first relaxation. The third T^ is defined toward the end of the full destr~ctlon only in the temperature range between 0.5 K and 0.65 K, corresponding to the range where the re-entrant transition occurs on slow cooling as seen in Fig. i. Moreover, the time T n from the rapid cooling till the appearance o~ the resistivity is also regarded as a klnd of relaxation time. In Fig. 3 is shown the temperature dependence of these four relaxation times. At low temperatures below 0.5 K, the relaxation times increase with decreasing temperature. The temperature dependence in the low temperature region below 0.3 K is given by t 0 = T-6"5' ~1 = T-7"2' ~ = T-7"6' respectively. In ~ h ~ + quenches modulated magnetic state, the Ho- magnetic moments are known to be aligned along the rhombohedral [lll] or [III] direction with a transverse and square modulation, propagating along a
found to be composed of microdomalns of sizes of the order of i000 ~ to 1500 ~. In the ferromagnetic state, therefore, the superconductivity may be considered to still survive in regions consisting of mlcrodomalns of relatively small sizes. The resistivity below T ~ seems strongly dependent not on the Bloch w ~ i s but on the size and distribution of the ferromagnetic microdomalns. According to this argument, sample dependence of the recovery rate of the resistivity in the reentrant normal state is also well understood.
3.2
HoMo6S 8
by Rapid
We have found that the superconductivity above T ~ Is quenched by rapid cooling from a cz hlgh temperature above T , down to a low temperature below T ~.15 ~l~is Just means that c the quenched modulated magnetic structure by rapid cooling, observed in neutron diffraction studles,ll, 12 coexists with the superconductivity. This quenched superconductivity is metastable and destroyed as a function of tlme t, as shown in Flg. 2. The relaxation tlme T from the superconducting metastable state to the normal stable one can be defined as p = o={l - exp(-t/z)} , (i) where p= is a saturated value of the resistivity after a sufficiently long time at each temperature. As seen in Flg. 2, three kinds of relaxation times are obtained. The first relaxation time ~I is defined in the begin-
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Fig. 2 : Time dependence of the electrical resistivity In the metastable state caused by rapid cooling down to various temperatures. p is a saturated value of the resistivity a~ter a sufficiently long time at each temperature.
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104
LOW TEMPERATURESBELOWTc2 IN SINGLE-CRYSTAL HoMo6SS
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T (K) Fig. 4 : Temperature dependence of the upper critical field in magnetic fields parallel to the rhombohedral Cl111 direction, namely to the easy axis of magnetization. Open circles are data in the usual superconducting state. Solid circles are data in the quenched superconducting state.
T-26
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dependence of the relaxFig. 3 : Temperature as the time from ation times: 0 - T defined the rapid cooling ? ill the appearance of the in the beginning resistlvlty; 7 - T1 defined of the full destruction of the superconducas a main relaxation tivity; . - T2 defined time after the first relaxation; A - T defined tovard the end of the full destru%tion of the superconductivity.
In regions consisting of microdomains of It follows that the process of large sizes. growth of the microdomains strongly depends on temperature, as given by Ts6e5, Tm7e2 or T-7.6. For the time being, these three relaxation times TV, TV and ~2, which have similar temperature dependence to each other, In the temperature cannot be told apart. range betveen 0.5 K and 0.65 K, corresponding to the range where the re-entrant transition the relaxation times occurs on slow cooling, This increase with increasing temperature. may be associated with critical slowing-dovn phenomena generally observed in phase transitions of the second order, though the reis widely believed entrant transition at T The order of the to be of the first order?. re-entrant transition should be reconsidered, taking account of no hysteresis effect at T c2 as mentioned in 3.1. The quenched superconductivity is also In Fig. 4 is destroyed by magnetic field. in magnetshown the upper critical field H direction, ic fields parallel to the clll’? namely to the easy axis of magnetization, determined by extrapolation to P = 0 of the As the linear part of the P vs H curve.
resistlvity in the quenched state is a function of time as well as magnetic field, H depends on time, namely on the sweep rate oc3 the magnetic field. The data in Fig. 4 have been obtained at the sweep rate of 2.3 Oelsec. The data in the temperature range between 0.3 K and 0.65 K are strongly affected by the time effect. The data at low temperatures below 0.3 K. on the other hand, are considered not to be affected by the time effect, for T is much longer than the sweep There H time of the gagnetic field. increases linearly with decreasing tempera% ure. The precise mechanism of the destruction of the quenched superconductivity by magnetic field is not yet clarified. It may be merely attributed to the enhancement of the growth the microdomains by magnetic field, of because it is known from neutron diffraction studies” that the modulated magnetic structure between T and T is suppressed by magnetic field %d tha? ferromagnetic order develops alternatively. On the other hand, it may be explained by a theory based on the modulated magnetic structure by analogy with antiferromagnetic superconductors.17 In Fig. 4 is also shown Hc2 in the usual superconducting state between T in magnetic fields parallel to the ?11”1;” dTf?ection. The demagnetization factor, which affects the H is not taken into accounf! value near Tc2, The anisotropy and temperature dependence of in the usual superconducting state will H bg2reported elsewhere. it may be worth while making a Finally, The ferromagnetic microdofollowing remark. main structure is just regarded as a square modulated magnetic structure of X = 2000 d to 3000 A, which is several times longer than in the real modulated one of X = 570 A. There is no essential difference between the ferromagnetic microdomain structure and the moduHowever, lated magnetic structure. it takes
Vol, 60, No. ]0
LOW TEMPERATURES BELOW Tc2 IN SINCLE-CRYSTAL HoMo6S 8
775
Acknowledgements- We w i s h to t h a n k P r o f . M. T a c h i k i and Dr. H. I w a s a k i f o r many h e l p f u l discussions. We a r e a l s o g r a t e f u l t o P r o f . Y. Muto, Mr. S. Sakatsume and t h e members o f C r y o n e n i c C e n t e r o f Tohoku U n i v e r s i t y f o r their aid in using the dilution refrigerator. T h i s work was s u p p o r t e d by t h e G r a n t - i n - A i d f o r S p e c i a l P r o j e c t R e s e a r c h on New S u p e r c o n d u c t i n g Materials No.61105001 from the Ministry of Education, Science and Culture, Japan.
long time for the modulated structure to change i n t o t h e mtcrodomain s t r u c t u r e , as o b s e r v e d a t T 2 on slow c o o l i n g and moreover as found i n t ~ e r e l a x a t i o n from t h e quenched s u p e r c o n d u c t i n g s t a t e t o t h e normal s t a t e . T h i s seems due t o t h e d i f f i c u l t y in large inversion of the magnetic moments between two ground states of IJz -+8> and IJz •-8> at low temperatures. More detailed experiments are under way to obtain a better understanding.
References 1.
2. 3. 4. 5. 6. 7.
8.
9.
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