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Magnetic ordering in PrNi2
Volume 79A, number 1
PHYSICS LETTERS
15 September 1980
MAGNETIC ORDERING IN PrNi2 H. MORI, T. FUJITA, T. SATOH and T. OHTSUKA Department of Physics, Faculty of Science, Tohoku University, Sendai, 980, Japan Received 17 April 1980 Revised manuscript received 1 July 1980
A peak has been observed in the magnetic susceptibility of the singlet ground state system PrNi2, indicating a magnetic ordering. The transition is believed to be of a mixed nuclear—electronic type.
Magnetic systems with singletground state ions differ from conventional systems in a number of ways. In order for magnetic ordering to occur, the exchange interaction must exceed a critical value determined by the crystal field splitting [1—3].If the exchange is smaller than the critical value, the system remains a Van even at absoluteis zero temperature.Vleck Whenparamagnet the exchange interaction weaker but very close to the threshold value, the coupling between the 4f electrons and the nuclei becomes essential in predicting its magnetic behavior [4—6]. The internuclear interaction is enhanced and a very high ordering temperature is realized for the nuclear spins, PrCu 2 [7], PrCu5 [8] and PrCu6 [9] belong to this category. Recent neutron diffraction measurements on HoGaG and ThGaG [10] demonstrate the characteristic temperature dependence of the spontaneous magnetization expected for hyperfine-induced systems. Various experiments above 1 K on PrNi2 mdicate that the exchange interaction is close to the critical value and that PrNi2 is a good candidate for combined nuclear—electronic order. Skrabek and Wallace [11] first reported that PrNi2 undergoes a ferromagnetic transition at 8 K but the ordered moment is much smaller than the free ion value. A few years later, McDermott and Marklund [12] observed a heat capacity2which varied temperabelow 0.35with K. They interture approximately as T preted it in terms of the internal field originating from the ordered electronic moment which sets in at 8 K. Contrary to the original report by Skrabek and Wallace,
however, subsequent measurements of the heat capacity, susceptibility and resistivity revealed no indication of order at 8 K or at any temperature above 1.8 K. Wallace and Mader [13] studied the magnetization and the susceptibility, and reported that PrNi2 remains a Van Vieck paramagnet down to 4.2 K. We are left, in 2 behavior therefore, with the question why the T heat capacity below 0.35 K occurs when the transition at 8 K is ruled out. A natural step toward the problem is to extend the experiments to lower ternperatures. We might recall in passing that a controversy still exists about the magnetic ordering in the elemental dhcp Pr [14]. Four different samples were used in the ac susceptibiity measurements, two powder (#1, #2) and two bulk (#3, #4) samples. The first three samples were prepared by arc-melting stoichiometric amounts of Pr and Ni metal. For the powder sample #1, no annealing was done after arc-melting. The powder sample #2 was annealed at 750°Cfor one week after powdering. The bulk sample #3 was annealed at 750°C for two weeks. The bulk sample #4 was prepared at the Matsushita Research Institute and had undergone a nominally identical heat treatment as #3. The ac susceptibility was measured by use of a 70 Hz Hartshorn bridge, the alternating field always being kept below I Oe. samples were of attached to copper foils leading to the The mixing chamber a dilution refrigerator. The volumes of the bulk samples #3 and #4 were 3 X 10—2 and 4 X 10~cm3, respectively, and the skin depth of the 70 Hz alternating field was estimated to be 121
Volume 79A, number 1
PHYSICS LETTERS ~ I
I
I
I
3.0
.
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T K Fig. 1. 70 Hz ac susceptibility Xac of the PrNi2 bulk samples #3 and #4 as a function of temperature.
much larger than the sample dimensions. The absolute value of Xac was calibrated with the help of a known amount of cerium magnesium nitrate replacing the samples. Preliminary ac susceptibility experiments on the unannealed powder sample showed a sharp peak at 3 K and a broad peak at about 0.2 K. For the annealed powder sample, the peak at 3 K was reduced considerably, indicating that it probably originates from an extraneous phase. The peak at the lower temperature became more pronounced. The peak at 3 K completely disappears for the bulk samples as shown in fig. 1. The observed broad peak in Xac resembles that of a behavior expected from a system with a magnetic excited level located at about 0.5 K above a nonmagnetic ground level. No Schottky anomaly, however, was found in the heat capacity at the corresponding temperature ofO.2 Moreover, heat capacity measurements ranging from 1 K to 80 K and the deduced entropy reveal that no such low-lying excited level exists. Therefore, the behavior of Xac cannot be due to a single-ion effect. In an effort to provide a more concrete basis for our conjecture that it reflects a cooperative transition, a dc measurement was carried out.
15 September 1980
The dc measurements incorporating a SQUID magnetometer differ from the ac measurements in the following aspects. The bulk sample #4 was immersed directly in the 4 side of the mixing chamber, and an astatic pair of superconducting coils and a singlelayered primary coil for dc field were wound around the sample. A carbon resistor thermometer was also placed in the mixing chamber. The SQUID magnetometer measures the static magnetization M induced by an applied field H. We define Xdc by M/H, where H 1 Oe at all temperatures. Xdc is peaked at 0.25 K, a slightly lower temperature than Xac The difference is believed to be related to the long relaxation time which we discuss below. In the course of the measurement, the time necessary for the induced magnetization M to reach its equilibrium value after switching on the external field was found to become very long near the temperature of the Xdc maximum. The time variation of M approximately followedM(t) Me I’ exp(—t/r), where Me is the equilibrium magnetization that the system finally attains. The temperature dependence of the 1relaxation time obtained is shown in fig. 2 together with Xdc• The maximum relaxation time becomes as long as about 2 mm. It has been reported that PrCu2 I
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Fig. 2. Dc susceptibility Xdc and relaxation time r of the PrNi2 bulk sample #4 as a function of temperature. An arbitrary scale is used for Xdc, and the zero of its ordinate is estimated to lie within the indicated interval.
Volume 79A, number 1
PHYSICS LETTERS
and PrCu6 exhibit a thermal relaxation time of about 10 mill at their ordering temperatures of 54 mK and 2.5 mK, respectively. Our experiment here is the direct observation of the magnetization itself and should be distinguished from these findings. The present result on PrNi2, to our knowledge, is the first detailed measurement of the magnetic relaxation time near the ordering temperature of a nuclear—electron coupled system. The fact that the temperature of the Xdc maximum does not coincide with that of the Xac maximum must be related to the relaxation effect, but a detailed analysis is left for future studies. Here we tentatively adopt 0.25 K to be the ordering ternperature of PrNi2. No measurable anomaly was found in the heat capacity near the temperature of the Xdc maximum. We conclude that PrNi2 undergoes a magnetic transition at 0.25 K around which both the ac and dc susceptibilities have a maximum. The cooperative character of the phenomenon is strongly supported by the anomalous behavior of the relaxation time. Further experiments are necessary to determine the type of magnetic ordering. We thank Dr. T. Yamadaya of the Matsushita Research Institute for providing us with sample #4, Dr. A. Sawada for constructing the ac bridge and Mr. S. Kobayashi for helping us with the dc susceptibility
15 September 1980
measurements. Thanks are also due to Dr. H. Suzuki, Professor T. Murao (Kyoto University) and Professor A. Yanase for useful discussions. References [1] T. Moriya, Phys. Rev. 117 (1960) 635. [2] G.T. Trammell, Phys. Rev. 131 (1963) 932. [3] B. Bleaney, Proc. Roy. Soc. A236 (1963) 19. [4] [5] [6]
T. 33 Murao, (1972) J.33.Phys. Soc. Japan 31(1971) 683; K. Andres, Phys. Rev. B7 (1973) 4295. B.B. Triplett and R.M. White, Phys. Rev. B7 (1973)
4938. [7] K. Andres, E. Bucher, J.P. Malta and A.S. Cooper, Phys. Rev. Lett. 28 (1972) 1652. [8] K. Andres, E. Bucher, J.P. Maita and S. Darack, Phys. Rev. 1311 (1975)4364. [9] J. Babcock, J. Kiely, T. Manley and W. Weyhman, Phys. Rev. Lett. 43 (1979) 380. [10] J. Hamman and M. Ocio, Physica 86—88B (1977) 1153. [11] E.A. Skrabek and W.E. Wallace, J. Appl. Phys. 34 (1963) 1356. [12] M.J. McDermott and K.K. Marklund, J. Appl. Phys. 40 (1969) 1007. [13] W.E. Wallace and K.H. Mader, borg. Chem. 7 (1968) 1627. [14] K. Andres, E. Bucher, J.P. Malta, L.D. Longinotti and R. Flukiger, Phys. Rev. B6 (1972) 313; P.E. Lindelof, I.E. Miller and G.R. Pickett, Phys. Rev. i~tt.35 (1975) 1297.
123
PHYSICS LETTERS
15 September 1980
MAGNETIC ORDERING IN PrNi2 H. MORI, T. FUJITA, T. SATOH and T. OHTSUKA Department of Physics, Faculty of Science, Tohoku University, Sendai, 980, Japan Received 17 April 1980 Revised manuscript received 1 July 1980
A peak has been observed in the magnetic susceptibility of the singlet ground state system PrNi2, indicating a magnetic ordering. The transition is believed to be of a mixed nuclear—electronic type.
Magnetic systems with singletground state ions differ from conventional systems in a number of ways. In order for magnetic ordering to occur, the exchange interaction must exceed a critical value determined by the crystal field splitting [1—3].If the exchange is smaller than the critical value, the system remains a Van even at absoluteis zero temperature.Vleck Whenparamagnet the exchange interaction weaker but very close to the threshold value, the coupling between the 4f electrons and the nuclei becomes essential in predicting its magnetic behavior [4—6]. The internuclear interaction is enhanced and a very high ordering temperature is realized for the nuclear spins, PrCu 2 [7], PrCu5 [8] and PrCu6 [9] belong to this category. Recent neutron diffraction measurements on HoGaG and ThGaG [10] demonstrate the characteristic temperature dependence of the spontaneous magnetization expected for hyperfine-induced systems. Various experiments above 1 K on PrNi2 mdicate that the exchange interaction is close to the critical value and that PrNi2 is a good candidate for combined nuclear—electronic order. Skrabek and Wallace [11] first reported that PrNi2 undergoes a ferromagnetic transition at 8 K but the ordered moment is much smaller than the free ion value. A few years later, McDermott and Marklund [12] observed a heat capacity2which varied temperabelow 0.35with K. They interture approximately as T preted it in terms of the internal field originating from the ordered electronic moment which sets in at 8 K. Contrary to the original report by Skrabek and Wallace,
however, subsequent measurements of the heat capacity, susceptibility and resistivity revealed no indication of order at 8 K or at any temperature above 1.8 K. Wallace and Mader [13] studied the magnetization and the susceptibility, and reported that PrNi2 remains a Van Vieck paramagnet down to 4.2 K. We are left, in 2 behavior therefore, with the question why the T heat capacity below 0.35 K occurs when the transition at 8 K is ruled out. A natural step toward the problem is to extend the experiments to lower ternperatures. We might recall in passing that a controversy still exists about the magnetic ordering in the elemental dhcp Pr [14]. Four different samples were used in the ac susceptibiity measurements, two powder (#1, #2) and two bulk (#3, #4) samples. The first three samples were prepared by arc-melting stoichiometric amounts of Pr and Ni metal. For the powder sample #1, no annealing was done after arc-melting. The powder sample #2 was annealed at 750°Cfor one week after powdering. The bulk sample #3 was annealed at 750°C for two weeks. The bulk sample #4 was prepared at the Matsushita Research Institute and had undergone a nominally identical heat treatment as #3. The ac susceptibility was measured by use of a 70 Hz Hartshorn bridge, the alternating field always being kept below I Oe. samples were of attached to copper foils leading to the The mixing chamber a dilution refrigerator. The volumes of the bulk samples #3 and #4 were 3 X 10—2 and 4 X 10~cm3, respectively, and the skin depth of the 70 Hz alternating field was estimated to be 121
Volume 79A, number 1
PHYSICS LETTERS ~ I
I
I
I
3.0
.
/
-
~°
,~‘
°~
2.O
-
><
••
•‘~ -i.o PrNi
2
T K Fig. 1. 70 Hz ac susceptibility Xac of the PrNi2 bulk samples #3 and #4 as a function of temperature.
much larger than the sample dimensions. The absolute value of Xac was calibrated with the help of a known amount of cerium magnesium nitrate replacing the samples. Preliminary ac susceptibility experiments on the unannealed powder sample showed a sharp peak at 3 K and a broad peak at about 0.2 K. For the annealed powder sample, the peak at 3 K was reduced considerably, indicating that it probably originates from an extraneous phase. The peak at the lower temperature became more pronounced. The peak at 3 K completely disappears for the bulk samples as shown in fig. 1. The observed broad peak in Xac resembles that of a behavior expected from a system with a magnetic excited level located at about 0.5 K above a nonmagnetic ground level. No Schottky anomaly, however, was found in the heat capacity at the corresponding temperature ofO.2 Moreover, heat capacity measurements ranging from 1 K to 80 K and the deduced entropy reveal that no such low-lying excited level exists. Therefore, the behavior of Xac cannot be due to a single-ion effect. In an effort to provide a more concrete basis for our conjecture that it reflects a cooperative transition, a dc measurement was carried out.
15 September 1980
The dc measurements incorporating a SQUID magnetometer differ from the ac measurements in the following aspects. The bulk sample #4 was immersed directly in the 4 side of the mixing chamber, and an astatic pair of superconducting coils and a singlelayered primary coil for dc field were wound around the sample. A carbon resistor thermometer was also placed in the mixing chamber. The SQUID magnetometer measures the static magnetization M induced by an applied field H. We define Xdc by M/H, where H 1 Oe at all temperatures. Xdc is peaked at 0.25 K, a slightly lower temperature than Xac The difference is believed to be related to the long relaxation time which we discuss below. In the course of the measurement, the time necessary for the induced magnetization M to reach its equilibrium value after switching on the external field was found to become very long near the temperature of the Xdc maximum. The time variation of M approximately followedM(t) Me I’ exp(—t/r), where Me is the equilibrium magnetization that the system finally attains. The temperature dependence of the 1relaxation time obtained is shown in fig. 2 together with Xdc• The maximum relaxation time becomes as long as about 2 mm. It has been reported that PrCu2 I
~
122
-
\
,/
200
—--------XdC~..
.s•~ 0 0
>~
0
0
-r
0 0 0
~.
~ The details will be published in a separate paper.
-~
0
-
0 0
0 0 00
o 0000
I
0.01
0
00
0
I
( K ) - -
Fig. 2. Dc susceptibility Xdc and relaxation time r of the PrNi2 bulk sample #4 as a function of temperature. An arbitrary scale is used for Xdc, and the zero of its ordinate is estimated to lie within the indicated interval.
Volume 79A, number 1
PHYSICS LETTERS
and PrCu6 exhibit a thermal relaxation time of about 10 mill at their ordering temperatures of 54 mK and 2.5 mK, respectively. Our experiment here is the direct observation of the magnetization itself and should be distinguished from these findings. The present result on PrNi2, to our knowledge, is the first detailed measurement of the magnetic relaxation time near the ordering temperature of a nuclear—electron coupled system. The fact that the temperature of the Xdc maximum does not coincide with that of the Xac maximum must be related to the relaxation effect, but a detailed analysis is left for future studies. Here we tentatively adopt 0.25 K to be the ordering ternperature of PrNi2. No measurable anomaly was found in the heat capacity near the temperature of the Xdc maximum. We conclude that PrNi2 undergoes a magnetic transition at 0.25 K around which both the ac and dc susceptibilities have a maximum. The cooperative character of the phenomenon is strongly supported by the anomalous behavior of the relaxation time. Further experiments are necessary to determine the type of magnetic ordering. We thank Dr. T. Yamadaya of the Matsushita Research Institute for providing us with sample #4, Dr. A. Sawada for constructing the ac bridge and Mr. S. Kobayashi for helping us with the dc susceptibility
15 September 1980
measurements. Thanks are also due to Dr. H. Suzuki, Professor T. Murao (Kyoto University) and Professor A. Yanase for useful discussions. References [1] T. Moriya, Phys. Rev. 117 (1960) 635. [2] G.T. Trammell, Phys. Rev. 131 (1963) 932. [3] B. Bleaney, Proc. Roy. Soc. A236 (1963) 19. [4] [5] [6]
T. 33 Murao, (1972) J.33.Phys. Soc. Japan 31(1971) 683; K. Andres, Phys. Rev. B7 (1973) 4295. B.B. Triplett and R.M. White, Phys. Rev. B7 (1973)
4938. [7] K. Andres, E. Bucher, J.P. Malta and A.S. Cooper, Phys. Rev. Lett. 28 (1972) 1652. [8] K. Andres, E. Bucher, J.P. Maita and S. Darack, Phys. Rev. 1311 (1975)4364. [9] J. Babcock, J. Kiely, T. Manley and W. Weyhman, Phys. Rev. Lett. 43 (1979) 380. [10] J. Hamman and M. Ocio, Physica 86—88B (1977) 1153. [11] E.A. Skrabek and W.E. Wallace, J. Appl. Phys. 34 (1963) 1356. [12] M.J. McDermott and K.K. Marklund, J. Appl. Phys. 40 (1969) 1007. [13] W.E. Wallace and K.H. Mader, borg. Chem. 7 (1968) 1627. [14] K. Andres, E. Bucher, J.P. Malta, L.D. Longinotti and R. Flukiger, Phys. Rev. B6 (1972) 313; P.E. Lindelof, I.E. Miller and G.R. Pickett, Phys. Rev. i~tt.35 (1975) 1297.
123