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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/21148完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 郭光宇(Guang-Yu Guo) | |
| dc.contributor.author | Fu-Yen Fan | en |
| dc.contributor.author | 范富硯 | zh_TW |
| dc.date.accessioned | 2021-06-08T03:27:45Z | - |
| dc.date.copyright | 2019-12-25 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-11-28 | |
| dc.identifier.citation | [1] N. A. Spaldin and M. Fiebig, “Materials science. the renaissance of magnetoelectric multiferroics,” Science, vol. 309, p. 391—392, Jul 2005.
[2] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, “Magnetic control of ferroelectric polarization,” Nature, vol. 426, pp. 55–8, Dec 2003. [3] N. A. Hill, “Why are there so few magnetic ferroelectrics?,” J. Phys. Chem. B, vol. 104, pp. 6694–6709, Jun 2000. [4] R. E. Cohen, “Origin of ferroelectricity in perovskite oxides,” Nature, vol. 358, pp. 136–138, Jul 1992. [5] J. Young, A. Stroppa, S. Picozzi, and J. M. Rondinelli, “Anharmonic lattice interactions in improper ferroelectrics for multiferroic design,” J. Phys. Condens. Matter, vol. 27, p. 283202, Jun 2015. [6] N. A. Benedek and C. J. Fennie, “Hybrid improper ferroelectricity: A mechanism for controllable polarization-magnetization coupling,” Phys. Rev. Lett., vol. 106, p. 107204, Mar 2011. [7] M. S. Senn, A. Bombardi, C. A. Murray, C. Vecchini, A. Scherillo, X. Luo, and S. W. Cheong, “Negative thermal expansion in hybrid improper ferroelectric ruddlesdenpopper perovskites by symmetry trapping,” Phys. Rev. Lett., vol. 114, p. 035701, Jan 2015. [8] M. V. Lobanov, M. Greenblatt, E. a. N. Caspi, J. D. Jorgensen, D. V. Sheptyakov, B. H. Toby, C. E. Botez, and P. W. Stephens, “Crystal and magnetic structure of the Ca3Mn2O7 ruddlesden–popper phase: neutron and synchrotron x-ray diffraction study,” J. Phys. Condens. Matter, vol. 16, pp. 5339–5348, Jul 2004. [9] P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Phys. Rev., vol. 136, pp. B864–B871, Nov 1964. [10] W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev., vol. 140, pp. A1133–A1138, Nov 1965. [11] D. M. Ceperley and B. J. Alder, “Ground state of the electron gas by a stochastic method,” Phys. Rev. Lett., vol. 45, pp. 566–569, Aug 1980. [12] J. P. Perdew and A. Zunger, “Self-interaction correction to density-functional approximations for many-electron systems,” Phys. Rev. B, vol. 23, pp. 5048–5079, May 1981. [13] J. P. Perdew and Y. Wang, “Accurate and simple analytic representation of the electron-gas correlation energy,” Phys. Rev. B, vol. 45, pp. 13244–13249, Jun 1992. [14] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, “Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation,” Phys. Rev. B, vol. 46, pp. 6671–6687, Sep 1992. [15] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett., vol. 77, pp. 3865–3868, Oct 1996. [16] A. D. Becke, “Density-functional exchange-energy approximation with correct asymptotic behavior,” Phys. Rev. A, vol. 38, pp. 3098–3100, Sep 1988. [17] C. Lee, W. Yang, and R. G. Parr, “Development of the colle-salvetti correlationenergy formula into a functional of the electron density,” Phys. Rev. B, vol. 37, pp. 785–789, Jan 1988. [18] J. Sun, A. Ruzsinszky, and J. P. Perdew, “Strongly constrained and appropriately normed semilocal density functional,” Phys. Rev. Lett., vol. 115, p. 036402, Jul 2015. [19] Y. Zhang, J. Sun, J. P. Perdew, and X. Wu, “Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA,” Phys. Rev. B, vol. 96, p. 035143, Jul 2017. [20] P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B, vol. 50, pp. 17953–17979, Dec 1994. [21] G. Kresse, J. Furthmüller, and J. Hafner, “Ab initioForce constant approach to phonon dispersion relations of diamond and graphite,” Europhysics Letters (EPL), vol. 32, pp. 729–734, Dec 1995. [22] K. Parlinski, Z. Q. Li, and Y. Kawazoe, “First-principles determination of the soft mode in cubic zro2,” Phys. Rev. Lett., vol. 78, pp. 4063–4066, May 1997. [23] A. Togo and I. Tanaka, “First principles phonon calculations in materials science,” Scr. Mater., vol. 108, pp. 1–5, Nov 2015. [24] J. Ziman, Electrons and Phonons The Theory of Transport Phenomena in Solids. Oxford scholarship online, Oxford: Oxford University Press, 2001. [25] G. Kresse and J. Hafner, “Ab initio molecular dynamics for liquid metals,” Phys. Rev. B, vol. 47, pp. 558–561, Jan 1993. [26] G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci., vol. 6, pp. 15 – 50, Jul 1996. [27] G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B, vol. 54, pp. 11169–11186, Oct 1996. [28] W. Nolting and A. Ramakanth, Quantum theory of magnetism. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2009. [29] A. Schrön, C. Rödl, and F. Bechstedt, “Energetic stability and magnetic properties of mno in the rocksalt, wurtzite, and zinc-blende structures: Influence of exchange and correlation,” Phys. Rev. B, vol. 82, p. 165109, Oct 2010. [30] S. F. Matar, V. Eyert, A. Villesuzanne, and M.-H. Whangbo, “First-principles study of the electronic and magnetic structures of the tetragonal and orthorhombic phases of Ca3X2O7,” Phys. Rev. B, vol. 76, p. 054403, Aug 2007. [31] E. C. Stoner, “Collective electron ferromagnetism ii. energy and specific heat,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 169, no. 938, pp. 339–371, 1939. [32] M. Liu, Y. Zhang, L.-F. Lin, L. Lin, S. Yang, X. Li, Y. Wang, S. Li, Z. Yan, X. Wang, X.-G. Li, S. Dong, and J.-M. Liu, “Direct observation of ferroelectricity in Ca3Mn2O7 and its prominent light absorption,” Appl. Phys. Lett, vol. 113, p. 022902, Jul 2018. [33] I. Dzyaloshinsky, “A thermodynamic theory of “weak”ferromagnetism of antiferromagnetics,” J. Phys. Chem. Solids, vol. 4, no. 4, pp. 241 – 255, 1958. [34] T. Moriya, “Anisotropic superexchange interaction and weak ferromagnetism,” Phys. Rev., vol. 120, pp. 91–98, Oct 1960. [35] B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, “ISODISPLACE: a web-based tool for exploring structural distortions,” J. Appl. Crystallogr., vol. 39, pp. 607–614, Aug 2006. [36] X. Gonze and C. Lee, “Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory,” Phys. Rev. B, vol. 55, pp. 10355–10368, Apr 1997. [37] M. H. Lee, C.-P. Chang, F.-T. Huang, G. Y. Guo, B. Gao, C. H. Chen, S.-W. Cheong, and M.-W. Chu, “Hidden antipolar order parameter and entangled néel-type charged domain walls in hybrid improper ferroelectrics,” Phys. Rev. Lett., vol. 119, p. 157601, Oct 2017. [38] A. Glamazda, D. Wulferding, P. Lemmens, B. Gao, S.-W. Cheong, and K.-Y. Choi, “Soft tilt and rotational modes in the hybrid improper ferroelectric Ca3Mn2O7,” Phys. Rev. B, vol. 97, p. 094104, Mar 2018. [39] X. Q. Liu, J. J. Lu, B. H. Chen, B. H. Zhang, and X. M. Chen, “Hybrid improper ferroelectricity and possible ferroelectric switching paths in Sr3Hf2O7,” J. Appl. Phys., vol. 125, p. 114105, Mar 2019. [40] S. Yoshida, K. Fujita, H. Akamatsu, O. Hernandez, A. Sen Gupta, F. G. Brown, H. Padmanabhan, A. S. Gibbs, T. Kuge, R. Tsuji, S. Murai, J. M. Rondinelli, V. Gopalan, and K. Tanaka, “Ferroelectric Sr3Zr2O7: Competition between hybrid improper ferroelectric and antiferroelectric mechanisms,” Adv. Funct. Mater., vol. 28, p. 1801856, May 2018. [41] A. B. Harris, “Symmetry analysis for the ruddlesden-popper systems Ca3Mn2O7 and Ca3Ti2O7,” Phys. Rev. B, vol. 84, p. 064116, Aug 2011. [42] M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B, vol. 73, p. 045112, Jan 2006. [43] S. Baroni and R. Resta, “Ab initio calculation of the macroscopic dielectric constant in silicon,” Phys. Rev. B, vol. 33, pp. 7017–7021, May 1986. [44] C. F. Li, S. H. Zheng, H. W. Wang, J. J. Gong, X. Li, Y. Zhang, K. L. Yang, L. Lin, Z. B. Yan, S. Dong, and J.-M. Liu, “Structural transitions in hybrid improper ferroelectric Ca3Mn2O7 tuned by site-selective isovalent substitutions: A first-principles study,” Phys. Rev. B, vol. 97, p. 184105, May 2018. [45] N. A. Benedek, A. T. Mulder, and C. J. Fennie, “Polar octahedral rotations: A path to new multifunctional materials,” J. Solid State Chem., vol. 195, pp. 11–20, Nov 2012. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/21148 | - |
| dc.description.abstract | 因為室溫下可由外加電場調控磁性的特性，多鐵過度金屬氧化物近年來被廣泛地研究。最近提出的一種混合非正規鐵電性(hybridimproper ferroelectricity, HIF)，其自發極化來自於混合兩個布里淵區邊界的非極性晶格不穩定性。做為HIF的原型材料，Ca3Mn2O7原本被認為是X+2和X−3聲子模混合凝聚的連續相變，但實驗卻發現了與對稱性違背的過渡態，因此其相變機制仍然不確定。
本文利用基於第一原理的密度泛函理論以及平面波贋勢法，計算Ca3Mn2O7的磁學、電子以及聲子特性。透過計算不同磁結構下的系統總能量，我們發現G型反鐵磁結構具有最低能量。根據海森堡模型，我們計算了交換耦合係數，並且用其估計Néel 溫度，得到了與實驗相當符合的結果。我們也計算了Ca3Mn2O7不同磁性結構下的電子結構，其中G型反鐵磁的電子結構顯示其具有弱鐵磁特性，因此我們再加入自旋軌道耦合效應，結果發現在G型反鐵磁下Ca3Mn2O7 會因為自旋傾斜出現淨總磁矩。進一步探討，發現自旋傾斜是源自於X−3聲子模造成的MnO6八面體傾斜。根據聲子色散關係的聲子軟化現象，我們發現X−3聲子模的軟化程度不及X−1聲子模，阻礙了X−3和X+2聲子模的混合凝聚，導致了與對稱性違背的相變路徑。布里淵區中心的聲子頻率顯示磁性會導致過度態的X−3聲子模軟化，驅動其發生往基態結構的相變。我們證明了Ca3Mn2O7的鐵電極化是由X+2和X−3所誘導，並透過計算得到極化強度為3.50 μC/cm2。 | zh_TW |
| dc.description.abstract | Because of the possibility of electric-field control of magnetism at room temperature, multiferroic transition metal oxides have been widely studied in recent years. Recently, hybrid improper ferroelectricity (HIF) have been reported as a new type of ferroelectricity. The spontaneous polarization of HIF originates from combining two nonpolar zone-boundary lattice instabilities. As a prototype of HIF materials, Ca3Mn2O7 considered to undergo continuous phase transition by hybrid condensation of X−3 and X+2 mode. However, a symmetry incompatible intermediate phase have been found, and thus the precise phase transition mechanism is still not determined.
In this thesis, ab initio calculations of phononic, magnetic and electronic properties have been performed within density functional theory and projected augmented-wave method. From calculating total energies of different magnetic configurations, we found G-type antiferromagnetic configuration have the lowest energy. By Heisenberg model, we have calculated the exchange coupling constants, and estimate the Néel temperature, the results agree with experiments. In order to study the electronic properties, we have calculated the density of states of NM, FM, A-AF and G-AF state. The results indicate G-AF state exhibits weak-ferromagnetism. By including spin-orbit coupling, we found there exists net magnetic moment in G-AF Ca3Mn2O7. A further study reveals that the spin-canted moment is due to X−3 tilt mode. According to soft phonon in phonon dispersion, we found that X−1 mode is softer than X−3 mode, impeding the hybrid condensation of X−2 and X−3 soft mode, thus transits in a symmetry incompatible pathway. The phonon frequencies calculated at Brillouin zone center indicate that magnetic ordering soften the X−3 tilt mode in the intermediate state, driving it to structural ground state. We have shown the ferroelectric polarization is induced by X−2 and X−3 mode, and the calculated polarization is 3.50 μC/cm2. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T03:27:45Z (GMT). No. of bitstreams: 1 ntu-108-R05222063-1.pdf: 4460686 bytes, checksum: f5fedc6564b06a6ac6b208622d7c0d50 (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 口試委員會審定書i
誌謝ii 摘要iii Abstract iv 1 Introduction 1 2 Theoretical background 4 2.1 Density funtional theory . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Hohenberg-Kohn theorems . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Kohn-Sham ansatz . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Exchange and correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Plane wave and Projector Augmented Wave method . . . . . . . . . . . . 10 2.3.1 Plane wave method . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Projector augmented wave method . . . . . . . . . . . . . . . . . 12 2.4 Finite displacement method . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Magnetic and electronic properties of Ca3Mn2O7 15 3.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Crystal structure and magnetic configuration . . . . . . . . . . . . . . . . 15 3.2.1 Theoretical lattice parameters . . . . . . . . . . . . . . . . . . . 16 3.2.2 Magnetic configuration . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.3 Exchange coupling parameter . . . . . . . . . . . . . . . . . . . 18 3.3 Density of states and band structure . . . . . . . . . . . . . . . . . . . . 20 4 Phononic and ferroelectric properties of Ca3Mn2O7 26 4.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Phononic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2.1 Phonon dispersion . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2.2 Energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 Ferroelectric polarization . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5 Summary 36 Bibliography 38 | |
| dc.language.iso | en | |
| dc.subject | 過度金屬氧化物 | zh_TW |
| dc.subject | 混和型非正規鐵電性 | zh_TW |
| dc.subject | 多鐵材料 | zh_TW |
| dc.subject | 聲子軟化 | zh_TW |
| dc.subject | 第一原理計算 | zh_TW |
| dc.subject | hybrid improper ferroelectricity | en |
| dc.subject | Multiferroics | en |
| dc.subject | soft phonon | en |
| dc.subject | first principles calculation | en |
| dc.subject | transition metal oxide | en |
| dc.title | 以第一原理計算研究Ca3Mn2O7的磁學、電子及聲子性質 | zh_TW |
| dc.title | An Ab Initio Computational Study of Magnetic, Electronic and Phononic Properties of Ca3Mn2O7 | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 胡崇德(Chong-Der Hu),朱明文(Ming-Wen Chu),陳威廷(Wei-tin Chen) | |
| dc.subject.keyword | 多鐵材料,混和型非正規鐵電性,過度金屬氧化物,聲子軟化,第一原理計算, | zh_TW |
| dc.subject.keyword | Multiferroics,hybrid improper ferroelectricity,transition metal oxide,soft phonon,first principles calculation, | en |
| dc.relation.page | 42 | |
| dc.identifier.doi | 10.6342/NTU201904201 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2019-11-28 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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