Journal of Magnetism and Magnetic Materials 29 (1982) 213-216 North-Holland Publishing Company
ac S U S C E P T I B I L I T Y AND E L E C T R I C A L R E S I S T I V I T Y O F Nd S I N G L E C R Y S T A L S H. B O G H O S S I A N and B.R. COLES Blackett Laboratory, Imperial College, London SW7, UK
As a contribution to our knowledge of the magnetic phase diagram of Nd measurements have been made of the ac susceptibility, of the effects on it of supersposed dc fields and changes in frequency, and of the electrical resistivity for different directions in single crystals. Only small effects are seen near the upper ordering temperature at 20 K, but a susceptibility maximum is found in all specimens near 8.3 K. Shoulders of various types are seen at lower temperatures. The dc field has its greatest effect on the 20 and 7.1 K shoulders. The c-axis resistivity data show an antiferromagnetic type anomaly at 20 K. In some specimens susceptibility effects are found near 30 K and are probably due to the presence of some fcc material.
The nature of the magnetic ordering in Nd is still not clearly understood, and it shows strong sensitivity to applied fields. Since the metal has the dhcp structure there are equal numbers of close packed planes perpendicular to the c-axis in which atoms have sites of either fcc or hcp local symmetry, and the two main magnetic transitions, at about 20 K and about 8 K have been ascribed to ordering of hexagonal and cubic sites respectively. Other anomalies have been observed in various properties, however, both as a function of temperature, especially below 8 K, and as a function of applied field. Neutron diffraction studies [1,2] show various types of satellite peaks including some formed by splitting below ~ 6.5 K of satellites associated with the hexagonal site ordering. Specific heat measurements [3,4] showed peaks associated with both main ordering temperatures, and effects at lower temperatures. Recent measurements [5,6] show a more complex set of anomalies (at ~ 8.3, 7.8, 6.3 and 5.8 K) but at different temperatures on heating and cooling, and these are greatly modified by applied fields. Elastic constant m e a s u r e m e n t s  show anomalies for longitudinal waves propagating in the basal plane at both the hexagonal and cubic site ordering temperatures, and also  anomalous
behaviour as a function of field for a number of elastic constants. Since the low field ac susceptibility is a sensitive indicator of magnetic ordering, and can be measured with or without a superposed dc field we have used such measurements on single crystal specimens of Nd to throw more light on the magnetic phase diagram. Our initial measurements have been in the temperature range 1.2-40 K and for dc fields up to 180 Oe. Some studies have also been made of the effect of varying the ac frequency, and of the behaviour of the electrical resistivity in different crystallographic directions.
2. Materials and methods
Four specimens cut from single crystals grown by Dr David Fort at the Materials Science Centre of Birmingham University have been examined. The characteristics of these are shown in table 1. The ac suspectibility measurements were made by a mutual inductance technique, observing the change in mutual inductance of a set of coils when the specimen was introduced into them. Use of a two-phase phase-sensitive detector enabled both the in-phase and in-quadrature components to be detected and the latter was always balanced. The value of the in-phase component was measured with a ratio transformer coupled to the secondary
0304-8853/82/0000-0000/$02.75 © 1982 North-Holland
H. Boghossian, B.R. Coles / Measurements on N d single crystals
Table 1 Specifications of Nd specimens used in ac susceptibility measurements, specimens 1, 2 and 3 were cut from a sample of residual resistivity ratio 50; specimen 4 was of lower purity with R R R ~ 25
Shape Dimensions (mm) Weight (g) Orientation
cylindrical ( 1.5 X 6) 0.1008 b-axis along specimen axis
rectangular (1.5 X 1.5 X 6) 0.0608 c-axis along specimen axis
cylindrical (1.5 x 4) 0.0824 specimen axis inclined to b and e axes
cylindrical (1.5 X 6) 0.0816 specimen axis at --45 ° to b and c axes
circuit. Measurements were normally made with an ac frequency of 300 Hz and field amplitude of 0.2 Oe after cooling to 1.2 K in zero field (earth's field nulled), readings being taken with increasing temperature in either zero field or a constant superposed dc field.
3. Results and discussion
Zero field susceptibility data are shown in fig. 1, and can be correlated to some extent with the 8
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Fig. I. Variation of x ' ( T ) with temperature: (a) specimen (1); (b) specimen (2); (c) specimen (3); (d) specimen (4). The earth's field in each case has been eliminated.
transitions indicated by neutrons and by calorimetry. It can be seen that a clear shoulder in the basal plane X (X±) is shown at the upper antiferromagnetic temperature but that little sign of it shows in X tl. This would suggest a strong component of basal plane ordering and a well-defined c-axis periodicity is consistent with our observation of a resistivity anomaly of antiferromagnetic superzone type for the resistivity of the c-axis specimen at that temperature. It is not possible from our results to decide whether two transitions exist between 19 and 20 K. A T 8.3 K also the peak in X± is much better defined than that in X II where the susceptibility falls slowly from 7.8 to 7.2 K and then more rapidly down to ~ 6.3 K, where another increase in slope is seen as the temperature falls. Some of these temperatures are close to those (8.3, 7.8 and 6.3 K) where anomalies are reported for the specific heat in similar circumstances, i.e. with rising temperature in zero field. In X± there are faint anomalies near the latter two temperatures, but in neither XH nor X± is there any significant effect at - 5 . 8 K where a calorimetric anomaly is found. A new feature of our results is evidence for considerable structure in X below 4.2 K, where no specific heat effects are found. This suggests that there are rapid changes at low temperatures in the low field anisotropy coefficients. While the behaviour of specimen number 3 is as might be expected, intermediate between that of specimens 1 and 2, the very different character of the less pure sample (number 4) suggests strong sensitivity of the main peak character to small amounts of impurity. It may be remarked that the value of X±/Xu increases, as the temperature is lowered, from about
H. Boghossian, B.R. Coles / Measurements on N d single crystals
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Fig. 2. Variation of x'(T, H ) with temperature at a steady field of 80 Oe applied parallel to the small alternating field: (a) specimen (1); (c) specimen (3); (d) specimen (4).
1.22 near 40 K to about 1.46 just below the 20 K anomaly, but falls again to about 1.28 at the peak temperature. Some effects of superposed dc fields are shown in fig. 2, although it is not possible to see the details at that scale. For x±(T) a slight broadening of the 8.3 K peak is produced by 80 Oe, but its slope is somewhat increased hear 7.8 K, and there is also more sign of structure between 5.8 and 6.3 K. For X Ir the 8.3 K peak (already broad) is not greatly affected by 80 Oe but the fall below 7.2 K is distinctly slower in the dc field as is that below 6.3 K. Where there is structure at low T this appears to be somewhat better defined in a field and in specimens 2, 3 and 4 a minimum tends to appear at about 3 K. In those specimens that showed a shoulder at 20 K this is significantly reduced by the dc field. The most obvious effect of applied fields is on the double peak of specimen 4, where progressive suppression of the lower peak is produced (fig. 3). Little change in the general mag-
Fig. 3. Variation of x ' ( T , H ) with temperature in specimen (4) at different dc fields applied parallel to the small alternating field• These data were taken sweeping the dc field up and down at each temperature.
nitudes of X are produced by our small fields. Some investigations have been made of the effects of changing the frequency of the ac field, mainly on the data for X of specimen 4 in a field of 80 Oe (fig. 4). The minimum originally found at 300 Hz for zero field between 7.1 and 8.3 K, which was partially suppressed by a field of 80 Oe is restored when the frequency is increased to 1 kHz, but at still higher frequencies the upper peak is relatively suppressed and the minimum disappears again. The behaviour around 20 K is little affected by change of frequency at constant dc field, but at the higher frequencies the low temperature behaviour is strongly modified. A surprising feature of the ac susceptibilities is the appearance (fig. l) in some of the specimens of a distinct anomaly (suppressed by superposed dc fields) close to 30 K. This corresponds to the temperature at which a ferromagnetic ordering has been reported  for fcc samples of Nd, and for some samples of nominally dhcp Nd and N d - Y alloys . This behaviour suggests that in our
H. Boghossian, B.R. Coles / Measurements on N d single crystals .%,
m a i n fall in p is below a b o u t 7.5 K, so that considerable spin disorder is clearly still present between 20 K a n d the susceptibility peak temperature. F u r t h e r m e a s u r e m e n t s of Xac are being u n d e r t a k e n with larger superposed dc fields, since drastic effects are shown in the specific heat, b u t it is clearly desirable that such m e a s u r e m e n t s should be m a d e o n the same samples as those used for calorimetry, especially since we fail to see effects at one of the characteristic temperatures seen in zero field.
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A m a j o r c o n t r i b u t i o n to the work has been m a d e by DL D. Fort of the B i r m i n g h a m Materials Science Centre, who grew a n d orientated the samples used.
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Fig. 4. Variation of x ( T , ~o) with temperature in specimen 4 in a steady state field of 80 Oe at frequencies of: (a) 300 Hz; (b) 1 kHz; (c) 3 kHz; (d) 5 kHz. specimens showing this effect there are local stacking fault densities large e n o u g h in some parts of the sample for macroscopic fcc character to show itself. It should be emphasized that only a small v o l u m e fraction of ferromagnetic material would b e needed to give effects clearly visible in the ac susceptibility. Resistivity m e a s u r e m e n t s were m a d e o n all the samples, b u t because of the unsatisfactory geometry (short fat samples) a n d large currents necessary precise low t e m p e r a t u r e data could n o t be obtained. The correlation of the c-axis resistivity a n o m a l y with the basal p l a n e has already b e e n m e n t i o n e d , b u t for both principal directions the
References  B. Lebech and B.D. Rainford, Proc. 9th Intern. Conf• on Magnetism (Nauka, Moscow, 1973) 3 (1974) 191.  B. Lebech, Proc. 26 Annual Conf. on Magn. and Magn. Materials, Dallas (1980).  D.H. Parkinson, F.E. Simon and F.H. Spedding, Proc. Roy. Soc. A207 (1951) 137.  O.V. Lounasmaa and L.J. Sundstrom, Phys. Rev. 158 (1967) 591.  E.M. Forgan, C.M. Muirhead, D.W. Jones and K.A. Gschneidner, J• Phys. F9 (1979) 651.  E.M. Forgan and C.M. Muirhead, J. de Phys. Colloq• 39, Suppl. 8, C6 (1978) C6794.  S.B. Palmer and J.T. Lenkkeri, Physica 86-88B (1977) 43.  S.B. Palmer and J.T. Lenkkeri, J. Phys. F8 (1978) 1359.  E. Bucher, C.W. Chu, J.P. Maita, K. Andres, A.S. Cooper, E. Buehler and K. Nassau, Phys. Rev. Lett. 22 (1969) 1260.  B. Sharif and B.R. Coles, J. Less Common Metals 62 (1978) 295.