J. Phys. Soc. Jpn. 77, 034713 (2008) [16 Pages]
FULL PAPERS

Magnetic, Optical, and Magnetooptical Properties of Spinel-Type ACr2X4 (A=Mn, Fe, Co, Cu, Zn, Cd; X=O, S, Se)

+ Affiliations
1Department of Applied Physics, University of Tokyo, Tokyo 113-86562Correlated Electron Research Center (CERC), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-85623Multiferroics Project, ERATO, Japan Science and Technology Agency (JST), c/o Department of Applied Physics, University of Tokyo, Tokyo 113-8656

A comprehensive study of magnetic, optical, and magnetooptical properties was carried out for single crystals of the spinel-type A Cr 2 X 4 ( A =Mn, Fe, Co, Cu, Zn, and Cd; X =O, S, and Se). The optical reflectivity measurements for 0.1–30 eV revealed a wide variation in electronic structures on a large energy scale between oxides ( X =O) and chalcogenides ( X =S and Se). For A =Fe and Co, we observed the intra-atomic d d transitions of A 2+ ions with a tetrahedral coordination, and successfully deduced the crystal field splitting Δ E , the Racah parameter B , and the spin–orbit coupling constant ζ by analysis based on the ligand field theory. A comparison of these optical parameters between oxides and chalcogenides indicated the strong covalency effect in the chalcogenides. In A =Cu, the insulator–metal transition between X =O and Se was clearly demonstrated by optical conductivity spectra. Magnetic properties were discussed in relation to electronic structures. A compound with a small optical gap is typically a ferrimagnet with antiparallel arrangements of A 2+ and Cr 3+ spins, whereas a compound with a large optical gap undergoes first-order phase transition into spiral spin ordering at a low temperature. We found that the magnetic anisotropy constants K 1 for A Cr 2 S 4 ( A =Mn, Fe, and Co) are approximately scaled by the inverse of the intra-atomic d d transition energies of A 2+ ions in agreement with the second-order perturbation theory for single-ion anisotropy. The magnetooptical spectra in a wide energy range (0.2–4.5 eV) were measured for chalcogenides focusing on the d d transition resonance. We observed gigantic magnetooptical signals up to 4.1° in the energy range of 4 A 2 4 T 2 and 4 A 2 4 T 1 transitions of Co 2+ ions for CoCr 2 S 4 , and analyzed them in the framework of the ligand field theory. We propose that the strong covalency of the ligand sulfur, as well as the local breakdown of inversion symmetry, in the tetrahedral site plays a crucial role in the enhancement of magnetooptical responses.

©2008 The Physical Society of Japan

References

  • 1 T. A.Kaplan and N.Menyuk: Philos. Mag. 87 (2007) 3711. CrossrefGoogle Scholar
  • 2 N.Menyuk, A.Wold, D.Rogers, and K.Dwight:J. Appl. Phys. 33 (1962) 1144. CrossrefGoogle Scholar
  • 3 E.Prince: Acta Crystallogr. 10 (1957) 554. CrossrefGoogle Scholar
  • 4 E.Prince:J. Appl. Phys. 32 (1961) 68S. CrossrefGoogle Scholar
  • 5 J. M.Hastings and L. M.Corliss:Phys. Rev. 126 (1962) 556. CrossrefGoogle Scholar
  • 6 G.Shirane, D. E.Cox, and S. J.Pickart:J. Appl. Phys. 35 (1964) 954. CrossrefGoogle Scholar
  • 7 G. L.Bacchella and M.Pinot: J. Phys. (Paris) 25 (1964) 537. CrossrefGoogle Scholar
  • 8 N.Menyuk, K.Dwight, and A.Wold: J. Phys. (Paris) 25 (1964) 528. CrossrefGoogle Scholar
  • 9 R.Plumier:J. Appl. Phys. 39 (1968) 635. CrossrefGoogle Scholar
  • 10 K.Dwight and N.Menyuk:J. Appl. Phys. 40 (1969) 1156. CrossrefGoogle Scholar
  • 11 S.Funahashi, Y.Morii, and H. R.Child:J. Appl. Phys. 61 (1987) 4114. CrossrefGoogle Scholar
  • 12 K.Tomiyasu and I.Kagomiya:J. Phys. Soc. Jpn. 73 (2004) 2539. LinkGoogle Scholar
  • 13 K.Tomiyasu, J.Fukunaga, and H.Suzuki:Phys. Rev. B 70 (2004) 214434. CrossrefGoogle Scholar
  • 14 T.Tsushima, Y.Kino, and S.Funahashi:J. Appl. Phys. 39 (1968) 626. CrossrefGoogle Scholar
  • 15 S.Funahashi, K.Siratori, and Y.Tomono:J. Phys. Soc. Jpn. 29 (1970) 1179. LinkGoogle Scholar
  • 16 T.Tsuda, A.Hirai, and T.Tsushima:Solid State Commun. 9 (1971) 2207. CrossrefGoogle Scholar
  • 17 T.Tsuda, H.Abe, and A.Hirai:J. Phys. Soc. Jpn. 38 (1975) 72. LinkGoogle Scholar
  • 18 E. F.Bertaut and J.Durac: Acta Crystallogr., Sect. A 28 (1972) 580. CrossrefGoogle Scholar
  • 19 Although a successive magnetic transition is also discerned in the magnetization measurement of NiCr2O4, no satellite peaks have been observed in the neutron diffraction profiles in the lowest-temperature phase. 12) Google Scholar
  • 20 D. H.Lyons, T. A.Kaplan, K.Dwight, and N.Menyuk:Phys. Rev. 126 (1962) 540. CrossrefGoogle Scholar
  • 21 M.Tanaka, T.Tokoro, and Y.Aiyama:J. Phys. Soc. Jpn. 21 (1966) 262. LinkGoogle Scholar
  • 22 K.Siratori:J. Phys. Soc. Jpn. 23 (1967) 948. LinkGoogle Scholar
  • 23 O.Crottaz, F.Kubel, and H.Schmid: J. Mater. Chem. 7 (1997) 143. CrossrefGoogle Scholar
  • 24 Z. G.Yé, O.Crottaz, F.Vaudano, F.Kubel, P.Tissot, and H.Schmid: Ferroelectrics 162 (1994) 103. CrossrefGoogle Scholar
  • 25 W. A.Dollase and H. St. C.O'Neill: Acta Crystallogr., Sect. C 53 (1997) 657. CrossrefGoogle Scholar
  • 26 J. B.Goodenough and A. L.Loeb:Phys. Rev. 98 (1955) 391. CrossrefGoogle Scholar
  • 27 J. B.Goodenough:J. Phys. Chem. Solids 25 (1964) 151. CrossrefGoogle Scholar
  • 28 J.Kanamori, M.Kataoka, and Y.Itoh:J. Appl. Phys. 39 (1968) 688. CrossrefGoogle Scholar
  • 29 M.Kataoka and J.Kanamori:J. Phys. Soc. Jpn. 32 (1972) 113. LinkGoogle Scholar
  • 30 Y.Yamasaki, S.Miyasaka, Y.Kaneko, J.-P.He, T.Arima, and Y.Tokura:Phys. Rev. Lett. 96 (2006) 207204. CrossrefGoogle Scholar
  • 31 A. B.Sushkov, O.Tchernyshyov, W.RatcliffII, S. W.Cheong, and H. D.Drew:Phys. Rev. Lett. 94 (2005) 137202. CrossrefGoogle Scholar
  • 32 S.-H.Lee, C.Broholm, W.Ratcliff, G.Gasparovic, Q.Huang, T. H.Kim, and S.-W.Cheong:Nature 418 (2002) 856. CrossrefGoogle Scholar
  • 33 S.-H.Lee, C.Broholm, T. H.Kim, W.RatcliffII , and S.-W.Cheong:Phys. Rev. Lett. 84 (2000) 3718. CrossrefGoogle Scholar
  • 34 H.Ueda, H. A.Katori, H.Mitamura, T.Goto, and H.Takagi:Phys. Rev. Lett. 94 (2005) 047202. CrossrefGoogle Scholar
  • 35 H.Ueda, H.Mitamura, T.Goto, and Y.Ueda:Phys. Rev. B 73 (2006) 094415. CrossrefGoogle Scholar
  • 36 H. W.Lehmann and M.Robbins:J. Appl. Phys. 37 (1966) 1389. CrossrefGoogle Scholar
  • 37 H. W.Lehmann:Phys. Rev. 163 (1967) 488. CrossrefGoogle Scholar
  • 38 C.Haas, A. M. J. G.van Rum, P. F.Bongers, and W.Albers:Solid State Commun. 5 (1967) 657. CrossrefGoogle Scholar
  • 39 C.Haas:Phys. Rev. 168 (1968) 531. CrossrefGoogle Scholar
  • 40 P. F.Bongers, C.Haas, A. M. J. G.van Rum, and G.Zanmarchi:J. Appl. Phys. 40 (1969) 958. CrossrefGoogle Scholar
  • 41 A.Amith and G. L.Gunsalus:J. Appl. Phys. 40 (1969) 1020. CrossrefGoogle Scholar
  • 42 T.Watanabe:J. Phys. Soc. Jpn. 37 (1974) 140. LinkGoogle Scholar
  • 43 T.Oguchi, T.Kambara, and K.Gondaira:Phys. Rev. B 24 (1981) 3441. CrossrefGoogle Scholar
  • 44 T.Oguchi, T.Kambara, and K.Gondaira:Phys. Rev. B 25 (1982) 2947. CrossrefGoogle Scholar
  • 45 W. J.Miniscalco, B. C.McCollum, N. G.Stoffel, and G.Margaritondo:Phys. Rev. B 25 (1982) 2947. CrossrefGoogle Scholar
  • 46 A.Continenza, T.de Pascale, F.Meloni, and M.Serra:Phys. Rev. B 49 (1994) 2503. CrossrefGoogle Scholar
  • 47 P. K.Baltzer, H. W.Lehmann, and M.Robbins:Phys. Rev. Lett. 15 (1965) 493. CrossrefGoogle Scholar
  • 48 P. K.Baltzer, P. J.Wojtowicz, M.Robbins, and E.Lopatin:Phys. Rev. 151 (1966) 367. CrossrefGoogle Scholar
  • 49 P. J.Plumier:J. Appl. Phys. 37 (1966) 964. CrossrefGoogle Scholar
  • 50 N.Menyuk, K.Dwight, and R. J.Arnott:J. Appl. Phys. 37 (1966) 1387. CrossrefGoogle Scholar
  • 51 J. M.Hastings and L. M.Corliss:J. Phys. Chem. Solids 29 (1968) 9. CrossrefGoogle Scholar
  • 52 K.Siratori:J. Phys. Soc. Jpn. 30 (1971) 709. LinkGoogle Scholar
  • 53 J.Akimitsu, K.Siratori, G.Shirane, M.Iizumi, and T.Watanabe:J. Phys. Soc. Jpn. 44 (1978) 172. LinkGoogle Scholar
  • 54 K.Siratori, J.Akimitsu, E.Kita, and M.Nishi:J. Phys. Soc. Jpn. 48 (1980) 1111. LinkGoogle Scholar
  • 55 G.Harbeke and H.Pinch:Phys. Rev. Lett. 17 (1966) 1090. CrossrefGoogle Scholar
  • 56 G.Busch, B.Magyar, and P.Wachter:Phys. Lett. 23 (1966) 438. CrossrefGoogle Scholar
  • 57 C. P.Wen, B.Hershenov, H.von Phillipsborn, and H.Pinch:Appl. Phys. Lett. 13 (1968) 188. CrossrefGoogle Scholar
  • 58 W.Lems, P. J.Rijnierse, P. F.Bongers, and U.Enz:Phys. Rev. Lett. 21 (1968) 1643. CrossrefGoogle Scholar
  • 59 S. B.Berger and L.Ekstrom:Phys. Rev. Lett. 23 (1969) 1499. CrossrefGoogle Scholar
  • 60 E. F.Steigmeier and G.Harbeke: Z. Phys. B 12 (1970) 1. Google Scholar
  • 61 R. K.Ahrenkiel, F.Moser, S.Lyu, and C. R.Pidgeon:J. Appl. Phys. 42 (1971) 1452. CrossrefGoogle Scholar
  • 62 H. W.Lehmann, G.Harbeke, and H.Pinch: J. Phys. (Paris), Colloq. 32 (1971) 932. CrossrefGoogle Scholar
  • 63 S. G.Stoyanov, M. N.Iliev, and S. P.Stoyanova:Phys. Status Solidi A 30 (1975) 133. CrossrefGoogle Scholar
  • 64 K.Sato:J. Phys. Soc. Jpn. 43 (1977) 719. LinkGoogle Scholar
  • 65 M.Zvara and V.Prosser:J. Magn. Magn. Mater. 12 (1979) 219. CrossrefGoogle Scholar
  • 66 M.Zvara, A.Schlegel, and P.Wachter:J. Appl. Phys. 50 (1979) 7463. CrossrefGoogle Scholar
  • 67 N.Koshizuka, S.Ushioda, and T.Tsushima:Phys. Rev. B 21 (1980) 1316. CrossrefGoogle Scholar
  • 68 S.Suga, S.Shin, M.Taniguchi, K.Inoue, M.Seki, I.Nakada, S.Shibuya, and T.Yamaguchi:Phys. Rev. B 25 (1982) 5486. CrossrefGoogle Scholar
  • 69 E.Mosiniewicz-Szablewska and H.Szymczak:Phys. Rev. B 47 (1993) 8700. CrossrefGoogle Scholar
  • 70 K.Siratori and E.Kita:J. Phys. Soc. Jpn. 48 (1980) 1443. LinkGoogle Scholar
  • 71 J.Hemberger, P.Lunkenheimer, R.Fichtl, H.-A. Krugvon Nidda, V.Tsurkan, and A.Loidl:Nature 434 (2005) 364. CrossrefGoogle Scholar
  • 72 N.Menyuk, K.Dwight, and A.Wold:J. Appl. Phys. 36 (1965) 1088. CrossrefGoogle Scholar
  • 73 C.Colominas:Phys. Rev. 153 (1967) 558. CrossrefGoogle Scholar
  • 74 P.Gibart, J.-L.Dormann, and Y.Pellerin: Phys. Status Solidi 36 (1969) 187. CrossrefGoogle Scholar
  • 75 J.Denis, Y.Allain, and R.Plumier:J. Appl. Phys. 41 (1970) 1091. CrossrefGoogle Scholar
  • 76 I.Nakatani, H.Nosé, and K.Masumoto:J. Phys. Chem. Solids 39 (1978) 743. CrossrefGoogle Scholar
  • 77 L. I.Koroleva and M. A.Shalimova: Sov. Phys. Solid State 21 (1979) 266. Google Scholar
  • 78 V.Tsurkan, M.Lohmann, H.-A. Krugvon Nidda, A.Loidl, S.Horn, and R.Tidecks:Phys. Rev. B 63 (2001) 125209. CrossrefGoogle Scholar
  • 79 V.Tsurkan, J.Hemberger, M.Klemm, S.Klimm, A.Loidl, S.Horn, and R.Tidecks:J. Appl. Phys. 90 (2001) 4639. CrossrefGoogle Scholar
  • 80 V.Tsurkan, M.Mucksch, V.Fritsch, J.Hemberger, M.Klemm, S.Klimm, S.Korner, H.-A. Krugvon Nidda, D.Samusi, E.-W.Scheidt, A.Loidl, S.Horn, and R.Tidecks:Phys. Rev. B 68 (2003) 134434. CrossrefGoogle Scholar
  • 81 O.Yamashita, Y.Yamaguchi, I.Nakatani, H.Watanabe, and K.Matsumoto:J. Phys. Soc. Jpn. 46 (1979) 1145. LinkGoogle Scholar
  • 82 J. C. Th.Hollander, G.Sawatzky, and C.Haas:Solid State Commun. 15 (1974) 747. CrossrefGoogle Scholar
  • 83 J.-S.Kang, S. J.Kim, C. S.Kim, C. G.Olson, and B. I.Min:Phys. Rev. B 63 (2001) 144412. CrossrefGoogle Scholar
  • 84 A.Kimura, J.Matsuno, J.Okabayashi, A.Fujimori, T.Shishidou, E.Kulatov, and T.Kanomata:Phys. Rev. B 63 (2001) 224420. CrossrefGoogle Scholar
  • 85 A.Deb, M.Mizumaki, T.Muro, Y.Sakurai, and V.Tsurkan:Phys. Rev. B 68 (2003) 014427. CrossrefGoogle Scholar
  • 86 V. N.Antonov, V. P.Antropov, B. N.Harmon, A. N.Yaresko, and A. Ya.Perlov:Phys. Rev. B 59 (1999) 14552. CrossrefGoogle Scholar
  • 87 T.Watanabe:Solid State Commun. 12 (1973) 355. CrossrefGoogle Scholar
  • 88 A. P.Ramirez, R. J.Cava, and J.Krajewski:Nature 386 (1997) 156. CrossrefGoogle Scholar
  • 89 Z.Chen, S.Tan, Z.Yang, and Y.Zhang:Phys. Rev. B 59 (1999) 11172. CrossrefGoogle Scholar
  • 90 Z.Yang, S.Tan, Z.Chen, and Y.Zhang:Phys. Rev. B 62 (2000) 13872. CrossrefGoogle Scholar
  • 91 V.Fritsch, J.Deisenhofer, R.Fichtl, J.Hemberger, H.-A. Krugvon Nidda, M.Mucksch, M.Nicklas, D.Samusi, J. D.Thompson, R.Tidecks, V.Tsurkan, and A.Loidl:Phys. Rev. B 67 (2003) 144419. CrossrefGoogle Scholar
  • 92 K.Oda, S.Yoshii, Y.Yasui, M.Ito, T.Ido, Y.Ohno, Y.Kobayashi, and M.Sato:J. Phys. Soc. Jpn. 70 (2001) 2999. LinkGoogle Scholar
  • 93 S.Iikubo, Y.Yasui, K.Oda, Y.Ohno, Y.Kobayashi, M.Sato, and K.Kakurai:J. Phys. Soc. Jpn. 71 (2002) 2792. LinkGoogle Scholar
  • 94 W.Lee, S.Watauchi, V. L.Miller, R. J.Cava, and N. P.Ong:Science 303 (2004) 1647. CrossrefGoogle Scholar
  • 95 T.Ogasawara, K.Ohgushi, Y.Tomioka, K. S.Takahashi, H.Okamoto, M.Kawasaki, and Y.Tokura:Phys. Rev. Lett. 94 (2005) 087202. CrossrefGoogle Scholar
  • 96 K.Ohgushi, T.Ogasawara, Y.Okimoto, S.Miyasaka, and Y.Tokura:Phys. Rev. B 72 (2005) 155114. CrossrefGoogle Scholar
  • 97 T.Ogasawara, K.Ohgushi, H.Okamoto, and Y.Tokura:J. Phys. Soc. Jpn. 75 (2006) 083707. LinkGoogle Scholar
  • 98 E.Carnall,Jr., D.Pearlman, T. J.Coburn, F.Moser, and T. W.Martin: Mater. Res. Bull. 7 (1972) 1361. CrossrefGoogle Scholar
  • 99 R. K.Ahrenkiel, T. H.Lee, S. L.Lyu, and F.Moser:Solid State Commun. 12 (1973) 1113. CrossrefGoogle Scholar
  • 100 R. K.Ahrenkiel, T. J.Corburn, and E.Carnali: IEEE Trans. Magn. 10 (1974) 2. CrossrefGoogle Scholar
  • 101 R. K.Ahrenkiel, S. L.Lyu, and T. J.Coburn:J. Appl. Phys. 46 (1975) 894. CrossrefGoogle Scholar
  • 102 H.Brändle, J.Schoenes, P.Wachter, F.Hulliger, and W.Reim:Appl. Phys. Lett. 56 (1990) 2602. CrossrefGoogle Scholar
  • 103 H.Brandle, J.Schoenes, P.Wachter, F.Hulliger, and W.Reim:J. Magn. Magn. Mater. 93 (1991) 207. CrossrefGoogle Scholar
  • 104 M. R.Spender and A. H.Morrish:Solid State Commun. 11 (1972) 1417. CrossrefGoogle Scholar
  • 105 M.Mertinat, V.Tsurkan, D.Samusi, R.Tidecks, and F.Haider:Phys. Rev. B 71 (2005) 100408. CrossrefGoogle Scholar
  • 106 R.Fichtl, V.Tsurkan, P.Lunkenheimer, J.Hemberger, V.Fritsch, H.-A. Krugvon Nidda, E.-W.Scheidt, and A.Loidl:Phys. Rev. Lett. 94 (2005) 027601. CrossrefGoogle Scholar
  • 107 H. V.Philipsborn:J. Cryst. Growth 9 (1971) 296. CrossrefGoogle Scholar
  • 108 L.Goldstein, J.Dormann, R.Druilhe, M.Guittard, and P.Gibart:J. Cryst. Growth 20 (1973) 24. CrossrefGoogle Scholar
  • 109 P.Gibart, L.Goldstein, J.Dormann, and M.Guittard:J. Cryst. Growth 24–25 (1974) 147. CrossrefGoogle Scholar
  • 110 F.Leccabue, B. E.Watts, D.Fiorani, A. M.Testa, J.Alvarez, V.Sagredo, and G.Bocelli:J. Mater. Sci. 28 (1993) 3945. CrossrefGoogle Scholar
  • 111 K.Sato: Jpn. J. Appl. Phys. 20 (1981) 2403. CrossrefGoogle Scholar
  • 112 L. A.Nafie and D. W.Vidrine: inFourier Transform Infrared Spectroscopy, ed. J. R.Ferraro and L. J.Basile (Academic Press, New York, 1982) Vol. 3. Google Scholar
  • 113 E. D.Lipp and L. A.Nafie: Appl. Spectrosc. 38 (1984) 20. CrossrefGoogle Scholar
  • 114 P. L.Polavarapu: Appl. Spectrosc. 38 (1984) 26. CrossrefGoogle Scholar
  • 115 V. G.Gregoriou, R.Hapanowicz, A. L.Clark, and P. T.Hammond: Appl. Spectrosc. 51 (1997) 470. CrossrefGoogle Scholar
  • 116 C. A.Mccoy and J. A.de Haseth: Appl. Spectrosc. 42 (1988) 336. CrossrefGoogle Scholar
  • 117 Z.Fang, N.Nagaosa, K. S.Takahashi, A.Asamitsu, R.Mathieu, T.Ogasawara, H.Yamada, M.Kawasaki, Y.Tokura, and K.Terakura:Science 302 (2003) 92 CrossrefGoogle Scholar
  • 118 I.Kezsmarki, S.Onoda, Y.Taguchi, T.Ogasawara, M.Matsubara, S.Iguchi, N.Hanasaki, N.Nagaosa, and Y.Tokura:Phys. Rev. B 72 (2005) 094427. CrossrefGoogle Scholar
  • 119 T.Arima and Y.Tokura:J. Phys. Soc. Jpn. 64 (1995) 2488. LinkGoogle Scholar
  • 120 S. K.Park, T.Ishikawa, and Y.Tokura:Phys. Rev. B 58 (1998) 3717. CrossrefGoogle Scholar
  • 121 M. L.Cohen and J. R.Chelikowsky:Electronic Structure and Optical Properties of Semiconductors (Springer-Verlag, Berlin, 1988). CrossrefGoogle Scholar
  • 122 L.Ley, R. A.Pollak, F. R.McFeely, S. P.Kowalczyk, and D. A.Shirley:Phys. Rev. B 9 (1974) 600. CrossrefGoogle Scholar
  • 123 J.Matsuno, A.Fujimori, and L. F.Mattheiss:Phys. Rev. B 60 (1999) 1607. CrossrefGoogle Scholar
  • 124 S.Wittekoek and P. F.Bongers:Solid State Commun. 7 (1969) 1719. CrossrefGoogle Scholar
  • 125 C. K.Jorgensen:Absorption Spectra of Molecules and Ions in Crystals (Academic Press, New York, 1959). Google Scholar
  • 126 J. S.Griffith:The Theory of Transition-Metal Ions (Cambridge University Press, Cambridge, U.K., 1961). Google Scholar
  • 127 S.Sugano, Y.Tanabe, and H.Kamimura:Multiplets of Transition-Metal Ions in Crystals (Academic Press, New York, 1970). Google Scholar
  • 128 R. G.Burns:Mineralogical Applications of Crystal Field Theory (Cambridge University Press, Cambridge, U.K., 1970). Google Scholar
  • 129 G. A.Slack, F. S.Ham, and R. M.Chrenko:Phys. Rev. 152 (1966) 376. CrossrefGoogle Scholar
  • 130 F. S.Ham and G. A.Slack:Phys. Rev. B 4 (1971) 777. CrossrefGoogle Scholar
  • 131 S.Wittekoek, R. P.van Stapele, and A. W. J.Wijma:Phys. Rev. B 7 (1973) 1667. CrossrefGoogle Scholar
  • 132 The intra-atomic d–d transitions of the Co2+ ion in a tetrahedral environment have been reported in many compounds. We list here several examples with their transition energies: Cs3CoCl5 (0.9 and 2.0 eV) [J. Ferguson:J. Chem. Phys.32(1960) 528]; ZnO:Co (0.9 and 2.0 eV), ZnS:Co (0.8 and 1.8 eV), and CdS:Co (0.8 and 1.8 eV) [H. A. Weakliem:J. Chem. Phys.36(1962) 2117]; CoCr2S4 (0.7 and 1.3 eV); 99–101) and CdTe:Co (0.7 and 1.4 eV) [J. Gardavský, A. Werner, and H. D. Hochheimer:Phys. Rev. B24(1981) 4972]. These bands have been discussed by the ligand field theory with weak-coupling approximation, where 4A2(e4t23), 4T2(e3t24), 4T1(e3t24), and 4T1(e2t25) in the strong-coupling scheme are respectively represented by 4A2(4F), 4T2(4F), 4T1(4F), and 4T1(4P). In most of the earlier articles, the two bands were ascribed to the 4A2(4F) →4T1(4F) and 4A2(4F) →4T1(4P) transitions; this assignment contradicts ours. According to the earlier interpretation, there is another lower excitation corresponding to the 4A2(4F) →4T2(4F) transition below 0.7 eV; this is actually insisted to be observed in ZnO:Co at around 0.5 eV [P. Koidl:Phys. Rev. B15(1977) 2493], and ZnS:Co and ZnSe:Co at around 0.5 eV [J. Dreyhsig and B. Litzenburger:Phys. Rev. B54(1996) 10516]. Nevertheless, we claim that our assignment is most plausible. It is unlikely that the two-particle excitation 4A2(e4t23) →4T1(e2t25) has a larger oscillator strength than the 4A2(e4t23) →4T2(e3t24) transition in CoCr2X4 (X=O and S). Moreover, it is reasonable to fo llow the well-established assignment of the d–d transitions of the Cr3+ ion in an octahedral environment, 125–128) which is a particle–hole analog of the Co2+ ion in a tetrahedral environment. Google Scholar
  • 133 A. S.Davydov:Theory of Molecular Excitons (Plenum Press, New York, 1971). CrossrefGoogle Scholar
  • 134 T.Inui, Y.Tanabe, and Y.Onodera:Group Theory and Its Applications in Physics (Springer-Verlag, Berlin, 1990). CrossrefGoogle Scholar
  • 135 J.Zaanen, G. A.Sawatzky, and J. W.Allen:Phys. Rev. Lett. 55 (1985) 418. CrossrefGoogle Scholar
  • 136 S.Chikazumi:Physics of Ferromagnetism (Clarendon, Oxford, U.K., 1997) 2nd ed. Google Scholar
  • 137 R. P.van Stapele, J. S.van Wieringen, and P. F.Bongers: J. Phys. Colloq. 32 (1971) C1-53. CrossrefGoogle Scholar
  • 138 B.Hoekstra, R. P.van Stapele, and A. B.Voermans:Phys. Rev. B 6 (1972) 2762. CrossrefGoogle Scholar
  • 139 A.Marais, M.Porte, L.Goldstein, and P.Gibart:J. Magn. Magn. Mater. 15–18 (1980) 1287. CrossrefGoogle Scholar
  • 140 Z.Yang, S.Tan, and Y.Zhang:Solid State Commun. 130 (2004) 511. CrossrefGoogle Scholar
  • 141 S. B.Berger and H. L.Pinch:J. Appl. Phys. 38 (1967) 949. CrossrefGoogle Scholar
  • 142 K.Yosida:Theory of Magnetism (Springer-Verlag, Berlin, 1996). CrossrefGoogle Scholar
  • 143 R. R.Birss:Symmetry and Magnetism (North-Holland, Amsterdam, 1966). Google Scholar
  • 144 H.Feil and C.Haas:Phys. Rev. Lett. 58 (1987) 65. CrossrefGoogle Scholar
  • 145 Spin–Orbit-Influenced Spectroscopies of Magnetic Solids, ed. H.Ebert and G.Schutz (Springer-Verlag, Berlin, 1996). CrossrefGoogle Scholar
  • 146 Magneto-Optics, ed. S.Sugano and N.Kojima (Springer-Verlag, Berlin, 1999). Google Scholar
  • 147 The sign of the εxy spectrum for the 5E→5T2 transition in FeCr2S4 is opposite of that for the 4A2→4T2 transition in CoCr2S4. This agrees with the difference in the manner of spin–orbit coupling splitting between the two T2 states (see Fig. 4). Google Scholar
  • 148 C. S.Wang and J.Callaway:Phys. Rev. B 9 (1974) 4897. CrossrefGoogle Scholar