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Spin-reorientation transitions in RFe11Mo (R=rare earth and Y) intermetallic compounds
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Journal of Magnetism and Magnetic Materials 313 (2007) 107–110 www.elsevier.com/locate/jmmm
Spin-reorientation transitions in RFe11Mo (R ¼ rare earth and Y) intermetallic compounds Y.C. Wang, Y.G. Xiao, J.Y. Zhang, G.Y. Liu, J.B. Li, G.H. Rao Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China Received 12 August 2006; received in revised form 30 October 2006 Available online 17 December 2006
Abstract A series of RFe11Mo compounds (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) with the ThMn12-type structure have been synthesized. The structural and magnetic properties of the compounds have been investigated by means of X-ray diffraction (XRD) and magnetic measurements. The lattice parameters a, c and the unit-cell volume V of the compounds decrease with decreasing the atomic radius of the rare earth element due to the lanthanide contraction. The spin-reorientation transition (SRT) was investigated in detail. For HoFe11Mo, no SRT was observed. For NdFe11Mo, TbFe11Mo and ErFe11Mo one SRT was observed, while for DyFe11Mo two SRTs were observed. By minimizing the magnetocrystalline anisotropy energy, theoretical SR temperatures of the compounds are derived, which show a reasonable agreement with the experimental values. r 2007 Elsevier B.V. All rights reserved. PACS: 75.50.y; 75.30.Kz; 75.10.Dg; 75.30.Gw Keywords: Rare-earth transition-metal compound; Magnetocrystalline anisotropy; Spin-reorientation transition; RFe11Mo compounds
1. Introduction Among the rare-earth (R)-transition-metal (T) intermetallic compounds, the R(Fe,M)12 (M ¼ transition metal or metalloids) compounds have been widely investigated during the past decades since some of the R(Fe,M)12 compounds exhibit various magnetic structures and magnetic anomalies, e.g., first-order magnetization process (FOMP), spin-glass-like transition, spin-reorientation transition (SRT) and magnetohistory effects [1–11]. These compounds crystallize in the tetragonal ThMn12-structure with space group I4/mmm. The binary RFe12 compounds are unstable and the third element M is needed to stabilize the crystal structure. In R(Fe,M)12 compounds, the Fe-sublattice has been found to exhibit a strong uniaxial anisotropy, while for the rare earth R with negative second-order Stevens factor aJ the R-sublattice shows a planar anisotropy [12]. The contribution of the R-sublattice to the magnetocrystalline Corresponding author. Tel.: +86 10 82648089.
E-mail address: [email protected] (G.H. Rao). 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.12.011
anisotropy of the compounds generally dominates at low temperature, whereas that of the Fe-sublattice anisotropy at high temperature. With increasing temperature, the Rsublattice anisotropy usually decreases much faster than the Fe-sublattice anisotropy. Therefore, a temperaturedriven SRT could be expected to occur in R(Fe, M)12 compounds due to the competition between the anisotropies of the R- and Fe-sublattices [12–14]. The R-sublattice contribution to the magnetic anisotropy energy can be described within the framework of the single-ion crystal-electric-field (CEF) model and the CEF parameters can be determined by fitting different experimental results to the CEF model. Hu et al. [15] have derived a set of five CEF parameters for the Dy3+ ion from the analysis of magnetization data of a DyFe11Ti single crystal. By assuming that the CEF coefficients Amn in an isostructural series were approximately constant, the CEF parameters Bmn for other R3+ were obtained by scaling with appropriate atomic parameters. Using the estimated Bnm(R3+) and by minimizing the magnetocrystalline anisotropy energy, theoretical SR temperature of other R(Fe, M)12 (M ¼ Ti, V, Nb and Si) compounds was
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derived from the temperature dependence of the tilting angle y between the magnetization and the c-axis. The SR temperatures obtained were in reasonable agreement with experimental observations. Recently, we reported the magnetic phase diagram of mixed rare-earth Nd1xTbxFe10.5Mo1.5 compounds and the change of easy-magnetization direction (EMD) of the compounds from easy cone, via an easy-plane range, to easy-axis with increasing temperature for x ¼ 0.2–0.8 [16]. In Ref. [17], we reported the variation of the SRT with nonmagnetic element Y concentration in Tb1xYxFe11Mo compounds. As a systematic research on the spin reorientation of R(Fe,Mo)12 compounds, in this paper we investigate the SRT of the RFe11Mo series in detail with R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er. 2. Experiment Polycrystalline samples of RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) were prepared by arc melting appropriate amounts of the pure metals under high-purity Ar atmosphere. An excess amount of R was added to compensate for the loss during melting and annealing. All the ingots were remelted at least four times to ensure homogeneity. The obtained ingots were wrapped in Ta foil, sealed into evacuated quartz tubes, annealed at 1373 K for 2 weeks, and then quenched in water. The samples were examined by means of X-ray powder diffraction (XRD) and thermo-magnetic analysis. The XRD data were collected on a Rigaku D/max-2500 diffractometer with Cu Ka radiation and a graphite monochromator. The temperature dependence of the magnetization of the samples was measured in a low field (0.05 T) with a superconducting quantum interference device (SQUID) magnetometer in the temperature range from 5 to 350 K and with a vibrating-sample magnetometer (VSM) from room temperature to above the Curie temperature. 3. Results and discussion XRD patterns of RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) compounds (Fig. 1) show that all the samples are single phase, crystallizing in the tetragonal ThMn12type structure with the space group I4/mmm, except for a very small amount of Fe phase in HoFe11Mo compound. The lattice parameters a, c and unit-cell volume V derived from the Rietveld refinement of the XRD pattern are listed in Table 1. The a, c and V decrease almost linearly with decreasing atomic radius of the rare earth element due to the lanthanide contraction, as shown in Fig. 2. From Nd to Er, the relative contraction of the c-axis (0.2%) is much smaller than that of the a-axis (1.2%). For YFe11Mo compounds, yttrium seems to exhibit a metallic radius between those of terbium and dysprosium, as observed in other yttrium-transition-metal intermetallic compounds with the CaCu5-type derivative structures [18]. Both the
Fig. 1. X-ray diffraction patterns of RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) compounds.
XRD pattern and the observed lanthanide contraction indicate the single-phase character of the synthesized light rare-earth compound NdFe11Mo, which used to be prepared by some special processes [19]. As shown below, the Curie temperature of NdFe11Mo is in excellent agreement with the report of Endoh et al. [19]. The temperature dependence of magnetization of RFe11Mo compounds was measured during warming under 0.05 T after cooling down from room temperature in the applied field (FC). The magnetization curves for RFe11Mo compounds are illustrated in Fig. 3. The curves exhibit some distinct peaks. These peaks correspond to the spin reorientation with increasing temperature. For DyFe11Mo, the FC M–T curve exhibits two anomalies in the investigated temperature range, which are associated with the change of the easy magnetization direction from easy plane, via an easy-cone range, to easy axis with increasing temperature [11,12]. Based on the thermo-magnetic measurements, the magnetic phase transition temperatures of the compounds, including the Curie temperature TC and the spin-reorientation temperature TSR, are determined and listed in Table 1. TC is obtained by plotting the M2–T curves and extrapolating M2 to zero. The spin- reorientation temperature TSR is determined from the peak on the FC M–T curve. The Curie temperature TC reaches a maximum value for R ¼ Gd. As shown in the inset of Fig. 3, for the heavy rare earth (Gd, Tb, Dy, Ho, Er) the TC increases linearly with the square-root of the de Gennes factor (equivalent to
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Table 1 Lattice parameters a, c, V, the Curie temperature TC, the experimental and calculated spin-reorientation temperatures TSR (exp) and TSR (cal) for RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) compounds R
Y
Nd
Gd
Tb
Dy
Ho
Er
a (A˚) c (A˚) V (A˚3) TC (K) TSR (exp)(K) TSR (cal)(K)
8.5174 (5) 4.7799 (3) 346.761 (5) 484 — —
8.5863 (2) 4.7814 (1) 352.512 (2) 499 178 232
8.5399 (1) 4.7822 (1) 348.759 (7) 542 — —
8.5265 (4) 4.7798 (3) 347.43 (4) 508 460 310
8.5077 (2) 4.7743 (1) 345.569 (2) 482 193, 244 184, 318
8.4976 (3) 4.7717 (2) 344.563 (3) 467 — —
8.4875 (2) 4.7706 (1) 343.667 (2) 456 40 109
Fig. 2. The lattice parameters a, c and the unit-cell volume V of RFe11Mo as functions of the atomic radius of R.
Fig. 4. Calculated canting angle (y) between magnetization and c-axis as a function of temperature for RFe11Mo compounds (R ¼ Nd, Gd, Tb, Dy, Ho and Er).
the calculation were described in our previous papers [16,17]. In present calculation, the temperature dependence of the anisotropy constant for the Fe-sublattice was derived from the magnetization data of the magnetically prealigned YFe11Mo powder [17]. The CEF parameters Bmn for Dy3+ derived from magnetization data of single-crystal DyFe11Ti by Hu et al. [15] were used and the Bmn for other R3+ were estimated according to the relation [20,21]: Bmn ðr3þ Þ ¼
Fig. 3. Temperature dependence of the magnetization of the RFe11Mo compounds at a low field of 0.05 T. The inset shows the dependence of the Curie temperature on the square-root of the de Gennes factor of R.
the effective spin of the rare earth ion), indicative of the consequence of the R–T exchange interaction. The temperature dependence of angle between the EMD and the c-axis for the RFe11Mo (R ¼ Nd, Tb, Dy, Er, Ho) compounds are calculated based on the single-ion CEF model and shown in Fig. 4. The calculated TSR is also listed in Table 1 and shows a reasonable agreement with that determined from magnetization measurements. Details of
ym hrm iðR3þ Þ Bmn ðDy3þ Þ, ym hrm iðDy3þ Þ
(1)
where ym is the Stevens coefficient (y2 ¼ aJ, y4 ¼ bJ, y6 ¼ gJ) and /rmS is the expectation value over the 4f shell. As showed in Fig. 4, the EMD of NdFe11Mo is easy cone below TSR and changes to easy axis with increasing temperature. The DyFe11Mo exhibit two SRTs, i.e. the EMD changes from easy plane, via an easy-cone range, to easy axis with increasing temperature, in consistent with magnetization measurements. For TbFe11Mo, the EMD changes from easy plane to easy axis with increasing temperature. However, the calculated TSR is about 150 K lower than the experimental one (Table 1). This discrepancy might result from the approximation nature of Eq. (1) when deriving the Bmn for Tb3+ from those for Dy3+. Reasonable agreement between the calculated and observed TSR could be achieved by using
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the Bmn for Tb derived from single-crystal TbFe11Ti by Wang et al. [17,22]. For HoFe11Mo, Fig. 4 shows that no SRT is anticipated, in consistent with the low-field magnetization measurement. Although the second- fourth- and sixth-order Stevens coefficients are all negative (aJo0, bJo0, gJo0), the EMD of HoFe11Mo is easy axis, indicating that the easy-axis anisotropy of the Fe-sublattice predominates and retards the tendency towards a SRT arising from the Hosublattice in the investigated temperature range. In fact, a SRT was observed in HoFe10Mo2 [13], probably due to the weakening of the Fe-sublattice anisotropy by the increased substitution of Mo for Fe. For ErFe11Mo, the second-order Steven coefficient of the Er3+ ion is positive (aJ40). Thus, both the Fe sublattice and the contribution of the second-order CEF favor an easy-axis EMD. The coned EMD of ErFe11Mo at low temperature seems arising from the contribution of higher order CEF terms, e.g., the fourth- or/and sixth-order Bmn. Therefore, the present calculation essentially gives correct order of the TSR, i.e., TSR (Tb)4TSR (Dy)4TSR (Nd)4TSR (Er), and reveals the character of the observed SRT in RFe11Mo compounds. However, the calculated TSRsare 54 K–74 K higher than the experimentally derived ones, except for the TbFe11Mo, for which the calculated TSR is 150 K lower than the experimental one. The CEF parameters Bmn for different R derived from those of the DyFe11Ti by Eq. (1) are in fact the same as those used for RFe11Ti. It is not a surprise that the temperature dependence of the tilting angle for RFe11Mo (Fig. 4) mimics that for RFe11Ti reported in Refs. [23,24], including the absence of any SRT in Ho counterpart, the occurrence of a SRT in Er counterpart and the discrepancy of the TSR between calculation and experiment for the Tb counterpart. Nevertheless, the calculated TSR of the RFe11Mo is obviously different from that of the RFe11Ti counterpart, owing to the use of the anisotropy constant KFe(T) derived from YFe11Mo [17] in our calculation and indicating the significant contribution of the KFe(T) to and the competition nature of the spin reorientation. In principle, Eq. (1) is valid exclusively under the assumption that the crystal-field coefficients Amn( ¼ Bmn/ymorm4) are independent of the rare earth and only determined by the crystallographic structure [23]. But the electronic influence on the Amn from the Fe-sublattice, which varies with M and its amount, cannot be neglected, as evidenced by the discrepancy between the calculated and experimental TSR for the DyFe11Mo in this work. The agreement between the calculated and experimental TSR of RFe11Mo is expected to be improved if the CEF parameters for one of the RFe11Mo were available. 4. Conclusion In present work, single-phase RFe11Mo compounds with the ThMn12-type structure are synthesized. The structural and magnetic properties, especially the magnetocrystalline
anisotropy of compounds, are studied by means of XRD and thermomagnetic measurements. The lattice parameters a, c and the unit-cell volume V decrease with the decrease of the atomic radius of the rare earth element. The spinreorientation temperatures of compounds are determined by thermomagnetic measurements. Theoretical calculations of the canting angle y vs. T curves have been performed, which reveals the nature of the observed SRT and shows a reasonable agreement with the experimental observations. Acknowledgments The work is supported by the National Natural Science Foundation of China (Grant no. 50371100) and the State Key Project of Fundamental Research (Grant no. 2006CB601101). References [1] M. Soizi, L. Pareti, O. Moze, W.L.F. David, J. Appl. Phys. 64 (1988) 15. [2] K.H.J. Buschow, J. Magn. Magn. Mater. 100 (1991) 79. [3] L.C.C.M. Nagamine, H.R. Rechenberg, P.A. Algarabel, M.R. Ibarra, J. Magn. Magn. Mater. 157/158 (1996) 11. [4] R. Vert, D. Fruchart, D. Gignoux, J. Magn. Magn. Mater. 242–245 (2002) 820. [5] K. Yu. Guslienko, X.C. Kou, R. Gro¨ssinger, J. Magn. Magn. Mater. 150 (1995) 383. [6] R. Lorenz, J. Hafiner, S.S. Jaswal, D.J. Sellmyer, Phys. Rev. Lett. 74 (1995) 3688. [7] H.-S. Li, Q.-z. Yang, Y.-z. Qiao, J. Magn. Magn. Mater. 208 (2000) 188. [8] C. Christides, A. Kostikas, G. Zouganelis, V. Psyharis, X.C. Kou, R. Gro¨ssinger, Phys. Rev. B 47 (1993) 11220. [9] C. Christides, A. Kostikas, X.C. Kou, R. Gro¨ssinger, J. Phys.: Condens. Matter 5 (1993) 8611. [10] Y.Z. Wang, B.P. Hu, G.C. Liu, J.H. Hu, L. Son, K.Y. Wang, W.Y. Lai, J. Appl. Phys. 76 (1994) 6383. [11] C.P. Yang, Y.Z. Wang, Y.Z. Wang, B.P. Hu, Z.X. Wang, J. Phys.: Condens. Matter 10 (1998) 4177. [12] J.M. Le Breton, N.H. Duc, V.T. Hien, N.P. Thuy, J. Teillet, J. Magn. Magn. Mater. 262 (2003) 452. [13] C. Christides, D. Niarchos, A. Kostikas, H.S. Li, B.P. Hu, J.M.D. Coey, Solid State Commun. 72 (1989) 839. [14] C.P. Yang, Y.Z. Wang, B.P. Hu, J.L. Wang, Z.X. Wang, Z.L. Jiang, C.L. Ma, J. Zhu, J. Alloys Compds. 290 (1999) 144. [15] B.P. Hu, H.S. Li, J.M.D. Coey, J.P. Gavigan, Phys. Rev. B 41 (1990) 2221. [16] Y.G. Xiao, G.H. Rao, Q. Zhang, Y. Zhang, G.Y. Liu, J.K. Liang, J. Magn. Magn. Mater. 302 (2006) 467. [17] Y.G. Xiao, G.H. Rao, Q. Zhang, Y. Zhang, G.Y. Liu, J.K. Liang, J. Phys. D. 39 (2006) 615. [18] K.H.J. Buschow, J. Less-Common Met. 11 (1966) 204. [19] M. Endoh, K. Nakamura, H. Mikami, IEEE Trans. Magn. 28 (1992) 2560. [20] J.M.D. Coey, J. Magn. Magn. Mater. 80 (1989) 9. [21] M. Yamada, H. Yamamoto, Y. Nakagawa, Phys. Rev. B 38 (1988) 620. [22] J.L. Wang, B. Garcı´ a-Landa, C. Marquina, M.R. Ibarra, F.M. Yang, G.H. Wu, Phys. Rev. B 67 (2003) 014417. [23] H.S. Li, J.M.D. Coey, In: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, vol. 6, North-Holland, Amsterdam, 1991, pp. 1–83. [24] B.P. Hu, Ph.D. Thesis, The University of Dublin, 1990.
Journal of Magnetism and Magnetic Materials 313 (2007) 107–110 www.elsevier.com/locate/jmmm
Spin-reorientation transitions in RFe11Mo (R ¼ rare earth and Y) intermetallic compounds Y.C. Wang, Y.G. Xiao, J.Y. Zhang, G.Y. Liu, J.B. Li, G.H. Rao Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China Received 12 August 2006; received in revised form 30 October 2006 Available online 17 December 2006
Abstract A series of RFe11Mo compounds (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) with the ThMn12-type structure have been synthesized. The structural and magnetic properties of the compounds have been investigated by means of X-ray diffraction (XRD) and magnetic measurements. The lattice parameters a, c and the unit-cell volume V of the compounds decrease with decreasing the atomic radius of the rare earth element due to the lanthanide contraction. The spin-reorientation transition (SRT) was investigated in detail. For HoFe11Mo, no SRT was observed. For NdFe11Mo, TbFe11Mo and ErFe11Mo one SRT was observed, while for DyFe11Mo two SRTs were observed. By minimizing the magnetocrystalline anisotropy energy, theoretical SR temperatures of the compounds are derived, which show a reasonable agreement with the experimental values. r 2007 Elsevier B.V. All rights reserved. PACS: 75.50.y; 75.30.Kz; 75.10.Dg; 75.30.Gw Keywords: Rare-earth transition-metal compound; Magnetocrystalline anisotropy; Spin-reorientation transition; RFe11Mo compounds
1. Introduction Among the rare-earth (R)-transition-metal (T) intermetallic compounds, the R(Fe,M)12 (M ¼ transition metal or metalloids) compounds have been widely investigated during the past decades since some of the R(Fe,M)12 compounds exhibit various magnetic structures and magnetic anomalies, e.g., first-order magnetization process (FOMP), spin-glass-like transition, spin-reorientation transition (SRT) and magnetohistory effects [1–11]. These compounds crystallize in the tetragonal ThMn12-structure with space group I4/mmm. The binary RFe12 compounds are unstable and the third element M is needed to stabilize the crystal structure. In R(Fe,M)12 compounds, the Fe-sublattice has been found to exhibit a strong uniaxial anisotropy, while for the rare earth R with negative second-order Stevens factor aJ the R-sublattice shows a planar anisotropy [12]. The contribution of the R-sublattice to the magnetocrystalline Corresponding author. Tel.: +86 10 82648089.
E-mail address: [email protected] (G.H. Rao). 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.12.011
anisotropy of the compounds generally dominates at low temperature, whereas that of the Fe-sublattice anisotropy at high temperature. With increasing temperature, the Rsublattice anisotropy usually decreases much faster than the Fe-sublattice anisotropy. Therefore, a temperaturedriven SRT could be expected to occur in R(Fe, M)12 compounds due to the competition between the anisotropies of the R- and Fe-sublattices [12–14]. The R-sublattice contribution to the magnetic anisotropy energy can be described within the framework of the single-ion crystal-electric-field (CEF) model and the CEF parameters can be determined by fitting different experimental results to the CEF model. Hu et al. [15] have derived a set of five CEF parameters for the Dy3+ ion from the analysis of magnetization data of a DyFe11Ti single crystal. By assuming that the CEF coefficients Amn in an isostructural series were approximately constant, the CEF parameters Bmn for other R3+ were obtained by scaling with appropriate atomic parameters. Using the estimated Bnm(R3+) and by minimizing the magnetocrystalline anisotropy energy, theoretical SR temperature of other R(Fe, M)12 (M ¼ Ti, V, Nb and Si) compounds was
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derived from the temperature dependence of the tilting angle y between the magnetization and the c-axis. The SR temperatures obtained were in reasonable agreement with experimental observations. Recently, we reported the magnetic phase diagram of mixed rare-earth Nd1xTbxFe10.5Mo1.5 compounds and the change of easy-magnetization direction (EMD) of the compounds from easy cone, via an easy-plane range, to easy-axis with increasing temperature for x ¼ 0.2–0.8 [16]. In Ref. [17], we reported the variation of the SRT with nonmagnetic element Y concentration in Tb1xYxFe11Mo compounds. As a systematic research on the spin reorientation of R(Fe,Mo)12 compounds, in this paper we investigate the SRT of the RFe11Mo series in detail with R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er. 2. Experiment Polycrystalline samples of RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) were prepared by arc melting appropriate amounts of the pure metals under high-purity Ar atmosphere. An excess amount of R was added to compensate for the loss during melting and annealing. All the ingots were remelted at least four times to ensure homogeneity. The obtained ingots were wrapped in Ta foil, sealed into evacuated quartz tubes, annealed at 1373 K for 2 weeks, and then quenched in water. The samples were examined by means of X-ray powder diffraction (XRD) and thermo-magnetic analysis. The XRD data were collected on a Rigaku D/max-2500 diffractometer with Cu Ka radiation and a graphite monochromator. The temperature dependence of the magnetization of the samples was measured in a low field (0.05 T) with a superconducting quantum interference device (SQUID) magnetometer in the temperature range from 5 to 350 K and with a vibrating-sample magnetometer (VSM) from room temperature to above the Curie temperature. 3. Results and discussion XRD patterns of RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) compounds (Fig. 1) show that all the samples are single phase, crystallizing in the tetragonal ThMn12type structure with the space group I4/mmm, except for a very small amount of Fe phase in HoFe11Mo compound. The lattice parameters a, c and unit-cell volume V derived from the Rietveld refinement of the XRD pattern are listed in Table 1. The a, c and V decrease almost linearly with decreasing atomic radius of the rare earth element due to the lanthanide contraction, as shown in Fig. 2. From Nd to Er, the relative contraction of the c-axis (0.2%) is much smaller than that of the a-axis (1.2%). For YFe11Mo compounds, yttrium seems to exhibit a metallic radius between those of terbium and dysprosium, as observed in other yttrium-transition-metal intermetallic compounds with the CaCu5-type derivative structures [18]. Both the
Fig. 1. X-ray diffraction patterns of RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) compounds.
XRD pattern and the observed lanthanide contraction indicate the single-phase character of the synthesized light rare-earth compound NdFe11Mo, which used to be prepared by some special processes [19]. As shown below, the Curie temperature of NdFe11Mo is in excellent agreement with the report of Endoh et al. [19]. The temperature dependence of magnetization of RFe11Mo compounds was measured during warming under 0.05 T after cooling down from room temperature in the applied field (FC). The magnetization curves for RFe11Mo compounds are illustrated in Fig. 3. The curves exhibit some distinct peaks. These peaks correspond to the spin reorientation with increasing temperature. For DyFe11Mo, the FC M–T curve exhibits two anomalies in the investigated temperature range, which are associated with the change of the easy magnetization direction from easy plane, via an easy-cone range, to easy axis with increasing temperature [11,12]. Based on the thermo-magnetic measurements, the magnetic phase transition temperatures of the compounds, including the Curie temperature TC and the spin-reorientation temperature TSR, are determined and listed in Table 1. TC is obtained by plotting the M2–T curves and extrapolating M2 to zero. The spin- reorientation temperature TSR is determined from the peak on the FC M–T curve. The Curie temperature TC reaches a maximum value for R ¼ Gd. As shown in the inset of Fig. 3, for the heavy rare earth (Gd, Tb, Dy, Ho, Er) the TC increases linearly with the square-root of the de Gennes factor (equivalent to
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Table 1 Lattice parameters a, c, V, the Curie temperature TC, the experimental and calculated spin-reorientation temperatures TSR (exp) and TSR (cal) for RFe11Mo (R ¼ Y, Nd, Gd, Tb, Dy, Ho and Er) compounds R
Y
Nd
Gd
Tb
Dy
Ho
Er
a (A˚) c (A˚) V (A˚3) TC (K) TSR (exp)(K) TSR (cal)(K)
8.5174 (5) 4.7799 (3) 346.761 (5) 484 — —
8.5863 (2) 4.7814 (1) 352.512 (2) 499 178 232
8.5399 (1) 4.7822 (1) 348.759 (7) 542 — —
8.5265 (4) 4.7798 (3) 347.43 (4) 508 460 310
8.5077 (2) 4.7743 (1) 345.569 (2) 482 193, 244 184, 318
8.4976 (3) 4.7717 (2) 344.563 (3) 467 — —
8.4875 (2) 4.7706 (1) 343.667 (2) 456 40 109
Fig. 2. The lattice parameters a, c and the unit-cell volume V of RFe11Mo as functions of the atomic radius of R.
Fig. 4. Calculated canting angle (y) between magnetization and c-axis as a function of temperature for RFe11Mo compounds (R ¼ Nd, Gd, Tb, Dy, Ho and Er).
the calculation were described in our previous papers [16,17]. In present calculation, the temperature dependence of the anisotropy constant for the Fe-sublattice was derived from the magnetization data of the magnetically prealigned YFe11Mo powder [17]. The CEF parameters Bmn for Dy3+ derived from magnetization data of single-crystal DyFe11Ti by Hu et al. [15] were used and the Bmn for other R3+ were estimated according to the relation [20,21]: Bmn ðr3þ Þ ¼
Fig. 3. Temperature dependence of the magnetization of the RFe11Mo compounds at a low field of 0.05 T. The inset shows the dependence of the Curie temperature on the square-root of the de Gennes factor of R.
the effective spin of the rare earth ion), indicative of the consequence of the R–T exchange interaction. The temperature dependence of angle between the EMD and the c-axis for the RFe11Mo (R ¼ Nd, Tb, Dy, Er, Ho) compounds are calculated based on the single-ion CEF model and shown in Fig. 4. The calculated TSR is also listed in Table 1 and shows a reasonable agreement with that determined from magnetization measurements. Details of
ym hrm iðR3þ Þ Bmn ðDy3þ Þ, ym hrm iðDy3þ Þ
(1)
where ym is the Stevens coefficient (y2 ¼ aJ, y4 ¼ bJ, y6 ¼ gJ) and /rmS is the expectation value over the 4f shell. As showed in Fig. 4, the EMD of NdFe11Mo is easy cone below TSR and changes to easy axis with increasing temperature. The DyFe11Mo exhibit two SRTs, i.e. the EMD changes from easy plane, via an easy-cone range, to easy axis with increasing temperature, in consistent with magnetization measurements. For TbFe11Mo, the EMD changes from easy plane to easy axis with increasing temperature. However, the calculated TSR is about 150 K lower than the experimental one (Table 1). This discrepancy might result from the approximation nature of Eq. (1) when deriving the Bmn for Tb3+ from those for Dy3+. Reasonable agreement between the calculated and observed TSR could be achieved by using
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the Bmn for Tb derived from single-crystal TbFe11Ti by Wang et al. [17,22]. For HoFe11Mo, Fig. 4 shows that no SRT is anticipated, in consistent with the low-field magnetization measurement. Although the second- fourth- and sixth-order Stevens coefficients are all negative (aJo0, bJo0, gJo0), the EMD of HoFe11Mo is easy axis, indicating that the easy-axis anisotropy of the Fe-sublattice predominates and retards the tendency towards a SRT arising from the Hosublattice in the investigated temperature range. In fact, a SRT was observed in HoFe10Mo2 [13], probably due to the weakening of the Fe-sublattice anisotropy by the increased substitution of Mo for Fe. For ErFe11Mo, the second-order Steven coefficient of the Er3+ ion is positive (aJ40). Thus, both the Fe sublattice and the contribution of the second-order CEF favor an easy-axis EMD. The coned EMD of ErFe11Mo at low temperature seems arising from the contribution of higher order CEF terms, e.g., the fourth- or/and sixth-order Bmn. Therefore, the present calculation essentially gives correct order of the TSR, i.e., TSR (Tb)4TSR (Dy)4TSR (Nd)4TSR (Er), and reveals the character of the observed SRT in RFe11Mo compounds. However, the calculated TSRsare 54 K–74 K higher than the experimentally derived ones, except for the TbFe11Mo, for which the calculated TSR is 150 K lower than the experimental one. The CEF parameters Bmn for different R derived from those of the DyFe11Ti by Eq. (1) are in fact the same as those used for RFe11Ti. It is not a surprise that the temperature dependence of the tilting angle for RFe11Mo (Fig. 4) mimics that for RFe11Ti reported in Refs. [23,24], including the absence of any SRT in Ho counterpart, the occurrence of a SRT in Er counterpart and the discrepancy of the TSR between calculation and experiment for the Tb counterpart. Nevertheless, the calculated TSR of the RFe11Mo is obviously different from that of the RFe11Ti counterpart, owing to the use of the anisotropy constant KFe(T) derived from YFe11Mo [17] in our calculation and indicating the significant contribution of the KFe(T) to and the competition nature of the spin reorientation. In principle, Eq. (1) is valid exclusively under the assumption that the crystal-field coefficients Amn( ¼ Bmn/ymorm4) are independent of the rare earth and only determined by the crystallographic structure [23]. But the electronic influence on the Amn from the Fe-sublattice, which varies with M and its amount, cannot be neglected, as evidenced by the discrepancy between the calculated and experimental TSR for the DyFe11Mo in this work. The agreement between the calculated and experimental TSR of RFe11Mo is expected to be improved if the CEF parameters for one of the RFe11Mo were available. 4. Conclusion In present work, single-phase RFe11Mo compounds with the ThMn12-type structure are synthesized. The structural and magnetic properties, especially the magnetocrystalline
anisotropy of compounds, are studied by means of XRD and thermomagnetic measurements. The lattice parameters a, c and the unit-cell volume V decrease with the decrease of the atomic radius of the rare earth element. The spinreorientation temperatures of compounds are determined by thermomagnetic measurements. Theoretical calculations of the canting angle y vs. T curves have been performed, which reveals the nature of the observed SRT and shows a reasonable agreement with the experimental observations. Acknowledgments The work is supported by the National Natural Science Foundation of China (Grant no. 50371100) and the State Key Project of Fundamental Research (Grant no. 2006CB601101). References [1] M. Soizi, L. Pareti, O. Moze, W.L.F. David, J. Appl. Phys. 64 (1988) 15. [2] K.H.J. Buschow, J. Magn. Magn. Mater. 100 (1991) 79. [3] L.C.C.M. Nagamine, H.R. Rechenberg, P.A. Algarabel, M.R. Ibarra, J. Magn. Magn. Mater. 157/158 (1996) 11. [4] R. Vert, D. Fruchart, D. Gignoux, J. Magn. Magn. Mater. 242–245 (2002) 820. [5] K. Yu. Guslienko, X.C. Kou, R. Gro¨ssinger, J. Magn. Magn. Mater. 150 (1995) 383. [6] R. Lorenz, J. Hafiner, S.S. Jaswal, D.J. Sellmyer, Phys. Rev. Lett. 74 (1995) 3688. [7] H.-S. Li, Q.-z. Yang, Y.-z. Qiao, J. Magn. Magn. Mater. 208 (2000) 188. [8] C. Christides, A. Kostikas, G. Zouganelis, V. Psyharis, X.C. Kou, R. Gro¨ssinger, Phys. Rev. B 47 (1993) 11220. [9] C. Christides, A. Kostikas, X.C. Kou, R. Gro¨ssinger, J. Phys.: Condens. Matter 5 (1993) 8611. [10] Y.Z. Wang, B.P. Hu, G.C. Liu, J.H. Hu, L. Son, K.Y. Wang, W.Y. Lai, J. Appl. Phys. 76 (1994) 6383. [11] C.P. Yang, Y.Z. Wang, Y.Z. Wang, B.P. Hu, Z.X. Wang, J. Phys.: Condens. Matter 10 (1998) 4177. [12] J.M. Le Breton, N.H. Duc, V.T. Hien, N.P. Thuy, J. Teillet, J. Magn. Magn. Mater. 262 (2003) 452. [13] C. Christides, D. Niarchos, A. Kostikas, H.S. Li, B.P. Hu, J.M.D. Coey, Solid State Commun. 72 (1989) 839. [14] C.P. Yang, Y.Z. Wang, B.P. Hu, J.L. Wang, Z.X. Wang, Z.L. Jiang, C.L. Ma, J. Zhu, J. Alloys Compds. 290 (1999) 144. [15] B.P. Hu, H.S. Li, J.M.D. Coey, J.P. Gavigan, Phys. Rev. B 41 (1990) 2221. [16] Y.G. Xiao, G.H. Rao, Q. Zhang, Y. Zhang, G.Y. Liu, J.K. Liang, J. Magn. Magn. Mater. 302 (2006) 467. [17] Y.G. Xiao, G.H. Rao, Q. Zhang, Y. Zhang, G.Y. Liu, J.K. Liang, J. Phys. D. 39 (2006) 615. [18] K.H.J. Buschow, J. Less-Common Met. 11 (1966) 204. [19] M. Endoh, K. Nakamura, H. Mikami, IEEE Trans. Magn. 28 (1992) 2560. [20] J.M.D. Coey, J. Magn. Magn. Mater. 80 (1989) 9. [21] M. Yamada, H. Yamamoto, Y. Nakagawa, Phys. Rev. B 38 (1988) 620. [22] J.L. Wang, B. Garcı´ a-Landa, C. Marquina, M.R. Ibarra, F.M. Yang, G.H. Wu, Phys. Rev. B 67 (2003) 014417. [23] H.S. Li, J.M.D. Coey, In: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, vol. 6, North-Holland, Amsterdam, 1991, pp. 1–83. [24] B.P. Hu, Ph.D. Thesis, The University of Dublin, 1990.