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Antiferromagnetic transition in CuRh2O4
Journal of Physics and Chemistry of Solids 60 (1999) 457–462
Antiferromagnetic transition in CuRh2O4 Ryo Endoh a, Osamu Fujishima b, Tooru Atake b, Nobuhiro Matsumoto a, Masanori Hayashi a, Shoichi Nagata a,* a
Department of Materials Science and Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, Hokkaido 050-8585, Japan b Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan Received 27 September 1998; accepted 5 October 1998
Abstract Heat-capacity and magnetic susceptibility measurements were carried out on the normal spinel-type compound CuRh2O4. A sharp heat capacity anomaly associated with an antiferromagnetic transition was first observed. The Ne´el temperature TN was 21.9 K which indicates the inflection point of the magnetic susceptibility x , being lower than the peak temperature of 24 K in x . The effective magnetic moment observed was 1.88 mB per molecule, which is close to the spin-only moment for Cu 2⫹ ion. The value of the magnetic entropy change was 2.72 J K ⫺1 mol ⫺1 which is much less than that expected for R ln(2S ⫹ 1): S 1/2. These results for CuRh2O4 based on the ionic picture have an important relevance to Cu-ternary chalcogenides with a similar structure. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: Antiferromagnetic transition in CuRh2O4; D. Magnetic properties; C. X-ray diffraction
1. Introduction Oxyspinels are in general semiconductors with antiferromagnetic interaction [1], while sulphospinels exhibit a wide variety of physical properties. We have discovered a metal– insulator transition at TM–I 226 K in CuIr2S4 [2–3]. The remarkable properties of this transition have stimulated a great deal of interest within the last decade leading to the publication of some related investigations [4–15]. In contrast, Rh-based compounds, CuRh2S4 and CuRh2Se4 become superconducting below transition temperatures of 4.70 and 3.48 K, respectively [16–23]. CuRh2O4 is a tetragonally distorted normal spinel-type compound at room temperature, in which Cu ions occupy the A (tetrahedral) sites and Rh ions occupy the B (octahedral) sites as shown in Fig. 1. The structural phase transition in CuRh2O4 at about 850 K from a high temperature cubic to a low temperature tetragonal symmetry has been reported [24–25]. This distortion is because of Jahn–Teller active Cu 2⫹ ions at A sites giving rise to cooperative distortion. * Corresponding author. Fax: ⫹ 81-143-46-5612. E-mail address: [email protected] (S. Nagata)
The axial ratio is c/a 0.9069 at room temperature and indicates the flattening of the tetrahedron to make c/a ⬍ 1.00, which is consistent with the expectation of the Jahn– Teller effect for Cu 2⫹(d 9) in the tetrahedral site [26–28]. CuRh2O4 plays a basic role of the physical properties from the viewpoint of fairly pure ionic picture without the covalence effect associated with the conductivity property. Many sulphides with a similar structure have only Cu ⫹ but no Cu 2⫹ in the valence state. As the valence state of the Cu ion has been the subject of controversy for each Cu-ternary chalcogenide with a spinel structure, CuRh2O4 has attracted experimentalists for many years primarily as a model magnetic compound. Unfortunately, no data on its accurate and precise magnetic property are currently available and there is no report concerning its thermal property. Its longrange magnetic order has not been confirmed as yet, and was only conjectured. We have successfully synthesized the spinel-type compound CuRh2O4 and have first studied systematically its structural, magnetic and thermal properties, which manifest itself as a sharp anomaly in the heat capacity and the magnetic susceptibility arising from the antiferromagnetic phase transition.
0022-3697/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(98)00310-2
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R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
adiabatic calorimeter. A full description of the experimental apparatus is available elsewhere [29–31]. A sample of 7.0535 g (0.021159 mol) was loaded into the calorimeter vessel. The heat capacity was determined with an accuracy of 0.10%. 3. Results and discussion
Fig. 1. The cubic unit cell of the spinel structure. Cu ions (A) lie on the tetrahedral sites and Rh ions (B) on the octahedral sites. Oxygen ions are indicated as open circles.
2. Experimental methods
x C= T ⫺ u ⫹ x0 ;
The samples were prepared by a solid state reaction CuO ⫹ Rh2 O3 ! CuRh2 O4 :
The powder X-ray diffraction pattern with the tetragonal symmetry of CuRh2O4 is shown in Fig. 2. Its lattice ˚ and c 7.930 A ˚ at room constants which are a 8.744 A temperature agree with previously published data [24,32– 33]. Fig. 3 shows the magnetic susceptibility of CuRh2O4. The inflection point in the susceptibility, which corresponds to the Ne´el temperature, TN 21.9 K, indicates the peak of the heat capacity as suggested by Fisher [34]. The molar susceptibility at high temperatures fits the Curie–Weiss law
1
The starting materials, CuO (purity 99.9%) and Rh2O3 (99.9%), were mixed in a calculated ratio. After mixing, the powder was pressed into rectangular bars which were heated to 1423 K for 20 h in a quartz tube under oxygen atmosphere. We also prepared the powder sample by heating at 1223 K for several days in air by using a silica boat. The d.c. magnetic susceptibility was measured with a Quantum Design superconducting quantum interference device (rf-SQUID) magnetometer in the range of 4 ⬍ T ⬍ 300 K in an applied magnetic field of 10 kOe. The heat capacity was measured using a laboratory-made
2
where x is the molar (formula-unit) susceptibility, C the Curie constant, u the Weiss temperature and x 0 the temperature-independent term. These values are C 0.443 emu K mol ⫺1, u ⫺ 116 K (antiferromagnetic), respectively. It should be noted that the value of u , which indicates the asymptotic value, is rather larger than TN. The presence of the temperature-independent term x 0 is experimentally evaluated to be ⫹ 0.50 × 10 ⫺4 emu mol ⫺1. The susceptibility x core of the orbital diamagnetism contribution resulting from ion cores for Cu 2⫹ ⫹ 2Rh 3⫹ ⫹ 4O 2⫺ is estimated to be ⫺ 1.03 × 10 ⫺4 emu mol ⫺1 [35]. The difference between x 0 and x core which is ⫹ 1.53 × 10 ⫺4 emu mol ⫺1, may be attributed to the Van Vleck paramagnetic contribution originating from Rh ions in the crystal field.
˚ and c 7.930 A ˚ at room Fig. 2. X-ray diffraction pattern of CuRh2O4 which has the tetragonal structure with the lattice constants a 8.744 A temperature.
R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
459
Fig. 3. Magnetic susceptibility versus temperature for powder specimens of CuRh2O4 as a function of temperature. The inset shows the susceptibility from 4 to 50 K.
Fig. 4. Inverse magnetic susceptibility versus temperature of CuRh2O4. The inset shows the same dependence from 4 to 50 K.
Fig. 5. Molar heat capacity of CuRh2O4 over a wide temperature range of 13 to 300 K.
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R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
Fig. 6. Heat capacity anomaly caused by the antiferromagetic phase transition in CuRh2O4.
Fig. 7. Variation of effective Debye characteristic temperature with T for CuRh2O4.
Fig. 8. Magnetic heat capacity of CuRh2O4.
R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
High-temperature Curie–Weiss behaviour arises from the existence of localized spins as shown in the inverse susceptibility in Fig. 4. The effective magnetic moment is evaluated from the Curie constant to be 1.88m B /formula unit, which is close to that of the spin-only moment 1.73m B expected for S 1/2 for Cu 2⫹ spins. The diamagnetic Rh 3⫹ ions have a low spin configuration 4d 6 on B sites. The irregular behaviour observed in the susceptibility below 10 K, as shown in Fig. 3, has also been detected in previous work [25]. Fig. 5 depicts the molar (formula-unit) heat capacity of CuRh2O4 as a function of temperature over the range of 13– 300 K. A sharp anomaly in the heat capacity is observed at 21.9 K and the background in the heat capacity gives the lattice contribution. Fig. 6 shows the expanded plot. Temperature dependence of the Debye characteristic temperature is shown in Fig. 7. Subtraction of the lattice heat capacity was made. The magnetic contribution to the heat capacity is shown in Fig. 8. The enthalpy resulting from the antiferromagnetic transition is 62.9 J mol ⫺1. The entropy change in the antiferromagnetic phase transition obtained is 2.72 J K ⫺1 mol ⫺1 which is nearly half of R ln(2S ⫹ 1) 5.763 J K ⫺1 mol ⫺1 for S 1/2, where R is the gas constant and S the spin per molecule. We have separated and subtracted the lattice heat capacity using a natural extrapolation of the smooth curve of the Debye characteristic temperature from a high temperature region to lower temperatures as indicated in Fig. 7. It is difficult to subtract the lattice contribution correctly. The magnetic entropy change from a completely ordered state to a completely disordered state is guaranteed to be R ln(2S ⫹ 1). The magnetic entropy consistency requires a matching technique. The magnetic heat capacity curve is obtained by subtracting more appropriate lattice contribution until the magnetic entropy change is brought into agreement with the theoretical entropy value of 5.763 J K ⫺1 mol ⫺1. It is finally noted that a possibility of the spin-pairing formation between the magnetic ions below the transition temperature of the Jahn–Teller distortion is not ruled out in CuRh2O4.
4. Summary In summary, the following aspects should be noted: 1. CuRh2O4 has a normal spinel structure. 2. The Jahn–Teller cooperative distortion at 850 K originates from the Cu 2⫹ ions at the A-site. 3. The tetragonal phase has an axial ratio c/a 0.9069 at room temperature. 4. TN is 21.9 K, indicating the peak of the heat capacity, where dx /dT is the maximum. It is stressed that there is no anomaly between 24 and 300 K. 5. The value of the effective magnetic moment per molecule is 1.88 m B/f.u. 6. The value of u is much larger than TN. 7. The increase in x below 10 K may be caused by mixing a
461
small amount of not-complete normal spinel for CuRh2O4. 8. The enthalpy and entropy changes arising from the antiferromagnetic phase transition are 62.9 J mol ⫺1 and 2.72 J K ⫺1 mol ⫺1. 9. The value of the magnetic entropy change is nearly half of the R ln(2S ⫹ 1): S 1/2. This fact may imply a slight tendency toward dimerization at low temperatures.
Acknowledgements The authors wish to thank Messrs. S. Kobayashi and J. Yamada for their help in these experiments. The authors would also like to thank Professor H. Kawaji and Dr. T. Tojo (Tokyo Institute of Technology) for heat capacity measurements and Professor K. Kumagai (Hokkaido University) and Mr. S. Tsuji for communicating their NMR results and for valuable discussion. The present work was financially supported by Nippon Sheet Glass Foundation for Materials Science and Engineering (1998, Tokyo, Japan). References [1] E.P. Wohlfarth (Eds.), Ferro-Magnetic Materials, Vol. 3, North-Holland, Amsterdam, New York, Oxford, 1982, pp. 603–746. [2] S. Nagata, T. Hagino, Y. Seki, T. Bitoh, Physica B 194-196 (1994) 1077. [3] S. Nagata, N. Matsumoto, Y. Kato, T. Furubayashi, T. Matsumoto, J.P. Sanchez, P. Vulliet, Phys. Rev. B 58 (1998) 6844. [4] T. Furubayashi, T. Matsumoto, T. Hagino, S. Nagata, J. Phys. Soc. Jpn. 63 (1994) 3333. [5] T. Hagino, T. Tojo, T. Atake, S. Nagata, Philos. Mag. B 71 (1995) 881. [6] T. Hagino, Y. Seki, S. Nagata, Physica C 235-240 (1994) 1303. [7] J. Matsuno, T. Mizokawa, A. Fujimori, D.A. Zatsepin, V.R. Galakhov, E.Z. Kurmaev, Y. Kato, S. Nagata, Phys. Rev. B 55 (1997) R15979. [8] K. Kumagai, S. Tsuji, T. Hagino, S. Nagata, in: A. Fujimori, Y. Tokura (Eds.), Spectroscopy of Mott Insulators and Correlated Metals, Springer Series in Solid-State Sciences, Vol. 119, 1995, pp. 255–264. [9] T. Oda, M. Shirai, N. Suzuki, K. Motizuki, J. Phys.: Condens. Matter. 7 (1995) 4433. [10] T. Oda, M. Shirai, N. Suzuki, K. Motizuki, Cryst. Res. Technol. 31 (1996) 877. [11] G. Oomi, T. Kagayama, I. Yoshida, T. Hagino, S. Nagata, J. Mag. Mag. Mater. 140-144 (1995) 157. [12] T. Furubayashi, T. Kosaka, J. Tang, T. Matsumoto, Y. Kato, S. Nagata, J. Phys. Soc. Jpn. 66 (1997) 1563. [13] S. Tsuji, K. Kumagai, N. Matsumoto, Y. Kato, S. Nagata, Physica B 237-238 (1997) 156. [14] S. Tsuji, K. Kumagai, N. Matsumoto, S. Nagata, Physica C 282-287 (1997) 1107. [15] S. Nagata, S. Yasuzuka, Y. Kato, T. Hagino, N. Matsumoto,
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R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462 N. Kijima, S. Ebisu, Czechoslovak J. of Phys. 46(Suppl.) (1996) 2425. N.H. Van Maaren, G.M. Schaeffer, F.K. Lotgering, Phys. Lett. 25A (1967) 238. M. Robbins, R.H. Willens, R.C. Miller, Solid State Commun. 5 (1967) 933. R.N. Shelton, D.C. Johnston, H. Adrian, Solid State Commun. 20 (1976) 1077. T. Hagino, Y. Seki, N. Wada, S. Tsuji, T. Shirane, K. Kumagai, S. Nagata, Phys. Rev. B 51 (1995) 12673. T. Bitoh, T. Hagino, Y. Seki, S. Chikazawa, S. Nagata, J. Phys. Soc. Jpn. 61 (1992) 3011. T. Shirane, T. Hagino, Y. Seki, T. Bitoh, S. Chikazawa, S. Nagata, J. Phys. Soc. Jpn. 62 (1993) 374. N. Matsumoto, H. Honma, Y. Kato, S. Yasuzuka, K. Morie, N. Kijima, S. Ebisu, S. Nagata, in: S. Nakajima, M. Murakami (Eds.), Proc. of the 9th Internat. Symp. on Superconductivity, Sappora, Japan, Vol. 9, Springer, Tokyo, 1997, p. 175. N. Kijima, H. Yashiro, S. Nagata, J. Phys. Chem. Solids 57 (1996) 1635.
[24] F. Bertaut, F. Forrat, J. Dulac, C. A. Acad. Sci. Paris (Compt. rend.) 249 (1959) 726. [25] G. Blasse, Philips Res. Repts 18 (1963) 383. [26] H.A. Jahn, E. Teller, Proc. Roy. Soc. A 161 (1937) 220. [27] J.D. Dunitz, L.E. Orgel, J. Phys. Chem. Solids 3 (1957) 20. [28] U. Opik, M.H.L. Pryce, Proc. Roy. Soc. A 238 (1957) 425. [29] T. Atake, H. Kawaji, A. Hamano, Y. Saito., Report Res. Lab. Eng. Mater., Tokyo Inst. Technology 15 (1990) 13. [30] T. Atake, H. Kawaji, M. Itoh, T. Nakamura, Y. Saito, Thermochimica Acta 183 (1991) 143. [31] S. Takai, T. Atake, K. Gesi, J. Phys. Chem. Chem. Solids 54 (1993) 213. [32] K.S.R.C. Murthy, J. Chose, J. Solid State Chem. 71 (1987) 441. [33] W.A. Dollase, H.St.C. O’Neill, Acta Cryst. C 53 (1997) 657. [34] M.E. Fisher, Philos. Mag. 7 (1962) 1731; Proc. Roy. Soc. A 254 (1960) 66; Proc. Roy. Soc. A 256 (1960) 502. [35] Landolt-Bo¨rnstein, in: K.-H. Hellwege, A.M. Hellwege (Eds.), New Series, Group 2, Vol. 8, Springer, Berlin, 1976, p. 27.
Antiferromagnetic transition in CuRh2O4 Ryo Endoh a, Osamu Fujishima b, Tooru Atake b, Nobuhiro Matsumoto a, Masanori Hayashi a, Shoichi Nagata a,* a
Department of Materials Science and Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, Hokkaido 050-8585, Japan b Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan Received 27 September 1998; accepted 5 October 1998
Abstract Heat-capacity and magnetic susceptibility measurements were carried out on the normal spinel-type compound CuRh2O4. A sharp heat capacity anomaly associated with an antiferromagnetic transition was first observed. The Ne´el temperature TN was 21.9 K which indicates the inflection point of the magnetic susceptibility x , being lower than the peak temperature of 24 K in x . The effective magnetic moment observed was 1.88 mB per molecule, which is close to the spin-only moment for Cu 2⫹ ion. The value of the magnetic entropy change was 2.72 J K ⫺1 mol ⫺1 which is much less than that expected for R ln(2S ⫹ 1): S 1/2. These results for CuRh2O4 based on the ionic picture have an important relevance to Cu-ternary chalcogenides with a similar structure. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: Antiferromagnetic transition in CuRh2O4; D. Magnetic properties; C. X-ray diffraction
1. Introduction Oxyspinels are in general semiconductors with antiferromagnetic interaction [1], while sulphospinels exhibit a wide variety of physical properties. We have discovered a metal– insulator transition at TM–I 226 K in CuIr2S4 [2–3]. The remarkable properties of this transition have stimulated a great deal of interest within the last decade leading to the publication of some related investigations [4–15]. In contrast, Rh-based compounds, CuRh2S4 and CuRh2Se4 become superconducting below transition temperatures of 4.70 and 3.48 K, respectively [16–23]. CuRh2O4 is a tetragonally distorted normal spinel-type compound at room temperature, in which Cu ions occupy the A (tetrahedral) sites and Rh ions occupy the B (octahedral) sites as shown in Fig. 1. The structural phase transition in CuRh2O4 at about 850 K from a high temperature cubic to a low temperature tetragonal symmetry has been reported [24–25]. This distortion is because of Jahn–Teller active Cu 2⫹ ions at A sites giving rise to cooperative distortion. * Corresponding author. Fax: ⫹ 81-143-46-5612. E-mail address: [email protected] (S. Nagata)
The axial ratio is c/a 0.9069 at room temperature and indicates the flattening of the tetrahedron to make c/a ⬍ 1.00, which is consistent with the expectation of the Jahn– Teller effect for Cu 2⫹(d 9) in the tetrahedral site [26–28]. CuRh2O4 plays a basic role of the physical properties from the viewpoint of fairly pure ionic picture without the covalence effect associated with the conductivity property. Many sulphides with a similar structure have only Cu ⫹ but no Cu 2⫹ in the valence state. As the valence state of the Cu ion has been the subject of controversy for each Cu-ternary chalcogenide with a spinel structure, CuRh2O4 has attracted experimentalists for many years primarily as a model magnetic compound. Unfortunately, no data on its accurate and precise magnetic property are currently available and there is no report concerning its thermal property. Its longrange magnetic order has not been confirmed as yet, and was only conjectured. We have successfully synthesized the spinel-type compound CuRh2O4 and have first studied systematically its structural, magnetic and thermal properties, which manifest itself as a sharp anomaly in the heat capacity and the magnetic susceptibility arising from the antiferromagnetic phase transition.
0022-3697/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(98)00310-2
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R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
adiabatic calorimeter. A full description of the experimental apparatus is available elsewhere [29–31]. A sample of 7.0535 g (0.021159 mol) was loaded into the calorimeter vessel. The heat capacity was determined with an accuracy of 0.10%. 3. Results and discussion
Fig. 1. The cubic unit cell of the spinel structure. Cu ions (A) lie on the tetrahedral sites and Rh ions (B) on the octahedral sites. Oxygen ions are indicated as open circles.
2. Experimental methods
x C= T ⫺ u ⫹ x0 ;
The samples were prepared by a solid state reaction CuO ⫹ Rh2 O3 ! CuRh2 O4 :
The powder X-ray diffraction pattern with the tetragonal symmetry of CuRh2O4 is shown in Fig. 2. Its lattice ˚ and c 7.930 A ˚ at room constants which are a 8.744 A temperature agree with previously published data [24,32– 33]. Fig. 3 shows the magnetic susceptibility of CuRh2O4. The inflection point in the susceptibility, which corresponds to the Ne´el temperature, TN 21.9 K, indicates the peak of the heat capacity as suggested by Fisher [34]. The molar susceptibility at high temperatures fits the Curie–Weiss law
1
The starting materials, CuO (purity 99.9%) and Rh2O3 (99.9%), were mixed in a calculated ratio. After mixing, the powder was pressed into rectangular bars which were heated to 1423 K for 20 h in a quartz tube under oxygen atmosphere. We also prepared the powder sample by heating at 1223 K for several days in air by using a silica boat. The d.c. magnetic susceptibility was measured with a Quantum Design superconducting quantum interference device (rf-SQUID) magnetometer in the range of 4 ⬍ T ⬍ 300 K in an applied magnetic field of 10 kOe. The heat capacity was measured using a laboratory-made
2
where x is the molar (formula-unit) susceptibility, C the Curie constant, u the Weiss temperature and x 0 the temperature-independent term. These values are C 0.443 emu K mol ⫺1, u ⫺ 116 K (antiferromagnetic), respectively. It should be noted that the value of u , which indicates the asymptotic value, is rather larger than TN. The presence of the temperature-independent term x 0 is experimentally evaluated to be ⫹ 0.50 × 10 ⫺4 emu mol ⫺1. The susceptibility x core of the orbital diamagnetism contribution resulting from ion cores for Cu 2⫹ ⫹ 2Rh 3⫹ ⫹ 4O 2⫺ is estimated to be ⫺ 1.03 × 10 ⫺4 emu mol ⫺1 [35]. The difference between x 0 and x core which is ⫹ 1.53 × 10 ⫺4 emu mol ⫺1, may be attributed to the Van Vleck paramagnetic contribution originating from Rh ions in the crystal field.
˚ and c 7.930 A ˚ at room Fig. 2. X-ray diffraction pattern of CuRh2O4 which has the tetragonal structure with the lattice constants a 8.744 A temperature.
R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
459
Fig. 3. Magnetic susceptibility versus temperature for powder specimens of CuRh2O4 as a function of temperature. The inset shows the susceptibility from 4 to 50 K.
Fig. 4. Inverse magnetic susceptibility versus temperature of CuRh2O4. The inset shows the same dependence from 4 to 50 K.
Fig. 5. Molar heat capacity of CuRh2O4 over a wide temperature range of 13 to 300 K.
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R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
Fig. 6. Heat capacity anomaly caused by the antiferromagetic phase transition in CuRh2O4.
Fig. 7. Variation of effective Debye characteristic temperature with T for CuRh2O4.
Fig. 8. Magnetic heat capacity of CuRh2O4.
R. Endoh et al. / Journal of Physics and Chemistry of Solids 60 (1999) 457–462
High-temperature Curie–Weiss behaviour arises from the existence of localized spins as shown in the inverse susceptibility in Fig. 4. The effective magnetic moment is evaluated from the Curie constant to be 1.88m B /formula unit, which is close to that of the spin-only moment 1.73m B expected for S 1/2 for Cu 2⫹ spins. The diamagnetic Rh 3⫹ ions have a low spin configuration 4d 6 on B sites. The irregular behaviour observed in the susceptibility below 10 K, as shown in Fig. 3, has also been detected in previous work [25]. Fig. 5 depicts the molar (formula-unit) heat capacity of CuRh2O4 as a function of temperature over the range of 13– 300 K. A sharp anomaly in the heat capacity is observed at 21.9 K and the background in the heat capacity gives the lattice contribution. Fig. 6 shows the expanded plot. Temperature dependence of the Debye characteristic temperature is shown in Fig. 7. Subtraction of the lattice heat capacity was made. The magnetic contribution to the heat capacity is shown in Fig. 8. The enthalpy resulting from the antiferromagnetic transition is 62.9 J mol ⫺1. The entropy change in the antiferromagnetic phase transition obtained is 2.72 J K ⫺1 mol ⫺1 which is nearly half of R ln(2S ⫹ 1) 5.763 J K ⫺1 mol ⫺1 for S 1/2, where R is the gas constant and S the spin per molecule. We have separated and subtracted the lattice heat capacity using a natural extrapolation of the smooth curve of the Debye characteristic temperature from a high temperature region to lower temperatures as indicated in Fig. 7. It is difficult to subtract the lattice contribution correctly. The magnetic entropy change from a completely ordered state to a completely disordered state is guaranteed to be R ln(2S ⫹ 1). The magnetic entropy consistency requires a matching technique. The magnetic heat capacity curve is obtained by subtracting more appropriate lattice contribution until the magnetic entropy change is brought into agreement with the theoretical entropy value of 5.763 J K ⫺1 mol ⫺1. It is finally noted that a possibility of the spin-pairing formation between the magnetic ions below the transition temperature of the Jahn–Teller distortion is not ruled out in CuRh2O4.
4. Summary In summary, the following aspects should be noted: 1. CuRh2O4 has a normal spinel structure. 2. The Jahn–Teller cooperative distortion at 850 K originates from the Cu 2⫹ ions at the A-site. 3. The tetragonal phase has an axial ratio c/a 0.9069 at room temperature. 4. TN is 21.9 K, indicating the peak of the heat capacity, where dx /dT is the maximum. It is stressed that there is no anomaly between 24 and 300 K. 5. The value of the effective magnetic moment per molecule is 1.88 m B/f.u. 6. The value of u is much larger than TN. 7. The increase in x below 10 K may be caused by mixing a
461
small amount of not-complete normal spinel for CuRh2O4. 8. The enthalpy and entropy changes arising from the antiferromagnetic phase transition are 62.9 J mol ⫺1 and 2.72 J K ⫺1 mol ⫺1. 9. The value of the magnetic entropy change is nearly half of the R ln(2S ⫹ 1): S 1/2. This fact may imply a slight tendency toward dimerization at low temperatures.
Acknowledgements The authors wish to thank Messrs. S. Kobayashi and J. Yamada for their help in these experiments. The authors would also like to thank Professor H. Kawaji and Dr. T. Tojo (Tokyo Institute of Technology) for heat capacity measurements and Professor K. Kumagai (Hokkaido University) and Mr. S. Tsuji for communicating their NMR results and for valuable discussion. The present work was financially supported by Nippon Sheet Glass Foundation for Materials Science and Engineering (1998, Tokyo, Japan). References [1] E.P. Wohlfarth (Eds.), Ferro-Magnetic Materials, Vol. 3, North-Holland, Amsterdam, New York, Oxford, 1982, pp. 603–746. [2] S. Nagata, T. Hagino, Y. Seki, T. Bitoh, Physica B 194-196 (1994) 1077. [3] S. Nagata, N. Matsumoto, Y. Kato, T. Furubayashi, T. Matsumoto, J.P. Sanchez, P. Vulliet, Phys. Rev. B 58 (1998) 6844. [4] T. Furubayashi, T. Matsumoto, T. Hagino, S. Nagata, J. Phys. Soc. Jpn. 63 (1994) 3333. [5] T. Hagino, T. Tojo, T. Atake, S. Nagata, Philos. Mag. B 71 (1995) 881. [6] T. Hagino, Y. Seki, S. Nagata, Physica C 235-240 (1994) 1303. [7] J. Matsuno, T. Mizokawa, A. Fujimori, D.A. Zatsepin, V.R. Galakhov, E.Z. Kurmaev, Y. Kato, S. Nagata, Phys. Rev. B 55 (1997) R15979. [8] K. Kumagai, S. Tsuji, T. Hagino, S. Nagata, in: A. Fujimori, Y. Tokura (Eds.), Spectroscopy of Mott Insulators and Correlated Metals, Springer Series in Solid-State Sciences, Vol. 119, 1995, pp. 255–264. [9] T. Oda, M. Shirai, N. Suzuki, K. Motizuki, J. Phys.: Condens. Matter. 7 (1995) 4433. [10] T. Oda, M. Shirai, N. Suzuki, K. Motizuki, Cryst. Res. Technol. 31 (1996) 877. [11] G. Oomi, T. Kagayama, I. Yoshida, T. Hagino, S. Nagata, J. Mag. Mag. Mater. 140-144 (1995) 157. [12] T. Furubayashi, T. Kosaka, J. Tang, T. Matsumoto, Y. Kato, S. Nagata, J. Phys. Soc. Jpn. 66 (1997) 1563. [13] S. Tsuji, K. Kumagai, N. Matsumoto, Y. Kato, S. Nagata, Physica B 237-238 (1997) 156. [14] S. Tsuji, K. Kumagai, N. Matsumoto, S. Nagata, Physica C 282-287 (1997) 1107. [15] S. Nagata, S. Yasuzuka, Y. Kato, T. Hagino, N. Matsumoto,
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