Correction to: Room temperature magneto-dielectric coupling in the CaMnO3 modified NBT lead-free ceramics (Applied Physics A, (2023), 129, 4, (237), 10.1007/s00339-023-06513-4)

Abstract

In this work we did Rietveld refinement using Full-Prof software to do the structural analysis of all the reported samples. In the previous analysis we did not consider the z-position of the O-atom to be fixed (1/12) while it is necessary for this type of structure to consider the fixed Oz position to avoid the problem of floating origin. Hence, realizing this mistake we have re-analyzed the XRD pattern and corrected the phase fraction (%), lattice parameters (a = b, c), Volume (V), tilt angle (ω), all the bond lengths and bond angles, A-atom/B-atom displacements values (s, t). Hence, with an inclusion of these modifications the Figs. 1b–f and 2 are corrected. A minor correction is made in the Raman spectroscopy and magnetism study section where these values were correlated to some physical parameters. Few sentences in the 1st and 2nd paragraphs of Sect. 3.1 (X-ray diffraction

page 3 &amp

4) are corrected as follows: X-Ray diffraction: The Rietveld analysis shows a presence of 18% Pnma and 82% R3c phase for x = 0.12. The lattice parameters (a = b), showed sporadic down and up with an increase in composition (Fig. 1f). On the other hand, the “c” parameter continuously decreased with an increase in CaMnO3 composition (Fig. 2a). The short B–O bond lengths decreased up to x = 0.06 followed by an increase for x = 0.12 (Fig. 1b). The A1–O bond length increased for x = 0.03 and thereafter continuously decreased for the other two compositions while an exactly opposite trend was observed for the A3–O bond (Fig. 2c). The variation of A2–O and A4–O bond lengths showed an opposite trend. The variation in the displacement of B-site atoms and A-site atoms affected various bond lengths (Fig. 2f). The last sentence in the 2nd, 4th, and 6th paragraphs of Sect. 3.3 (Raman spectroscopy

page 9) are corrected as follows: Raman Spectroscopy: This could be associated with the variation of A4–O bond length. Such variation could be associated with modifying the long O–B–O bond angles. Such variation is associated with the modification in the B–O bond strength. The 7th paragraph of Sect. 3.6 (magnetism

page 13) 3rd, 5th, and 6th sentences are corrected as follows: Magnetism: In the R3c structure, the B–O–B bond angle increased from 160.97° for x = 0 to 166.85° for x = 0.03 followed by continuous decrease to164.23 for x = 0.06 and 162.96 for the x = 0.12 composition. The deviation from this angle decreased from x = 0.03 to x = 0.09. This indicates the introduction of antiferromagnetism in the x = 0.03, x = 0.06, and x = 0.12 compositions. The Fig. 1b–f are corrected as follows: (Figure presented.) a XRD pattern of (1 − x) Na0.5Bi0.5TiO3-xCaMnO3 (x = 0, 0.03, 0.06, and 0.12), Rietveld plot of bx = 0, cx = 0.03, dx = 0.06, ex = 0.12, f tilt angle and strain with composition

inset shows variation of volume with composition The Fig. 2a–f are corrected as follows: (Figure presented.) a Variation of lattice parameters with composition. b Variation of B–O bond lengths with composition. c Variation of A–O bond lengths with composition. d Variation of O–B–O bond angles with composition. e Variation of O–A–O bond angles with composition. f Variation of off-centering of the A-atom and B-atoms The Figure caption of Fig. 2f is corrected as given below: The original article has been corrected. © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2024.