Appl. Phys. A 74 [Suppl.], S686–S688 (2002) / Digital Object Identifier (DOI) 10.1007/s003390201623
Applied Physics A Materials Science & Processing
Geometrical frustration and incommensurate magnetic ordering in CePdAl: a low-temperature neutron-diffraction study L. Keller1,∗ , A. Dönni2 , H. Kitazawa3 , B. van den Brandt4 1 Laboratory for Neutron Scattering, ETHZ & PSI, 5232 Villigen PSI, Switzerland 2 Department of Physics, Niigata University, Niigata 950-2181, Japan 3 National Research Institute for Materials Science (NIMS), Tsukuba 305-0047, Japan 4 Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
Received: 16 July 2001/Accepted: 11 December 2001 – Springer-Verlag 2002
Abstract. The ordering of the Ce3+ magnetic moments in the heavy-fermion compound CePdAl was investigated by means of neutron powder diffraction measurements of high-quality polycrystalline samples at temperatures down to 180 mK. The triangular coordination symmetry of the magnetic ions gives rise to geometrical frustration and leads to an incommensurate antiferromagnetic structure, exhibiting a coexistence of ordered and frustrated disordered Ce moments. The magnetic propagation vector shows a pronounced temperature depen dence below TN and locks in to k = 12 , 0, τ , τ = 0.351, below 1.9 K. The magnetic structure at 180 mK could unambiguously be determined and the coexistence of ordered and disordered Ce moments is observed even at the lowest temperatures. A second magnetic phase transition can be excluded. PACS: 61.12.Ld; 75.25.+z; 75.50.Ee The ternary intermetallic compounds RXAl (R = rare earth, X = Ni, Pd) adopt the ZrNiAl-type structure (hexagonal space group P 6¯ 2m). The triangular coordination symmetry of the metallic rare earth atoms gives rise to geometrical frustration and leads to a rich and complex behavior of the magnetic ordering phenomena in this class of compounds. A common feature for the nickel compounds RNiAl (R = Tb, Dy, Ho) [1, 2] is the existence of at least two magnetic phase transitions. Below TN1 the ordered magnetic moment of one out of three R atoms appears strongly reduced but acquires the same size as the others below TN2 , accompanied by a change of the magnetic propagation vector. Recently, we have investigated the magnetic ordering phenomena of PrPdAl and NdPdAl by means of specific heat and neutron scattering experiments [3, 4]. Both compounds undergo two magnetic phase transitions to incommensurate magnetic phases that are dominated by the geometrical frustrations inherent to the symmetry and structure of these compounds. At temperatures below TN1 , the magnetic ordering of PrPdAl ∗ Corresponding
author. (Fax: +41-56/3102939, E-mail:
[email protected])
is characterized by a frustrated but commensurate antiferromagnetic arrangement of the Pr3+ magnetic moments in the a-b plane with an incommensurate triple-k modulation along c ki = 12 , 0, τi ). The incommensurate magnetic propagation vector k of NdPdAl shows a pronounced temperature dependence below TN1 and locks in to k = 14 , 0, 49 at TN2 . CePdAl has been investigated by neutron diffraction at temperatures down to 1.3 K [5]. A magnetic phase transition at TN = 2.7 K was found with an incommensurate an tiferromagnetic propagation vector k = 12 , 0, τ , τ = 0.35 at 1.5 K, exhibiting coexistence of two third magnetically ordered Ce3+ moments with one third frustrated disordered moments. The experimentally determined magnetic structure was shown to be in agreement with group theoretical symmetry analysis considerations, calculated by the program MODY, which confirmed that for the geometrically frustrated one third of Ce atoms an ordered magnetic moment parallel to the magnetically easy c-axis is forbidden by symmetry. CePdAl shows physical properties which are typical for heavy-fermion compounds. A tail of the λ-type specific heat anomaly extends to considerably higher temperatures than the ordering temperature and the magnetic entropy at TN is only 38% of Rln2. This reduction of Smag is not only due to magnetic short-range order above TN but also due to Kondo hybridization. Theoretical considerations [6] showed the importance of the Kondo effect to the magnetic structure appearing in CePdAl: a model including Kondo screening and first-nearest neighbor ( J1 ) and second-nearest neighbor (J2 ) in-plane exchange interactions explains the magnetic ordering of CePdAl below TN with J1 > 0 and J2 < 0. Geometrical frustration on a Kagom´e-like lattice and the Kondo effect in CePdAl has attracted much interest. Especially the nature of the magnetic order at very low temperatures has been a disputed topic. Preliminary neutron scattering data with a poor signal to background ratio of less than 10% suggested a possible second magnetic phase transition between 1.3 and 0.6 K [5]. A recent NMR study [7] favored disordered Ce moments coexisting with ordered ones down to 30 mK and suggested that a possible second magnetic phase transition would only appear as a change of the incommensurate structure along c, leaving the disordered mo-
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ments untouched. Neutron diffraction is the method of choice for investigating long-range magnetic order. Therefore we decided to perform a low-temperature powder diffraction study on a new high-quality sample of CePdAl in order to clarify the magnetism in CePdAl at temperatures far below TN .
1 Experimental A large amount (18 g) of polycrystalline CePdAl sample was synthesized by the arc-melting technique using high quality Ce-4N material. The neutron diffraction experiments were performed at the spallation neutron source SINQ of the Paul Scherrer Institute in Villigen, Switzerland. The low temperature measurements were done on the cold neutron powder diffractometer DMC with a vertically focusing graphite monochromator C(002) and the wavelengths 2.564 Å and 4.201 Å. In order to remove higher-order neutron wavelengths a graphite (2.564 Å) and Be (4.201 Å) filter was placed between the monochromator and the sample. An oscillating radial collimator between sample and multidetector suppresses Bragg peaks from the sample environment and reduces the background. Temperatures down to 1.4 K were reached with a standard 4 He cryostat, temperatures down to 180 mK with a 3 He/4 He dilution cryostat designed by the Low Temperature Facilities Group of the Paul Scherrer Institute. The refinements of the powder diffraction patterns were done using the Rietveld method and the program FULLPROF [8].
2 Results and discussion The low-Q part of the paramagnetic neutron powder diffraction pattern of CePdAl at T = 3.50 K and neutron wavelength λ = 4.2 Å is shown in Fig. 1, showing the observed, calculated and difference (observed - calculated) patterns. The refinement confirmed the ZrNiAl-type structure, the lattice parameters turn out to be a = 7.1846(6) Å and c = 4.2348(5) Å, c/a = 0.5894. The low-Q part of the data for magnetically
Fig. 2. Observed, calculated and difference neutron diffraction patterns (λ = 4.20 Å) of magnetically ordered CePdAl at T = 1.44 K. The vertical bars indicate the Bragg peak positions due to the chemical and magnetic structure, respectively
ordered CePdAl at T = 1.44 K is shown in Fig. 2. The refinement confirms the incommensurate antiferromagnetic structure k = 12 , 0, τ with a LSW modulated spin arrangement and coexistence of ordered moments of Ce(1) and Ce(3) with disordered moments of Ce(2) (Table 1). We have investigated the temperature evolution of the magnetic structure of CePdAl. The temperature dependence of the integrated intensity of the 12 , 0, τ magnetic Bragg peak describes a second-order phase transition with N´eel temperature TN = 2.87(3) K (Fig. 3). Also shown is the pronounced temperature dependence of the incommensurate component τ of the magnetic propagation vector k. Below TN τ decreases with decreasing temperature but locks in at T = 1.9 K. A similar behavior has been observed for NdPdAl [3]. The neutron powder diffraction pattern at T = 0.18 K and λ = 2.56 Å is shown in Fig. 4. The change of background as compared to Fig. 2 is due to the different sample environment. Also shown is the difference data (0.18 K–3.50 K), displaying the magnetic scattering only. We were able to refine the data with a similar magnetic structure model as at 1.44 K but with increased ordered moments (Table 1). This strongly supports the suggestion that even at lowest temperatures CePdAl shows coexistence of ordered and disordered moments. Such a magnetic structure leads to extinction rules for the magnetic Bragg peaks. If Ce(2) has no orderedmagnetic component then the extinction rule −h 2 , h, k ± τ is valid. A break of this rule, i.e. appearance of Bragg peaks with forbidden indices, is identical to the onset of an ordered Ce3+ moTable 1. The refined magnetic parameters. τ: incomm. component of magnetic propagation vector k = 12 , 0, τ , Ce(1): coordinates (0.58, 0, 0), Ce(2): (0, 0.58, 0), Ce(3): (0.42, 0.42, 0), µz : component of magnetic moment µ = (0, 0, µz )
Fig. 1. Observed, calculated and difference neutron diffraction patterns (λ = 4.20 Å) of CePdAl in its paramagnetic state. The vertical bars indicate the Bragg peak positions
T [K]
τ
2.60 K 1.44 K 0.18 K
0.3544(2) 0.3511(2) 0.3511(2)
Ce(1)
µz Ce(2)
Ce(3)
1.16(1) 1.69(1) 1.77(1)
0 0 0
1.16(1) 1.69(1) 1.77(1)
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Fig. 3. Temperature evolution of the incommensurate component τ of the magnetic propagation vector k = 12 , 0, τ for CePdAl, showing the lock-in behavior around 1.9 K (•). Temperature evolution of the ordered magnetic moment of Ce(1) and Ce(3) in CePdAl (◦)
ment for Ce(2). A careful analysis of the low-temperature pattern as well as of the difference pattern (0.18 K–3.50 K) shows no trace of magnetic Bragg peaks that are incompatible with the extinction rule mentioned above. This unambiguously proves that even at lowest temperatures the coexistence of ordered and disordered magnetic Ce moments survives. 3 Summary New neutron diffraction experiments were performed on high-quality powder samples of CePdAl in the temperature range 180 mK < T < 3.5 K. High count rate yielded very good counting statistics which enabled us to unambiguously determine the low-temperature magnetic structure. The magnetic propagation vector k shows a pronounced temperature dependence including lock-in behavior at T = 1.9 K. Down to 180 mK the extinction rule −h , h, k ± τ remains valid 2 and a second phase transition can be excluded. CePdAl is confirmed to be an extreme case where the Ce atoms located on the crystallographic (3 f ) site exhibit a coexistence of ordered moments (2/3) and disordered moments (1/3). Reasons are effects of geometrical frustration [5] and/or the interplay of Kondo screening and exchange interaction [6].
Fig. 4. Low-temperature powder diffraction data of CePdAl at T = 180 mK, measured with neutron wavelength 2.56 Å (top). Refinement of the difference data (0.18 K–3.50 K), displaying the magnetic scattering only (bottom)
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