- Full text:
- PDF (eReader) / PDF (Download) (864 kB)
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.
References
- 1 T. A.Kaplan and N.Menyuk: Philos. Mag. 87 (2007) 3711. Crossref, Google Scholar
- 2 N.Menyuk, A.Wold, D.Rogers, and K.Dwight:J. Appl. Phys. 33 (1962) 1144. Crossref, Google Scholar
- 3 E.Prince: Acta Crystallogr. 10 (1957) 554. Crossref, Google Scholar
- 4 E.Prince:J. Appl. Phys. 32 (1961) 68S. Crossref, Google Scholar
- 5 J. M.Hastings and L. M.Corliss:Phys. Rev. 126 (1962) 556. Crossref, Google Scholar
- 6 G.Shirane, D. E.Cox, and S. J.Pickart:J. Appl. Phys. 35 (1964) 954. Crossref, Google Scholar
- 7 G. L.Bacchella and M.Pinot: J. Phys. (Paris) 25 (1964) 537. Crossref, Google Scholar
- 8 N.Menyuk, K.Dwight, and A.Wold: J. Phys. (Paris) 25 (1964) 528. Crossref, Google Scholar
- 9 R.Plumier:J. Appl. Phys. 39 (1968) 635. Crossref, Google Scholar
- 10 K.Dwight and N.Menyuk:J. Appl. Phys. 40 (1969) 1156. Crossref, Google Scholar
- 11 S.Funahashi, Y.Morii, and H. R.Child:J. Appl. Phys. 61 (1987) 4114. Crossref, Google Scholar
- 12 K.Tomiyasu and I.Kagomiya:J. Phys. Soc. Jpn. 73 (2004) 2539. Link, Google Scholar
- 13 K.Tomiyasu, J.Fukunaga, and H.Suzuki:Phys. Rev. B 70 (2004) 214434. Crossref, Google Scholar
- 14 T.Tsushima, Y.Kino, and S.Funahashi:J. Appl. Phys. 39 (1968) 626. Crossref, Google Scholar
- 15 S.Funahashi, K.Siratori, and Y.Tomono:J. Phys. Soc. Jpn. 29 (1970) 1179. Link, Google Scholar
- 16 T.Tsuda, A.Hirai, and T.Tsushima:Solid State Commun. 9 (1971) 2207. Crossref, Google Scholar
- 17 T.Tsuda, H.Abe, and A.Hirai:J. Phys. Soc. Jpn. 38 (1975) 72. Link, Google Scholar
- 18 E. F.Bertaut and J.Durac: Acta Crystallogr., Sect. A 28 (1972) 580. Crossref, Google 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. Crossref, Google Scholar
- 21 M.Tanaka, T.Tokoro, and Y.Aiyama:J. Phys. Soc. Jpn. 21 (1966) 262. Link, Google Scholar
- 22 K.Siratori:J. Phys. Soc. Jpn. 23 (1967) 948. Link, Google Scholar
- 23 O.Crottaz, F.Kubel, and H.Schmid: J. Mater. Chem. 7 (1997) 143. Crossref, Google Scholar
- 24 Z. G.Yé, O.Crottaz, F.Vaudano, F.Kubel, P.Tissot, and H.Schmid: Ferroelectrics 162 (1994) 103. Crossref, Google Scholar
- 25 W. A.Dollase and H. St. C.O'Neill: Acta Crystallogr., Sect. C 53 (1997) 657. Crossref, Google Scholar
- 26 J. B.Goodenough and A. L.Loeb:Phys. Rev. 98 (1955) 391. Crossref, Google Scholar
- 27 J. B.Goodenough:J. Phys. Chem. Solids 25 (1964) 151. Crossref, Google Scholar
- 28 J.Kanamori, M.Kataoka, and Y.Itoh:J. Appl. Phys. 39 (1968) 688. Crossref, Google Scholar
- 29 M.Kataoka and J.Kanamori:J. Phys. Soc. Jpn. 32 (1972) 113. Link, Google Scholar
- 30 Y.Yamasaki, S.Miyasaka, Y.Kaneko, J.-P.He, T.Arima, and Y.Tokura:Phys. Rev. Lett. 96 (2006) 207204. Crossref, Google Scholar
- 31 A. B.Sushkov, O.Tchernyshyov, W.RatcliffII, S. W.Cheong, and H. D.Drew:Phys. Rev. Lett. 94 (2005) 137202. Crossref, Google Scholar
- 32 S.-H.Lee, C.Broholm, W.Ratcliff, G.Gasparovic, Q.Huang, T. H.Kim, and S.-W.Cheong:Nature 418 (2002) 856. Crossref, Google Scholar
- 33 S.-H.Lee, C.Broholm, T. H.Kim, W.RatcliffII , and S.-W.Cheong:Phys. Rev. Lett. 84 (2000) 3718. Crossref, Google Scholar
- 34 H.Ueda, H. A.Katori, H.Mitamura, T.Goto, and H.Takagi:Phys. Rev. Lett. 94 (2005) 047202. Crossref, Google Scholar
- 35 H.Ueda, H.Mitamura, T.Goto, and Y.Ueda:Phys. Rev. B 73 (2006) 094415. Crossref, Google Scholar
- 36 H. W.Lehmann and M.Robbins:J. Appl. Phys. 37 (1966) 1389. Crossref, Google Scholar
- 37 H. W.Lehmann:Phys. Rev. 163 (1967) 488. Crossref, Google Scholar
- 38 C.Haas, A. M. J. G.van Rum, P. F.Bongers, and W.Albers:Solid State Commun. 5 (1967) 657. Crossref, Google Scholar
- 39 C.Haas:Phys. Rev. 168 (1968) 531. Crossref, Google Scholar
- 40 P. F.Bongers, C.Haas, A. M. J. G.van Rum, and G.Zanmarchi:J. Appl. Phys. 40 (1969) 958. Crossref, Google Scholar
- 41 A.Amith and G. L.Gunsalus:J. Appl. Phys. 40 (1969) 1020. Crossref, Google Scholar
- 42 T.Watanabe:J. Phys. Soc. Jpn. 37 (1974) 140. Link, Google Scholar
- 43 T.Oguchi, T.Kambara, and K.Gondaira:Phys. Rev. B 24 (1981) 3441. Crossref, Google Scholar
- 44 T.Oguchi, T.Kambara, and K.Gondaira:Phys. Rev. B 25 (1982) 2947. Crossref, Google Scholar
- 45 W. J.Miniscalco, B. C.McCollum, N. G.Stoffel, and G.Margaritondo:Phys. Rev. B 25 (1982) 2947. Crossref, Google Scholar
- 46 A.Continenza, T.de Pascale, F.Meloni, and M.Serra:Phys. Rev. B 49 (1994) 2503. Crossref, Google Scholar
- 47 P. K.Baltzer, H. W.Lehmann, and M.Robbins:Phys. Rev. Lett. 15 (1965) 493. Crossref, Google Scholar
- 48 P. K.Baltzer, P. J.Wojtowicz, M.Robbins, and E.Lopatin:Phys. Rev. 151 (1966) 367. Crossref, Google Scholar
- 49 P. J.Plumier:J. Appl. Phys. 37 (1966) 964. Crossref, Google Scholar
- 50 N.Menyuk, K.Dwight, and R. J.Arnott:J. Appl. Phys. 37 (1966) 1387. Crossref, Google Scholar
- 51 J. M.Hastings and L. M.Corliss:J. Phys. Chem. Solids 29 (1968) 9. Crossref, Google Scholar
- 52 K.Siratori:J. Phys. Soc. Jpn. 30 (1971) 709. Link, Google Scholar
- 53 J.Akimitsu, K.Siratori, G.Shirane, M.Iizumi, and T.Watanabe:J. Phys. Soc. Jpn. 44 (1978) 172. Link, Google Scholar
- 54 K.Siratori, J.Akimitsu, E.Kita, and M.Nishi:J. Phys. Soc. Jpn. 48 (1980) 1111. Link, Google Scholar
- 55 G.Harbeke and H.Pinch:Phys. Rev. Lett. 17 (1966) 1090. Crossref, Google Scholar
- 56 G.Busch, B.Magyar, and P.Wachter:Phys. Lett. 23 (1966) 438. Crossref, Google Scholar
- 57 C. P.Wen, B.Hershenov, H.von Phillipsborn, and H.Pinch:Appl. Phys. Lett. 13 (1968) 188. Crossref, Google Scholar
- 58 W.Lems, P. J.Rijnierse, P. F.Bongers, and U.Enz:Phys. Rev. Lett. 21 (1968) 1643. Crossref, Google Scholar
- 59 S. B.Berger and L.Ekstrom:Phys. Rev. Lett. 23 (1969) 1499. Crossref, Google 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. Crossref, Google Scholar
- 62 H. W.Lehmann, G.Harbeke, and H.Pinch: J. Phys. (Paris), Colloq. 32 (1971) 932. Crossref, Google Scholar
- 63 S. G.Stoyanov, M. N.Iliev, and S. P.Stoyanova:Phys. Status Solidi A 30 (1975) 133. Crossref, Google Scholar
- 64 K.Sato:J. Phys. Soc. Jpn. 43 (1977) 719. Link, Google Scholar
- 65 M.Zvara and V.Prosser:J. Magn. Magn. Mater. 12 (1979) 219. Crossref, Google Scholar
- 66 M.Zvara, A.Schlegel, and P.Wachter:J. Appl. Phys. 50 (1979) 7463. Crossref, Google Scholar
- 67 N.Koshizuka, S.Ushioda, and T.Tsushima:Phys. Rev. B 21 (1980) 1316. Crossref, Google 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. Crossref, Google Scholar
- 69 E.Mosiniewicz-Szablewska and H.Szymczak:Phys. Rev. B 47 (1993) 8700. Crossref, Google Scholar
- 70 K.Siratori and E.Kita:J. Phys. Soc. Jpn. 48 (1980) 1443. Link, Google Scholar
- 71 J.Hemberger, P.Lunkenheimer, R.Fichtl, H.-A. Krugvon Nidda, V.Tsurkan, and A.Loidl:Nature 434 (2005) 364. Crossref, Google Scholar
- 72 N.Menyuk, K.Dwight, and A.Wold:J. Appl. Phys. 36 (1965) 1088. Crossref, Google Scholar
- 73 C.Colominas:Phys. Rev. 153 (1967) 558. Crossref, Google Scholar
- 74 P.Gibart, J.-L.Dormann, and Y.Pellerin: Phys. Status Solidi 36 (1969) 187. Crossref, Google Scholar
- 75 J.Denis, Y.Allain, and R.Plumier:J. Appl. Phys. 41 (1970) 1091. Crossref, Google Scholar
- 76 I.Nakatani, H.Nosé, and K.Masumoto:J. Phys. Chem. Solids 39 (1978) 743. Crossref, Google 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. Crossref, Google Scholar
- 79 V.Tsurkan, J.Hemberger, M.Klemm, S.Klimm, A.Loidl, S.Horn, and R.Tidecks:J. Appl. Phys. 90 (2001) 4639. Crossref, Google 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. Crossref, Google Scholar
- 81 O.Yamashita, Y.Yamaguchi, I.Nakatani, H.Watanabe, and K.Matsumoto:J. Phys. Soc. Jpn. 46 (1979) 1145. Link, Google Scholar
- 82 J. C. Th.Hollander, G.Sawatzky, and C.Haas:Solid State Commun. 15 (1974) 747. Crossref, Google Scholar
- 83 J.-S.Kang, S. J.Kim, C. S.Kim, C. G.Olson, and B. I.Min:Phys. Rev. B 63 (2001) 144412. Crossref, Google Scholar
- 84 A.Kimura, J.Matsuno, J.Okabayashi, A.Fujimori, T.Shishidou, E.Kulatov, and T.Kanomata:Phys. Rev. B 63 (2001) 224420. Crossref, Google Scholar
- 85 A.Deb, M.Mizumaki, T.Muro, Y.Sakurai, and V.Tsurkan:Phys. Rev. B 68 (2003) 014427. Crossref, Google Scholar
- 86 V. N.Antonov, V. P.Antropov, B. N.Harmon, A. N.Yaresko, and A. Ya.Perlov:Phys. Rev. B 59 (1999) 14552. Crossref, Google Scholar
- 87 T.Watanabe:Solid State Commun. 12 (1973) 355. Crossref, Google Scholar
- 88 A. P.Ramirez, R. J.Cava, and J.Krajewski:Nature 386 (1997) 156. Crossref, Google Scholar
- 89 Z.Chen, S.Tan, Z.Yang, and Y.Zhang:Phys. Rev. B 59 (1999) 11172. Crossref, Google Scholar
- 90 Z.Yang, S.Tan, Z.Chen, and Y.Zhang:Phys. Rev. B 62 (2000) 13872. Crossref, Google 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. Crossref, Google 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. Link, Google Scholar
- 93 S.Iikubo, Y.Yasui, K.Oda, Y.Ohno, Y.Kobayashi, M.Sato, and K.Kakurai:J. Phys. Soc. Jpn. 71 (2002) 2792. Link, Google Scholar
- 94 W.Lee, S.Watauchi, V. L.Miller, R. J.Cava, and N. P.Ong:Science 303 (2004) 1647. Crossref, Google Scholar
- 95 T.Ogasawara, K.Ohgushi, Y.Tomioka, K. S.Takahashi, H.Okamoto, M.Kawasaki, and Y.Tokura:Phys. Rev. Lett. 94 (2005) 087202. Crossref, Google Scholar
- 96 K.Ohgushi, T.Ogasawara, Y.Okimoto, S.Miyasaka, and Y.Tokura:Phys. Rev. B 72 (2005) 155114. Crossref, Google Scholar
- 97 T.Ogasawara, K.Ohgushi, H.Okamoto, and Y.Tokura:J. Phys. Soc. Jpn. 75 (2006) 083707. Link, Google Scholar
- 98 E.Carnall,Jr., D.Pearlman, T. J.Coburn, F.Moser, and T. W.Martin: Mater. Res. Bull. 7 (1972) 1361. Crossref, Google Scholar
- 99 R. K.Ahrenkiel, T. H.Lee, S. L.Lyu, and F.Moser:Solid State Commun. 12 (1973) 1113. Crossref, Google Scholar
- 100 R. K.Ahrenkiel, T. J.Corburn, and E.Carnali: IEEE Trans. Magn. 10 (1974) 2. Crossref, Google Scholar
- 101 R. K.Ahrenkiel, S. L.Lyu, and T. J.Coburn:J. Appl. Phys. 46 (1975) 894. Crossref, Google Scholar
- 102 H.Brändle, J.Schoenes, P.Wachter, F.Hulliger, and W.Reim:Appl. Phys. Lett. 56 (1990) 2602. Crossref, Google Scholar
- 103 H.Brandle, J.Schoenes, P.Wachter, F.Hulliger, and W.Reim:J. Magn. Magn. Mater. 93 (1991) 207. Crossref, Google Scholar
- 104 M. R.Spender and A. H.Morrish:Solid State Commun. 11 (1972) 1417. Crossref, Google Scholar
- 105 M.Mertinat, V.Tsurkan, D.Samusi, R.Tidecks, and F.Haider:Phys. Rev. B 71 (2005) 100408. Crossref, Google 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. Crossref, Google Scholar
- 107 H. V.Philipsborn:J. Cryst. Growth 9 (1971) 296. Crossref, Google Scholar
- 108 L.Goldstein, J.Dormann, R.Druilhe, M.Guittard, and P.Gibart:J. Cryst. Growth 20 (1973) 24. Crossref, Google Scholar
- 109 P.Gibart, L.Goldstein, J.Dormann, and M.Guittard:J. Cryst. Growth 24–25 (1974) 147. Crossref, Google 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. Crossref, Google Scholar
- 111 K.Sato: Jpn. J. Appl. Phys. 20 (1981) 2403. Crossref, Google 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. Crossref, Google Scholar
- 114 P. L.Polavarapu: Appl. Spectrosc. 38 (1984) 26. Crossref, Google Scholar
- 115 V. G.Gregoriou, R.Hapanowicz, A. L.Clark, and P. T.Hammond: Appl. Spectrosc. 51 (1997) 470. Crossref, Google Scholar
- 116 C. A.Mccoy and J. A.de Haseth: Appl. Spectrosc. 42 (1988) 336. Crossref, Google 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 Crossref, Google 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. Crossref, Google Scholar
- 119 T.Arima and Y.Tokura:J. Phys. Soc. Jpn. 64 (1995) 2488. Link, Google Scholar
- 120 S. K.Park, T.Ishikawa, and Y.Tokura:Phys. Rev. B 58 (1998) 3717. Crossref, Google Scholar
- 121 M. L.Cohen and J. R.Chelikowsky:Electronic Structure and Optical Properties of Semiconductors (Springer-Verlag, Berlin, 1988). Crossref, Google Scholar
- 122 L.Ley, R. A.Pollak, F. R.McFeely, S. P.Kowalczyk, and D. A.Shirley:Phys. Rev. B 9 (1974) 600. Crossref, Google Scholar
- 123 J.Matsuno, A.Fujimori, and L. F.Mattheiss:Phys. Rev. B 60 (1999) 1607. Crossref, Google Scholar
- 124 S.Wittekoek and P. F.Bongers:Solid State Commun. 7 (1969) 1719. Crossref, Google 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. Crossref, Google Scholar
- 130 F. S.Ham and G. A.Slack:Phys. Rev. B 4 (1971) 777. Crossref, Google Scholar
- 131 S.Wittekoek, R. P.van Stapele, and A. W. J.Wijma:Phys. Rev. B 7 (1973) 1667. Crossref, Google 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). Crossref, Google Scholar
- 134 T.Inui, Y.Tanabe, and Y.Onodera:Group Theory and Its Applications in Physics (Springer-Verlag, Berlin, 1990). Crossref, Google Scholar
- 135 J.Zaanen, G. A.Sawatzky, and J. W.Allen:Phys. Rev. Lett. 55 (1985) 418. Crossref, Google 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. Crossref, Google Scholar
- 138 B.Hoekstra, R. P.van Stapele, and A. B.Voermans:Phys. Rev. B 6 (1972) 2762. Crossref, Google Scholar
- 139 A.Marais, M.Porte, L.Goldstein, and P.Gibart:J. Magn. Magn. Mater. 15–18 (1980) 1287. Crossref, Google Scholar
- 140 Z.Yang, S.Tan, and Y.Zhang:Solid State Commun. 130 (2004) 511. Crossref, Google Scholar
- 141 S. B.Berger and H. L.Pinch:J. Appl. Phys. 38 (1967) 949. Crossref, Google Scholar
- 142 K.Yosida:Theory of Magnetism (Springer-Verlag, Berlin, 1996). Crossref, Google 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. Crossref, Google Scholar
- 145 Spin–Orbit-Influenced Spectroscopies of Magnetic Solids, ed. H.Ebert and G.Schutz (Springer-Verlag, Berlin, 1996). Crossref, Google 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. Crossref, Google Scholar