Crystal-field excitations in the visible spectrum of Nd2CuO4

Journal of Alloys and Compounds 374 (2004) 14–17

Crystal-field excitations in the visible spectrum of Nd2 CuO4 P. Richard a , S. Jandl a , J. Hölsä b , V. Nekvasil c,∗ a

b

Centre de Recherche sur les Propriétés Électroniques des Matériaux Avancés, Département de Physique, Université de Sherbrooke, Sherbrooke, Canada J1K 2R1 Department of Chemistry, Laboratory of Inorganic Chemistry, University of Turku, Turku FIN-20014, Finland c Institute of Physics ASCR, Cukrovarnická 10, CZ-162 53 Praha 6, Czech Republic

Abstract A phenomenological simulation was carried out for 41 experimental crystal-field (CF) levels within the 4 I9/2–15/2 , 4 F3/2–9/2 , 4 S3/2 and H9/2 J manifolds, including the available infrared (IR) data up to ∼15 000 cm−1 for the Nd3+ ions in the Nd2 CuO4 single crystals. The CF Hamiltonian for the tetragonal C4v symmetry was diagonalized together with the free-ion Hamiltonian in a basis that spans the entire 4f3 configuration. A rms error of 9 cm−1 between the calculated and experimental energy level schemes was obtained. A comparison of the spectra in the visible region between the insulating Nd2 CuO4 and the metallic Nd2−x Cex CuO4 , allowed identifying the absorption bands associated with the development of the charge-doping induced local structural distortions in the superconducting regime. © 2003 Elsevier B.V. All rights reserved. 2

Keywords: Crystal-field excitations; Optical absorption; Cuprate superconductors

1. Introduction Electron Raman scattering and infrared (IR) absorption provided a powerful experimental tool to study the crystal-field (CF) excitations in Nd2−x Cex CuO4 [1–4]. They complement inelastic neutron experiments (see ref. [5], and references therein) in detecting the intermanifold f–f transitions and determining reliable sets of the CF parameters. The CF excitations in R2−x Cex CuO4 (R: rare earth) are frequently being used as a probe for phenomena associated with the Ce-doping, turning the system from an insulating to a metallic state which becomes superconducting below Tc ∼ 25 K [6]. The infrared absorption studies of the CF excitations in Nd2−x Cex CuO4 do not serve well for this particular purpose, as the metallic phase is opaque in the IR region for a transmission in the ab plane. It is thus desirable to extend the measurements of the CF excitations into the visible range, where both the metallic and superconducting phases are transparent [7]. The purpose of the present communication is threefold. First, we report the experimentally determined CF energy levels of the Nd3+ ion in the insulating parent compound Nd2 CuO4 in the visible region up to ∼15 000 cm−1 . To ∗

Corresponding author. Fax: +420-2-3123184. E-mail address: [email protected] (V. Nekvasil).

0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.11.043

the set of the 25 levels within the four lowest-energy 4 IJ (J = 9/2, 11/2, 13/2, and 15/2) manifolds, deduced earlier from the IR absorption spectra [3], additional 16 levels are included for the six 4 FJ (J = 3/2, 5/2, 7/2, and 9/2), 4S 2 3/2 and H9/2 manifolds. Second, experimental spectra are analyzed theoretically diagonalizing the many parameter free-ion Hamiltonian, together with the CF Hamiltonian, in a basis that spans the entire 4f3 configuration of Nd3+ . Third, based on this CF study, discussed is the nature of new lines at ∼13 000–14 000 cm−1 , appearing below Tc in the absorption spectra of the electron-type superconductor Nd1.85 Ce0.15 CuO4 [8].

2. Experimental The Nd2 CuO4 single crystal sample was grown by the flux method [9]. The CF excitations of the Nd3+ ion in Nd2 CuO4 were detected between 4.2 and 300 K, by infrared transmission spectroscopy with the unpolarized incident beam perpendicular to the ac plane. The Nd2 CuO4 100 ␮m thick sample was mounted on a closed cycle cryostat cold finger and 0.5 cm−1 resolution transmission spectra were obtained in the range of 11 000–15 000 cm−1 with a BOMEM DA3.002 Fourier transform interferometer equipped with InSb and Si detectors, quartz-halogen and globar sources as well as CaF2

P. Richard et al. / Journal of Alloys and Compounds 374 (2004) 14–17

15

and quartz beamsplitters. The crystal structure of Nd2 CuO4 belongs to the T phase with the I4/mmm (#139) space group [6]. The Nd3+ ion occupies in Nd2 CuO4 the Wyckoff 4e position with C4v point symmetry.

3. Energy level calculations The effective free-ion Hamiltonian HFI considered comprises the Coulomb interaction, the spin-orbit coupling and the electrostatic two- and three body interactions described respectively by the Slater integrals Fk (k = 0, 2, 4, and 6), the spin-orbit radial integral ζ 4f , the Trees parameters α, β and γ and the Judd parameters Tk (k = 2, 3, 4, 6, 7, 8):
HFI = F k (nf, nf)fk + ζ4f ASO + αL(L + 1) k

+ βG(G2 ) + γG(R7 ) +




T k tk ,

(1)

k

where the angular parts fk, ASO , L, G(G2 ), G(R7 ), and tk have their usual meanings [10,11]. The CF Hamiltonian HCF is written in the Wybourne notation [10]:
HCF = Bqk Cqk , (2) k

where the parameters Bqk are coefficients of the CF expansion, and Cqk ’s are the components of tensor operators of rank k = 2, 4, 6. For the Nd3+ C4v symmetry site in Nd2 CuO4 there are 19 parameters to be determined from the experimental data. Due to their sparseness–41 CF levels spanning over four terms–the Judd parameters Tk were fixed to their usual values [12]. The Trees parameters were optimized individually. The initial free-ion parameter values were taken from [13] for NdOF and those of the CF parameter from a previous study of the 4 I ground term [3]. The phenomenological free-ion and CF parameters (Eqs. (1) and (2)) were determined by using the program REEL [14].

Fig. 1. The 4 I9/2 → 4 F3/2 transition range in the absorption spectrum of Nd2 CuO4 at 4.2 K. Arrows correspond to regular site Nd3+ CF excitations.

lowed character. This was evidenced by the calculations for the Γ 7 component of the 4 S3/2 manifold. Forty-one CF levels were finally deduced from the absorption spectra of Nd2 CuO4 (Table 1). At the beginning of the fitting procedure only unambiguously assigned experimental levels were included. At this step the set consisting of the electron repulsion parameters (F2 , F4 , F6 ), the spin-orbit coupling constant ζ 4f and the five CF parameters were adjusted. The remaining free-ion parameters (α, β, and γ) were varied individually then, as well. When the additional energy levels were included into the refinement, the iteration procedure was repeated. Practically without exception (Table 1),

4. Results and discussion The 4f3 electron configuration of the Nd3+ ion gives rise to 41 2S+1 LJ levels all of which situate below 67 000 cm−1 . However, only a fraction of all these levels are accessible in Nd2 CuO4 by one photon absorption because of the limited transparency of the host lattice. The absorption techniques used in this work yielded the transitions in the Nd2 CuO4 single crystals from the 4 I9/2 ground level to the excited 4F 4 2 3/2–9/2 , S3/2 and H9/2 manifolds (Figs. 1–4). The resulting experimental CF levels, together with the available data for the 4 I9/2–15/2 manifolds are given in Table 1. In some cases the absorption to some levels with the Γ 7 representation was weak and masked by stronger bands of al-

Fig. 2. The 4 I9/2 → 4 F5/2 , 2 H9/2 transition range in the absorption spectrum of Nd2 CuO4 at 4.2 K. Arrows correspond to regular site Nd3+ CF excitations while stars are associated with defects.

16

P. Richard et al. / Journal of Alloys and Compounds 374 (2004) 14–17 Table 1 Experimental and calculated energy level schemes for Nd2 CuO4 (in cm−1 ) Level

Fig. 3. The 4 I9/2 → 4 F7/2 , 4 S3/2 transition range in the absorption spectrum of Nd2 CuO4 at 4.2 K. Arrows correspond to regular site Nd3+ CF excitations.

it was possible to label the calculated CF levels with the irreducible representations [15] determined from the spectral measurements. In the final simulation both the free-ion and the CF interactions were treated simultaneously. The high quality and reliability of the simulation is reflected in the low (9 cm−1 ) rms deviation (Table 1). All the adjusted parameters reached stable and physically acceptable values. The absence of systematic discrepancies between the calculated and experimental energy level schemes indicates that the free-ion effects are well reproduced. As for the individual CF splittings, with the exception of the Γ 6 component of the 4F −1 7/2 manifold at 13 277 cm , there are no discrepancies significantly larger than the rms value. An anomalous CF

4I

9/2

4I

11/2

4I

13/2

4I

15/2

Experimental

Calculated

Γ6 Γ7 Γ6 Γ7 Γ6

0 119 168 216 747

10 130 177 230 755

−10 −11 −9 −14 −8

Γ6 Γ6 Γ7 Γ7 Γ6 Γ7

1995 2006 2013 2077 2383 2414

1988 2002 2008 2069 2377 2409

7 4 5 8 6 5

Γ6 Γ7 Γ6 Γ7 Γ6 Γ7 Γ7

3918 3924 3950 3964 4329 4329 4410

3912 3917 3944 3955 4328 4326 4407

6 7 6 9 1 3 3

Γ7 Γ7 Γ6 Γ6 Γ6 Γ7 Γ7 Γ6

5754 5824 5868 5914 6400 – 6570 6585

5756 5827 5872 5920 6403 6463 6578 6588

−2 −3 −4 −6 −3 – −8 −3

Γ7 Γ6

11 322 11 389

11 322 11 380

Γ7 Γ6 Γ6 Γ7 Γ6 Γ7 Γ7 Γ6

12 12 12 12 12 12 12 –

12 12 12 12 12 12 12 12

7/2

Γ6 Γ7

4S

3/2

4F

7/2

4F

3/2

4F

5/2

4F

4F

9/2

+ 2 H9/2

Difference

272 290 340 454 510 544 607

0 9

270 287 342 456 508 528 607 649

2 3 −2 −2 2 16a 0b –

13 277 13 304

13 303 13 315

−26 −11b

Γ7 Γ6

– 13 446

13 428 13 436

– 10b

Γ6 Γ7

13 458 –

13 458 13 526

–

Γ6 Γ7 Γ6 Γ7 Γ6

14 525 14 565 14 632 – –

14 14 14 14 14

−6 −6 13 – –

531 571 619 722 781

0

Number of levels: 41/182; rms σ: 9; average deviation: 8. a Experimental symmetry Γ . 6 b Ref. [7].

Fig. 4. The 4 I9/2 → 4 F9/2 transition range in the absorption spectrum of Nd2 CuO4 at 4.2 K. Arrows correspond to regular site Nd3+ CF excitations.

splitting has been reported earlier for the 2 H9/2 and 2 H11/2 manifolds in various compounds (see e.g., refs. [16,17]) and discussed in terms of the two electron CF interaction [18]. However, of these two manifolds the latter was not observed experimentally and the former was reproduced quite

P. Richard et al. / Journal of Alloys and Compounds 374 (2004) 14–17 Table 2 Free-ion and crystal-field parameters for Nd3+ in Nd2 CuO4

the local structural distortions when entering into the superconducting regime.

Parameter

Valuea,b (cm−1 )

Parameter

Valuea (cm−1 )

[3]

F0

23 332(1) 71 323(6) 50 241(16) 34 933(34) [21.02] [−604] [1532]

ζ 4f B20 B40 B44 B60 B64

867.43(55) −344(26) −2157(38) 1566(29) 234(22) 1507(13)

−335 −2219 1634 224 1494

F2 F4 F6 α β γ

17

The Trees parameters α, β, and γ were not varied freely but optimized individually. No practical change from starting values was observed. The Judd parameters T 2 = 303, T 3 = 41, T 4 = 66, T 6 = −289, T 7 = 317 and T 8 = 301 were not varied. a The values in brackets are the estimated standard deviations of the parameters. b The parameter values in square brackets were not varied in the simulations.

normally. Thus, the need of the inclusion of the two electron CF terms to describe these CF splittings for Nd2 CuO4 could not be tested. The best-fit CF parameters (Table 2) are very close to those obtained in earlier IR study where only the nearly pure Russell-Saunders term 4 I (97–100% in 4 I) was involved [3]. The preliminary ab plane reflectance data on Nd1.85 Ce15 CuO4 revealed two extra absorption bands at ∼13 517 and 13 659 cm−1 , absent in Nd2 CuO4 . These bands appear in Nd1.85 Ce0.15 CuO4 below Tc in the cooling process and disappear in the warming cycle above Tc [7]. This finding is compatible with the EXAFS study of Nd1.85 Ce0.15 CuO4 and Nd2 CuO4 [19], indicating that the Ce-doping induced broadening of the in-plane Cu–O–Cu angle distribution in the superconducting compound is enhanced below Tc . The present study supports these considerations: the energy gap between the 13 659 cm−1 band and the nearest regular CF transition band is as large as ∼130 cm−1 (Table 1).

5. Conclusions The absorption spectra of the Nd3+ ions in the Nd2 CuO4 single crystals were measured and analysed in the IR and visible regions up to 15 000 cm−1 . The CF energy level scheme of the 4 I9/2–15/2 , 4 F3/2–9/2 , 4 S3/2 and 2 H9/2 free-ion levels was simulated successfully according to the tetragonal C4v symmetry by using 41 experimental CF levels. A low rms error of 9 cm−1 between the calculated and experimental energy level schemes indicates the reliability of the results. The CF parameter set obtained is consistent with that given by the analysis carried out for the ground 4 I term only. A comparison of the CF analyses between the insulating Nd2 CuO4 and the metallic Nd2−x Cex CuO4 suggests enhancement of

Acknowledgements Financial support from the National Science and Engineering Research Council of Canada (NSERC), le Fonds Québécois de la Recherche sur la Nature et les Technologies (P.R. and S.J.), the Academy of Finland (J.H.), and the Grant Agency of the Czech republic (Grant No. 202/03/0552-V.N.) is gratefully acknowledged. The work in Prague was also supported by the institutional project AV0Z1-010-914.

References [1] S. Jandl, P. Dufour, T. Strach, T. Ruf, M. Cardona, V. Nekvasil, C. Chen, B.M. Wanklyn, Phys. Rev. B 52 (1995) 15558. [2] S. Jandl, P. Dufour, T. Strach, T. Ruf, M. Cardona, V. Nekvasil, C. Chen, B.M. Wanklyn, S. Piñol, Phys. Rev. B 53 (1996) 8632. [3] S. Jandl, P. Dufour, P. Richard, V. Nekvasil, D.I. Zhigunov, S.N. Barilo, S.V. Shiryaev, J. Lumin. 78 (1998) 197. [4] S. Jandl, P. Richard, M. Poirier, V. Nekvasil, A.A. Nugroho, A.A. Menovsky, D.I. Zhigunov, S.N. Barilo, S.V. Shiryaev, Phys. Rev. B 61 (2000) 12882. [5] U. Staub, L. Soderholm, in: K.A. Gschneidner Jr., L. Eyring, M.B. Maple (Eds.), Handbook Phys. Chem. Rare Earths: High Temperature Rare Earths Superconductors, Part I, vol. 30, North Holland, Amsterdam, 2000, p. 491. [6] Y. Tokura, H. Takagi, S. Uchida, Nature 337 (1989) 345. [7] M.L. Jones, D.W. Shortt, B.W. Sterling, A.L. Schawlow, R.M. Macfarlane, Phys. Rev. B 46 (1992) 611. [8] S. Jandl, P. Richard, P. Fournier, V. Nekvasil, A.A. Nugroho, A.A. Menovsky, in: Proceedings of the 10th International Ceramics Congress and 3rd Forum on New Materials, Florence, Italy, 2002. [9] S.N. Barilo, D.N. Zhigunov, Phys. Chem. Technol. 2 (1989) 138. [10] B.G. Wybourne, Spectroscopic Properties of Rare Earths, Interscience, New York, 1965. [11] W.T. Carnall, H. Crosswhite, H.M. Crosswhite, J.P. Hessler, N. Edelstein, J.G. Conway, G.V. Shalimoff, R. Sarup, J. Chem. Phys. 72 (1980) 5089. [12] C. Görller-Walrand, K. Binnemans, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook Phys. Chem. Rare Earths, vol. 23, Elsevier, Amsterdam, 1996 (Chapter 155). [13] J. Hölsä, E. Säilynoja, P. Ylhä, E. Antic-Fidancev, M. Lemaˆıtre-Blaise, P. Porcher, J. Chem. Soc., Faraday Trans. 94 (1998) 481. [14] P. Porcher, Computer Program REEL/IMAGE for the Simulation of dN and fN Configurations Involving the Real/Complex Crystal Field Parameters, C.N.R.S., Meudon, France, 1989, unpublished. [15] J.L. Prather, Monograph 19, US National Bureau of Standards, Washington, 1961. [16] G.W. Burdick, C.K. Jayasankar, F.S. Richardson, Phys. Rev. B 50 (1994) 16309. [17] J.B. Gruber, M.E. Hills, T.H. Allik, C.K. Jayasankar, J.R. Quagliano, F.S. Richardson, Phys. Rev. B 41 (1990) 7999. [18] M.F. Reid, J. Chem. Phys. 87 (1987) 2875. [19] F. Spernadini, A. Di Cicco, M. Gazda, Phys. Rev. B 57 (1998) 6067.