Optical study of 4f excitations in rare earth cuprates

Several recent examples are used to demonstrate that Raman and infrared spectroscopy can be successfully used as a novel experimental tool to study microscopic processes involving 4f electrons in rare earth (RE) cuprates. Raman-active crystal field (CF) excitations in Nd₂CuO₄ were measured under hyd...

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spelling	nasplib_isofts_kiev_ua-123456789-1302302025-02-09T17:22:02Z Optical study of 4f excitations in rare earth cuprates Nekvasil, V. Магнетизм Several recent examples are used to demonstrate that Raman and infrared spectroscopy can be successfully used as a novel experimental tool to study microscopic processes involving 4f electrons in rare earth (RE) cuprates. Raman-active crystal field (CF) excitations in Nd₂CuO₄ were measured under hydrostatic pressure up to ∼7 GPa. The observed pressure-induced shifts of the CF levels were interpreted using density-functional-theory-based ab initio calculations and the superposition model. An infrared transmission study of the ⁴Ij, J=9/2, 11/2, 13/2 multiplets of Nd³⁺ in Nd₂CuO₄ reveals a splitting of the Kramers doublets of the order of a few cm⁻¹ due to the Nd-Cu exchange interaction. This study shows that these splittings can be described by an effective anisotropic exchange Hamiltonian for the Nd³⁺ ion expressed in terms of spherical tensor operators up to the sixth order. The isotropic term in the exchange Hamiltonian vanishes for symmetry reasons in this case. An analysis of the infrared transmission spectra in RE₁₊xBa₂₋xCu3O₆₊δ (RE=Nd,Sm) up to ∼ 10 000 cm⁻¹ indicates that, besides the regular sites, the RE ions also occupy Ba sites, even in the samples with the cation stoichiometry 1–2–3. The assistance of the Grant Agency of the Czech Republic in the form of its grant No. 202/00/1602 is gratefully acknowledged. 2002 Article Optical study of 4f excitations in rare earth cuprates / V.Nekvasil // Физика низких температур. — 2002. — Т. 28, № 7. — С. 739-744. — Бібліогр.: 28 назв. — англ. 0132-6414 PACS: 78.30.-j, 71.70.-d https://nasplib.isofts.kiev.ua/handle/123456789/130230 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language	English
topic	Магнетизм Магнетизм
spellingShingle	Магнетизм Магнетизм Nekvasil, V. Optical study of 4f excitations in rare earth cuprates Физика низких температур
description	Several recent examples are used to demonstrate that Raman and infrared spectroscopy can be successfully used as a novel experimental tool to study microscopic processes involving 4f electrons in rare earth (RE) cuprates. Raman-active crystal field (CF) excitations in Nd₂CuO₄ were measured under hydrostatic pressure up to ∼7 GPa. The observed pressure-induced shifts of the CF levels were interpreted using density-functional-theory-based ab initio calculations and the superposition model. An infrared transmission study of the ⁴Ij, J=9/2, 11/2, 13/2 multiplets of Nd³⁺ in Nd₂CuO₄ reveals a splitting of the Kramers doublets of the order of a few cm⁻¹ due to the Nd-Cu exchange interaction. This study shows that these splittings can be described by an effective anisotropic exchange Hamiltonian for the Nd³⁺ ion expressed in terms of spherical tensor operators up to the sixth order. The isotropic term in the exchange Hamiltonian vanishes for symmetry reasons in this case. An analysis of the infrared transmission spectra in RE₁₊xBa₂₋xCu3O₆₊δ (RE=Nd,Sm) up to ∼ 10 000 cm⁻¹ indicates that, besides the regular sites, the RE ions also occupy Ba sites, even in the samples with the cation stoichiometry 1–2–3.
format	Article
author	Nekvasil, V.
author_facet	Nekvasil, V.
author_sort	Nekvasil, V.
title	Optical study of 4f excitations in rare earth cuprates
title_short	Optical study of 4f excitations in rare earth cuprates
title_full	Optical study of 4f excitations in rare earth cuprates
title_fullStr	Optical study of 4f excitations in rare earth cuprates
title_full_unstemmed	Optical study of 4f excitations in rare earth cuprates
title_sort	optical study of 4f excitations in rare earth cuprates
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2002
topic_facet	Магнетизм
url	https://nasplib.isofts.kiev.ua/handle/123456789/130230
citation_txt	Optical study of 4f excitations in rare earth cuprates / V.Nekvasil // Физика низких температур. — 2002. — Т. 28, № 7. — С. 739-744. — Бібліогр.: 28 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT nekvasilv opticalstudyof4fexcitationsinrareearthcuprates
first_indexed	2025-11-28T13:46:21Z
last_indexed	2025-11-28T13:46:21Z
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fulltext	Fizika Nizkikh Temperatur, 2002, v. 28, No. 7, p. 739–744 Optical study of 4f excitations in rare earth cuprates V. Nekvasil Institute of Physics, Czech Academy of Sciences, Cukrovarnická 10, 162 53 Prague 6, Czech Republic E-mail: nekvasil@fzu.cz Received February 2, 2002 Several recent examples are used to demonstrate that Raman and infrared spectroscopy can be successfully used as a novel experimental tool to study microscopic processes involving 4f electrons in rare earth (RE) cuprates. Raman-active crystal field (CF) excitations in Nd CuO2 4 were measured under hydrostatic pressure up to ~ 7 GPa. The observed pressure-in- duced shifts of the CF levels were interpreted using density-functional-theory-based ab initio calculations and the superposition model. An infrared transmission study of the 4IJ , J � 9/2, 11/2, 13/2 multiplets of Nd3+ in Nd CuO2 4 reveals a splitting of the Kramers doublets of the order of a few cm–1 due to the Nd–Cu exchange interaction. This study shows that these splittings can be described by an effective anisotropic exchange Hamiltonian for the Nd3+ ion expressed in terms of spherical tensor operators up to the sixth order. The isotropic term in the exchange Hamiltonian vanishes for symmetry reasons in this case. An analysis of the infra- red transmission spectra in RE1+xBa2–xCu3O6+� (RE = Nd, Sm) up to ~ 10 000 cm–1 indicates that, besides the regular sites, the RE ions also occupy Ba sites, even in the samples with the cation stoichiometry 1-2-3. PACS: 78.30.–j, 71.70.–d 1. Introduction The presence of magnetic rare earth (RE) ions has no detrimental effect on superconductivity of the high-Tc cuprates. Therefore, the 4f states in RE cuprates have been widely used as a noninteracting probe for examination of superconductivity-related phenomena, including the doping-induced charge transfer from the charge reservoir to the «supercon- ducting» CuO2 planes, the phase-separation-related charge inhomogeneities and local structure defor- mations, and the pseudogap openings (for recent surveys see Refs. 1,2). The RE subsystem also ex- hibits interesting magnetic properties, including strongly anisotropic magnetic moments, Ising-like antiferromagnetism, magnetostriction, or carrier- concentration-dependent spin and lattice dimensio- nality of the magnetic order [3–7]. An important prerequisite for the study of physi- cal properties of the RE cuprates is an understand- ing of the microscopic interactions involving 4f electrons: the crystal field (CF) interaction, the magnetic exchange interaction, and the coupling of 4f excitations and phonons. The principal experi- mental tool for examining these interactions, by measurements of the 4f excitation spectra, has been inelastic neutron scattering [1,2]. Despite the widespread belief that optical methods are not ap- propriate in opaque materials, sharp and well-re- solved 4f excitations in RE cuprates have been re- vealed by infrared (IR) [8] and Raman [9] spectroscopies. Surveyed in this article are recent results illustrating how these two techniques have been used to study microscopic processes involving 4f electrons in RE cuprates. This article is organized as follows. The effect of hydrostatic pressure on the Raman active 4f state excitations in Nd CuO42 is studied in the next Sec- tion. The splitting of the Kramers doublets in this compound, revealed using the IR spectroscopy, are described in terms of the anisotropic Nd–Cu ex- change Hamiltonian in Sec. 3. The 4f excitations spectra in REBa Cu O2 3 6��(RE = Nd, Sm) are dis- cussed in Sec. 4. © V. Nekvasil, 2002 2. 4f spectra in Nd CuO2 4 under pressure An interaction with the crystal field produced by the neighboring core charges and valence elec- tronic density is the strongest perturbation of the free ion 4f-shell state of trivalent RE ions in cu- prates. The CF interaction Hamiltonian is usually considered in the form [10]: H B C CCF kq q k q k k q � � �� ( )[ ] [ ] , , (1) where the functions Cq k[ ] transform as tensor ope- rators under simultaneous rotation of the coordi- nates of all the f electrons, Bkq are the so-called CF parameters. The above-mentioned optical methods have ma- de possible the determination of a sufficient num- ber of CF energy levels in Nd CuO2 4 to ensure re- liability of the phenomenological parameters Bkq calculated by solving numerically the inverse secu- lar problem [9,11]. Recently, CF excitations of the Nd3+ ions in Nd CuO2 4 were measured under hydrostatic pres- sure using Raman spectroscopy [12]. Two relatively intense CF peaks near 750 cm–1 and 1995 cm–1 were detected in applied pressure up to ~ 7 GPa. The energy of the 750 cm–1 CF excitation within the ground state J multiplet increases nearly lin- early as a function of pressure at an average rate of 12.9(5) cm–1/GPa (Fig. 1). It shows much larger pressure dependence than the transitions at 1992/1997 cm–1 from the ground state to the ex- change-split Kramers doublet within the first ex- cited J multiplet (Fig. 2). The energies of this doublet increase at rates of 1.7(2) cm–1 and 2.0(2) cm–1/GPa. Two theoretical methods were used to interpret the pressure dependence of the CF interaction. The k = 4 and 6 CF parameters were predicted using the superposition model [13] that has proved to be effi- cient in the CF modeling in cuprates [4]. The model makes it possible to describe the parameters Bkq in Eq. (2) in terms of intrinsic (pair) CF pa- rameters bk(R): B S i b Rkq kq k i i � � ( ) ( ), (2) where S ikq( ) is the geometrical factor determined by the angular coordinates of the ligands at the same distance Ri from the RE ion. The superposition model does not apply to the k � 2 parameters, where the long-range electrostatic contribution dominates. Therefore, the CF parame- ter B20 was calculated using the ab initio method, in which the electronic structure and related distri- bution of the ground state charge density are ob- tained from calculations based on the density func- tional theory (DFT). Within the DFT, the CF parameter B20 , originating from the effective po- tential V inside the crystal, can be written as [14]: � � � �B a R r V r r drf20 2 0 4 2 2 0 2 0 � ( ) , (3) where nonspherical components � �V r2 0 reflect not only the nuclear potentials and Hartree part of the inter-electronic interaction but also the exchange correlation term, which accounts for many-particle 740 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 V. Nekvasil In te n si ty 0 1 2 3 4 5 Pressure, GPaRaman shift, cm – 1 P e a k p o si tio n , cm – 1 4 4 9/2 11/2 bT = 5 K P, GPa 5.8 4.7 3.2 2.5 0.8 a theory exp 2010 2005 2000 1995 1990 �6 �6 1950 2000 2050 Fig. 2. (a) Raman spectra of Nd CuO2 4 in the spectral range of the 1995-cm–1 CF excitation for pressures of 0.8–5.8 GPa (T = 5 K). (b) Experimental and calcu- lated pressure dependences of the peak positions of the CF excitations. The filled and unfilled triangles repre- sent peak positions measured at 5 and 44 K, respectively. The lines represent linear regressions of the data [12]. In te n si ty 0 1 2 3 4 5 6 7700 800750 850 Pressure, GPa T = 5 K P, GPa 5.8 4.7 3.2 2.5 0.8 830 810 790 770 750 4 9/2 theory Raman shift, cm – 1 P e a k p o si tio n , cm – 1 ba �6 �6 exp. Fig. 1. (a) Raman spectra of Nd CuO2 4 in the spectral range of the 750-cm–1 CF excitation for pressures of 0.8–5.8 GPa (T = 5 K). (b) Experimental (■, solid li- ne) and calculated (�, dashed line) pressure dependen- ces of the peak position of the CF excitation. The lines in (b) are guides to the eye [12]. effects. The radial wave function R4f describes the radial shape of the localized 4f charge density of the RE3+ ion in the compound studied. The calculation of the pressure dependence of the CF parameters included two steps. First, Eqs. (2), (3) were used to calculate the theoretical ratio Bkq(P)/Bkq(0) with allowance for the data on the pressure evolution of the Nd CuO2 4 crystal structure measured by synchrotron x-ray powder diffraction [15] and the available superposition model parameters [4]. The effect of pressure on the underlying electronic density of states (DOS) is shown in Fig. 3. It is worth noting that the DOS curve is broadened by ~ 0.5 eV at an applied pres- sure of 7 GPa. This broadening is connected with a slight redistribution of the charge density, which results in an increase of the absolute value of the calculated parameter B20 . In the second step each phenomenological parameter Bkq [11] was multi- plied by the theoretical ratio Bkq(P)/Bkq(0). As an illustration, the CF parameters obtained in this way for the applied pressure 7 GPa are compared with the ambient pressure parameters in Table 1. The absolute values of the individual CF parame- ters are increased by ~ 6–18 % at 7 GPa compared to those at zero pressure. The theoretical approach described above gives transition frequencies increasing nearly linearly at rates of ~ 11.7 and ~ 0.7 cm–1/GPa for excitations near 750 and 1992(1997) cm–1, respectively. Re- garding the lower-energy transition, very good ag- reement is achieved with the experimental result of 12.9 cm–1 (Fig. 1). The calculated value of the pressure dependence of the higher energy transi- tions is smaller than the experimental values of ~ 1.7 and 2.0 cm–1 for the peaks at 1992 and 1997 cm–1 (Fig. 2), respectively. It bears noting that these transitions include the ground-state level and the lowest energy level in the J � 11/2 multiplet. The CF calculation shows that the pres- sure dependences of these levels are very similar, –4.5 and –3.8 cm–1/GPa, respectively. This ex- plains why the resulting pressure-induced shift of the transition energy is small. The remaining dis- crepancy between the experimental and calculated values is ascribed to a small pressure-induced shift of the free ion levels, not taken into account in the above calculations. A detailed analysis of the pressure-induced in- crease in the separation of the doublet near 1995 cm–1 (Fig. 2) indicated that in addition to the CF parameters the parameters �kq of the Hamil- tonian of the anisotropic Nd–Cu exchange interac- tion, Eq. (4), are pressure dependent [12]. 3. Anisotropy of the Nd–Cu exchange interaction in RE cuprates The IR transmission study of the 4f spectra in the antiferromagnet Nd CuO2 4 yielded a splitting of the CF Kramers doublets of the order of a few cm–1 due to the exchange interaction between Nd and Cu (see the third column of Table 2) [16]. An example of the experimental spectra of the transi- tion from the ground state to an exchange-split Kramers doublet at ~ 5870 cm–1 is shown in Fig. 4. The exchange anisotropy due to the orbital mo- ments of the f electrons is pronounced in this case: the isotropic Heisenberg-type exchange alone ap- pears to be completely incapable of explaining the observed doublet splittings [11]. To account for these splittings one has to consider the complete Hamiltonian within the molecular field approxima- tion describing the exchange interaction of the 4f Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 741 Optical study of 4f excitations in rare earth cuprates Fig. 3. Total density of electron states (DOS) of Nd CuO2 4 calculated at ambient pressure and at 7 GPa [12]. Table 1 CF parameters Bkq in Nd CuO2 4 (in cm–1) obtained from a fit to IR absorption data at ambient pressure [11] and calculated at 7 GPa using the superposition model and the DFT based ab initio method (see text) Parameter P � 0 [11] P � 7 GPa [12] B 20 –335 –373 B 40 –2219 –2574 B 44 1634 1935 B 60 224 246 B 64 1494 1584 electrons of an Nd ion with the magnetically pola- rized Cu sublattice [17,18]. Table 2 Splitting of the Nd3+ Kramers doublets in Nd CuO2 4 as measured by infrared transmission [16] and calculated using Eq. (4) [19] (all energies in cm–1) J multiplet CF level [10] Observed splitting Calculated splitting 9/2 Ground state 5.5 5.7 11/2 1995 2006 2013 2077 2414 3.5 3.5 4.0 2.0 3.0 3.7 3.5 3.7 2.1 2.9 13/2 3950 2.5 2.7 15/2 5868 2.0 1.3 The perturbation single-ion Hamiltonian under consideration then includes, besides the standard CF term HCF from Eq. (1), an exchange term Hexch : H T i ikq q k ik q exch � � ��2 [ ] , ( ) ( )s n, (4) where �kq are the exchange parameters, T ik[ ]( ) are the irreducible unit tensor operators which act on the orbital part of the Nd wave function, s(i) is the spin of a Nd electron, and n is the unit vector directed along the magnetization of the Cu sub- lattice. There are six independent parameters �kq in Hexch for Nd ions occupying the tetragonal sym- metry sites in Nd CuO2 4. A least-squares procedure has been utilized to fit the splitting of the eight observed Kramers doublet splittings using the above-mentioned perturbation Hamiltonian [19]. The results of the final fit are summarized in Table 2; the corresponding best-fit values of �kq are given in Table 3. It is worthwhile to note that the contributions of the second- and fourth-order terms to the splittings are two orders of magnitude larger than that of the isotropic term (k q� � 0) in the exchange operator. This finding is compatible with the symmetry considerations indi- cating that the isotropic term in the exchange Hamiltonian vanishes when only the nearest Cu neighbors of Nd are considered [20]. It also shows the importance of the higher-order terms in Eq. (4), neglected in magnetic studies in which the ani- sotropic RE–Cu coupling in Nd CuO2 4 [20,21] and PrBa Cu O2 3 6�� [22,23] is represented by a pseu- do-dipolar term. Table 3 The best-fit values of the exchange parameters �kq (in cm–1) in Eq. (4) [19] Exchange parameter � kq � 00 –7(4) � 20 –491(130) � 40 –177(33) � �� –257(12) � 60 15(16) � 64 47(13) 4. Crystal field study in RE Ba Cu O1 2 3 6� � �x x � (RE = Nd, Sm) In this Section we report a systematic study of CF transitions in NdBa Cu O2 3 6�� (� ~ 0) and Sm Ba Cu O1 2 3 6� � �x x � (x � 0.01, x = 0.03, 0.05, and 0.11; � ~ 0) by IR absorption [24,25]. The tran- sitions involving Kramers doublets within the low- 742 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 V. Nekvasil Fig. 4. Nd CuO2 4 IR transmission as a function of tem- perature [16]. est-energy 4I term and 6H term in the Nd and Sm compounds, respectively, were determined. Exam- ples of these transitions are shown in Figs. 5 and 6. The large number of peaks in the experimental spectra indicates that there exists more than one type of RE site. We observe that the f–f transitions are electric-dipole forbidden for the RE ions at re- gular D4h-symmetry sites in ideal REBa2Cu3O6 . A phenomenological CF analysis of the IR data (Sec. 2), including the neutron scattering data for the J � 9/2 multiplet in NdBa2Cu3O6 [26], al- lowed identification and fitting of the CF spectra of Nd and Sm ions at regular sites. Detailed CF cal- culations using the superposition model and the ab initio method based on the density-functional the- ory described in Sec. 2 indicate [27] that additional bands in the IR spectra correspond to the RE3+ ions in the C4� -symmetry Ba sites. The sets of the CF parameters for regular as well as Ba sites obtained using the above-mentioned methods are summarized in Table 4. Concluding this part, we note that the CF tran- sitions at RE/Ba sites have been observed in all RE1+xBa2–xCu3O6+� samples studied, including those with x = 0. This finding supports recent data indicating that the presence of a relatively small quantity of the magnetic Pr3+ ions at the Ba sites is the main reason for anomalous behavior of PrBa2Cu3O7 , including the suppression of super- conductivity as well as the appearance of the anti- ferromagnetic ordering in the Pr sublattice at a Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 743 Optical study of 4f excitations in rare earth cuprates Fig. 6. IR spectra of CF transitions (6H5/2 � 6H13/2) in Sm1+xBa2–xCu3O6+� in the 4800–5050 cm–1 range. The dashed arrows indicate CF transitions associated with Sm/Ba sites. See Ref. 25 for additional details. Table 4 CF parameters (in cm–1) in Sm1+xBa2–xCu3O6 [6] and Nd1+xBa2–xCu3O6 [5] obtained by an analysis of the IR spectra (see text) B kq D 4h site C 4v site k q Sm Nd Sm 2 0 282(5) 380(28) –227 4 0 –2481(12) –2956(34) 24 4 4 1307(10) 1664(25) –331 6 0 321(12) 526(15) –427 6 4 1931(6) 2021(10) 624 Fig. 5. IR spectra of CF transitions in NdBa2Cu3O6 from the ground state multiplet 4I9/2 to the second excited multiplet 4I13/2 (ab and ac platelets at 4.2 K). The filled circles and asterisks indicate strong and weak absorption bands, respectively. See Ref. 24 for additio- nal details. temperature at least one order of magnitude higher than for other RE elements [28]. Acknowledgements The assistance of the Grant Agency of the Czech Republic in the form of its grant No. 202/00/1602 is gratefully acknowledged. 1. U. Staub and L. Soderholm, in: Handbook on the Physics and Chemistry of Rare Earth, Vol. 30, K. A. Gschneidner, Jr., L. Eyering, and M. B. Maple (eds.), North Holland, Amsterdam (2001), p. 491. 2. J. Mesot and A. Furrer, J. Supercond. 10, 623 (1997). 3. T. W. Clinton and J. W. Lynn, Phys. Rev. B51, 15429 (1995). 4. V. Nekvasil, J. Magn. Magn. Mater. 140–144, 1265 (1995); Nekvasil, M. Divis, G. Hilscher, and E. Holland-Moritz, J. Alloys Comps. 225, 578 (1995). 5. V. Nekvasil, S. Jandl, T. Strach, T. Ruf, and M. Cardona, J. Magn. Magn. Mater. 177–181, 535 (1998). 6. I. K. Aminov, B. Z. Malkin, and M. A. Teplov, in: Handbook on the Physics and Chemistry of Rare Earth, Vol. 22, K. A. Schneider, Jr. and L. Eyering, (eds.), North-Holland, Amsterdam (1996), p. 295. 7. V. V. Eremenko, T. V. Sukhareva, and V. N. Samo- varov, Phys. Solid State 42, 816 (2000). 8. M. L. Jones, D. W. Shortt, B. W. Sterling, A. L. Schawlow, and R. M. Macfarlane, Phys. Rev. B46, 611 (1992). 9. S. Jandl, M. Iliev, C. Thomsen, M. Cardona, B. M. Wanklyn, and C. Changkang, Solid State Commun. 87, 609 (1993); S. Jandl, P. Dufour, T. Strach, T. Ruf, M. Cardona, V. Nekvasil, C. Chen, and B. M. Wanklyn, Phys. Rev. B52, 15558 (1995). 10. B. G. Wybourne, Spectroscopic Properties of Rare Earths, Wiley, New York (1965). 11. S. Jandl, P. Dufour, P. Richard, V. Nekvasil, D. I. Zhigunov, S. A. Barilo, and S. V. Shiryaev, J. Lumin. 78, 197 (1998). 12. I. Loa, K. Syassen, M. Divis, V. Nekvasil, S. Jandl, A. A. Nugroho, and A. A. Menovsky, Phys. Rev. B64, 214106 (2001). 13. D. J. Newman and Betty Ng, Rep. Prog. Phys. 52, 699 (1989). 14. M. Divis, V. Nekvasil, and J. Kuriplach, Physica C301, 23 (2998); M. Divis and V. Nekvasil, J. Al- loys Comps. 323–324, 567 (2001). 15. H. Wilhelm, C. Cross, E. Reny, G. Demazeau, and M. Hanfland, J. Mater. Chem. 8, 2729 (1998). 16. S. Jandl, P. Richard, V. Nekvasil, D. I. Zhigunov, S. N. Barilo, and S. V. Shiryaev, Physica C314 189 (1999). 17. P. M. Levy, Phys. Rev. 135, 155 (1964). 18. W. P. Wolf, J. Phys. (Paris) 32, C1–26 (1971). 19. A. A. Nugroho, V. Nekvasil, I. Veltrusky, S. Jandl, P. Richard, A. A. Menovsky, F. R. de Boer, and J. J. M. Franse, J. Magn. Magn. Mater. 226–230, 973 (2001). 20. R. Sachidanandam, T. Yilidirim, A. B. Harris, A. Aharony, and O. Entin-Wohlman, Phys. Rev. B56, 260 (1997). 21. Ph. Bourges, L. Boudarene, and D. Petitgrand, Physica B180–181, 128 (1992). 22. S. V. Maleev, JETP Lett. 67, 947 (1998). 23. S. J. S. Lister, A. T. Boothroyd, N. H. Andersen, B. H. Larsen, A. A. Zhokhov, A. N. Christensen, and A. R. Wildes, Phys. Rev. Lett. 86, 5994 (2001). 24. A. A. Martin, T. Ruf, M. Cardona, S. Jandl, D. Barba, V. Nekvasil, M. Divis, and T. Wolf, Phys. Rev. B59, 6528 (999). 25. D. Barba, S. Jandl, V. Nekvasil, M. Marysko, M. Divis, T. Wolf, A. A. Martin, C. T. Lin, and M. Cardona, Phys. Rev. B63, 54528 (2001). 26. P. Allenspach, J. Mesot, U. Staub, M. Guillaume, A. Furrer, S.-I. Yoo, M. J. Kramer, R. W. McCal- lum, H. Maletta, H. Blank, H. Mutka, R. Osborn, M. Arai, Z. Bowden, and A. D. Taylor, Z. Phys. B95, 301 (1995). 27. M. Divis and V. Nekvasil, J. Alloys Comps. 323–324, 567 (2001). 28. H. A. Blackstead, J. D. Dow, I. Felner, and W. B. Yelon, Phys. Rev. B63, 094517 (2001). 744 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 V. Nekvasil

Optical study of 4f excitations in rare earth cuprates

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