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Metastable characteristics in ferromagnetic TbPdIn and DyPdIn
Journal of Magnetism and Magnetic Materials 241 (2002) 17–24
Metastable characteristics in ferromagnetic TbPdIn and DyPdIn D.X. Lia,*, Y. Shiokawaa, T. Nozueb, T. Kamimurab, K. Sumiyamac a
Oarai Branch, Institute for Materials Research, Tohoku University, Oarai-machi, Ibaraki 311-1313, Japan b Department of Physics, Tohoku University, Sendai 980-8578, Japan c Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan Received 30 May 2001; received in revised form 19 September 2001
Abstract Equiatomic ternary compounds, TbPdIn and DyPdIn, have been studied by means of DC magnetization, AC susceptibility, magnetic relaxation, specific heat and electrical resistivity measurements. The two compounds are ferromagnets below a transition temperature TC ¼ 74 K for TbPdIn and TC ¼ 38 K for DyPdIn with metastable magnetic properties, behaving as the irreversibility of the temperature dependence of magnetization below a characteristic temperature Tir and the long-time magnetic relaxation behavior below TC when changing the magnetic field at a constant temperature. DyPdIn shows the second phase transition at TN ¼ 23 K, caused by the antiferromagnetic coupling. For both compounds, the ground state is not a collinear ferromagnet, but some canted one with antiferromagnetic component. The observed metastable magnetic properties are discussed in terms of domainwall pinning model. The complex magnetic structures in DyPdIn and TbPdIn are compared with those of isostructural DyNiAl and HoNiAl. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.30.Cr; 75.60.Ch; 75.60.Es; 72.15.Eb Keywords: Magnetization; Magnetic relaxation; Metastable state; Irreversibility
1. Introduction RPdIn (R=rare-earth elements) compounds belong to a large family of ternary rare-earth alloys with an equiatomic ration. Most members of these materials crystallize in the ZrNiAl-type hexagonal structure, which is an ordered ternary derivative of the Fe2P structure. The lattice shown schematically in Fig. 1 is built up of two types of basal-plane layers with and without rare-earth *Corresponding author. E-mail address: [email protected] (D.X. Li).
atoms, (3R+Pd) and (3In+2Pd), respectively, alternating along the c-axis. The atomic arrangement in these compounds may be described in the p6% 2m space group with following atomic positions [1]: 3R at 3g ðx; 0; 12; 0; x; 12; x; x; 12Þ; 3In at 3f (y; 0; 0; 0; y; 0; y; y; 0); 2Pd at 2c ð13; 23; 0; 23; 13; 0Þ; 1Pd at 1b ð0; 0; 12Þ: The important feature in this structure is that the crystalline electric field (CEF) around the rare-earth ion often induces strong anisotropy due to the distinct layered character of the crystal structure, while within one magnetic layer rare-earth atoms form triangles of nearest neighbors, in the case of antiferromagnetic
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and explained as spin-glass behavior [6]. However, recent neutron diffraction measurements [1,10] indicate the occurrence of long-range ferromagnetic order at TC for both TbPdIn and DyPdIn. These results motivated us to consider if the domain-wall pinning effects could be used to explain the ‘‘spin-glass-like’’ magnetic properties of TbPdIn and DyPdIn, because the ordered crystal structure in both systems is hard to induce sufficient site randomness or bond randomness necessary for a spin glass. We have performed a systematic investigation on the well-annealed polycrystalline TbPdIn and DyPdIn samples by AC susceptibility, DC magnetization, magnetic relaxation, specific heat and electrical resistivity measurements. The results indicate that ferromagnetic TbPdIn and DyPdIn show metastable magnetic ground states with complex magnetic structures. The domain-wall pinning effects may be responsible for the observed irreversible magnetism.
2. Experimental
Fig. 1. Schematic representation of RPdIn (R=rare-earth elements except Eu) crystallizing in the ZrNiAl-type hexagonal structure.
coupling between nearest neighbor frustration of the magnetic interactions could be induced by this topology [2]. In recent years, magnetic properties have been reported for some of RPdIn compounds [3–9]. CePdIn is an antiferromagnetic Kondolattice compound [7,8]. SmPdIn shows a ferromagnetic behavior with strong 4f CEF anisotropy [3]. YbPdIn is a mixed-valent system [9], and EuPdIn that crystallizes in a different structure behaves like an antiferromagnet with weak magnetocrystalline anisotropy [5]. For TbPdIn and DyPdIn, the difference between field cooling (FC) and zero-field cooling (ZFC) magnetization was observed below a characteristic temperature TC
Polycrystalline samples of TbPdIn and DyPdIn were prepared by arc melting high-purity raw metals (Tb and Dy: 3N; Pd: 4N; In: 5N) in a titanium-gettered argon atmosphere. The buttons were flipped and remelted three to four times to ensure homogeneity, and then were annealed at 8001C for 240 h in high vacuum. From the powder X-ray diffraction pattern, the ZrNiAl-type structure was confirmed for both samples with the ( c ¼ 3:842 A ( for lattice parameters a ¼ 7:645 A, ( c ¼ 3:817 A ( for DyPdIn. TbPdIn and a ¼ 7:636 A, The samples used in the experiments are small pieces cut from the annealed buttons. The low field magnetization, AC susceptibility and magnetic relaxation measurements were carried out by a SQUID magnetometer (Quantum Design, MPMS-5P). Using a hybrid magnet, the high-field magnetizations in a steady magnetic field up to 2.18 107 A/m were measured at 4.2 K with an induction method. Electrical resistivity measurements were performed between 1.6 and 300 K using a standard four-terminal DC method. The adiabatic heat pulse method was employed for
D.X. Li et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 17–24
specific heat measurements over the temperature range between 1.7 and 100 K.
3. Results Fig. 2 shows the temperature dependence of AC susceptibility of DyPdIn and TbPdIn measured in an AC field of 80 A/m at the frequency range 0:1pf p1000 Hz. For DyPdIn, the main feature seen in Fig. 2(a) is a two-peak behavior of both the real, w0 ; and the imaginary, w00 ; components of the AC susceptibility. The first peak of both w0 and w00 ; occurring at the same temperature Tm ¼ 36 K, is almost independent of the frequency. This feature gives evidence for long-range ferromagnetic order
Fig. 2. Real, w0 ; and imaginary, w0 ; components of the SI volume AC susceptibility of TbPdIn and DyPdIn in an AC magnetic field of 80 A/m (using the lattice parameters, the unit transformation of wac can be made as 1 emu/g=1.2530 103 and 1.2081 103 (SI) for DyPdIn and TbPdIn, respectively).
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with the Curie temperature TC ¼ 38 K. For convenience, here, TC is defined as the temperature below which w00 appears (in other words, at which w00 falls to zero with increasing T). Note that TC is a little higher than the peak temperature of w0 ðTÞ; and dw0 =dT has a maximum at TC : The second peak of w0 ; at about TN ¼ 23 K, is also independent of the frequency. It is worth noting that w00 does not show evident anomaly at TN ; instead, a frequency-dependent peak is observed around Tf ¼ 13 K (f ¼ 1000 Hz). These characteristics suggest that the second peak in w0 at TN may be due to the antiferromagnetic correlation between Dy moments. For TbPdIn, w0 shows a pronounced maximum near Tm ¼ 68 K, while a kink appears in w00 near this temperature. Tm appears to be much less f dependent. This anomaly may be originated from ferromagnetic transition. The Curie temperature is determined to be TC ¼ 74 K in the way used for DyPdIn. A frequency-dependent peak is also detected around Tf B50 K in w00 similar to that observed for DyPdIn. One likely source for the observed frequency-dependent peak in w00 is the presence of a few stacking faults resulted from the randomly placed impurities or defects. These stacking faults can cause the relative orientation of moments in different Tb/Dy–Pd layers near the stacking faults being randomly parallel or antiparallel, and thus leading to the formation of spinglass like states at low temperatures [11]. However, this effect is so weak that no response could be detected in w0 ðTÞ: The demagnetizing limited value of w0 ; 1=N; is 2.46 for DyPdIn and 3.42 for TbPdIn, where N is the estimated demagnetizing factor. For DyPdIn, we observed the largest w0 value at TN but not near TC : When the sample was rotated at an angle of about 90 degrees in the direction of the AC field, w0 shows the largest value near TC and a small and broad anomaly around TN ; which seems to originate from the preferred orientations of moments in the sample. This is further confirmed by the experimental results measured on a single crystal sample by Nisgigori et al. [6] in spite of the different TC and TN values due to the sample dependence. They reported that w0 of DyPdIn shows the largest value at TC (they define TC as the peak temperature of w0 ) and no any anomaly near TN in the case of H AC jjc-axis.
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Whereas, the largest value of w0 was observed at TN and only slight increase appears at TC ; when the AC magnetic field is applied parallel to the aaxis. The temperature dependence of the DC magnetization, M; of TbPdIn and DyPdIn was measured in both FC and in ZFC modes in several magnetic fields, H: Fig. 3 shows the low-temperature results in plot of M=H vs. T: For TbPdIn, a sharp increase is observed at TC ¼ 74 K for both MZFC and MFC signaling the onset of ferromagnetic ordering. The MFC curve is reversible and independent of the time of the measurement. In contrast, a cusp-like maximum is observed for the low-field MZFC curve just below TC : MZFC is smaller than MFC and time dependent below a characteristic temperature Tir (at which MZFC and MFC bifurcate). It is interesting to note that the characteristic temperature Tir shifts to high temperature side with decreasing H: In fact, for the very low applied fields the deviation between MZFC and MFC starts at TC itself (Tir ¼ TC ). This observation is very significant, because it means
Fig. 3. Temperature variation of the FC (J) and ZFC (K) magnetization of TbPdIn and DyPdIn, in plot of M=H vs. T; measured at different magnetic fields (SI units were used. The unit transformation of M=H can be done as same as that in wac ; see the caption of Fig. 1).
that the irreversible magnetism resulted from the formation of ferromagnetic state. Similar behaviors are also observed for DyPdIn. Note that in a field of 8 103 A/m, MZFC curve of DyPdIn shows a kink at 35 K followed by a broad maximum near TN ¼ 23 K. From the approximate Curie–Weiss behavior at higher temperatures, the effective moment, meff ; and paramagnetic Curie temperature, yP ; are estimated to be 9.73 mB and 60 K for TbPdIn and 10.50 mB and 29 K for DyPdIn, respectively. The meff values are very close to those expected for tripositive Tb and Dy ions (9.72 mB for Tb+3 and 10.63 mB for Dy+3), indicating that the 4f electrons are well localized in the Tb/Dy atoms. The large positive yP values suggest the existence of strong ferromagnetic exchange interaction in these compounds. For the measurement of the isothermal remnant magnetization MðtÞ as a function of time t; the samples were first zero-field cooled from 200 K, much higher than TC ; to 20 K. Then a magnetic field of 8 104 A/m was applied for 5 min and switched off at t ¼ 0: As shown in Fig. 4, the decay of MðtÞ is remarkably slow for both samples: a nonzero MðtÞ could still be detected after 3 h. The observed relaxational results are consistent with a fractional exponential law MðtÞpexp½ðt=tÞ1n (see the solid lines in Fig. 4). The long-time magnetic relaxation behaviors indicate that the ferromagnetic states of TbPdIn and DyPdIn are metastable with many possible configurations.
Fig. 4. Time dependence of the isothermal remanent magnetization MðtÞ=Mð0Þ of TbPdIn and DyPdIn measured at 20 K.
D.X. Li et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 17–24
For both TbPdIn and DyPdIn, the plot of the high-field isothermal magnetization measured at 4.2 K shows ferromagnetic behavior as illustrated in Fig. 5. To make a connection with the neutron diffraction data mentioned in the following, the magnetization scale in Fig. 5 is given in the Bohr magnetons per formula unit. M(HÞ does not saturate up to 2.18 107 A/m. The inset of Fig. 5 shows the low-field results measured at 2 and 5 K for TbPdIn. It may be seen that the magnetization at 5 K is larger than that at 2 K for fields below 5 105 A/m. This feature may be related to magnetic anisotropy of TbPdIn. The temperature dependence of specific heat CðTÞ of TbPdIn and DyPdIn is shown in Fig. 6. A pronounced anomaly is observed near 70 and 36 K for TbPdIn and DyPdIn, respectively, corresponding to the long-range ferromagnetic phase transition. These results agree with the AC and DC susceptibility measurements (Figs. 2 and 3). It is noted that a frequency-dependent peak in w00 is detected at Tf B50 K for TbPdIn and at Tf B13 K for DyPdIn. However, no anomaly is observed at the same temperatures for both CðTÞ curves. Moreover, there is no singularity in CðTÞ curve of DyPdIn around TN ¼ 23 K at which w0 shows a maximum originated from the antiferromagnetic
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Fig. 6. Temperature dependence of the specific heat CðTÞ of TbPdIn and DyPdIn. The inset shows the low-temperature results of the electrical resistivity rðTÞ of TbPdIn and DyPdIn.
correlation. At low temperatures, assuming no CEF effect and neglecting the magnetic specific heat, the C=T vs. T 2 plot yields the g (the specific heat coefficient of T-linear term) values of 35 and 52 mJ (mol R)1 K2 for TbPdIn and DyPdIn, respectively. The relative large g values may be related to the presence of a few stacking faults as described above. Otherwise, the g values of TbPdIn and DyPdIn are evidently smaller than those observed for most of the rare earth or uranium-based spin-glass systems which show larger g values, near or greater than 100 mJ (mol)1 K2 due to the magnetic specific heat is also linear in T (for examples see Refs. [12– 14]). The inset of Fig. 6 shows the low-temperature results of electrical resistivity rðTÞ: A distinct knee in rðTÞ curve at TC for both compounds also characterizes the ferromagnetic ordering. No peak or singularity can be found in rðTÞ at Tf for TbPdIn and DyPdIn or at TN for DyPdIn.
4. Discussion Fig. 5. High-field magnetization MðHÞ up to 2.18 107 A/m of TbPdIn and DyPdIn at 4.2 K. The low-field results of TbPdIn measured at 2 and 5 K are shown in the inset (1(A/ m)=6.9410 106 (mB/Tb) and 6.8795 106 (mB/Dy) for DyPdIn and TbPdIn, respectively).
Metastable magnetic properties, e.g., the difference between field-cooled and zero-field-cooled magnetizations at low temperatures, and long-time magnetic relaxation effect, are usually observed in rare earth or uranium compounds and explained
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as either the formation of spin-glass states [15,16] or the domain-wall pinning effects [17–19]. For TbPdIn and DyPdIn, however, it is evident that there cannot be a simple spin-glass transition (paramagnetic state-spin glass), because a ferromagnetic phase transition from the paramagnetic state occurs at TC : Even for a ‘‘re-entrant spin glass’’ (paramagnetic state-ferromagnetic state-spin glass, also called as ferroglass [20]), to form spin-glass states, one needs two ingredients, i.e., the existences of frustration and randomness [15]. As described in the introduction, TbPdIn and DyPdIn crystallize in the hexagonal ZrNiAltype crystal structure, an ordered derivative of the Fe2P-type structure [21], where all three constituent elements occur at crystallographically nonequivalent positions. This crystal structure is hard to provide bulk randomness of atomic arrangement. On the other hand, the results of our AC susceptibility (peak position is independent of the frequency), specific heat (the g values are evidently smaller than those found for common rare-earth spin glasses) and electrical resistivity (characterized by a relatively small residual resistivity rðT0Þ and strong temperature dependence) measurements are normal for metallic polycrystals, but distinctly strange for metallic spin glasses. These results suggest that the metastable magnetic properties of TbPdIn and DyPdIn cannot be explained on the spin-glass model. Recently, the powder neutron diffraction measurements were preformed by Javorsky et al. [1,10]. Their results reveal that DyPdIn and TbPdIn exhibit ferromagnetic ordering below 31 and 66 K, respectively. For DyPdIn, two different magnetic phases were detected. In the hightemperature one, 15 KoTo31 K; ferromagnetically ordered Dy moments (mF ) were observed along the c-axis. Below 15 K, basal-plane components of Dy moments (mAF ) order antiferromagnetically with the propagation vector k~ ¼ ð12; 0; 12Þ: The magnitudes of the magnetic moments are mF ¼ 7:1ð4Þ mB and mAF ¼ 3:8ð3Þ mB at 1.6 K. The total Dy magnetic moments, given as ~ m ¼~ mF þ ~ m AF ; are canted with each other. For TbPdIn, Tb moments lie within the basal plane and order ferromagnetically below 66 K. Though no antiferromagnetic phase transition is observed, the
reflection pattern measured at 1.5 K shows several additional peaks. Altogether our measurements and the neutron diffraction results prove that the ground state of both compounds is not collinear ferromagnet, but some canted one with antiferromagnetic component. Thus, the ferromagnetic domain in the compounds should be such a region in which the canted spin structure is a combination of the ferromagnetic and antiferromagnetic components with a net magnetization Ms ðT; HÞ: Ms is a function of T and H due to the canted spin structure in the domain, and increases with field at low temperatures. It may be one reason for unsaturated magnetization at 4.2 K even in high fields. The question now arises as to the source of the metastable magnetic properties of TbPdIn and DyPdIn. Although a straightforward answer to this question is not possible at this moment, we point out that the domain-wall pinning effects might be responsible for it. It is known that systems with high magnetic anisotropy have narrow domain walls [18,19]. Domain-wall energy is different when its center coincides with an atomic plan from where it is located between the two planes [22,23]. The energy difference DE between different domain walls hinders the wall motion, leading to domain-wall pinning. Based on this model, the observed magnetic properties on TbPdIn and DyPdIn can be understood as follows: below TC ; two competing effects on the temperature dependence of magnetization come into play. Firstly, the thermal fluctuation in the spin system is reduced with decreasing temperature and thereby MZFC increases. Secondly, the movement of the domain walls also slows down which results in the decrease in MZFC : These two opposite processes give rise to the observed peak in the MZFC curve for TbPdIn and DyPdIn. The FC curves showed in Fig. 3 exhibits a tendency to saturate at low temperatures instead of the maximum, indicating the absence of domain-wall effects. This means that at TC ; even a small field could cause domain wall movements. Note that due to the canted spin structure in the domain, Ms could increase as decreasing T in a constant H; and thus MFC does not saturate at TC : This is clearly different from that in usual collinear ferromagnet where magnetic
D.X. Li et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 17–24
moments inside the domains orient along the same direction and Ms is almost a constant below TC : The observed magnetic relaxation phenomena are a consequence of the metastable magnetic states separated by some potential energy barriers due to the pinning of domain walls. Similar ferromagnetic domains and domain-wall pinning effects may also exist in single-crystal TbPdIn and DyPdIn, because the irreversibility of the temperature dependence of magnetization has been observed in the single-crystalline samples [6]. Note that the metastable magnetic behavior has been found in several uranium and rare-earth based magnetic systems, such as UCu2Ge2, and explained in terms of the intrinsic domain-wall pinning model [11,17–19,23]. It is well known that the domain-wall pinning effects are usually observed in materials with high magnetic anisotropy and large coercive field HC : Our TbPdIn and DyPdIn samples, however, show small values of HC (B4.4 104 and 1.0 104 A/m at 4.2 K for TbPdIn and DyPdIn, respectively). Recently, Joy et al. [24] reported the very similar properties for substituted manganate La0.9Ca0.1MnO3 that shows evident domain-wall pinning effects with a very small HC (B2.0 103 A/m at temperatures much below TC ). They consider that it is indicative of the multidomain ferromagnetic character of the compounds. Isostructural compounds DyNiAl and HoNiAl exist with similar metastable magnetic properties [2,25–26], where AC susceptibility and DC magnetization measurements show two magnetic phases with transition temperatures TC ¼ 31 and 13 K, and TN ¼ 15 and 5 K for DyNiAl and HoNiAl, respectively. Neutron diffraction experiments have also been performed for powder sample of DyNiAl [2] and single-crystalline HoNiAl [26], and confirmed the existence of two magnetic phases for both samples. The canted spin structures in DyNiAl and HoNiAl are combinations of the antiferromagnetically coupled basal-plane components and the c-axis ferromagnetic ones as same as that in DyPdIn. Ehlers and Maletta [2] attributed the metastable magnetic behavior observed for DyNiAl and HoNiAl below TC to domain-wall pinning. While they pointed out that the existence of frustrated magnetic moments, which is induced by the topology and the partially antiferromagnetic
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coupling between nearest neighbors of rare-earth moments, is a common phenomenon in the hexagonal RNiAl series. It is also an interesting physical problem whether similar frustrated magnetic moments exist and contribute to the metastable magnetic behavior in isostructural DyPdIn and TbPdIn. In conclusion, our experimental results of magnetic, transport and thermal properties of polycrystalline TbPdIn and DyPdIn show typical metastable features of ferromagnetic behaviors, which could be explained as domain-wall pining effects. New specific heat and high-field magnetization measurements give further evidence for this. Complex magnetic orders are observed for both samples, in particular, AC susceptibility measurements indicate that the second phase transition in DyPdIn at TN originates from the antiferromagnetic coupling consistent with the neutron diffraction results. However, the present data allow us to make only tentative conclusion. Since the samples used in the present work are small pieces cut from the annealed buttons, we cannot quantitatively discuss the true value of magnetic moment per Tb or Dy atom at ordered states using the magnetization data, due to the preferred orientations of moments in the pieces. For a more detailed interpretation of the observed results, we should also consider the shape effect of the samples and further experimental works on single crystals or fixed isotropic powder samples are necessary.
Acknowledgements We would like to thank Prof. A.V. Andreev and Dr. P. Javorsk"y for helpful discussions. A part of this work was performed at Laboratory for Developmental Research of Advanced Materials, and High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University.
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[2] G. Ehlers, H. Maletta, Z. Phys. B 101 (1996) 317. [3] T. Ito, K. Ohkubo, T. Hirasawa, J. Takeuchi, I. Hiromitsu, M. Kurisu, J. Magn. Magn. Mater. 140–144 (1995) 873. [4] R. Mullmann, . B.D. Mosel, H. Eckert, G. Kotzyba, R. . Pottgen, J. Solid State Chem. 137 (1998) 174. [5] T. Ito, S. Nishigori, I. Hiromitsu, M. Kurisu, J. Magn. Magn. Mater. 177–181 (1998) 1079. [6] S. Nishigori, Y. Hirooka, T. Ito, J. Magn. Magn. Mater. 177–181 (1998) 137. [7] E. Bruck, . M. van Sprang, J.C.P. Klasse, F.R. de Boer, J. Appl. Phys. 63 (1998) 3417. [8] K. Satoh, T. Fujita, Y. Maeno, Y. Uwatoko, H. Fujii, J. Phys. Soc. Japan 59 (1990) 692. [9] S. Cirafici, A. Palenzona, F. Canepa, J. Less-Common Met. 107 (1985) 179. [10] P. Javorsk"y, S. Nishigori, B. Ouladdiaf, Physica B 276–278 (2000) 730. [11] S.B. Roy, A.K. Pradhan, P. Chaddah, Philos. Mag. B 71 (1995) 97. . [12] D.X. Li, Y. Shiokawa, Y. Homma, A. Uesawa, A. Donni, T. Suzuki, Y. Haga, E. Yamamoto, T. Homma, Y. Onuki, Phys. Rev. B 57 (1998) 7434. [13] C. Tien, J.J. Lu, C.S. Wur, Phys. Rev. B 60 (1999) 6692.
[14] C. Tien, L. Luo, Solid State Commun. 107 (1998) 295. [15] J.A. Mydosh, Spin Glass: an experimental introduction, Taylar & Francis, London, 1993. [16] K. Binder, A.P. Young, Rev. Mod. Phys. 58 (1986) 801. [17] W. Zhong, J. Lan, Z. Liu, J. Magn. Magn. Mater. 68 (1987) 197. [18] L.C. Sampaio, S.F. da Cunha, J. Magn. Magn. Mater. 99 (1991) 145. [19] K.M.B. Alves, L.C. Sampaio, A.P. Guimaraes, S.F. da Cunha, J. Alloys Compounds 210 (1994) 325. [20] R.B. Goldfarb, K.V. Rao, H.S. Chen, Solid State Commun. 54 (1985) 799. [21] R. Ferro, R. Marazza, G. Rambaldi, Z. Metall. 65 (1974) 37. [22] J.J. Van den Broeck, H. Zijlstra, IEEE Trans. 7 (1971) 226. [23] T.V.C. Rao, P. Raj, Sk.M. Yusuf, L.M. Rao, A. Sathyamoorthy, V.C. Sahni, Philos. Mag. B 74 (1996) 275. [24] P.A. Joy, S.K. Date, J. Magn. Magn. Mater. 220 (2000) 106. [25] P. Javorsk"y, P. Burlet, E. Ressouche, V. Sechovsk"y, G. Lapertot, J. Magn. Magn. Mater. 159 (1996) 324. [26] P. Javorsk"y, H. Sugaware, D. Rafaja, F. Bourdarot, H. Sato, J. Alloys Compounds 323–324 (2001) 472.
Metastable characteristics in ferromagnetic TbPdIn and DyPdIn D.X. Lia,*, Y. Shiokawaa, T. Nozueb, T. Kamimurab, K. Sumiyamac a
Oarai Branch, Institute for Materials Research, Tohoku University, Oarai-machi, Ibaraki 311-1313, Japan b Department of Physics, Tohoku University, Sendai 980-8578, Japan c Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan Received 30 May 2001; received in revised form 19 September 2001
Abstract Equiatomic ternary compounds, TbPdIn and DyPdIn, have been studied by means of DC magnetization, AC susceptibility, magnetic relaxation, specific heat and electrical resistivity measurements. The two compounds are ferromagnets below a transition temperature TC ¼ 74 K for TbPdIn and TC ¼ 38 K for DyPdIn with metastable magnetic properties, behaving as the irreversibility of the temperature dependence of magnetization below a characteristic temperature Tir and the long-time magnetic relaxation behavior below TC when changing the magnetic field at a constant temperature. DyPdIn shows the second phase transition at TN ¼ 23 K, caused by the antiferromagnetic coupling. For both compounds, the ground state is not a collinear ferromagnet, but some canted one with antiferromagnetic component. The observed metastable magnetic properties are discussed in terms of domainwall pinning model. The complex magnetic structures in DyPdIn and TbPdIn are compared with those of isostructural DyNiAl and HoNiAl. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.30.Cr; 75.60.Ch; 75.60.Es; 72.15.Eb Keywords: Magnetization; Magnetic relaxation; Metastable state; Irreversibility
1. Introduction RPdIn (R=rare-earth elements) compounds belong to a large family of ternary rare-earth alloys with an equiatomic ration. Most members of these materials crystallize in the ZrNiAl-type hexagonal structure, which is an ordered ternary derivative of the Fe2P structure. The lattice shown schematically in Fig. 1 is built up of two types of basal-plane layers with and without rare-earth *Corresponding author. E-mail address: [email protected] (D.X. Li).
atoms, (3R+Pd) and (3In+2Pd), respectively, alternating along the c-axis. The atomic arrangement in these compounds may be described in the p6% 2m space group with following atomic positions [1]: 3R at 3g ðx; 0; 12; 0; x; 12; x; x; 12Þ; 3In at 3f (y; 0; 0; 0; y; 0; y; y; 0); 2Pd at 2c ð13; 23; 0; 23; 13; 0Þ; 1Pd at 1b ð0; 0; 12Þ: The important feature in this structure is that the crystalline electric field (CEF) around the rare-earth ion often induces strong anisotropy due to the distinct layered character of the crystal structure, while within one magnetic layer rare-earth atoms form triangles of nearest neighbors, in the case of antiferromagnetic
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and explained as spin-glass behavior [6]. However, recent neutron diffraction measurements [1,10] indicate the occurrence of long-range ferromagnetic order at TC for both TbPdIn and DyPdIn. These results motivated us to consider if the domain-wall pinning effects could be used to explain the ‘‘spin-glass-like’’ magnetic properties of TbPdIn and DyPdIn, because the ordered crystal structure in both systems is hard to induce sufficient site randomness or bond randomness necessary for a spin glass. We have performed a systematic investigation on the well-annealed polycrystalline TbPdIn and DyPdIn samples by AC susceptibility, DC magnetization, magnetic relaxation, specific heat and electrical resistivity measurements. The results indicate that ferromagnetic TbPdIn and DyPdIn show metastable magnetic ground states with complex magnetic structures. The domain-wall pinning effects may be responsible for the observed irreversible magnetism.
2. Experimental
Fig. 1. Schematic representation of RPdIn (R=rare-earth elements except Eu) crystallizing in the ZrNiAl-type hexagonal structure.
coupling between nearest neighbor frustration of the magnetic interactions could be induced by this topology [2]. In recent years, magnetic properties have been reported for some of RPdIn compounds [3–9]. CePdIn is an antiferromagnetic Kondolattice compound [7,8]. SmPdIn shows a ferromagnetic behavior with strong 4f CEF anisotropy [3]. YbPdIn is a mixed-valent system [9], and EuPdIn that crystallizes in a different structure behaves like an antiferromagnet with weak magnetocrystalline anisotropy [5]. For TbPdIn and DyPdIn, the difference between field cooling (FC) and zero-field cooling (ZFC) magnetization was observed below a characteristic temperature TC
Polycrystalline samples of TbPdIn and DyPdIn were prepared by arc melting high-purity raw metals (Tb and Dy: 3N; Pd: 4N; In: 5N) in a titanium-gettered argon atmosphere. The buttons were flipped and remelted three to four times to ensure homogeneity, and then were annealed at 8001C for 240 h in high vacuum. From the powder X-ray diffraction pattern, the ZrNiAl-type structure was confirmed for both samples with the ( c ¼ 3:842 A ( for lattice parameters a ¼ 7:645 A, ( c ¼ 3:817 A ( for DyPdIn. TbPdIn and a ¼ 7:636 A, The samples used in the experiments are small pieces cut from the annealed buttons. The low field magnetization, AC susceptibility and magnetic relaxation measurements were carried out by a SQUID magnetometer (Quantum Design, MPMS-5P). Using a hybrid magnet, the high-field magnetizations in a steady magnetic field up to 2.18 107 A/m were measured at 4.2 K with an induction method. Electrical resistivity measurements were performed between 1.6 and 300 K using a standard four-terminal DC method. The adiabatic heat pulse method was employed for
D.X. Li et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 17–24
specific heat measurements over the temperature range between 1.7 and 100 K.
3. Results Fig. 2 shows the temperature dependence of AC susceptibility of DyPdIn and TbPdIn measured in an AC field of 80 A/m at the frequency range 0:1pf p1000 Hz. For DyPdIn, the main feature seen in Fig. 2(a) is a two-peak behavior of both the real, w0 ; and the imaginary, w00 ; components of the AC susceptibility. The first peak of both w0 and w00 ; occurring at the same temperature Tm ¼ 36 K, is almost independent of the frequency. This feature gives evidence for long-range ferromagnetic order
Fig. 2. Real, w0 ; and imaginary, w0 ; components of the SI volume AC susceptibility of TbPdIn and DyPdIn in an AC magnetic field of 80 A/m (using the lattice parameters, the unit transformation of wac can be made as 1 emu/g=1.2530 103 and 1.2081 103 (SI) for DyPdIn and TbPdIn, respectively).
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with the Curie temperature TC ¼ 38 K. For convenience, here, TC is defined as the temperature below which w00 appears (in other words, at which w00 falls to zero with increasing T). Note that TC is a little higher than the peak temperature of w0 ðTÞ; and dw0 =dT has a maximum at TC : The second peak of w0 ; at about TN ¼ 23 K, is also independent of the frequency. It is worth noting that w00 does not show evident anomaly at TN ; instead, a frequency-dependent peak is observed around Tf ¼ 13 K (f ¼ 1000 Hz). These characteristics suggest that the second peak in w0 at TN may be due to the antiferromagnetic correlation between Dy moments. For TbPdIn, w0 shows a pronounced maximum near Tm ¼ 68 K, while a kink appears in w00 near this temperature. Tm appears to be much less f dependent. This anomaly may be originated from ferromagnetic transition. The Curie temperature is determined to be TC ¼ 74 K in the way used for DyPdIn. A frequency-dependent peak is also detected around Tf B50 K in w00 similar to that observed for DyPdIn. One likely source for the observed frequency-dependent peak in w00 is the presence of a few stacking faults resulted from the randomly placed impurities or defects. These stacking faults can cause the relative orientation of moments in different Tb/Dy–Pd layers near the stacking faults being randomly parallel or antiparallel, and thus leading to the formation of spinglass like states at low temperatures [11]. However, this effect is so weak that no response could be detected in w0 ðTÞ: The demagnetizing limited value of w0 ; 1=N; is 2.46 for DyPdIn and 3.42 for TbPdIn, where N is the estimated demagnetizing factor. For DyPdIn, we observed the largest w0 value at TN but not near TC : When the sample was rotated at an angle of about 90 degrees in the direction of the AC field, w0 shows the largest value near TC and a small and broad anomaly around TN ; which seems to originate from the preferred orientations of moments in the sample. This is further confirmed by the experimental results measured on a single crystal sample by Nisgigori et al. [6] in spite of the different TC and TN values due to the sample dependence. They reported that w0 of DyPdIn shows the largest value at TC (they define TC as the peak temperature of w0 ) and no any anomaly near TN in the case of H AC jjc-axis.
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Whereas, the largest value of w0 was observed at TN and only slight increase appears at TC ; when the AC magnetic field is applied parallel to the aaxis. The temperature dependence of the DC magnetization, M; of TbPdIn and DyPdIn was measured in both FC and in ZFC modes in several magnetic fields, H: Fig. 3 shows the low-temperature results in plot of M=H vs. T: For TbPdIn, a sharp increase is observed at TC ¼ 74 K for both MZFC and MFC signaling the onset of ferromagnetic ordering. The MFC curve is reversible and independent of the time of the measurement. In contrast, a cusp-like maximum is observed for the low-field MZFC curve just below TC : MZFC is smaller than MFC and time dependent below a characteristic temperature Tir (at which MZFC and MFC bifurcate). It is interesting to note that the characteristic temperature Tir shifts to high temperature side with decreasing H: In fact, for the very low applied fields the deviation between MZFC and MFC starts at TC itself (Tir ¼ TC ). This observation is very significant, because it means
Fig. 3. Temperature variation of the FC (J) and ZFC (K) magnetization of TbPdIn and DyPdIn, in plot of M=H vs. T; measured at different magnetic fields (SI units were used. The unit transformation of M=H can be done as same as that in wac ; see the caption of Fig. 1).
that the irreversible magnetism resulted from the formation of ferromagnetic state. Similar behaviors are also observed for DyPdIn. Note that in a field of 8 103 A/m, MZFC curve of DyPdIn shows a kink at 35 K followed by a broad maximum near TN ¼ 23 K. From the approximate Curie–Weiss behavior at higher temperatures, the effective moment, meff ; and paramagnetic Curie temperature, yP ; are estimated to be 9.73 mB and 60 K for TbPdIn and 10.50 mB and 29 K for DyPdIn, respectively. The meff values are very close to those expected for tripositive Tb and Dy ions (9.72 mB for Tb+3 and 10.63 mB for Dy+3), indicating that the 4f electrons are well localized in the Tb/Dy atoms. The large positive yP values suggest the existence of strong ferromagnetic exchange interaction in these compounds. For the measurement of the isothermal remnant magnetization MðtÞ as a function of time t; the samples were first zero-field cooled from 200 K, much higher than TC ; to 20 K. Then a magnetic field of 8 104 A/m was applied for 5 min and switched off at t ¼ 0: As shown in Fig. 4, the decay of MðtÞ is remarkably slow for both samples: a nonzero MðtÞ could still be detected after 3 h. The observed relaxational results are consistent with a fractional exponential law MðtÞpexp½ðt=tÞ1n (see the solid lines in Fig. 4). The long-time magnetic relaxation behaviors indicate that the ferromagnetic states of TbPdIn and DyPdIn are metastable with many possible configurations.
Fig. 4. Time dependence of the isothermal remanent magnetization MðtÞ=Mð0Þ of TbPdIn and DyPdIn measured at 20 K.
D.X. Li et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 17–24
For both TbPdIn and DyPdIn, the plot of the high-field isothermal magnetization measured at 4.2 K shows ferromagnetic behavior as illustrated in Fig. 5. To make a connection with the neutron diffraction data mentioned in the following, the magnetization scale in Fig. 5 is given in the Bohr magnetons per formula unit. M(HÞ does not saturate up to 2.18 107 A/m. The inset of Fig. 5 shows the low-field results measured at 2 and 5 K for TbPdIn. It may be seen that the magnetization at 5 K is larger than that at 2 K for fields below 5 105 A/m. This feature may be related to magnetic anisotropy of TbPdIn. The temperature dependence of specific heat CðTÞ of TbPdIn and DyPdIn is shown in Fig. 6. A pronounced anomaly is observed near 70 and 36 K for TbPdIn and DyPdIn, respectively, corresponding to the long-range ferromagnetic phase transition. These results agree with the AC and DC susceptibility measurements (Figs. 2 and 3). It is noted that a frequency-dependent peak in w00 is detected at Tf B50 K for TbPdIn and at Tf B13 K for DyPdIn. However, no anomaly is observed at the same temperatures for both CðTÞ curves. Moreover, there is no singularity in CðTÞ curve of DyPdIn around TN ¼ 23 K at which w0 shows a maximum originated from the antiferromagnetic
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Fig. 6. Temperature dependence of the specific heat CðTÞ of TbPdIn and DyPdIn. The inset shows the low-temperature results of the electrical resistivity rðTÞ of TbPdIn and DyPdIn.
correlation. At low temperatures, assuming no CEF effect and neglecting the magnetic specific heat, the C=T vs. T 2 plot yields the g (the specific heat coefficient of T-linear term) values of 35 and 52 mJ (mol R)1 K2 for TbPdIn and DyPdIn, respectively. The relative large g values may be related to the presence of a few stacking faults as described above. Otherwise, the g values of TbPdIn and DyPdIn are evidently smaller than those observed for most of the rare earth or uranium-based spin-glass systems which show larger g values, near or greater than 100 mJ (mol)1 K2 due to the magnetic specific heat is also linear in T (for examples see Refs. [12– 14]). The inset of Fig. 6 shows the low-temperature results of electrical resistivity rðTÞ: A distinct knee in rðTÞ curve at TC for both compounds also characterizes the ferromagnetic ordering. No peak or singularity can be found in rðTÞ at Tf for TbPdIn and DyPdIn or at TN for DyPdIn.
4. Discussion Fig. 5. High-field magnetization MðHÞ up to 2.18 107 A/m of TbPdIn and DyPdIn at 4.2 K. The low-field results of TbPdIn measured at 2 and 5 K are shown in the inset (1(A/ m)=6.9410 106 (mB/Tb) and 6.8795 106 (mB/Dy) for DyPdIn and TbPdIn, respectively).
Metastable magnetic properties, e.g., the difference between field-cooled and zero-field-cooled magnetizations at low temperatures, and long-time magnetic relaxation effect, are usually observed in rare earth or uranium compounds and explained
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as either the formation of spin-glass states [15,16] or the domain-wall pinning effects [17–19]. For TbPdIn and DyPdIn, however, it is evident that there cannot be a simple spin-glass transition (paramagnetic state-spin glass), because a ferromagnetic phase transition from the paramagnetic state occurs at TC : Even for a ‘‘re-entrant spin glass’’ (paramagnetic state-ferromagnetic state-spin glass, also called as ferroglass [20]), to form spin-glass states, one needs two ingredients, i.e., the existences of frustration and randomness [15]. As described in the introduction, TbPdIn and DyPdIn crystallize in the hexagonal ZrNiAltype crystal structure, an ordered derivative of the Fe2P-type structure [21], where all three constituent elements occur at crystallographically nonequivalent positions. This crystal structure is hard to provide bulk randomness of atomic arrangement. On the other hand, the results of our AC susceptibility (peak position is independent of the frequency), specific heat (the g values are evidently smaller than those found for common rare-earth spin glasses) and electrical resistivity (characterized by a relatively small residual resistivity rðT0Þ and strong temperature dependence) measurements are normal for metallic polycrystals, but distinctly strange for metallic spin glasses. These results suggest that the metastable magnetic properties of TbPdIn and DyPdIn cannot be explained on the spin-glass model. Recently, the powder neutron diffraction measurements were preformed by Javorsky et al. [1,10]. Their results reveal that DyPdIn and TbPdIn exhibit ferromagnetic ordering below 31 and 66 K, respectively. For DyPdIn, two different magnetic phases were detected. In the hightemperature one, 15 KoTo31 K; ferromagnetically ordered Dy moments (mF ) were observed along the c-axis. Below 15 K, basal-plane components of Dy moments (mAF ) order antiferromagnetically with the propagation vector k~ ¼ ð12; 0; 12Þ: The magnitudes of the magnetic moments are mF ¼ 7:1ð4Þ mB and mAF ¼ 3:8ð3Þ mB at 1.6 K. The total Dy magnetic moments, given as ~ m ¼~ mF þ ~ m AF ; are canted with each other. For TbPdIn, Tb moments lie within the basal plane and order ferromagnetically below 66 K. Though no antiferromagnetic phase transition is observed, the
reflection pattern measured at 1.5 K shows several additional peaks. Altogether our measurements and the neutron diffraction results prove that the ground state of both compounds is not collinear ferromagnet, but some canted one with antiferromagnetic component. Thus, the ferromagnetic domain in the compounds should be such a region in which the canted spin structure is a combination of the ferromagnetic and antiferromagnetic components with a net magnetization Ms ðT; HÞ: Ms is a function of T and H due to the canted spin structure in the domain, and increases with field at low temperatures. It may be one reason for unsaturated magnetization at 4.2 K even in high fields. The question now arises as to the source of the metastable magnetic properties of TbPdIn and DyPdIn. Although a straightforward answer to this question is not possible at this moment, we point out that the domain-wall pinning effects might be responsible for it. It is known that systems with high magnetic anisotropy have narrow domain walls [18,19]. Domain-wall energy is different when its center coincides with an atomic plan from where it is located between the two planes [22,23]. The energy difference DE between different domain walls hinders the wall motion, leading to domain-wall pinning. Based on this model, the observed magnetic properties on TbPdIn and DyPdIn can be understood as follows: below TC ; two competing effects on the temperature dependence of magnetization come into play. Firstly, the thermal fluctuation in the spin system is reduced with decreasing temperature and thereby MZFC increases. Secondly, the movement of the domain walls also slows down which results in the decrease in MZFC : These two opposite processes give rise to the observed peak in the MZFC curve for TbPdIn and DyPdIn. The FC curves showed in Fig. 3 exhibits a tendency to saturate at low temperatures instead of the maximum, indicating the absence of domain-wall effects. This means that at TC ; even a small field could cause domain wall movements. Note that due to the canted spin structure in the domain, Ms could increase as decreasing T in a constant H; and thus MFC does not saturate at TC : This is clearly different from that in usual collinear ferromagnet where magnetic
D.X. Li et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 17–24
moments inside the domains orient along the same direction and Ms is almost a constant below TC : The observed magnetic relaxation phenomena are a consequence of the metastable magnetic states separated by some potential energy barriers due to the pinning of domain walls. Similar ferromagnetic domains and domain-wall pinning effects may also exist in single-crystal TbPdIn and DyPdIn, because the irreversibility of the temperature dependence of magnetization has been observed in the single-crystalline samples [6]. Note that the metastable magnetic behavior has been found in several uranium and rare-earth based magnetic systems, such as UCu2Ge2, and explained in terms of the intrinsic domain-wall pinning model [11,17–19,23]. It is well known that the domain-wall pinning effects are usually observed in materials with high magnetic anisotropy and large coercive field HC : Our TbPdIn and DyPdIn samples, however, show small values of HC (B4.4 104 and 1.0 104 A/m at 4.2 K for TbPdIn and DyPdIn, respectively). Recently, Joy et al. [24] reported the very similar properties for substituted manganate La0.9Ca0.1MnO3 that shows evident domain-wall pinning effects with a very small HC (B2.0 103 A/m at temperatures much below TC ). They consider that it is indicative of the multidomain ferromagnetic character of the compounds. Isostructural compounds DyNiAl and HoNiAl exist with similar metastable magnetic properties [2,25–26], where AC susceptibility and DC magnetization measurements show two magnetic phases with transition temperatures TC ¼ 31 and 13 K, and TN ¼ 15 and 5 K for DyNiAl and HoNiAl, respectively. Neutron diffraction experiments have also been performed for powder sample of DyNiAl [2] and single-crystalline HoNiAl [26], and confirmed the existence of two magnetic phases for both samples. The canted spin structures in DyNiAl and HoNiAl are combinations of the antiferromagnetically coupled basal-plane components and the c-axis ferromagnetic ones as same as that in DyPdIn. Ehlers and Maletta [2] attributed the metastable magnetic behavior observed for DyNiAl and HoNiAl below TC to domain-wall pinning. While they pointed out that the existence of frustrated magnetic moments, which is induced by the topology and the partially antiferromagnetic
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coupling between nearest neighbors of rare-earth moments, is a common phenomenon in the hexagonal RNiAl series. It is also an interesting physical problem whether similar frustrated magnetic moments exist and contribute to the metastable magnetic behavior in isostructural DyPdIn and TbPdIn. In conclusion, our experimental results of magnetic, transport and thermal properties of polycrystalline TbPdIn and DyPdIn show typical metastable features of ferromagnetic behaviors, which could be explained as domain-wall pining effects. New specific heat and high-field magnetization measurements give further evidence for this. Complex magnetic orders are observed for both samples, in particular, AC susceptibility measurements indicate that the second phase transition in DyPdIn at TN originates from the antiferromagnetic coupling consistent with the neutron diffraction results. However, the present data allow us to make only tentative conclusion. Since the samples used in the present work are small pieces cut from the annealed buttons, we cannot quantitatively discuss the true value of magnetic moment per Tb or Dy atom at ordered states using the magnetization data, due to the preferred orientations of moments in the pieces. For a more detailed interpretation of the observed results, we should also consider the shape effect of the samples and further experimental works on single crystals or fixed isotropic powder samples are necessary.
Acknowledgements We would like to thank Prof. A.V. Andreev and Dr. P. Javorsk"y for helpful discussions. A part of this work was performed at Laboratory for Developmental Research of Advanced Materials, and High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University.
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