- Email: [email protected]
Multiple-q magnetic structure of praseodymium at millikelvin temperatures
EB 6
Physica 107B (1981) 259-260 North-Holland Publishing Company
MULTIPLE-Q MAGNETIC STRUCTURE OF PRASEODYMIUM AT MILLIKELVlN TEMPERATURES
K A McEwen1, W G S t i r l i n g 2, C V e t t i e r 2, J L Ragazzoni 2, D F o r t 3 and D W Jones 3 (I) Department of Physics, University of Salford, Salford M5 4WT, England (2) Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex, France (3) Centre for Materials Science, University of Birmingham, England The development of magnetic ordering in high-purity, single-crystal dhcp Pr has been revealed by neutron scattering studies in the temperature range 0.03 - 4.2K. Satellite reflections with wavevector O.13~i00 originating from a sinusoidally modulated magnetic structure were clearly observed at temperatures well below IK. Below 2OOmK, sets of six satellites split transversely into twelve satellites, whose modulation wavevector is no longer along a high symmetry direction. The results of additional neutron polarisation analysis experiments provide evidence for the multiple-q nature of the magnetic structure in Pr.
i.
INTRODUCTION
Comprehensive neutron scattering and magnetization studies have established that the ions in double-hexagonal close-packed Pr metal experience a crystalline electric fie~d which produces singlet ground states at both the locally hexagonal and cubic sites.(l,2) For many years, it was assumed that this element remained paramagnetic down to T = O as a result of the subcritical ratio of the exchange coupling to the crystal field splitting between the ground and first excited states. However, in a recent paper (to be referred to as I) McEwen and Stirling reported the development, below IK, of a sinusoidally modulated magnetic structure.(3) A moment of some 0.08 ~B was induced at 3OmK. The development of this moment was attributed in I to an enhancement of the ionic exchange coupling via the hyperfine interaction, in a mechanism discussed by Murao. (4)
meter IN 12 at the Institut Laue-Langevin, using a fixed incident neutron wavelength of 3.142 ~. 3.
RESULTS AND DISCUSSION
A series of longitudinal (L) scans were made through the (iOO) dhcp reciprocal lattice point, parallel to the ~ O 4 , [O10] and [i~0] directions. Figure I shows the results of such an L-scan parallel to [O1d at 36mK. In agreement with studies around (OO£) and (hO£) described in I, two peaks are observed. The data were fitted to the sum of two gaussians and a background. The "broad peak" at Q1 is consistently broader than the resolution and is still detectable, though weak, at 4.2K. The satellite peak at Q2 is interpreted as arising from long-range magnetic ordering in a modulated structure of wavevector Q2 = O.135x010. Pr 3 6 i n K " L - s c a n " through ( 1.0,-0.13,0
2600
We report here further high-resolution studies on another Pr crystal of higher purity, mounted in a complementary crystallographic orientation. Although a detailed analysis of the date has not yet been completed, the results for the temperature dependence of the magnetic moment are in good qualitative agreement with those of I. Furthermore, we have observed a new splitting of the satellites at the lowest temperatures. 2.
)
Satellile (02) 2400
.(100) nuclear peak ~
2200
oz
8 z
2000
z
1800
o
q I
,
/-~P
Broad Peak
C~ = 0.135 FWHM =0.016
o,=OlO,
F'WHM = 0.029L a
,
~
•
Y.F
a
~,
...,,_.
EXPERIMENTAL DETAILS
The Pr single crystal (size 4x4x6 mm 3) was spark cut from a rod purified by the solid state electrotransport technique. (5) Mass spectrographic analysis indicated a total metallic impurity concentration of 70 ppm(atomic), of which 20 ppm was magnetic, including 6 ppm of neodymium. The crystal was mounted with its c-direction vertical in a dilution refrigerator. Details of the thermometry etc are given in I. Measurements were made with the 3-axis spectro-
03784363/81/0000-0000/$0250
© North-HollandPublishingCompany
(1.0;0.13,0) I
QK -0.05
I
-0.10 WAVEVECTOR
'~'
I
- 0.15
I
-0.20
( r. ~.u3
Figure I. Elastic scattering scan through the reciprocal lattice position (1,-O.13,O) parallel to ~iO] at a temperature of 36mK. The centres and widths of the peaks are given in reciRr?cal lattice units, i r.l.u. = 4~/a/3 = 1.976~- •
259
260
Broad peaks and satellites were observed at the equivalent positions (I,±Q,O), (I±Q,~Q,O). Because of geometrical factors in the neutron scattering cross-section, the intensity of the (I+Q,O,O) peaks are expected to be an order of magnitude weaker and were indeed not clearly detected. Scans were also performed through the satellit~ position (I,Q2,0) in a direction parallel to ~ T ~ i.e. transverse to the L-scan through the satellite. The satellite peaks split in this transverse direction as the temperature is reduced. Fitting the data to two gaussians yields a maximum separation which corresponds to a 3 o tilt of the modulation wavevector away from ~ i ~ . All the satellites observed around (iO0) were found to split in this manner. Above 28OmK, the data were fitted to a s%ngle gaussian of width considerably wider than the experimental resolution in this direction (O.Ol~-i). The presence of 12 satellites around a reciprocal lattice point may arise from either (i) a multidomain structure each with a single wavevector or (ii) a linear combination of the modulations along each wavevector, comprising a multiple-q structure which extends throughout the crystal.(6) The multiple-q structure should be characterized by the existence of long-range lattice modulations due to the strong magnetoelastic coupling. Studies of stress-induced magnetic ordering in Pr (7,8) have revealed satellites at (±Q202) and (±Q206). No broad peaks were found near these positions. In a recent investigation using polarisation analysis and an unstressed Pr crystal, we have verified that satellites such as (Q202) arise from a modulation of the lattice, rather than the magnetic moments.(8) This observation provides direct support for the multiple-q model of the magnetic structure in Pr.
u') I-Z 0 0 Z 0 hI.-
I.U Z
r
,
o
2
~o
330mK-
4.
ACKNOWLEDGEMENTS AND REFERENCES
We wish to thank D Brochier, S Burke, K Gobrecht, D Puschner and P Suttling for their help in this experiment. We are indebted to the Neutron Division, Rutherford and Appleton Laboratories for the use of the dilution refrigerator. Financial support from the SRC is also gratefully acknowledged. o
"
o°o
, QH QK
0.90 0.18
0.95 0.155
Oooo
4.2K
°°
-I
, 0.,? ,ooo o o0
1.00 0.13
1.05 0.105
1.10 0.08
WAVEVECTOR ( r. ,e. u.) Figure 2. Transverse scans through (1,O.13,0) at various temperatures, showing the splitting of the (I,Q2,O) satellite. The full lines represent the fitted gaussians plus background.
(I) Houmann J G, Rainford B D, Jensen J and Mackintosh A R, Phys Rev B20 (1979), 11051118. (2) Jensen J, J Physique 40 (1979) C5, 1-7 (3) McEwen K A and Stirling W G, J Phys C: Solid State Phys 14 (1981), 157-165 (4) Murao T, J Phys Soc Japan 46 (1979), 40-44 and references therein (5) Muirhead C M and Jones D W, J Less-Con~non Met 50 (1976), 73-83 (6) Bak P and Lebech B, Phys Rev Lett 40 (1978), 800-803 (7) McEwen K A, Stirling W G and Vettier C, Phys Rev Lett 41 (1978), 343-346 (8) McEwen K A, Stirling W G, Vettier C and Burke S, to be published.
Physica 107B (1981) 259-260 North-Holland Publishing Company
MULTIPLE-Q MAGNETIC STRUCTURE OF PRASEODYMIUM AT MILLIKELVlN TEMPERATURES
K A McEwen1, W G S t i r l i n g 2, C V e t t i e r 2, J L Ragazzoni 2, D F o r t 3 and D W Jones 3 (I) Department of Physics, University of Salford, Salford M5 4WT, England (2) Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex, France (3) Centre for Materials Science, University of Birmingham, England The development of magnetic ordering in high-purity, single-crystal dhcp Pr has been revealed by neutron scattering studies in the temperature range 0.03 - 4.2K. Satellite reflections with wavevector O.13~i00 originating from a sinusoidally modulated magnetic structure were clearly observed at temperatures well below IK. Below 2OOmK, sets of six satellites split transversely into twelve satellites, whose modulation wavevector is no longer along a high symmetry direction. The results of additional neutron polarisation analysis experiments provide evidence for the multiple-q nature of the magnetic structure in Pr.
i.
INTRODUCTION
Comprehensive neutron scattering and magnetization studies have established that the ions in double-hexagonal close-packed Pr metal experience a crystalline electric fie~d which produces singlet ground states at both the locally hexagonal and cubic sites.(l,2) For many years, it was assumed that this element remained paramagnetic down to T = O as a result of the subcritical ratio of the exchange coupling to the crystal field splitting between the ground and first excited states. However, in a recent paper (to be referred to as I) McEwen and Stirling reported the development, below IK, of a sinusoidally modulated magnetic structure.(3) A moment of some 0.08 ~B was induced at 3OmK. The development of this moment was attributed in I to an enhancement of the ionic exchange coupling via the hyperfine interaction, in a mechanism discussed by Murao. (4)
meter IN 12 at the Institut Laue-Langevin, using a fixed incident neutron wavelength of 3.142 ~. 3.
RESULTS AND DISCUSSION
A series of longitudinal (L) scans were made through the (iOO) dhcp reciprocal lattice point, parallel to the ~ O 4 , [O10] and [i~0] directions. Figure I shows the results of such an L-scan parallel to [O1d at 36mK. In agreement with studies around (OO£) and (hO£) described in I, two peaks are observed. The data were fitted to the sum of two gaussians and a background. The "broad peak" at Q1 is consistently broader than the resolution and is still detectable, though weak, at 4.2K. The satellite peak at Q2 is interpreted as arising from long-range magnetic ordering in a modulated structure of wavevector Q2 = O.135x010. Pr 3 6 i n K " L - s c a n " through ( 1.0,-0.13,0
2600
We report here further high-resolution studies on another Pr crystal of higher purity, mounted in a complementary crystallographic orientation. Although a detailed analysis of the date has not yet been completed, the results for the temperature dependence of the magnetic moment are in good qualitative agreement with those of I. Furthermore, we have observed a new splitting of the satellites at the lowest temperatures. 2.
)
Satellile (02) 2400
.(100) nuclear peak ~
2200
oz
8 z
2000
z
1800
o
q I
,
/-~P
Broad Peak
C~ = 0.135 FWHM =0.016
o,=OlO,
F'WHM = 0.029L a
,
~
•
Y.F
a
~,
...,,_.
EXPERIMENTAL DETAILS
The Pr single crystal (size 4x4x6 mm 3) was spark cut from a rod purified by the solid state electrotransport technique. (5) Mass spectrographic analysis indicated a total metallic impurity concentration of 70 ppm(atomic), of which 20 ppm was magnetic, including 6 ppm of neodymium. The crystal was mounted with its c-direction vertical in a dilution refrigerator. Details of the thermometry etc are given in I. Measurements were made with the 3-axis spectro-
03784363/81/0000-0000/$0250
© North-HollandPublishingCompany
(1.0;0.13,0) I
QK -0.05
I
-0.10 WAVEVECTOR
'~'
I
- 0.15
I
-0.20
( r. ~.u3
Figure I. Elastic scattering scan through the reciprocal lattice position (1,-O.13,O) parallel to ~iO] at a temperature of 36mK. The centres and widths of the peaks are given in reciRr?cal lattice units, i r.l.u. = 4~/a/3 = 1.976~- •
259
260
Broad peaks and satellites were observed at the equivalent positions (I,±Q,O), (I±Q,~Q,O). Because of geometrical factors in the neutron scattering cross-section, the intensity of the (I+Q,O,O) peaks are expected to be an order of magnitude weaker and were indeed not clearly detected. Scans were also performed through the satellit~ position (I,Q2,0) in a direction parallel to ~ T ~ i.e. transverse to the L-scan through the satellite. The satellite peaks split in this transverse direction as the temperature is reduced. Fitting the data to two gaussians yields a maximum separation which corresponds to a 3 o tilt of the modulation wavevector away from ~ i ~ . All the satellites observed around (iO0) were found to split in this manner. Above 28OmK, the data were fitted to a s%ngle gaussian of width considerably wider than the experimental resolution in this direction (O.Ol~-i). The presence of 12 satellites around a reciprocal lattice point may arise from either (i) a multidomain structure each with a single wavevector or (ii) a linear combination of the modulations along each wavevector, comprising a multiple-q structure which extends throughout the crystal.(6) The multiple-q structure should be characterized by the existence of long-range lattice modulations due to the strong magnetoelastic coupling. Studies of stress-induced magnetic ordering in Pr (7,8) have revealed satellites at (±Q202) and (±Q206). No broad peaks were found near these positions. In a recent investigation using polarisation analysis and an unstressed Pr crystal, we have verified that satellites such as (Q202) arise from a modulation of the lattice, rather than the magnetic moments.(8) This observation provides direct support for the multiple-q model of the magnetic structure in Pr.
u') I-Z 0 0 Z 0 hI.-
I.U Z
r
,
o
2
~o
330mK-
4.
ACKNOWLEDGEMENTS AND REFERENCES
We wish to thank D Brochier, S Burke, K Gobrecht, D Puschner and P Suttling for their help in this experiment. We are indebted to the Neutron Division, Rutherford and Appleton Laboratories for the use of the dilution refrigerator. Financial support from the SRC is also gratefully acknowledged. o
"
o°o
, QH QK
0.90 0.18
0.95 0.155
Oooo
4.2K
°°
-I
, 0.,? ,ooo o o0
1.00 0.13
1.05 0.105
1.10 0.08
WAVEVECTOR ( r. ,e. u.) Figure 2. Transverse scans through (1,O.13,0) at various temperatures, showing the splitting of the (I,Q2,O) satellite. The full lines represent the fitted gaussians plus background.
(I) Houmann J G, Rainford B D, Jensen J and Mackintosh A R, Phys Rev B20 (1979), 11051118. (2) Jensen J, J Physique 40 (1979) C5, 1-7 (3) McEwen K A and Stirling W G, J Phys C: Solid State Phys 14 (1981), 157-165 (4) Murao T, J Phys Soc Japan 46 (1979), 40-44 and references therein (5) Muirhead C M and Jones D W, J Less-Con~non Met 50 (1976), 73-83 (6) Bak P and Lebech B, Phys Rev Lett 40 (1978), 800-803 (7) McEwen K A, Stirling W G and Vettier C, Phys Rev Lett 41 (1978), 343-346 (8) McEwen K A, Stirling W G, Vettier C and Burke S, to be published.