(Nd,Y)BaMn2O6, and CuB2O4 display interesting magnetic, charge/orbital, and structural phase transitions. These complex phases open up new and exciting functionalities (e.g. colossal magnetoresistance, high-temperature superconductivity, magnetocaloric effect, metal-insulator transition, etc.) that are not fully understood. Recognizing and determining the strengths of these correlations is fundamental and important for practical technological applications. Optical spectroscopy is a sensitive tool that can probe the intricate interactions between the spin, charge, and lattice of these materials. In this study, we employed spectroscopic ellipsometry and Raman scattering spectroscopy to investigate the electronic structure and lattice dynamics of (Nd,Y)BaMn2O6, and CuB2O4 single crystals.
The room-temperature optical absorption spectra of NdBaMn2O6 and YBaMn2O6 revealed d–d transitions in Mn ions positioned at 0.88 and 1.50 eV, respectively. The d–d transition peak for RBaMn2O6 compounds was observed to increase as R radii were decreased. Temperature-dependent d–d transition energy of NdBaMn2O6 exhibited anomalies at the charge/orbital ordering phase transition (290 K) and the magnetic phase transition (235 K). Furthermore, the temperature-dependent Raman scattering spectra revealed anomalies at the phase transition temperatures. In NdBaMn2O6, phonon modes appeared at approximately 440 cm−1. This correlated with the spike of the 270 cm-1 phonon mode at 290 K, which is also the onset of the charge/orbital ordering. Additionally, new phonon peaks appeared at temperatures < 200 K, indicating charge and orbital ordering in YBaMn2O6. Magnetic order-induced changes were observed in the breathing and Jahn-Teller modes. The octahedral breathing mode of NdBaMn2O6 at 610 cm−1 shifted to lower frequencies below 235 K along with a reduced intensity of the 620 cm-1 and an increase of the 644 cm-1 phonon peaks. Hardening of the Jahn-Teller mode of YBaMn2O6 at approximately 496 cm-1 was observed at temperature < 200 K. These phenomena revealed the occurrence of spin-phonon coupling in NdBaMn2O6 and YBaMn2O6.
The room-temperature optical absorption spectrum of CuB2O4 displayed charge-transfer transitions from the 2p states of O to the 3d states of Cu at approximately 4.49 and 5.90 eV. A direct band gap for CuB2O4 was extrapolated at 3.88 ± 0.01 eV. We noted isotopic-induced changes upon the replacement of heavier boron. Optical absorption data of Cu11B2O4 revealed a shift to lower energies in the charge-transfer bands. The band gap of Cu11B2O4 was also slightly lower than that of CuB2O4. The temperature-dependent band gap and the peak energy of charge-transfer bands exhibited anomalies through the canted antiferromagnetic ordering temperature at 21 K. The Raman phonon frequencies of Cu11B2O4 shifted lower, whereas the linewidth displayed minor discrepancies. The isotopic shift in frequencies conferred with the inverse square root dependence of the mean atomic mass. The Cu stretching vibrations of CuB2O4 and Cu11B2O4 exhibited a softening below 21 K, indicating a spin-phonon interaction.
We have demonstrated the correlations between the temperature-dependent optical response and the complex phase transitions in (Nd,Y)BaMn2O6, and CuB2O4. These results highlight the intricate spin, charge, and lattice interactions in these materials.

[1] Y. Ueda and T. Nakajima, The A-site ordered manganese perovskite and its colossal magnetoresistance, Prog. Solid State Chem. 35, 397 (2007).
[2] Y. Moritomo, A. Asamitsu, H. Kuwahara, and Y. Tokura, Giant magnetoresistance of manganese oxides with a layered perovskite structure, Nature 380, 141 (1996).
[3] Millis, Shraiman, and Mueller, Dynamic Jahn-Teller Effect and Colossal Magnetoresistance in La 1-xSrxMnO3, Phys. Rev. Lett. 77, 175 (1996).
[4] T. Nakajima and Y. Ueda, 1000% colossal magnetoresistance at room temperature in the A-site ordered perovskite manganites, Sm1−xLax+yBa1−yMn2O6, J. Appl. Phys. 98, 046108 (2005).
[5] T. Nakajima, H. Kageyama, and Y. Ueda, Successive phase transitions in a metal-ordered manganite perovskite YBaMn2O6, J. Phys. Chem. Solids 63, 913 (2002).
[6] Y. Tomioka, T. Okuda, Y. Okimoto, A. Asamitsu, H. Kuwahara, and Y. Tokura, Charge/orbital ordering in perovskite manganites, J. Alloys Compd. (2001), pp. 27–35.
[7] Y. Tokura, S. Seki, and N. Nagaosa, Multiferroics of spin origin, Reports Prog. Phys. 77, (2014).
[8] E. A. Ekimov, V. A. Sidorov, A. V Zoteev, J. B. Lebed, J. D. Thompson, and S. M. Stishov, Structure and superconductivity of isotope-enriched boron-doped diamond, Sci. Technol. Adv. Mater. 9, 044210 (2008).
[9] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of Superconductivity, Phys. Rev. 108, 1175 (1957).
[10] Y. Tomioka, Y. Okimoto, J. H. Jung, R. Kumai, and Y. Tokura, Phase diagrams of perovskite-type manganese oxides, J. Phys. Chem. Solids 67, 2214 (2006).
[11] V. N. Antonov, L. V. Bekenov, and A. N. Yaresko, Electronic structure of strongly correlated systems, Adv. Condens. Matter Phys. 2011, (2011).
[12] T. M. Hsu and J. H. Lin, Anomalous temperature-dependent band gaps in CuInS2 studied by surface-barrier electroreflectance, Phys. Rev. B 37, 4106 (1988).
[13] S. Singh, C. Li, F. Panzer, K. L. Narasimhan, A. Graeser, T. P. Gujar, A. Köhler, M. Thelakkat, S. Huettner, and D. Kabra, Effect of Thermal and Structural Disorder on the Electronic Structure of Hybrid Perovskite Semiconductor CH3NH3PbI3, J. Phys. Chem. Lett. 7, 3014 (2016).
[14] V. M. Loktev and Y. G. Pogorelov, Peculiar physical properties and the colossal magnetoresistance of manganites (Review), Low Temp. Phys. 26, 171 (2000).
[15] R. J. D. Tilley, Perovskites: Structure–Property Relationships, (John and Wiley Ltd., 2017).
[16] T. Nakajima, H. Kageyama, H. Yoshizawa, and Y. Ueda, Structures and Electromagnetic Properties of New Metal-Ordered Manganites: RBaMn2O6 ( R =Y and Rare-Earth Elements), J. Phys. Soc. Japan 71, 2843 (2002).
[17] T. Nakajima, H. Kageyama, H. Yoshizawa, K. Ohoyama, and Y. Ueda, Ground State Properties of the A -site Ordered Manganites, RBaMn2O6 ( R = La, Pr and Nd), J. Phys. Soc. Japan 72, 3237 (2003).
[18] Y. Ueda and T. Nakajima, Novel structures and electromagnetic properties of the A-site-ordered/disordered manganites RBaMn2O6/R0.5Ba0.5MnO3 (R = Y and rare earth elements)J. Phys. Condens. Matter 16, (2004).
[19] A. J. Williams and J. P. Attfield, Ferro-orbital order in the charge- and cation-ordered manganite YBaMn2O6, Phys. Rev. B 72, 024436 (2005).
[20] M. N. Iliev, M. V. Abrashev, J. Laverdière, S. Jandl, M. M. Gospodinov, Y. Q. Wang, and Y. Y. Sun, Distortion-dependent Raman spectra and mode mixing in RMnO3 perovskites (R=La,Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Y), Phys. Rev. B - Condens. Matter Mater. Phys. (2006).
[21] G.-H. H. Gweon, T. Sasagawa, S. Y. Y. Zhou, J. Graf, H. Takagi, D.-H. H. Lee, and A. Lanzara, An unusual isotope effect in a high-transition-temperature superconductor, Nature 430, 187 (2004).
[22] S. L. Bud’ko, G. Lapertot, C. Petrovic, C. E. Cunningham, N. Anderson, and P. C. Canfield, Boron Isotope Effect in Superconducting MgB2, Phys. Rev. Lett. 86, 1877 (2001).
[23] V. G. Plekhanov, Isotopic and disorder effects in large exciton spectroscopy, Uspekhi Fiz. Nauk 167, 577 (1997).
[24] D. G. Hinks, H. Claus, and J. D. Jorgensen, The complex nature of superconductivity in MgB2 as revealed by the reduced total isotope effect, Nature 411, 457 (2001).
[25] R. D. Mero, K. Ogawa, S. Yamada, and H.-L. Liu, Optical study of the electronic structure and lattice dynamics of NdBaMn2O6 single crystals, Sci. Rep. 9, 18164 (2019).
[26] S. Yamada, H. Sagayama, K. Higuchi, T. Sasaki, K. Sugimoto, and T. Arima, Physical properties and crystal structure analysis of double-perovskite NdBaMn2O6 by using single crystals, Phys. Rev. B (2017).
[27] D. Akahoshi, Y. Okimoto, M. Kubota, R. Kumai, T. Arima, Y. Tomioka, and Y. Tokura, Charge-orbital ordering near the multicritical point in A-site ordered perovskites SmBaMn2O6 and NdBaMn2O6, Phys. Rev. B 70, 064418 (2004).
[28] H. Kageyama, T. Nakajima, M. Ichihara, Y. Ueda, H. Yoshizawa, and K. Ohoyama, New Stacking Variations of the Charge and Orbital Ordering in the Metal-Ordered Manganite YBaMn2O6, J. Phys. Soc. Japan 72, 241 (2003).
[29] T. Nakajima and Y. Ueda, Structures and electromagnetic properties of the A-site disordered Ba-based manganites; R0.5Ba0.5MnO3 (R = Y and rare earth elements), in J. Alloys Compd. (2004), pp. 135–139.
[30] S. Yamada, H. Sagayama, K. Sugimoto, and T. Arima, Successive phase transitions and magnetic fluctuation in a double-perovskite NdBaMn2O6 single crystal, J. Phys. Conf. Ser. 969, 012103 (2018).
[31] T. Nakajima, H. Kageyama, M. Ichihara, K. Ohoyama, H. Yoshizawa, and Y. Ueda, Anomalous octahedral distortion and multiple phase transitions in the metal-ordered manganite YBaMn2O6, J. Solid State Chem. 177, 987 (2004).
[32] Q.-Q. Gao, J.-B. Li, G.-N. Li, G.-H. Rao, J. Luo, G.-Y. Liu, and J.-K. Liang, Spin glass behavior in A-site ordered YBaMn2O6 compound, J. Appl. Phys. 114, 053901 (2013).
[33] A. J. Williams, J. P. Attfield, and S. A. T. Redfern, High-temperature orbital, charge, and structural phase transitions in the cation-ordered manganites TbBaMn2O6, Phys. Rev. B 72, 184426 (2005).
[34] M. Martinez-Ripoll, S. Martínez-Carrera, and S. García-Blanco, The crystal structure of copper metaborate, CuB2O4, Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem. 27, 677 (1971).
[35] G. A. Petrakovskiǐ, A. I. Pankrats, M. A. Popov, A. D. Balaev, D. A. Velikanov, A. M. Vorotynov, K. A. Sablina, B. Roessli, J. Schefer, A. Amato, U. Staub, M. Boehm, and B. Ouladdiaf, Magnetic properties of copper metaborate CuB2O4 , Low Temp. Phys. 28, 606 (2002).
[36] M. Boehm, B. Roessli, J. Schefer, A. S. Wills, B. Ouladdiaf, E. Lelièvre-Berna, U. Staub, and G. A. Petrakovskii, Complex magnetic ground state of CuB2O4, Phys. Rev. B 68, 024405 (2003).
[37] N. D. Khanh, N. Abe, K. Kubo, M. Akaki, M. Tokunaga, T. Sasaki, and T. Arima, Magnetic control of electric polarization in the noncentrosymmetric compound (Cu,Ni)B2O4 Phys. Rev. B - Condens. Matter Mater. Phys. 87, 184416 (2013).
[38] R. V. Pisarev, K. N. Boldyrev, M. N. Popova, A. N. Smirnov, V. Y. Davydov, L. N. Bezmaternykh, M. B. Smirnov, and V. Y. Kazimirov, Lattice dynamics of piezoelectric copper metaborate CuB2O4, Phys. Rev. B - Condens. Matter Mater. Phys. 88, 024301 (2013).
[39] V. G. Ivanov, M. V. Abrashev, N. D. Todorov, V. Tomov, R. P. Nikolova, A. P. Litvinchuk, and M. N. Iliev, Phonon and magnon Raman scattering in CuB2O4, Phys. Rev. B - Condens. Matter Mater. Phys. 88, 094301 (2013).
[40] S. Toyoda, N. Abe, S. Kimura, Y. H. Matsuda, T. Nomura, A. Ikeda, S. Takeyama, and T. Arima, One-Way Transparency of Light in Multiferroic CuB2O4, Phys. Rev. Lett. 115, 1 (2015).
[41] B. Roessli, J. Schefer, G. A. Petrakovskii, B. Ouladdiaf, M. Boehm, U. Staub, A. Vorotinov, and L. Bezmaternikh, Formation of a magnetic soliton lattice in copper metaborate, Phys. Rev. Lett. 86, 1885 (2001).
[42] T. Fujita, Y. Fujimoto, S. Mitsudo, T. Idehara, K. Inoue, J. Kishine, Y. Kousaka, S. Yano, J. Akimitsu, and M. Motokawa, High field ESR measurements on the chiral spin system CuB2O4, J. Phys. Conf. Ser. 51, 111 (2006).
[43] M. Saito, K. Taniguchi, and T. H. Arima, Gigantic optical magnetoelectric effect in CuB2O4, J. Phys. Soc. Japan 77, 1 (2008).
[44] K. N. Boldyrev, R. V. Pisarev, L. N. Bezmaternykh, and M. N. Popova, Antiferromagnetic dichroism and Davydov splitting of 3d-excitons in a complex multisublattice magnetoelectric CuB2O4, Phys. Rev. Lett. 114, 247210 (2014).
[45] M. Fiebig, I. Sänger, and R. V. Pisarev, Magnetic phase diagram of CuB2O4, J. Appl. Phys. 93, 6960 (2003).
[46] R. V. Pisarev, I. Sänger, G. A. Petrakovskii, and M. Fiebig, Magnetic-field induced second harmonic generation in CuB2O4, Phys. Rev. Lett. 93, 2 (2004).
[47] G. Nénert, L. N. Bezmaternykh, A. N. Vasiliev, and T. T. M. Palstra, Magnetic, structural, and dielectric properties of CuB2O4, Phys. Rev. B - Condens. Matter Mater. Phys. 76, 3 (2007).
[48] M. Saito, K. Ishikawa, K. Taniguchi, and T. Arima, Magnetic control of crystal chirality and the existence of a large magneto-optical dichroism effect in CuB2O4, Phys. Rev. Lett. 101, 1 (2008).
[49] G. A. Petrakovskii, K. A. Sablina, D. A. Velikanov, A. M. Vorotynov, N. V. Volkov, and A. F. Bovina, Synthesis and magnetic properties of copper metaborate single crystals, CuB2O4, Crystallogr. Reports 45, 853 (2000).
[50] G. Zhao, K. K. Singh, and D. E. Morris, Oxygen isotope effect on Néel temperature in various antiferromagnetic cuprates, Phys. Rev. B 50, 4112 (1994).
[51] E. Amit, A. Keren, J. S. Lord, and P. King, A precise measurement of the oxygen isotope effect on the néel temperature in cuprates, Adv. Condens. Matter Phys. 2011, 1 (2011).
[52] R. V. Pisarev, A. M. Kalashnikova, O. Schöps, and L. N. Bezmaternykh, Electronic transitions and genuine crystal-field parameters in copper metaborate CuB2O4, Phys. Rev. B - Condens. Matter Mater. Phys. 84, 1 (2011).
[53] S. W. Lovesey and U. Staub, Reply to comment on ‘Calculated chiral and magneto-electric dichroic signals for copper metaborate (CuB2O4) in an applied magnetic field’ J. Phys. Condens. Matter 21, 498002 (2009).
[54] T. Arima and M. Saito, Comment on ‘Calculated chiral and magneto-electric dichroic signals for copper metaborate (CuB2O4 ) in an applied magnetic field’, J. Phys. Condens. Matter 21, 498001 (2009).
[55] V. Tomov, P. M. Rafailov, and L. Yankova, Raman spectroscopy investigation of the polar vibrational modes in CuB2O4, J. Phys. Conf. Ser. 682, 012028 (2016).
[56] H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (2007).
[57] F. Wooten, Optical Properties of Solids (Academic Press, New York, 1972).
[58] J. A. Woollam and P. G. Snyder, Fundamentals and applications of variable angle spectroscopic ellipsometry, Mater. Sci. Eng. B. 5, 279-283 (1990).
[59] D. Gonçalves and E. A. Irene, Fundamentals and applications of spectroscopic ellipsometry, Quim. Nova 25, 794 (2002).
[60] J.A. Woollam Co., Guide to using WVASE spectroscopic ellipsometry data acquisition and analysis software.WVASE Man. (2012).
[61] Z. V. Popović, Raman Scattering in Materials Science, Mater. Sci. Forum 214, 11 (1996).
[62] T. W. W. Noh, J. H. H. Jung, H. J. J. Lee, K. H. H. Kim, J. Yu, E. J. J. Choi, Y. Moritomo, and Y. Moritomo, Optical properties of perovskite manganites, J. Korean Phys. Soc. 36, 392 (2000).
[63] H. L. Liu, K. S. Lu, M. X. Kuo, L. Uba, S. Uba, L. M. Wang, and H.-T. Jeng, Magneto-optical properties of La0.7Sr0.3MnO3, J. Appl. Phys. 99, 043908 (2006).
[64] S. G. Kaplan, M. Quijada, H. D. Drew, D. B. Tanner, G. C. Xiong, R. Ramesh, C. Kwon, and T. Venkatesan, Optical evidence for the dynamic Jahn-teller effect in Nd0.7Sr0.3MnO3, Phys. Rev. Lett. 77, 2081 (1996).
[65] Arima, Tokura, and Torrance, Variation of optical gaps in perovskite-type 3d transition-metal oxides, Phys. Rev. B. Condens. Matter 48, 17006 (1993).
[66] J. H. Jung, K. H. Kim, D. J. Eom, T. W. Noh, E. J. Choi, J. Yu, Y. S. Kwon, and Y. Chung, Determination of electronic band structures of CaMnO3, Phys. Rev. B 55, 15489 (1997).
[67] M. W. Kim, S. J. Moon, J. H. Jung, J. Yu, S. Parashar, P. Murugavel, J. H. Lee, and T. W. Noh, Effect of orbital rotation and mixing on the optical properties of orthorhombic RMnO3 (R= Pr, Nd, Gd, and Tb), Phys. Rev. Lett. 96, 247205 (2006).
[68] S. Yamada, N. Abe, H. Sagayama, K. Ogawa, T. Yamagami, and T. Arima, Room-temperature low-field colossal magneto-resistance in a double-perovskite manganite, Phys. Rev. Lett. 123, 126602 (2019).
[69] W. G. Fateley, N. T. McDevitt, and F. F. Bentley, Infrared and Raman Selection Rules for Lattice Vibrations: The Correlation Method (1971).
[70] S. Asselin, S. Jandl, P. Fournier, A. A. Mukhin, V. Y. Ivanov, and A. M. Balbashov, Resonant micro-Raman study of Nd0.5Sr0.5MnO3, J. Phys. Condens. Matter 17, 5247 (2005).
[71] M. N. Iliev, M. V. Abrashev, A. P. Litvinchuk, V. G. Hadjiev, H. Guo, and A. Gupta, Raman spectroscopy of ordered double perovskite La2CoMnO6, Phys. Rev. B 75, 104118 (2007).
[72] M. Abrashev, J. Bäckström, L. Börjesson, M. Pissas, N. Kolev, and M. Iliev, Raman spectroscopy of the charge- and orbital-ordered state in La0.5Ca0.5MnO3, Phys. Rev. B 64, 144429 (2001).
[73] K.-Y. Choi, P. Lemmens, G. Guntherodt, M. Pattabiraman, G. Rangarajan, V. P. Gnezdilov, G. Balakrishnan, D. McK Paul, and M. R. Lees, Raman scattering study of Nd1 − x SrxMnO3 (x=0.3, 0.5), J. Phys. Condens. Matter 15, 3333 (2003).
[74] E. Granado, A. García, J. A. Sanjurjo, C. Rettori, I. Torriani, F. Prado, R. D. Sánchez, A. Caneiro, and S. B. Oseroff, Magnetic ordering effects in the Raman spectra of La1-xMn1-xO3, Phys. Rev. B 60, 11879 (1999).
[75] M. N. Iliev, M. V. Abrashev, V. N. Popov, and V. G. Hadjiev, Role of Jahn-Teller disorder in Raman scattering of mixed-valence manganites, Phys. Rev. B 67, 212301 (2003).
[76] M. Balkanski, R. F. Wallis, and E. Haro, Anharmonic effects in light scattering due to optical phonons in silicon, Phys. Rev. B 28, 1928 (1983).
[77] M. Nabi and D. C. Gupta, Study of the magneto-electronic, optical, thermal and thermoelectric applications of double perovskites Ba2MTaO6 (M = Er, Tm), RSC Adv. 9, 15852 (2019).
[78] S. Yamada, H. Sagayama, K. Higuchi, T. Sasaki, K. Sugimoto, and T. Arima, Physical properties and crystal structure analysis of double-perovskite NdBaMn2O6 by using single crystals, Phys. Rev. B 95, 035101 (2017).
[79] J. Q. Li, Structural properties of the perovskite manganites, J. Appl. Phys. 90, 637 (2001).
[80] S. Mansouri, S. Jandl, A. Mukhin, V. Y. Ivanov, and A. Balbashov, A comparative Raman study between PrMnO3, NdMnO3, TbMnO3 and DyMnO3, Sci. Rep. 7, 13796 (2017).
[81] R. B. M. Filho, D. A. B. Barbosa, H. Reichlova, X. Marti, A. S. de Menezes, A. P. Ayala, and C. W. A. Paschoal, Role of rare-earth ionic radii on the spin-phonon coupling in multiferroic ordered double perovskites, Mater. Res. Express 2, 075201 (2015).
[82] P. K. Pandey, R. J. Choudhary, D. K. Mishra, V. G. Sathe, and D. M. Phase, Signature of spin-phonon coupling in Sr2CoO4 thin film: A Raman spectroscopic study, Appl. Phys. Lett. 102, 142401 (2013).
[83] Q. Zhang, F. Guillou, A. Wahl, Y. Bŕard, and V. Hardy, Coexistence of inverse and normal magnetocaloric effect in A-site ordered NdBaMn2O6, Appl. Phys. Lett. 96, (2010).
[84] A. B. Sushkov, O. Tchernyshyov, W. R. II, S. W. Cheong, and H. D. Drew, Probing spin correlations with phonons in the strongly frustrated magnet ZnCrO4, Phys. Rev. Lett. 94, 137202 (2005).
[85] S.-H. Lee, C. Broholm, T. H. Kim, W. Ratcliff, and S.-W. Cheong, Local spin resonance and spin-peierls-like phase transition in a geometrically frustrated antiferromagnet, Phys. Rev. Lett. 84, 3718 (2000).
[86] S. Elsässer, J. Geurts, A. A. Mukhin, and A. M. Balbashov, Lattice dynamics and spin-phonon coupling in orthorhombic Eu1−xHoxMnO3 (x =0.3) studied by Raman spectroscopy Phys. Rev. B 93, 054301 (2016).
[87] D. Kumar, S. Kumar, and V. G. Sathe, Spin-phonon coupling in ordered double perovskites A2CoMnO6(A=La, Pr, Nd) probed by micro-Raman spectroscopy, Solid State Commun. 194, 59 (2014).
[88] B. S. Araújo, A. M. Arévalo-López, J. P. Attfield, C. W. A. Paschoal, and A. P. Ayala, Spin-phonon coupling in melanothallite Cu2OCl2, Appl. Phys. Lett. 113, 222901 (2018).
[89] T. M. H. Nguyen, X. N. Nguyen, X.-B. Chen, X. T. To, S. Lee, T. H. Nguyen, and I.-S. Yang, Study of spin-phonon coupling in multiferroic BiFeO3 through Raman spectroscopy, J. Mol. Struct. 1222, 128884 (2020).
[90] E. Aytan, B. Debnath, F. Kargar, Y. Barlas, M. M. Lacerda, J. X. Li, R. K. Lake, J. Shi, and A. A. Balandin, Spin-phonon coupling in antiferromagnetic nickel oxide, Appl. Phys. Lett. 111, 252402 (2017).
[91] A. D. Molchanova, M. A. Prosnikov, R. M. Dubrovin, V. Y. Davydov, A. N. Smirnov, R. V. Pisarev, K. N. Boldyrev, and M. N. Popova, Lattice dynamics and electronic transitions in a structurally complex layered copper borate Cu3(BO3)2, Phys. Rev. B 96, 1 (2017).
[92] J. I. Pankove and D. A. Kiewit, Optical processes in semiconductors, J. Electrochem. Soc. 119, 156C (1972).
[93] D. S. Murali, S. Kumar, R. J. Choudhary, A. D. Wadikar, M. K. Jain, and A. Subrahmanyam, Synthesis of Cu2O from CuO thin films: Optical and electrical properties, AIP Adv. 5, 047143 (2015).
[94] W. Y. Ching, Y.-N. Xu, and K. W. Wong, Ground-state and optical properties of Cu2O and CuO crystals, Phys. Rev. B 40, 7684 (1989).
[95] S. C. Ray, Preparation of copper oxide thin film by the sol–gel-like dip technique and study of their structural and optical properties, Sol. Energy Mater. Sol. Cells 68, 307 (2001).
[96] R. D. Mero, C.-H. Lai, C.-H. Du, and H.-L. Liu, Anomalous boron isotope effects on electronic structure and lattice dynamics of CuB2O4, RSC Adv. 10, 41891 (2020).
[97] V. G. Plekhanov, Wannier-Mott excitons in isotope-disordered crystals, Reports Prog. Phys. 61, 1045 (1998).
[98] V. G. Plekhanov, Fundamentals and applications of isotope effect in solids, Prog. Mater. Sci. 51, 287 (2006).
[99] A. T. Collins, S. C. Lawson, G. Davies, and H. Kanda, Indirect energy gap of C13 diamond, Phys. Rev. Lett. 65, 891 (1990).
[100] S. Zollner, M. Cardona, and S. Gopalan, Isotope and temperature shifts of direct and indirect band gaps in diamond-type semiconductors, Phys. Rev. B 45, 3376 (1992).
[101] G. Davies, E. C. Lightowlers, T. S. Hui, V. Ozhogin, K. M. Itoh, W. L. Hansen, and E. E. Haller, Isotope dependence of the lowest direct energy gap in crystalline germanium, Semicond. Sci. Technol. (1993).
[102] D. Rönnow, L. F. Lastras-Martínez, and M. Cardona, Isotope effects on the electronic critical points of germanium: Ellipsometric investigation of the and transitions, Eur. Phys. J. B 5, 29 (1998).
[103] A. Göbel, T. Ruf, M. Cardona, C. T. Lin, J. Wrzesinski, M. Steube, K. Reimann, J.-C. Merle, and M. Joucla, Effects of the isotopic composition on the fundamental gap of CuCl, Phys. Rev. B 57, 15183 (1998).
[104] L. Viña, S. Logothetidis, and M. Cardona, Temperature dependence of the dielectric function of germanium, Phys. Rev. B (1984).
[105] C. Keffer, T. M. Hayes, and A. Bienenstock, PbTe Debye-Waller Factors and Band-Gap Temperature Dependence, Phys. Rev. Lett. 21, 1676 (1968).
[106] H. J. Lian, A. Yang, M. L. W. Thewalt, R. Lauck, and M. Cardona, Effects of sulfur isotopic composition on the band gap of PbS, Phys. Rev. B - Condens. Matter Mater. Phys. (2006).
[107] C. Yu, Z. Chen, J. J. Wang, W. Pfenninger, N. Vockic, J. T. Kenney, and K. Shum, Temperature dependence of the band gap of perovskite semiconductor compound CsSnI3, J. Appl. Phys. 110, 063526 (2011).
[108] L. Y. Huang and W. R. L. Lambrecht, Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl3, CsSnBr3, and CsSnI3, Phys. Rev. B - Condens. Matter Mater. Phys. (2013).
[109] F. Ruf, A. Magin, M. Schultes, E. Ahlswede, H. Kalt, and M. Hetterich, Excitonic nature of optical transitions in electroabsorption spectra of perovskite solar cells, Appl. Phys. Lett. 112, 083902 (2018).
[110] R. D. Mero, C.-H. Lai, C.-H. Du, and H.-L. Liu, Spectroscopic Signature of Spin–Charge–Lattice Coupling in CuB2O4, J. Phys. Chem. C 125, 4322 (2021).
[111] B. J. Foley, D. L. Marlowe, K. Sun, W. A. Saidi, L. Scudiero, M. C. Gupta, and J. J. Choi, Temperature dependent energy levels of methylammonium lead iodide perovskite, Appl. Phys. Lett. 106, 243904 (2015).
[112] W. S. Choi, K. Taniguchi, S. J. Moon, S. S. A. Seo, T. Arima, H. Hoang, I. S. Yang, T. W. Noh, and Y. S. Lee, Phys. Rev. B - Condens. Matter Mater. Phys. 81, 1 (2010).
[113] W. S. Choi, S. J. Moon, S. S. A. Seo, D. Lee, J. H. Lee, P. Murugavel, T. W. Noh, and Y. S. Lee, Optical spectroscopic investigation on the coupling of electronic and magnetic structure in multiferroic hexagonal RMnO3, Phys. Rev. B 78, 054440 (2008).
[114] R. C. Rai, A. Delmont, A. Sprow, B. Cai, and M. L. Nakarmi, Spin-charge-orbital coupling in multiferroic LuFe2O4 thin films, Appl. Phys. Lett. 100, 212904 (2012).
[115] G. Lawes and G. Srinivasan, Introduction to magnetoelectric coupling and multiferroic films, J. Phys. D. Appl. Phys. 44, 243001 (2011).
[116] J. Lu, A. Günther, F. Schrettle, F. Mayr, S. Krohns, P. Lunkenheimer, A. Pimenov, V. D. Travkin, A. A. Mukhin, and A. Loidl, On the room temperature multiferroic BiFeO 3: magnetic, dielectric and thermal properties, Eur. Phys. J. B 75, 451 (2010).
[117] M. Giar, M. Heinemann, and C. Heiliger, Phonon properties of copper oxide phases from first principles, Phys. Rev. B 96, 075202 (2017).