Physica C 509 (2015) 5–7

Contents lists available at ScienceDirect

Physica C

journal homepage: www.elsevier .com/locate /physc

Studies on the EPR g factors for the oxygenated and nonoxygenatedBaCuO2+x

http://dx.doi.org/10.1016/j.physc.2014.11.0070921-4534/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: ykcheng166@126.com (Y.-K. Cheng).

Yong-Kun Cheng ⇑, Shao-Yi Wu, Chang-Chun Ding, Li-Juan ZhangDepartment of Applied Physics, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, PR China

a r t i c l e i n f o

Article history:Received 30 September 2014Received in revised form 5 November 2014Accepted 27 November 2014Available online 6 December 2014

Keywords:Electron paramagnetic resonance (EPR)Cu2+

BaCuO2+x

a b s t r a c t

The EPR g factors for the oxygenated and nonoxygenated BaCuO2+x are theoretically studied from theperturbation formulas of the g factors for an orthorhombically elongated octahedral 3d9 complex basedon the cluster approach. The relative axial elongation ratios (�1% and 0.6%) along c axis and the relativeplanar bond length variations (�6.9% and 8.9%) are found for the oxygenated and nonoxygenatedsystems, respectively. The above local orthorhombic distortions of the Jahn–Teller nature around Cu2+

can suitably account for the axial and perpendicular anisotropies of the observed g factors. The presentstudies can be useful to understand the influences of this parasitic phase BaCuO2+x on the EPR behavioursand superconductivity of the R123 high Tc superconductors.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

BaCuO2+x has unique magnetic [1–3] and ferromagnetic [4,5]properties. As the parasitic phase often occurring in the prepara-tion of R123 high Tc superconductors, oxygenated and nonoxygen-ated BaCuO2+x may bring forward influences on the magnetic andspectroscopic analysis (e.g., magnetic susceptibility and magneticresonance measurements) for intrinsic R123 systems [2,3,6,7].Generally speaking, the above properties and behaviours may beclosely related to the local structures (e.g., low symmetrical distor-tions) of the paramagnetic Cu2+ site, which can be effectively ana-lyzed with the aid of electron paramagnetic resonance (EPR)technique. The EPR experiments were employed for the powdersamples of oxygenated and nonoxygenated BaCuO2+x at room tem-perature, and the anisotropic g factors gx, gy and gz were measuredfor the orthorhombic Cu2+ in the disordered part of the systems [2].Until now, however, the above EPR experimental results have notbeen quantitatively explained. Furthermore, the local structuralinformation of copper sites in these systems has not been obtainedso far.

It is known that analysis on the EPR spectra for oxygenated andnonoxygenated BaCuO2+x can provide useful information aboutmicroscopic mechanism of spectroscopic behaviours and localstructures of the paramagnetic Cu2+ sites of this parasitic phase,which would be helpful to reveal spectroscopic, structural andsuperconducting properties of the primary R123 systems.

Therefore, the theoretical investigations of the g factors and localstructures for the oxygenated and nonoxygenated BaCuO2+x areof specific fundamental and practical significance. In this work,the high order perturbation formulas of the g factors for a 3d9

ion in orthorhombically elongated octahedra based on the clusterapproach are applied to the analysis of the oxygenated and nonox-ygenated BaCuO2+x. The suitable local lattice distortions due to theJahn–Teller effect are taken into account from the superpositionmodel. The results are discussed.

2. Calculations

For the Cu2+ site in BaCuO2+x, there are six nearest neighbouringoxygen ions with the average (reference) Cu–O distance R(�2.113 Å [2]). As a Jahn–Teller ion, Cu2+ may undergo the Jahn–Teller effect via the vibration interactions. For example, the[CuO6]10� cluster may stretch or contract parallel or perpendicularCu–O bonds along c axis (characterized by a relative elongationratio q) and modify the planar bond lengths (characterized by arelative variation ratio s) along a and b axes, yielding an ortho-rhombically elongated octahedron. For convenience, the immedi-ate structures in the vicinity of the copper sites in the studiedsystems can be suitably described by the local structural distortionparameters q and s. For an orthorhombically elongated octahedral3d9(Cu2+) cluster, the original cubic ground state 2Eg may split intotwo orbital singlets 2A01g(e) and 2A1g(h), with the former lying low-est. Meanwhile, the original cubic excited state 2T2g can be sepa-rated into three orbital singlets 2B1g(f), 2B2g(g) and 2B3g(n) [8,9].Since the systems have moderate covalency, the ligand orbital

6 Y.-K. Cheng et al. / Physica C 509 (2015) 5–7

and spin–orbit coupling contributions can be important and shouldbe included in the EPR analysis. To investigate the EPR spectra andlocal structures of the oxygenated and nonoxygenated BaCuO2+x,the high order perturbation formulas of the g factors for a 3d9

ion in orthorhombically elongated octahedra containing the ligandcontributions from the cluster approach can be adopted here. Thus,we have [10]:

gx ¼ gs þ 2kf0=E2 � 4kff0=ðE1E3Þ þ k0ff0½2=ðE1E2Þ � 1=ðE2E3Þ�þ gsff

0½2=E21 � ð1=E2

2 � 1=E23Þ=2� þ kff02

� fð1=E2 � 1=E3Þð1=E3 þ 1=E2Þ=ð2E1Þþ ð2=E1 � 1=E2Þð2=E1 þ 1=E2Þ=ð2E3Þ � ð1=E2 � 1=E3Þ=ð2E2E4Þgþ ðgsff

02=4Þ½ð1=E3 � 2=E1Þ=E22 þ ð2=E3 � 1=E2Þ=E2

3

þ 2ð1=E2 � 1=E3Þ=E21 þ 2ð1=E2

2 � 1=E23Þ=E1�;

gy ¼ gs þ 2kf0=E3 � 4kff0=ðE1E2Þ þ k0ff0½2=ðE1E3Þ � 1=ðE2E3Þ�

þ gsff0½2=E2

1 þ ð1=E22 � 1=E2

3Þ=2� þ kff02

� fð1=E3 � 1=E2Þð1=E3 þ 1=E2Þ=ð2E1Þþ ð2=E1 � 1=E3Þð2=E1 þ 1=E3Þ=ð2E2Þþ ð1=E2 � 1=E3Þ=ð2E3E4Þg þ ðgsff

02=4Þ½ð1=E2 � 2=E1Þ=E23

þ ð2=E2 � 1=E3Þ=E22 þ 2ð1=E3 � 1=E2Þ=E2

1 þ 2ð1=E23 � 1=E2

2Þ=E1�;

gz ¼ gs þ 8k0f0=E1 þ kf02=ðE3E2Þ þ 2k0f02½ð1=E1E2 þ 1=E1E3Þ�� gsff

0½1=E21 � ð1=E2

2 þ 1=E23Þ=4�

þ k0ff02½8=E1 � ð1=E2 þ 1=E3Þ�=ð2E2E3Þ � 2k0ff02½1=ðE1E2Þþ 1=ðE1E3Þ � 1=ðE2E3Þ�=E1 þ ðgsff

02=4Þ½2ð1=E22 þ 1=E2

3Þ=E1

� ð1=E2 þ 1=E3Þ=ðE2E3Þ�; ð1Þ

where gs (�2.0023) is the pure spin value. The spin–orbit couplingcoefficients f, f0 and the orbital reduction factors k, k0 stand for theanisotropic interactions of the spin–orbit coupling and the orbitalangular momentum operators within the irreducible representa-tions c (=e and t denoting Eg and T2g) of cubic group Oh. They canbe determined from the cluster approach [11]:

f ¼ Ntðf0d þ k2

t f0p=2Þ; f0 ¼ ðNtNeÞ1=2ðf0

d � ktkef0p=2Þ;

k ¼ Ntð1þ k2t =2Þ; k0 ¼ ðNtNeÞ1=2½1� ktðke þ ksAÞ=2�;

ð2Þ

where fd0 and fp

0 are, respectively, the spin–orbit coupling coeffi-cients of the free 3d9 and the ligand ions. A denotes the integral Rh3s|o/ox|3pxi with the reference Cu–O distance R. Nc and kc are thenormalization factors and the orbital admixture coefficients, respec-tively, which are usually obtained from the normalization condi-tions [11]

Ntð1� 2ktSdpt þ k2t Þ ¼ 1;

Neð1� 2keSdpe � 2ksSds þ k2e þ k2

s Þ ¼ 1 ð3Þ

and the approximate relationships [11]

N2 ¼ N2t ½1þ k2

t S2dpt � 2ktSdpt�;

N2 ¼ N2e ½1þ k2

e S2dpe þ k2

s S2ds � 2keSdpe � 2ksSds�: ð4Þ

Here Sdpc (and Sds) are the group overlap integrals. N is the averagecovalency factor, indicating covalency of the systems. Normally, theorbital admixture coefficients have the coincident tendency withthe group overlap integrals as the distance R increases. So one canapproximately adopt the proportionality relationship ks/ke � Sds/Sdpe

between the orbital admixture coefficients and the relevant groupoverlap integrals for the same Eg state.

The denominators Ei (i = 1–4) in Eq. (1) are the energy separa-tions between the excited 2A1g(h), 2B1g(f), 2B2g(g) and 2B3g(n) and

the ground 2A01g(e) states [10], which can be obtained from theenergy matrix for a 3d9 ion in orthorhombic symmetry:

E1 ¼ 10Dq;

E2 ¼ 10Dq� 3Dsþ 5Dt � 3Dn þ 4Dg;

E3 ¼ 10Dq� 3Dsþ 5Dt þ 3Dn � 4Dg;

E4 ¼ �4Ds� 5Dt: ð5Þ

Here Dq is the cubic field parameter, and Ds, Dt, Dn and Dg are theorthorhombic field parameters, respectively. In view of the Jahn–Teller effect, the local Cu–O bond lengths along the crystalline a, band c axes are expressed in terms of the reference distance R andthe local structural distortion parameters q and s:

Ra ¼ Rð1� qþ sÞ;Rb ¼ Rð1� q� sÞ;Rc ¼ Rð1þ 2qÞ: ð6Þ

From the local geometry and the superposition model [12], theorthorhombic field parameters can be written as:

Ds � ð�2=7ÞA2½ðR=RaÞt2 þ ðR=RbÞt2 � 2ðR=RcÞt2�;Dn � ð2=7ÞA2½ðR=RaÞt2 � ðR=RbÞt2�;Dt � ð8=21ÞA4½2ðR=RcÞt4 � ðR=RaÞt4 � ðR=RbÞt4�;Dg � ð5=21ÞA4½ðR=RaÞt4 � ðR=RbÞt4�: ð7Þ

Here t2 (�3) and t4 (�5) are the power-law exponents [12]. �A2 and�A4 are the intrinsic parameters. For 3dn ions in octahedra, theexpressions �A4 � (3/4) Dq and �A2 � 10.8�A4 [13–15] have beenproved sound in many systems and can be reasonably utilizedhere. Therefore, the axial and perpendicular anisotropiesDg (=gz � (gx + gy)/2) and dg (=gy � gx) of the g factors are correlatedto the orthorhombic field parameters and hence to the local struc-tures of the studied systems.

From the optical absorption data for Cu2+ in oxides [16], the spec-tral parameters Dq � 1260 cm�1 and N � 0.745 can be obtained forthe studied BaCuO2+x. Using the reference (average) Cu–O distanceR, the group overlap integrals are computed from the Slater-typeself-consistent field (SCF) functions [17,18]: Sdpt � 0.0062, Sdpe �0.0218, Sds � 0.0174 and A � 1.3167. The normalization factors andthe orbital admixture coefficients can be determined from Eqs. (3)and (4), i.e., Nt � 0.748 and Ne � 0.758, kt � 0.587, ke � 0.465 andks � 0.371. Applying the free-ion values fd

0 (Cu2+) � 829 cm–1 [19]and fp

0 (O2–) � 151 cm–1 [20], the spin–orbit coupling coefficientsf � 639 cm�1, f0 � 608 cm�1 and the orbital reduction factorsk � 0.877 and k0 � 0.542 are calculated from Eq. (2). Thus, onlythe local structural distortion parameters q and s are unknownin the g formulas. Inputting the above values into Eq. (1) and fittingthe theoretical g factors to the experimental data, one can obtain

q � 1:0% and 0:6%;

s � 6:9% and 8:9% ð8Þ

for oxygenated and nonoxygenated BaCuO2+x, respectively. The cal-culated g factors (Cal.b) are given in Table 1. To clarify importance ofcovalency and ligand contributions, the results (Cal.a) based onomission of the ligand contributions (i.e., taking f = f0 = fd

0 N andk = k0 = N) are obtained and shown in Table 1.

3. Discussion

According to Table 1, the calculated g factors (Cal.b) for the oxy-genated and nonoxygenated BaCuO2+x based on the local structuraldistortion parameters q and s in Eq. (8) and inclusion of the ligandcontributions are in good agreement with the experimental data.However, those (Cal.a) based on omission of the ligand contributions

Table 1The anisotropic g factors for oxygenated and nonoxygenated BaCuO2+x at roomtemperature.

Oxygenated Nonoxygenated

Cal.a Cal.b Expt. [2] Cal.a Cal.b Expt. [2]

gx 2.062 2.044 2.041 (3) 2.062 2.050 2.057 (3)gy 2.147 2.104 2.103 (3) 2.177 2.127 2.120 (3)gz 2.307 2.222 2.223 (3) 2.318 2.235 2.21 (3)

a Calculations based on omission of the ligand orbital and spin–orbit couplingcontributions.

b Calculations based on inclusion of the ligand contributions from the clusterapproach.

Y.-K. Cheng et al. / Physica C 509 (2015) 5–7 7

are not so good. Therefore, the observed EPR spectra for oxygenatedand nonoxygenated BaCuO2+x are satisfactorily explained here in auniform way, and the information about the local structures aroundcopper sites is also obtained.

(1) The local distortions of Cu2+ sites in the oxygenated andnonoxygenated BaCuO2+x are described by the relative axialelongation ratio q and the relative planar bond length vari-ation ratio s due to the Jahn–Teller effect, resulting in ortho-rhombically elongated octahedra. According to Eqs. (1), (5)and (6), the axial and perpendicular anisotropies Dg (=gz –(gx + gy)/2) and dg (=gy – gx) of the g factors originate mainlyfrom the axial (related to Ds. and Dt arising from q) and per-pendicular (related to Dn and Dg arising from s). Moreover,the larger Dg (or dg) for oxygenated (or nonoxygenated)BaCuO2+x can be suitably ascribed to the higher q (or s) ofthe respective system. The above differences in the localorthorhombic distortions and g anisotropies may be furtherillustrated by the distinct oxygen arrangement at the disor-dered part with variation of oxygen content.

(2) The studied [CuO6]10– clusters in BaCuO2+x exhibit moderatecovalency due to the moderate Cu–O distance R (�2 Å [2]),as supported by the small N (�0.745 < 1) and the moderatekc (�0.4–0.6). Furthermore, the relative anisotropies (k –k0)/k0 (�62%) and (f – f0)/f0 (�5%) can be obtained for theorbital reduction factors and the spin–orbit coupling coeffi-cients, respectively, on the basis of the cluster approach cal-culations. In view of covalency and anisotropic expansions ofCu2+ 3d orbitals in covalent environments [21,22], the ligandorbital and spin–orbit coupling contributions should be con-sidered in the theoretical analysis. It is understandable thatthe g factors and the anisotropies Dg and dg (Cal.a) basedon omission of the ligand contributions are larger than theexperimental data, in consideration of the errors under thescheme of the conventional g formulas.

(3) The parasitic phase BaCuOx often appears in the preparationof R123 high Tc superconductors. Because of the similar EPRsignals within the same resonance magnetic field range tothose of the copper sites in R123 systems, the spectroscopicbehaviours of BaCuOx would bring forward influences on the

studies of R123 superconductors. The present analysiswould be useful to understand the influences of this para-sitic phase BaCuO2+x on the EPR behaviours and supercon-ductivity of the R123 high Tc superconductors.

4. Conclusion

The g factors are theoretically investigated for the oxygenatedand nonoxygenated BaCuO2+x using the perturbation calculations.The [CuO6]10– clusters are found to suffer the relative axial elonga-tion ratios (�1% and 0.6%) along c axis and the relative planar bondlength variations (�6.9% and 8.9%) for the oxygenated and nonoxy-genated systems, respectively. The above local orthorhombic distor-tions of the Jahn–Teller nature around Cu2+ sites suitably accountfor the axial and perpendicular anisotropies Dg and dg of the exper-imental g factors. The present studies can be useful to understandthe influences of this parasitic phase BaCuO2+x on the EPR behav-iours and superconductivity of the R123 high Tc superconductors.

Acknowledgments

This work was financially supported by the Sichuan Province Aca-demic and Technical Leaders Support Fund [Y02028023601015] andthe Fundamental Research Funds for the Central Universities[ZYGX2012YB018].

References

[1] A. Yamamoto, T. Koyama, T. Mito, S. Wada, R.A. Fisher, N.E. Phillips, Z.P. Wang,D.C. Johnston, J. Phys.: Condens. Matter 15 (2003) 8587.

[2] N. Guskos, V. Likodimos, C.A. Londos, J. Solid State Chem. 119 (1995) 50.[3] W.E. Farneth, R.S. McLean, E.M. McCarron III, F. Zuo, Y. Lu, R. Patton, A.J.

Epstein, Phys. Rev. B 39 (1989) 6594.[4] K. Shreedhar, P. Ganguly, Inorg. Chem. 27 (1988) 2261.[5] P. Ganguly, K. Shreedhar, A.R. Raju, G. Demazeau, P. Hagenmuller, J. Phys.:

Condens. Matter 1 (1989) 213.[6] D.C. Vier, S.B. Oseroff, C.T. Salling, S. Schultz, Y. Dalichaouch, B.W. Lee, M.B.

Maple, Z. Fisk, J.D. Thompson, Phys. Rev. B 36 (1987) 8888.[7] J. Genossar, D. Shaltiel, V. Zevin, A. Grayevski, B. Fisher, J. Phys.: Condens.

Matter 1 (1989) 9471.[8] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions,

Oxford University Press, London, 1970.[9] A.S. Chakravarty, Introduction to the Magnetic Properties of Solids, John Wiley

& Sons Inc. Press, New York, 1980.[10] H.M. Zhang, S.Y. Wu, M.Q. Kuang, Z.H. Zhang, J. Phys. Chem. Solids 73 (2012)

846.[11] Y.X. Hu, S.Y. Wu, X.F. Wang, Philos. Magn. 90 (2010) 1391.[12] D.J. Newman, B. Ng, Rep. Prog. Phys. 52 (1989) 699.[13] M. Açıkgöz, P. Gnutek, C. Rudowicz, Chem. Phys. Lett. 524 (2012) 49.[14] Z.Y. Yang, J. Phys.: Condens. Matter 12 (2000) 4091.[15] H.N. Dong, P. Li, Spectrochim. Acta A 76 (2010) 33.[16] C.K. Jorgensen, Absorption Spectra and Chemical Bonding in Complexes,

second ed., Pergamon Press, Oxford, London, New York and Paris, 1964.[17] E. Clementi, D.L. Raimondi, J. Chem. Phys. 38 (1963) 2686.[18] E. Clementi, D.L. Raimondi, W.P. Reinhardt, J. Chem. Phys. 47 (1967) 1300.[19] J.S. Griffith, The Theory of Transition-Metal Ions, Cambridge University Press,

London, 1964.[20] E.K. Hodgson, I. Fridovich, Biochem. Biophys. Res. Commun. 54 (1973) 270.[21] N. Gemma, J. Phys. C 17 (1984) 2333.[22] A. Fazzio, M.J. Caldas, A. Zunger, Phys. Rev. B 30 (1984) 3430;

A. Fazzio, M.J. Caldas, A. Zunger, Phys. Rev. B 29 (1984) 5999.