- Email: [email protected]
Dilatometric study of NdCu2 in magnetic fields
Journal of Magnetism and Magnetic Materials 140-144 (1995) 1129-1130
~ H journalof magnetism and magnetic ~ I ~ materials
ELSEVIER
Dilatometric study of
NdCu 2
in magnetic fields
S.W. Zochowski a,., M. Rotter b, E. Gratz b, K.A. M c E w e n a a Department of Physics, Birkbeck College, UniL,ersity of London, Malet Street, London WC1E 7HX, UK b . . . . Instttut fiir Expertmentalphyszk, Technische Universitiit Wien, A-I 040 Wien, Austria Abstract Single crystals of the orthorhombic intermetallic NdCu 2 have been used to measure the thermal expansion and longitudinal magnetostriction. Measurements were made parallel to the crystallographic b-direction in the temperature range 1.5-30 K and in magnetic fields up to 7 T. A comparison of the measurements with the results of a mean-field calculation indicate a negative magnetoelastic constant. A magnetic phase diagram of NdCu 2 has been deduced from the anomalies observed in the dilatometric measurements.
The magnetic structures, and phase diagrams, of RCu 2 alloys, where R is a rare-earth metal, appear to be complex, generally of an antiferromagnetic nature. The orthorhombic (CeCuz-type) NdCu 2 has been reported to exhibit four antiferromagnetic phases below its N6el temperature, T N = 6.5 K, in its magnetoresistance and magnetisation, measured along the b-axis of a single crystal [1]. In a recent neutron diffraction experiment [2], the zero-field magnetic structure of NdCu 2 was investigated between 1.4 and 8 K. Only two magnetic phases were observed, with the moments constrained to the b - c plane: an antiferromagnetic incommensurate phase between T N and 4 K and a commensurate phase down to 1.4 K. Here, we report on the results of our single-crystal magnetic dilatometric investigation on NdCu 2, including model calculations, the details of which will be published elsewhere. Two single crystals were measured in this experiment. Both were cut from the same ingot which was grown using the Czochralski method. In each case, faces were cut perpendicular to the b-direction with lengths 0.745 cm and 0.310 cm, respectively. Measurements of strain were made relative to the body of a capacitance dilatometer The temperature was controlled and measured using a calibrated carbon-glass sensing element. For field-dependent thermal expansion and magnetostriction measurements, a magnetic field with H < 7 T was applied parallel to the measurement direction. Fig. 1 shows representative thermal expansion data at H = 0.0, 0.25, 1.0, 1.7 and 3.5 T. Note that the relative positions of the curves in Figs. 1 and 2 have been altered
for ease of viewing. In zero field, the N4el temperature is observed to be near 6.7 K; a small anomaly is found 0.2 K below TN when the derivative of A l / l is analysed. A second anomaly, at 4.2 K, marks the transition from an incommensurate to commensurate structure, as observed in neutron diffraction work [2]. As shown for H = 3.5 T, the general shape of the A l / l curves remains the same until H > 3.0 T, where it is observed to rise before decreasing at a constant rate after T = 7 K. The inset shows data for H = 0.0 T up to 80 K, with an upward turn observed near 34 K.
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TEMPERATURE (K)
* Corresponding author. [email protected].
Fax:
+44-71-631 6220; email:
Fig. 1. Thermal expansion of NdCu2, measured in increasing temperature along the b-axis, at various applied magnetic fields. The arrows mark the locations of the zero-field transitions. The inset shows extended H = 0.0 T results.
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 0 7 8 5 - 3
1130
S. W. Zochowski et al. / Journal of Magnetism and Magnetic Materials 140-144 (1995) 1129-1130
Also shown in Fig. 1 is an overscaled representation of the calculation of ( O ° ) for zero applied magnetic field. Using a simple model [3] and previously published crystal-field parameters [4], the thermal expansion can be described by a linear combination of the expectation values of the Stevens operators ( O °) and (O22). Although the ( 0 2o ) term describes the zero-field data reasonably well, it is necessary to include a second nearest neighbour calculation, (JiJi+2), in order to model the turn at 34 K. The first-order transition at 4.2 K is not reproduced in this calculation because of the incommensurate nature of the ordering structure. Representative magnetostriction results are shown in Fig. 2. At T = 2.0 K, four anomalies indicate transitions at 0.77, 2.55, 2.76 and 2.94 K. These transitions are seen to gradually disappear as the temperature is increased, until at T = 7.0 K a paramagnetic response is observed. The magnetostriction has been found to be best modelled by assuming a strong strain dependence of the coupling constant between second nearest neighbouring planes (-0.1699 T), neglecting the strain dependence of all other magnetic coupling constants. A plot of the thermal expectation value (JiJi+2), at 1.7 K, is also shown in Fig. 2. If a negatively signed magnetoelastic constant is chosen, the calculation is found to be in general agreement with the observed data.
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TEMPERATURE (K)
Fig. 3. Magnetic phase diagram of NdCu2, measured with field along the b-axis. The open circles and filled squares mark anomalies observed in magnetostriction and thermal expansion measurements, respectively. The magnetic phase diagram for NdCu2, as deduced from the anomalies observed in the single-crystal thermal expansion and magnetostriction measurements, is shown in Fig. 3. The lines are drawn as a guide only. The incommensurate (I-AF) and commensurate (AF) phases are identified by zero-field neutron diffraction results [2]. The mixed phase (MIX) between these antiferromagnetic phases is a region of co-existence also observed in the neutron study. The area marked F-I is clearly a ferromagnetic region, because of the positive slope of the adjacent boundary lines. F-II is also ferromagnetic. A phase line, not shown, was observed to come out of the upper boundary and increase with increasing temperature. The boundary between I-AF and U is deduced from very weak anomalies. The area U itself is of unknown structure, indicating that the phase diagram of NdCu 2 requires more attention. Acknowledgements: We acknowledge financial support from The Royal Society and the UK Science and Engineering Research Council. This work was also supported by the Austrian FWF project No. P9203. References
2, ,4
0
1
2
3
7:7 4
5
6
7
APPLIED MAGNETIC FIELD (T)
Fig. 2. Magnetostriction of NdCu 2, measured in increasing applied magnetic fields along the b-axis, at various temperatures. The arrows mark the location of the T = 2.0 K transitions.
[1] P. Svoboda, M. Divi~, A.V. Andreev, N.V. Baranov, M.I. Bartashevich and P.E. Martin, J. Magn. Magn. Mater. 104-107 (1992) 1329. [2] R.R. Axons, M. Loewenhaupt, Th. Reif and E. Gratz, J. Phys.: Condens, Matter., submitted [3] M. Divig, P. Lukfic and P. Svoboda, J. Phys.: Condens. Matter 2 (1990) 7569. [4] E. Gratz, M. Loewenhaupt, M. Divig, W. Steiner, E. Bauer, N. Pillmayr, H. Miiller, H. Nowotny and B. Frick, J. Phys.: Condens. Matter 3 (1991) 9297.
~ H journalof magnetism and magnetic ~ I ~ materials
ELSEVIER
Dilatometric study of
NdCu 2
in magnetic fields
S.W. Zochowski a,., M. Rotter b, E. Gratz b, K.A. M c E w e n a a Department of Physics, Birkbeck College, UniL,ersity of London, Malet Street, London WC1E 7HX, UK b . . . . Instttut fiir Expertmentalphyszk, Technische Universitiit Wien, A-I 040 Wien, Austria Abstract Single crystals of the orthorhombic intermetallic NdCu 2 have been used to measure the thermal expansion and longitudinal magnetostriction. Measurements were made parallel to the crystallographic b-direction in the temperature range 1.5-30 K and in magnetic fields up to 7 T. A comparison of the measurements with the results of a mean-field calculation indicate a negative magnetoelastic constant. A magnetic phase diagram of NdCu 2 has been deduced from the anomalies observed in the dilatometric measurements.
The magnetic structures, and phase diagrams, of RCu 2 alloys, where R is a rare-earth metal, appear to be complex, generally of an antiferromagnetic nature. The orthorhombic (CeCuz-type) NdCu 2 has been reported to exhibit four antiferromagnetic phases below its N6el temperature, T N = 6.5 K, in its magnetoresistance and magnetisation, measured along the b-axis of a single crystal [1]. In a recent neutron diffraction experiment [2], the zero-field magnetic structure of NdCu 2 was investigated between 1.4 and 8 K. Only two magnetic phases were observed, with the moments constrained to the b - c plane: an antiferromagnetic incommensurate phase between T N and 4 K and a commensurate phase down to 1.4 K. Here, we report on the results of our single-crystal magnetic dilatometric investigation on NdCu 2, including model calculations, the details of which will be published elsewhere. Two single crystals were measured in this experiment. Both were cut from the same ingot which was grown using the Czochralski method. In each case, faces were cut perpendicular to the b-direction with lengths 0.745 cm and 0.310 cm, respectively. Measurements of strain were made relative to the body of a capacitance dilatometer The temperature was controlled and measured using a calibrated carbon-glass sensing element. For field-dependent thermal expansion and magnetostriction measurements, a magnetic field with H < 7 T was applied parallel to the measurement direction. Fig. 1 shows representative thermal expansion data at H = 0.0, 0.25, 1.0, 1.7 and 3.5 T. Note that the relative positions of the curves in Figs. 1 and 2 have been altered
for ease of viewing. In zero field, the N4el temperature is observed to be near 6.7 K; a small anomaly is found 0.2 K below TN when the derivative of A l / l is analysed. A second anomaly, at 4.2 K, marks the transition from an incommensurate to commensurate structure, as observed in neutron diffraction work [2]. As shown for H = 3.5 T, the general shape of the A l / l curves remains the same until H > 3.0 T, where it is observed to rise before decreasing at a constant rate after T = 7 K. The inset shows data for H = 0.0 T up to 80 K, with an upward turn observed near 34 K.
.-- , ~ ~ .
illlllltlllllllll2
3
4
5
6
7
8
9
10
TEMPERATURE (K)
* Corresponding author. [email protected].
Fax:
+44-71-631 6220; email:
Fig. 1. Thermal expansion of NdCu2, measured in increasing temperature along the b-axis, at various applied magnetic fields. The arrows mark the locations of the zero-field transitions. The inset shows extended H = 0.0 T results.
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 0 7 8 5 - 3
1130
S. W. Zochowski et al. / Journal of Magnetism and Magnetic Materials 140-144 (1995) 1129-1130
Also shown in Fig. 1 is an overscaled representation of the calculation of ( O ° ) for zero applied magnetic field. Using a simple model [3] and previously published crystal-field parameters [4], the thermal expansion can be described by a linear combination of the expectation values of the Stevens operators ( O °) and (O22). Although the ( 0 2o ) term describes the zero-field data reasonably well, it is necessary to include a second nearest neighbour calculation, (JiJi+2), in order to model the turn at 34 K. The first-order transition at 4.2 K is not reproduced in this calculation because of the incommensurate nature of the ordering structure. Representative magnetostriction results are shown in Fig. 2. At T = 2.0 K, four anomalies indicate transitions at 0.77, 2.55, 2.76 and 2.94 K. These transitions are seen to gradually disappear as the temperature is increased, until at T = 7.0 K a paramagnetic response is observed. The magnetostriction has been found to be best modelled by assuming a strong strain dependence of the coupling constant between second nearest neighbouring planes (-0.1699 T), neglecting the strain dependence of all other magnetic coupling constants. A plot of the thermal expectation value (JiJi+2), at 1.7 K, is also shown in Fig. 2. If a negatively signed magnetoelastic constant is chosen, the calculation is found to be in general agreement with the observed data.
-'
[ ' I ' I J I ' I T=7.0K ' I J [1 T=6.0K
4-" b
4
E £
F-II
NdCu 2 b-axis
w3
,'7
%o
U
°'"k
PARA
E,
<0
ikll
1
II
2
J[I
3
I
4
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5
III
6
II
7
TEMPERATURE (K)
Fig. 3. Magnetic phase diagram of NdCu2, measured with field along the b-axis. The open circles and filled squares mark anomalies observed in magnetostriction and thermal expansion measurements, respectively. The magnetic phase diagram for NdCu2, as deduced from the anomalies observed in the single-crystal thermal expansion and magnetostriction measurements, is shown in Fig. 3. The lines are drawn as a guide only. The incommensurate (I-AF) and commensurate (AF) phases are identified by zero-field neutron diffraction results [2]. The mixed phase (MIX) between these antiferromagnetic phases is a region of co-existence also observed in the neutron study. The area marked F-I is clearly a ferromagnetic region, because of the positive slope of the adjacent boundary lines. F-II is also ferromagnetic. A phase line, not shown, was observed to come out of the upper boundary and increase with increasing temperature. The boundary between I-AF and U is deduced from very weak anomalies. The area U itself is of unknown structure, indicating that the phase diagram of NdCu 2 requires more attention. Acknowledgements: We acknowledge financial support from The Royal Society and the UK Science and Engineering Research Council. This work was also supported by the Austrian FWF project No. P9203. References
2, ,4
0
1
2
3
7:7 4
5
6
7
APPLIED MAGNETIC FIELD (T)
Fig. 2. Magnetostriction of NdCu 2, measured in increasing applied magnetic fields along the b-axis, at various temperatures. The arrows mark the location of the T = 2.0 K transitions.
[1] P. Svoboda, M. Divi~, A.V. Andreev, N.V. Baranov, M.I. Bartashevich and P.E. Martin, J. Magn. Magn. Mater. 104-107 (1992) 1329. [2] R.R. Axons, M. Loewenhaupt, Th. Reif and E. Gratz, J. Phys.: Condens, Matter., submitted [3] M. Divig, P. Lukfic and P. Svoboda, J. Phys.: Condens. Matter 2 (1990) 7569. [4] E. Gratz, M. Loewenhaupt, M. Divig, W. Steiner, E. Bauer, N. Pillmayr, H. Miiller, H. Nowotny and B. Frick, J. Phys.: Condens. Matter 3 (1991) 9297.