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Specific heat and frequency-dependent ac-susceptibility of PrNi2 below 1 K
92
Physica 112B (1982) 92-97 North-Holland Publishing Company
LETTER
TO THE
EDITOR
SPECIFIC HEAT AND FREQUENCY-DEPENDENT AC-SUSCEPTIBILITY OF PrNiz BELOW 1 K F.J.A.M.
GREIDANUS,
L.J. DE JONGH
and W.J. HUISKAMP
Kamerlingh Onnes Laboratory, University of Leiden, 7he Neiherlands
K.H.J.
BUSCHOW
Philips Research Laboratories, Eindhoven, The Netherlands Received
19 August
1981
AC-susceptibility measurements on PrNi2 show broad anomalies, the temperature of the susceptibility maximum shifting from 0.3-0.5 K as the frequency is varied in between 3 Hz and 3 kHz. On the other hand the specific heat is featureless in the same temperature range. The behaviour is interpreted in terms of a mixed electronic-nuclear phase transition. Strong relaxation effects are observed in the susceptibility at temperatures close to the maxima.
1. Introduction The study
of enhanced nuclear and mixedelectronic nuclear magnetic order in Van Vleck paramagnetic compounds, in particular of praseodymium, is of current theoretical [l-5] and experimental [6-lo] interest. In these systems the electronic ground state of P?’ is a singlet (F1) or a non-magnetic doublet (F,), the next higher energy levels being at a distance A large enough compared to the exchange J to exclude conventional electronic magnetic ordering. The hyperfine interaction, Hh.f. = AI-J, between electronic (J) and nuclear (1) spins then becomes of prime importance, since it induces a moment in the electronic ground state through mixing of the higher energy levels. The induced 4f moments of neighbouring Pr atoms may interact via the RKKY interaction (plus dipolar interactions), which may result in magnetic ordering at a transition temperature T, considerably lower than would be observed for conventional electronic ordering. The nuclear moments in turn become ordered through the hyperfine interaction. Thus, depending on the ratio of A and J,
we may characterize the type of magnetic ordering as: (i) purely electronic for J S- A ; (ii) enhanced 037%4363/82/0000-0000/$02.75
@ 1982 North-Holland
nuclear for J GA ; and (iii) mixed electronicnuclear for J = A. Examples of the latter two types have so far been very few. As regards enhanced nuclear ordering, a clear experimental example appears to have been found in PrCud [lo]. Magnetization data on this compound indicate a ferromagnetic transition near T,= 2.5 mK. At the same temperature the specific heat shows a very high and sharp peak, indicating that all of the nuclear entropy is involved in the cooperative transition (the electronic entropy is already removed at very much higher temperatures via crystal field single-ion interactions). This contrasts with the specific heat behaviour found for PrCuz and PrCuS, which show mixed electronic-nuclear transitions (type iii) at T, = 54 mK and 24 mK, respectively [6,7,9, 111. These transition temperatures were deduced from peaks in the lowfield or ac-susceptibility measured as a function of temperature. Near T, the specific heat of both compounds is featureless; for PrCus a Schottkytype hyperfine anomaly is observed [7] with a maximum at about 0.6T,. This behaviour is not inconsistent with existing theoretical predictions within the effective field framework, which indicate that the specific heat ordering anomaly may
Specific heat and susceptibility
become
unmeasurably
small
excited
in the intermediate
region of mixed electronic-nuclear In this note we present what
order. we believe
of PrNi2 below 1 K
is
another example of the mixed electronic-nuclear type of order, namely the intermetallic compound PrNir. PrNi* belongs to the series PrX2, in which X can be Mg, Al, Co, Ni, Rh, Ru, Ir, Pt. Each of these materials has the Cl5 structure, and the rare earth ions are situated at sites of cubic symmetry. It has been shown by several authors [12-151 that the compounds with X= Mg, Al, Co, Rh, Ru, Ir, Pt exhibit phase transitions in the range 4.2-40 K. In this respect PrNiz is an exception. Although earlier magnetic measurements 1161 and specific heat data [17] in the temperature range 150 mK-1 K were interpreted in terms of a phase transition around 8 K, more recent susceptibility, magnetization and specific heat data [18-201 prove PrN& to be paramagnetic at 4.2 K. The contribution of a substantial exchange interaction was, however, clearly manifest. In 1974 Bucher et al. [21] claimed a transition temperature of 0.33 K. In the course of our experiments of PrNi*, Mori et al. independently published their data on the acand dc-susceptibility [22]. They showed that both reached a maximum in between 0.2 K and 0.3 K. Strong relaxation effects were also observed at the same temperature. A knowledge of the nature of the ground state is of primary importance in understanding the low temperature behaviour of PrNi*. Wallace [19] and Bucher et al. [21] claimed rl to be the ground state with the r, level at 45 K and the r, level at 77 K, inferred from specific heat [21]. This was in agreement with thermopower measurements, although a r, ground state could not be ruled out completely. In order to study this problem in more detail we have recently performed inelastic neutron scattering experiments on a triple axis spectrometer at the E.I.R. in Wiirenlingen, in cooperation with A. Furrer. A preliminary analysis of the data indicates the non-magnetic doublet r, to be the ground state, with a first
state
93
at 35 K+ 10 K. Further
details
will
be published elsewhere [23]. This would contradict previous assignments of the r1 singlet to be the PP’ ground state in PrNi*. Also, it would present
a difference
above
mentioned
three
are claimed
In the present ments on various dependent provide
temperature
PrNi*
compounds,
to be r1 singlet
and
the
which
all
systems.
letter specific heat measuresamples, as well as frequency-
susceptibility more
between
Pr-Cu
insight
studies
are presented,
into the nature
to
of the low
transition.
2. Experimental
techniques
Various samples of PrNir were studied, prepared by arc melting of 99.9% pure Pr and in an atmosphere of purified argon gas. For samples labelled I and II stoichiometric ratios
all Ni the of
the starting materials were used, while a third sample, labelled III, was prepared starting from Pr and Ni in atomic ratio 1:2.04. All samples were vacuum annealed (wrapped in Ta foil) first at 600” C for two weeks, subsequently 4 weeks at 700°C and 4 weeks at 800°C. After the annealing the condition of the samples was carefully checked by X-ray diffraction. Samples I and II showed small traces of the impurity phase PrNi. In sample II the impurity concentration was lower than in sample I and was estimated to be less than 5%. In sample III no impurity phases could be detected. The specific heat measurements were performed on the bulk polycrystalline materials. The sample was mounted in an adiabatic demagnetization apparatus, described more extensively elsewhere [24]. Heat contact was provided by electrolytically coating the ingot with a thin layer of copper, and then soldering it with indium to the cooling device. Both resistance and magnetic thermometry were applied. Susceptibility measurements were performed on a powdered specimen of about 100 mg taken from sample III. A conventional 3He-4He dilu-
94
Specific heat and susceptibility
tion refrigerator cryostat was used. Heat contact with the mixing chamber was provided by means of liquid 4He. The ac-susceptibility was measured with a bridge, in which a SQUID was employed as a null detector [25]. The available frequency range was l-3000Hz, the amplitude of the measuring ac-field being always smaller than 0.01 Oe. The same circuitry could also be used to measure changes in the magnetization by monitoring the dc-output of the SQUID, and using the primary coil of the mutual inductance as a field coil. In this apparatus the temperature was measured with a CMN thermometer, calibrated against the 4He vapour pressure scale. Below 30 mK the CMN thermometer readings were checked with a @‘CoCo single crystal [26] nuclear orientation thermometer. Details of the apparatus and the SQUID-bridge circuitry will be published at a later date.
of RNiz
below 1 K
l
SAMPLE
0 SAMPLE
001
01
II III
10
TEMPERATURE
50
(Kl
Fig. 1. Specific heat C/R of sample II and sample III. A line with a T-* slope has been drawn through the data at the lowest temperatures.
3. Results of the measurements The specific heat data on the samples II and
III are shown in fig. 1. (the addenda being already subtracted). The results on these two samples are seen to agree within a few percent. Qualitatively, the data on sample I were found to show the same behaviour. At temperatures below 600 mK, however, the data on sample I were substantially higher than for II and III. We attribute this to a contribution of an impurity phase, whose presence was established by means of X-ray diffraction, as obtained in section 2. With reference to the discussion below we remark that the observed relaxation times never exceeded a few seconds in the specific heat experiments. We cannot exclude however the occurrence of relaxation times of several minutes, or longer. Susceptibility measurements, taken at different frequencies between v = 3 Hz and v = 3000 Hz are shown in fig. 2. Plotted are the real ($) and imaginary (J$‘) parts of the complex frequency dependent ac-susceptibility X(V) = X’(V) - ix”(v).
Because the x” signal shows similar behaviour for various frequencies, only the 600 Hz signal has been shown, for clarity of representation. With increasing frequency the position of the x’ maximum is found to shift from 330 & 10 mK to 450 220 mK, whereas its height is decreasing. I
““m
““““I
20
l. . .
F
l.
. I
Aa&* fi_
I
15-
3 15 64 600 3000
Hz Hz Hz Hz Hz
5-
O001
10
01 TEMPERATURE
(Kl
Fig. 2. In-phase part x’ of the susceptibility for frequencies in between 3-3000 Hz. The out-of-phase part x0 for a frequency of 600 Hz is also shown.
Specific heat and susceptibility of PrNi2 below 1 K
Finally, in fig. 3, the change in the magnetization signal as a function of temperature is shown, using a field of about 0.5 Oe as the magnetizing field. Every time the temperature was changed, the system was allowed to’ come to equilibrium. While performing measurements it proved to be essential to apply the magnetizing field before cooling the sample. If not, the behaviour of the out magnetization sample, when carrying measurements in a warm up run, was completely undefined. For example, the change in the output of the SQUID-magnetometer could change sign, depending on the rate at which heat was applied. In addition we performed dc-susceptibility measurements by applying instantaneously a constant magnetic field (6 1 Oe) at a fixed temperature and monitoring the output of the SQUID-electronics as a function of time. A preliminary analysis indicates that the dc-susceptibility reaches a maximum at 270 mK& 20 mK. Strong relaxation effects were observed,
0 0 I
0 01
00 I
I11111
1.0
01 TEMPERATURE
10
(K)
Fig. 3. Change in magnetization as a function of temperature, as monitored at the dc-output of the SQUIDmagnetometer during a warming up run. The zero is chosen at T = 1.27 K.
95
as was reported previously by Mori et al. [22]. However, our measurements cannot be described with a single time constant. It seems more likely that two processes take place on different time scales. At about 270 mK the time constant related to the slow process reaches a value of about 1000 s, i.e. an order of magnitude larger than reported by Mori et al. The time constant related to the fast process could not yet be determined.
4. Discussion and conclusion As was outlined in the introduction, the ground state of PrNiz probably is the non-magnetic r3-doublet with a first excited state at a distance of about 35 K ? 10 K. Because no sign of a phase transition is found at temperatures above 1 K, one concludes that the ratio of the exchange interaction J to the crystal field splitting A must be close to its threshold value. It is therefore tempting to explain the observed susceptibility peak in terms of a mixed electronic-nuclear ordering phenomenon, as previously suggested for PrCu* and PrCu5 [7,9,11]. Although the specific heat data show no anomaly in the temperature range of the x maxima, this does not necessarily contradict such an explanation. From the theoretical calculation within the effectivefield approach [l, 21, it follows that for certain combinations of J, A and the hyperfine coupling constant A, the anomaly in the heat capacity associated with such a type of ordering may become extremely small. For instance Murao [l], predicts for AID = 10m3and D/J = 2 a specific heat jump of the order of lo-* R only. This obviously is far outside the presently attainable experimental accuracy. Thus the state of affairs for PrNi* appears to be rather similar to that for the singlet-ground state systems PrCu, and PrCu5. The huge increase in the relaxation time observed near the transition is a feature that appears to be common to nuclear-induced
96
Specific heat and suscepfibilify
ordering transitions. PrCuh [lo] relaxation
Both for PrCu, [6] and for times near T, of the order
of 5-10 min have been order
reported,
as what we observe
process
in PrNi*.
Since
i.e. of the same
for the slow relaxation the nuclear
spin-lattice
relaxation normally
times in intermetallic substances are quite small, i.e. < 10e3 s, the strong
relaxation
could find its origin
in the coupling
of
the nuclei to (and via) the nearly fully quenched 4f-moments. Memory effects, such as observed in monitoring the magnetization as a function of temperature may originate from a different mechanism. They might, for example, be caused by the existence of a domain structure at low temperatures, in which the walls are blocked. A low ratio of the exchange energy to the crystal field splitting, as is presently observed, favours the existence of such a domain structure. Another puzzling feature is the fact that the position of the x’ maximum on the temperature axis depends rather strongly on the frequency. For a transition to long-range magnetic order, whether antiferromagnetic or ferromagnetic, a drastic effect on the height of the x- maximum could be expected indeed, but the temperature at which it occurs would be fairly insensitive to the ac-frequency. The frequency effects observed, as well as the broadness of the x maxima, are in fact quite similar to what is commonly observed magnetic glasses or superfor spinglasses, paramagnetic substances. In these materials there is no long-range magnetic order but instead a frozen-in state of magnetic clusters resulting e.g. from competitive magnetic interactions (spinglasses) or from chemical clustering (superparamagnetism). Memory effects are likewise commonly observed in such systems. Although the occurrence of such a frozen-in short range ordered magnetic state in PrNiz would be rather unexpected, it is clear that additional experiments would be highly desirable to establish more firmly the nature of the magnetic phase. Lastly, we comment on the fact that the heat capacity of PrNiz below 0.5 K depends less
of PrNiz below 1 K
strongly on temperature than the expected behaviour. In fig. 1 the solid curve represents
Tez
the
T-* tail of the hyperfine Schottky-type anomaly in case the ordered electronic moment would be 8% of the full Pr” moment. The situation con-
trasts
with those
for the Pr-Cu
compounds
(see
e.g. fig. 2 of ref. lo), for which the heat capacity shows a steeper dependence than the T-* law in the region of interest. To explain the different behaviour of the specific heat of PrNi2, one could think of impurity effects, e.g. hyperfine contributions of traces of ferromagnetic PrNi. However, as mentioned, the data in fig. 1 are for two differently prepared samples and yet yield the same curve within the errors. Another possibility would be that the temperature dependence of the specific heat is related to the fact that the Plj’ ground state in PrNi2 probably is the non-magnetic r3 doublet. Our conclusion is that PrNi2 shows a mixed electronic-nuclear phase transition at a temperature of 270 mK 2 20 mK. This is mainly inferred from magnetization and susceptibility data. Obviously an extension of the specific heat data to still lower temperatures would be highly desirable for a better understanding of the phase transition. Such experiments are presently under way.
Acknowledgements This investigation is part of the research program of the “Stichting F.O.M.” with financial support from “Z.W.O.“.
References [l] T. Murao, J. Phys. Sot. Japan 33 (1972) 33. [2] K. Andres, Phys. Rev. B7 (1973) 4295. [3] B.B. Triplett and R.M. White, Phys. Rev. B7 (1973) 4938. [4] J. Hammann and P. Manneville, J. Phys. 34 (1973) 615. [5] T. Murao, preprint. [6] K. Andres, E. Bucher, J.P. Maita and A.S. Cooper, Phys. Rev. L&t. 28 (1972) 1652.
Specific heat and susceptibility
[7] K. Andres, E. Bucher, P.H. Schmidt, J.P. Maita and S. Darack, Phys. Rev. Bll (1975) 4364. [S] J. Hammann and M. Ocio, Physica 86-88B (1977) 1153. [9] J.L. Genicon, J.L. Tholence and R. Tournier, J. Phys. 39 Coil. C6 (1978) 798. [IO] J. Babcock, J. Kiely, T. Manley and W. Weyhmann, Phys. Rev. Lett. 43 (1979) 380. [ll] A. Benoit, P. Convert, J. Flouquet and J. Palleau, Annual Report 1980, Inst. Von Laue-Langevin (Grenoble), and to be published. [12] J.C.M. van Dongen, H.W.M. van der Linden, F.J.A.M. Greidanus, G.J. Nieuwenhuys, J.A. Mydosh and K.H.J. Buschow, J. Magn. Magn. Mat. 15-18 (1980) 1245. [13] L.J. de Jongh, J. Bartolome, F.J.A.M. Greidanus, H. de Groot, H.L. Stipdonk and K.H.J. Buschow, submitted to J. Magn. Magn. Mat. [14] P. Bak, Rise Report No. 312 (1974). [15] A. Loidl, K. Knorr, M. Mtillner and K.H.J. Buschow, J. Appl. Phys. 53 (1981) 1433. [16] E.A. Skrabek and W.E. Wallace, J. Appl. Phys. 34 (1963) 1356. [17] M.J. McDermott and K.K. Marklund, J. Appl. Phys. 40 (1969) 1007.
of PrNi2 below 1 K
97
[18] W.E. Wallace and K.H. Mader, Inorg. Chem. 7 (1%8) 1627. [19] W.E. Wallace, Rare Earth Intermetallics (Academic Press, New York, 1973). [20] W.E. Wallace, R.S. Craig, A. Thompson, C. Deenadas, M. Dixon, M. Aoyagi and N. Marzouk, Les Elements des Terres Rares, Coll. Int. C.N.R.S. No. 180 (1970) 427. [21] E. Bucher, J.P. Maita, G.W. Hull jr., J. Sierro, C.W. Chu and B. Liithi, Proc. 1st Conf. on Crystalline Electr. Field Eff. in Metals and Alloys, R.A.B. Devine, ed., Montreal (1974) 221. [22] H. Mori, T. Fujita, T. Satoh and T. Ohtsuka, Phys. Lett. 79A (1980) 121. [23] F.J.A.M. Greidanus, L.J. de Jongh, W.J. Huiskamp, A. Furrer and K.H.J. Buschow, to be published. [24] H.A. Algra, L.J. de Jongh, W.J. Huiskamp and R.L. Carlin, Physica 92B (1977) 187. [25] R.P. Giffard, R.A. Webb and J.C. Wheatley, J. Low Temp. Phys. 6 (1972) 533. [26] The @Co in 59Co single crystal y-ray thermometer was kindly supplied by Dr. H. Marshak at the National Bureau of Standards.
Physica 112B (1982) 92-97 North-Holland Publishing Company
LETTER
TO THE
EDITOR
SPECIFIC HEAT AND FREQUENCY-DEPENDENT AC-SUSCEPTIBILITY OF PrNiz BELOW 1 K F.J.A.M.
GREIDANUS,
L.J. DE JONGH
and W.J. HUISKAMP
Kamerlingh Onnes Laboratory, University of Leiden, 7he Neiherlands
K.H.J.
BUSCHOW
Philips Research Laboratories, Eindhoven, The Netherlands Received
19 August
1981
AC-susceptibility measurements on PrNi2 show broad anomalies, the temperature of the susceptibility maximum shifting from 0.3-0.5 K as the frequency is varied in between 3 Hz and 3 kHz. On the other hand the specific heat is featureless in the same temperature range. The behaviour is interpreted in terms of a mixed electronic-nuclear phase transition. Strong relaxation effects are observed in the susceptibility at temperatures close to the maxima.
1. Introduction The study
of enhanced nuclear and mixedelectronic nuclear magnetic order in Van Vleck paramagnetic compounds, in particular of praseodymium, is of current theoretical [l-5] and experimental [6-lo] interest. In these systems the electronic ground state of P?’ is a singlet (F1) or a non-magnetic doublet (F,), the next higher energy levels being at a distance A large enough compared to the exchange J to exclude conventional electronic magnetic ordering. The hyperfine interaction, Hh.f. = AI-J, between electronic (J) and nuclear (1) spins then becomes of prime importance, since it induces a moment in the electronic ground state through mixing of the higher energy levels. The induced 4f moments of neighbouring Pr atoms may interact via the RKKY interaction (plus dipolar interactions), which may result in magnetic ordering at a transition temperature T, considerably lower than would be observed for conventional electronic ordering. The nuclear moments in turn become ordered through the hyperfine interaction. Thus, depending on the ratio of A and J,
we may characterize the type of magnetic ordering as: (i) purely electronic for J S- A ; (ii) enhanced 037%4363/82/0000-0000/$02.75
@ 1982 North-Holland
nuclear for J GA ; and (iii) mixed electronicnuclear for J = A. Examples of the latter two types have so far been very few. As regards enhanced nuclear ordering, a clear experimental example appears to have been found in PrCud [lo]. Magnetization data on this compound indicate a ferromagnetic transition near T,= 2.5 mK. At the same temperature the specific heat shows a very high and sharp peak, indicating that all of the nuclear entropy is involved in the cooperative transition (the electronic entropy is already removed at very much higher temperatures via crystal field single-ion interactions). This contrasts with the specific heat behaviour found for PrCuz and PrCuS, which show mixed electronic-nuclear transitions (type iii) at T, = 54 mK and 24 mK, respectively [6,7,9, 111. These transition temperatures were deduced from peaks in the lowfield or ac-susceptibility measured as a function of temperature. Near T, the specific heat of both compounds is featureless; for PrCus a Schottkytype hyperfine anomaly is observed [7] with a maximum at about 0.6T,. This behaviour is not inconsistent with existing theoretical predictions within the effective field framework, which indicate that the specific heat ordering anomaly may
Specific heat and susceptibility
become
unmeasurably
small
excited
in the intermediate
region of mixed electronic-nuclear In this note we present what
order. we believe
of PrNi2 below 1 K
is
another example of the mixed electronic-nuclear type of order, namely the intermetallic compound PrNir. PrNi* belongs to the series PrX2, in which X can be Mg, Al, Co, Ni, Rh, Ru, Ir, Pt. Each of these materials has the Cl5 structure, and the rare earth ions are situated at sites of cubic symmetry. It has been shown by several authors [12-151 that the compounds with X= Mg, Al, Co, Rh, Ru, Ir, Pt exhibit phase transitions in the range 4.2-40 K. In this respect PrNiz is an exception. Although earlier magnetic measurements 1161 and specific heat data [17] in the temperature range 150 mK-1 K were interpreted in terms of a phase transition around 8 K, more recent susceptibility, magnetization and specific heat data [18-201 prove PrN& to be paramagnetic at 4.2 K. The contribution of a substantial exchange interaction was, however, clearly manifest. In 1974 Bucher et al. [21] claimed a transition temperature of 0.33 K. In the course of our experiments of PrNi*, Mori et al. independently published their data on the acand dc-susceptibility [22]. They showed that both reached a maximum in between 0.2 K and 0.3 K. Strong relaxation effects were also observed at the same temperature. A knowledge of the nature of the ground state is of primary importance in understanding the low temperature behaviour of PrNi*. Wallace [19] and Bucher et al. [21] claimed rl to be the ground state with the r, level at 45 K and the r, level at 77 K, inferred from specific heat [21]. This was in agreement with thermopower measurements, although a r, ground state could not be ruled out completely. In order to study this problem in more detail we have recently performed inelastic neutron scattering experiments on a triple axis spectrometer at the E.I.R. in Wiirenlingen, in cooperation with A. Furrer. A preliminary analysis of the data indicates the non-magnetic doublet r, to be the ground state, with a first
state
93
at 35 K+ 10 K. Further
details
will
be published elsewhere [23]. This would contradict previous assignments of the r1 singlet to be the PP’ ground state in PrNi*. Also, it would present
a difference
above
mentioned
three
are claimed
In the present ments on various dependent provide
temperature
PrNi*
compounds,
to be r1 singlet
and
the
which
all
systems.
letter specific heat measuresamples, as well as frequency-
susceptibility more
between
Pr-Cu
insight
studies
are presented,
into the nature
to
of the low
transition.
2. Experimental
techniques
Various samples of PrNir were studied, prepared by arc melting of 99.9% pure Pr and in an atmosphere of purified argon gas. For samples labelled I and II stoichiometric ratios
all Ni the of
the starting materials were used, while a third sample, labelled III, was prepared starting from Pr and Ni in atomic ratio 1:2.04. All samples were vacuum annealed (wrapped in Ta foil) first at 600” C for two weeks, subsequently 4 weeks at 700°C and 4 weeks at 800°C. After the annealing the condition of the samples was carefully checked by X-ray diffraction. Samples I and II showed small traces of the impurity phase PrNi. In sample II the impurity concentration was lower than in sample I and was estimated to be less than 5%. In sample III no impurity phases could be detected. The specific heat measurements were performed on the bulk polycrystalline materials. The sample was mounted in an adiabatic demagnetization apparatus, described more extensively elsewhere [24]. Heat contact was provided by electrolytically coating the ingot with a thin layer of copper, and then soldering it with indium to the cooling device. Both resistance and magnetic thermometry were applied. Susceptibility measurements were performed on a powdered specimen of about 100 mg taken from sample III. A conventional 3He-4He dilu-
94
Specific heat and susceptibility
tion refrigerator cryostat was used. Heat contact with the mixing chamber was provided by means of liquid 4He. The ac-susceptibility was measured with a bridge, in which a SQUID was employed as a null detector [25]. The available frequency range was l-3000Hz, the amplitude of the measuring ac-field being always smaller than 0.01 Oe. The same circuitry could also be used to measure changes in the magnetization by monitoring the dc-output of the SQUID, and using the primary coil of the mutual inductance as a field coil. In this apparatus the temperature was measured with a CMN thermometer, calibrated against the 4He vapour pressure scale. Below 30 mK the CMN thermometer readings were checked with a @‘CoCo single crystal [26] nuclear orientation thermometer. Details of the apparatus and the SQUID-bridge circuitry will be published at a later date.
of RNiz
below 1 K
l
SAMPLE
0 SAMPLE
001
01
II III
10
TEMPERATURE
50
(Kl
Fig. 1. Specific heat C/R of sample II and sample III. A line with a T-* slope has been drawn through the data at the lowest temperatures.
3. Results of the measurements The specific heat data on the samples II and
III are shown in fig. 1. (the addenda being already subtracted). The results on these two samples are seen to agree within a few percent. Qualitatively, the data on sample I were found to show the same behaviour. At temperatures below 600 mK, however, the data on sample I were substantially higher than for II and III. We attribute this to a contribution of an impurity phase, whose presence was established by means of X-ray diffraction, as obtained in section 2. With reference to the discussion below we remark that the observed relaxation times never exceeded a few seconds in the specific heat experiments. We cannot exclude however the occurrence of relaxation times of several minutes, or longer. Susceptibility measurements, taken at different frequencies between v = 3 Hz and v = 3000 Hz are shown in fig. 2. Plotted are the real ($) and imaginary (J$‘) parts of the complex frequency dependent ac-susceptibility X(V) = X’(V) - ix”(v).
Because the x” signal shows similar behaviour for various frequencies, only the 600 Hz signal has been shown, for clarity of representation. With increasing frequency the position of the x’ maximum is found to shift from 330 & 10 mK to 450 220 mK, whereas its height is decreasing. I
““m
““““I
20
l. . .
F
l.
. I
Aa&* fi_
I
15-
3 15 64 600 3000
Hz Hz Hz Hz Hz
5-
O001
10
01 TEMPERATURE
(Kl
Fig. 2. In-phase part x’ of the susceptibility for frequencies in between 3-3000 Hz. The out-of-phase part x0 for a frequency of 600 Hz is also shown.
Specific heat and susceptibility of PrNi2 below 1 K
Finally, in fig. 3, the change in the magnetization signal as a function of temperature is shown, using a field of about 0.5 Oe as the magnetizing field. Every time the temperature was changed, the system was allowed to’ come to equilibrium. While performing measurements it proved to be essential to apply the magnetizing field before cooling the sample. If not, the behaviour of the out magnetization sample, when carrying measurements in a warm up run, was completely undefined. For example, the change in the output of the SQUID-magnetometer could change sign, depending on the rate at which heat was applied. In addition we performed dc-susceptibility measurements by applying instantaneously a constant magnetic field (6 1 Oe) at a fixed temperature and monitoring the output of the SQUID-electronics as a function of time. A preliminary analysis indicates that the dc-susceptibility reaches a maximum at 270 mK& 20 mK. Strong relaxation effects were observed,
0 0 I
0 01
00 I
I11111
1.0
01 TEMPERATURE
10
(K)
Fig. 3. Change in magnetization as a function of temperature, as monitored at the dc-output of the SQUIDmagnetometer during a warming up run. The zero is chosen at T = 1.27 K.
95
as was reported previously by Mori et al. [22]. However, our measurements cannot be described with a single time constant. It seems more likely that two processes take place on different time scales. At about 270 mK the time constant related to the slow process reaches a value of about 1000 s, i.e. an order of magnitude larger than reported by Mori et al. The time constant related to the fast process could not yet be determined.
4. Discussion and conclusion As was outlined in the introduction, the ground state of PrNiz probably is the non-magnetic r3-doublet with a first excited state at a distance of about 35 K ? 10 K. Because no sign of a phase transition is found at temperatures above 1 K, one concludes that the ratio of the exchange interaction J to the crystal field splitting A must be close to its threshold value. It is therefore tempting to explain the observed susceptibility peak in terms of a mixed electronic-nuclear ordering phenomenon, as previously suggested for PrCu* and PrCu5 [7,9,11]. Although the specific heat data show no anomaly in the temperature range of the x maxima, this does not necessarily contradict such an explanation. From the theoretical calculation within the effectivefield approach [l, 21, it follows that for certain combinations of J, A and the hyperfine coupling constant A, the anomaly in the heat capacity associated with such a type of ordering may become extremely small. For instance Murao [l], predicts for AID = 10m3and D/J = 2 a specific heat jump of the order of lo-* R only. This obviously is far outside the presently attainable experimental accuracy. Thus the state of affairs for PrNi* appears to be rather similar to that for the singlet-ground state systems PrCu, and PrCu5. The huge increase in the relaxation time observed near the transition is a feature that appears to be common to nuclear-induced
96
Specific heat and suscepfibilify
ordering transitions. PrCuh [lo] relaxation
Both for PrCu, [6] and for times near T, of the order
of 5-10 min have been order
reported,
as what we observe
process
in PrNi*.
Since
i.e. of the same
for the slow relaxation the nuclear
spin-lattice
relaxation normally
times in intermetallic substances are quite small, i.e. < 10e3 s, the strong
relaxation
could find its origin
in the coupling
of
the nuclei to (and via) the nearly fully quenched 4f-moments. Memory effects, such as observed in monitoring the magnetization as a function of temperature may originate from a different mechanism. They might, for example, be caused by the existence of a domain structure at low temperatures, in which the walls are blocked. A low ratio of the exchange energy to the crystal field splitting, as is presently observed, favours the existence of such a domain structure. Another puzzling feature is the fact that the position of the x’ maximum on the temperature axis depends rather strongly on the frequency. For a transition to long-range magnetic order, whether antiferromagnetic or ferromagnetic, a drastic effect on the height of the x- maximum could be expected indeed, but the temperature at which it occurs would be fairly insensitive to the ac-frequency. The frequency effects observed, as well as the broadness of the x maxima, are in fact quite similar to what is commonly observed magnetic glasses or superfor spinglasses, paramagnetic substances. In these materials there is no long-range magnetic order but instead a frozen-in state of magnetic clusters resulting e.g. from competitive magnetic interactions (spinglasses) or from chemical clustering (superparamagnetism). Memory effects are likewise commonly observed in such systems. Although the occurrence of such a frozen-in short range ordered magnetic state in PrNiz would be rather unexpected, it is clear that additional experiments would be highly desirable to establish more firmly the nature of the magnetic phase. Lastly, we comment on the fact that the heat capacity of PrNiz below 0.5 K depends less
of PrNiz below 1 K
strongly on temperature than the expected behaviour. In fig. 1 the solid curve represents
Tez
the
T-* tail of the hyperfine Schottky-type anomaly in case the ordered electronic moment would be 8% of the full Pr” moment. The situation con-
trasts
with those
for the Pr-Cu
compounds
(see
e.g. fig. 2 of ref. lo), for which the heat capacity shows a steeper dependence than the T-* law in the region of interest. To explain the different behaviour of the specific heat of PrNi2, one could think of impurity effects, e.g. hyperfine contributions of traces of ferromagnetic PrNi. However, as mentioned, the data in fig. 1 are for two differently prepared samples and yet yield the same curve within the errors. Another possibility would be that the temperature dependence of the specific heat is related to the fact that the Plj’ ground state in PrNi2 probably is the non-magnetic r3 doublet. Our conclusion is that PrNi2 shows a mixed electronic-nuclear phase transition at a temperature of 270 mK 2 20 mK. This is mainly inferred from magnetization and susceptibility data. Obviously an extension of the specific heat data to still lower temperatures would be highly desirable for a better understanding of the phase transition. Such experiments are presently under way.
Acknowledgements This investigation is part of the research program of the “Stichting F.O.M.” with financial support from “Z.W.O.“.
References [l] T. Murao, J. Phys. Sot. Japan 33 (1972) 33. [2] K. Andres, Phys. Rev. B7 (1973) 4295. [3] B.B. Triplett and R.M. White, Phys. Rev. B7 (1973) 4938. [4] J. Hammann and P. Manneville, J. Phys. 34 (1973) 615. [5] T. Murao, preprint. [6] K. Andres, E. Bucher, J.P. Maita and A.S. Cooper, Phys. Rev. L&t. 28 (1972) 1652.
Specific heat and susceptibility
[7] K. Andres, E. Bucher, P.H. Schmidt, J.P. Maita and S. Darack, Phys. Rev. Bll (1975) 4364. [S] J. Hammann and M. Ocio, Physica 86-88B (1977) 1153. [9] J.L. Genicon, J.L. Tholence and R. Tournier, J. Phys. 39 Coil. C6 (1978) 798. [IO] J. Babcock, J. Kiely, T. Manley and W. Weyhmann, Phys. Rev. Lett. 43 (1979) 380. [ll] A. Benoit, P. Convert, J. Flouquet and J. Palleau, Annual Report 1980, Inst. Von Laue-Langevin (Grenoble), and to be published. [12] J.C.M. van Dongen, H.W.M. van der Linden, F.J.A.M. Greidanus, G.J. Nieuwenhuys, J.A. Mydosh and K.H.J. Buschow, J. Magn. Magn. Mat. 15-18 (1980) 1245. [13] L.J. de Jongh, J. Bartolome, F.J.A.M. Greidanus, H. de Groot, H.L. Stipdonk and K.H.J. Buschow, submitted to J. Magn. Magn. Mat. [14] P. Bak, Rise Report No. 312 (1974). [15] A. Loidl, K. Knorr, M. Mtillner and K.H.J. Buschow, J. Appl. Phys. 53 (1981) 1433. [16] E.A. Skrabek and W.E. Wallace, J. Appl. Phys. 34 (1963) 1356. [17] M.J. McDermott and K.K. Marklund, J. Appl. Phys. 40 (1969) 1007.
of PrNi2 below 1 K
97
[18] W.E. Wallace and K.H. Mader, Inorg. Chem. 7 (1%8) 1627. [19] W.E. Wallace, Rare Earth Intermetallics (Academic Press, New York, 1973). [20] W.E. Wallace, R.S. Craig, A. Thompson, C. Deenadas, M. Dixon, M. Aoyagi and N. Marzouk, Les Elements des Terres Rares, Coll. Int. C.N.R.S. No. 180 (1970) 427. [21] E. Bucher, J.P. Maita, G.W. Hull jr., J. Sierro, C.W. Chu and B. Liithi, Proc. 1st Conf. on Crystalline Electr. Field Eff. in Metals and Alloys, R.A.B. Devine, ed., Montreal (1974) 221. [22] H. Mori, T. Fujita, T. Satoh and T. Ohtsuka, Phys. Lett. 79A (1980) 121. [23] F.J.A.M. Greidanus, L.J. de Jongh, W.J. Huiskamp, A. Furrer and K.H.J. Buschow, to be published. [24] H.A. Algra, L.J. de Jongh, W.J. Huiskamp and R.L. Carlin, Physica 92B (1977) 187. [25] R.P. Giffard, R.A. Webb and J.C. Wheatley, J. Low Temp. Phys. 6 (1972) 533. [26] The @Co in 59Co single crystal y-ray thermometer was kindly supplied by Dr. H. Marshak at the National Bureau of Standards.