鈦鐵礦 MTiO3（M = Fe、Co、Ni），具有蜂巢狀結構。 CoTiO3 在中子散射光譜中呈現狄拉克磁振子(Dirac magnons) [1][2]。在這篇論文中，我們將報告使用光學浮區爐製作 NiTiO3 及Co0.5Ni0.5TiO3單晶。透過X射線勞厄衍射法確認了晶體結構和品質。隨後，我們進行了直流磁化率和比熱測量，以研究樣品的物理性質。
NiTiO3在 23.5 K 處觀察到與磁有序相關的直流磁化率的明顯峰值，與ab平面及c軸中的磁異相性。低溫下磁比熱數據的積分熵估計為R ln3，表示存在 spin - 1 系統。並藉由非彈性中子散射實驗來研究狄拉克磁振子激發。並確認到能帶結構線性交叉於K點，並透過使用 SpinW 軟體擬合自旋波來獲得交換常數。
Co0.5Ni0.5TiO3在 28 K 處觀察到與磁有序相關的直流磁化率的明顯峰值及磁異相性。低溫下磁比熱數據的積分熵接近為 R(ln2+ln3)。以及進行的CoxNi1-x¬TiO3 (0≤x≤1)的各種參雜比例，進行X光繞射及磁化率量測，了解晶格常數、尼爾溫度及有效磁矩的變化趨勢。

MTiO3 (M = Fe, Co, Ni) possesses a honeycomb structure. CoTiO3 exhibits Dirac magnons in neutron scattering spectra [1][2]. Here, we report the growth of NiTiO3 and Co0.5Ni0.5TiO3 single crystals using an optical floating zone furnace. The crystal structure and quality were confirmed by X-ray Laue diffraction. Subsequently, we conducted DC magnetic susceptibility and specific heat measurements to investigate the physical properties of the samples.
NiTiO3 shows a pronounced peak in the DC magnetic susceptibility at 23.5 K related to magnetic ordering, with magnetic anisotropy between the ab plane and c-axis. Integration of the low-temperature magnetic specific heat data estimates an entropy of Rln3, indicating the presence of a spin-1 system. Dirac magnon excitations were studied using inelastic neutron scattering technique. Linear band crossings were confirmed at the K and K’ point, and the exchange constants were obtained by fitting spin waves using SpinW software.
Co0.5Ni0.5TiO3 exhibits a pronounced peak in DC magnetic susceptibility at 28 K associated with magnetic ordering and magnetic anisotropy. The integrated entropy from low-temperature magnetic specific heat data approaches R(ln2+ln3). Additionally, various doping ratios of CoxNi1-xTiO3 were studied through X-rays diffraction and magnetic susceptibility measurements to understand the trends in lattice constants, Néel temperatures, and effective magnetic moments.

[1] B. Yuan, I. Khait, G.-J. Shu, F. Chou, M. Stone, J. Clancy, A. Paramekanti, and Y.-J. Kim, Physical Review X 10, 011062 (2020).
[2] B. Yuan, E. Horsley, M. Stone, N. P. Butch, G. Xu, G.-J. Shu, J. Clancy, and Y.-J. Kim, Physical Review B 109, 174440 (2024).
[3] R. Kubo, Physical Review 87, 568 (1952).
[4] F. Bloch, Zeitschrift für Physik 61, 206 (1930)
[5] S. Katsura, Physical Review 127, 1508 (1962).
[6] S. M. Blinder, Introduction to quantum mechanics (Academic Press, 2020).
[7] W. Heisenberg, Zeitschrift für Physik 38, 411 (1926).
[8] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Nature physics 11, 453 (2015).
[9] P. A. M. Dirac, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 117, 610 (1928).
[10] J. Fransson, A. M. Black-Schaffer, and A. V. Balatsky, Physical Review B 94, 075401 (2016).
[11] D. Boyko, A. V. Balatsky, and J. Haraldsen, Physical Review B 97, 014433 (2018).
[12] P. A. McClarty, Annual Review of Condensed Matter Physics 13, 171 (2022).
[13] D. Boyko, A. Saxena, and J. T. Haraldsen, Annalen der Physik 532, 1900350 (2020).
[14] Zhai and Y. M. Blanter, Physical Review B 102, 075407 (2020).
[15] N Okuma, Physical Review Letters 119, 107205 (2017).
[16] L. Chen, M. B. Stone, A. I. Kolesnikov, B. Winn, W. Shon, P. Dai, and J.-H. Chung, 2D Materials 9, 015006 (2021).
[17] S.-H. Do, Joseph A. M. Paddison, Gabriele Sala, Travis J. Williams, Koji Kaneko, Keitaro Kuwahara, Jiaqiang Yan, Michael A. McGuire, Andrew F. May, Matthew B. Stone, Mark D. Lumsden, Andrew D. Christianson, Physical Review B 106, L060408 (2022).
[18] L. Chen, J.-H. Chung, B. Gao, T. Chen, M. B. Stone, A. I. Kolesnikov, Q. Huang, and P. Dai, Physical Review X 8, 041028 (2018).
[19] W. Yao, C. Li, L. Wang, S. Xue, Y. Dan, K. Iida, K Kamazawa, K. Li, C. Fang, and Y. L., Nature Physics 14, 1011 (2018).
[20] S. Bao, J. Wang, W. Wang. Cai, S. Li, Z. Ma, D. Wang, K. Ran, Z.-Y. Dong, D. L. Abernathy, S.-L. Yu X. Wan, J.-X. Li, and J. Wen, Nat. Commun. 9, 2591(2018).
[21] N. Wilson, J. Muscat, D. Mkhonto, P. Ngoepe, and N. Harrison, Physical Review B—Condensed Matter and Materials Physics 71, 075202 (2005).
[22] L. Trengove, Annals of Science 29, 361 (1972).
[23] J. B. Goodenough and J. J. Stickler, Phys. Rev. 164, 768 (1967).
[24] J. J. Stickler, S. Kern, A. Wold, and G. S. Heller, Phys. Rev.164, 765 (1967).
[25] H. Watanabe, H. Yamauchi, and H. Takei, Journal of Magnetism and Magnetic Materials 15, 549 (1980).
[26] G. S. Heller, J. J. Stickler, S. Kern, and A. Wold, Journal of Applied Physics 34, 1033 (1963).
[27] G. Shirane, P. SJ, and Y. Ishikawa, Journal of the Physical Society of Japan 14, 1352 (1959).
[28] R. Newnham, J. Fang, and R. Santoro, Acta Crystallographica 17, 240 (1964).
[29] Y. Yamaguchi, H. Kato, H. Takei, A. Goldman, and G. Shirane, Solid state communications 59, 865 (1986).
[30] M. Charilaou, D. Sheptyakov, J. F. Löffler, and A. Gehring, Physical Review B—Condensed Matter and Materials Physics 86, 024439 (2012).
[31] G. Shirane, P. SJ, and Y. Ishikawa, Journal of the Physical Society of Japan 14, 1352 (1959).
[32] R. E. Newnham, J. H. Fang, and R. P. Santoro, Acta Crystallogr.17, 240 (1964).
[33] Y. Li Y. Li, T. T. Mai, M. Karaki, E. V. Jasper, K. F. Garrity, C. Lyon, Physical Review B 109, 184436 (2024).
[34] T. F. Barth and E. Posnjak, Zeitschrift für Kristallographie-Crystalline Materials 88, 265 (1934).
[35] J.-H. Chung, K. Shin, T. R. Yokoo, D. Ueta, M. Imai, H.-s. Kim, D. H. Kiem, M. J. Han, and S.-i. Shamoto, Scientific Reports 15, 5978 (2025).
[36] B. E. Warren, X-ray Diffraction (Courier Corporation, 1990).
[37] A. A. Bunaciu, E. G. UdriŞTioiu, and H. Y. Aboul-Enein, Critical reviews in analytical chemistry 45, 289 (2015).
[38] G. Jauncey, Proceedings of the national academy of sciences 10, 57 (1924).
[39] P. P. Ewald, Annalen der physik 369, 253 (1921).
[40] P. Ewald, Foundations of Crystallography 25, 103 (1969).
[41] W. Zachariasen, Acta Crystallographica 23, 558 (1967).
[42] ̎ProductIntroduction Model PPMS-16: 16 Tesla PPMS ̎
[43] Physical Property Measurement System Hardware Manual. (Quantum Design, USA, 2008).
[44] PPMS Heat capacity Option User’s Manual. Quantum Design, Inc (2004)
[45] Physical Property Measurement System Heat Capacity Option User’s Manual. (Quantum Design, USA, 2004).
[46] PPMS AC Measurement System (ACMS) Option User’s Manual (Quantum Design, Inc, USA, 2003).
[47] C. Kittel and P. McEuen, Introduction to solid state physics (John Wiley & Sons, 2018).
[48] J. R. Christman, J. R. Christman, J. R. Christman, J. R. Christman, and E.-U. Physicien, Fundamentals of solid state physics. Wiley New York (1988).
[49] D. Averin, Y. V. Nazarov, and A. Odintsov, "Incoherent tunneling of the Cooper pairs and magnetic flux quanta in ultrasmall Josephson junctions," Physica B: Condensed Matter 165, 945 (1990).
[50] W. Schmidt and M. Ohl, Physica B: Condensed Matter 385, 1073 (2006).
[51] ILL IN12 -cold neutron three-axis spectrometer.
Instrument layout - ILL Neutrons for Society
[52] K.-H. Beckurts and K. Wirtz, Neutron physics (Springer Science & Business Media, 2013).
[53] J. Chadwick, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 136, 692 (1932).
[54] G. Shirane, S. M. Shapiro, and J. M. Tranquada, Neutron scattering with a triple-axis spectrometer: basic techniques (Cambridge University Press, 2002).
[55] L. Li, Technical white paper (2014)
[56] U. Boesl, Mass spectrometry reviews 36, 86 (2017).
[57] K. Schmalzl, W. Schmidt, S. Raymond, H. Feilbach, C. Mounier, B. Vettard, and T. Brueckel, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 819, 89 (2016).
[58] M. Ruiz-Preciado, A. Kassiba, A. Gibaud, and A. Morales-Acevedo, Materials Science in Semiconductor Processing 37, 171 (2015).
[59] J. Rodríguez-Carvajal, Laboratoire Léon Brillouin (CEA-CNRS), CEA/Saclay 91191 (2003).
[60] J. Rodriguez-Carvajal, CEA/Saclay, France 1045, 132 (2001).
[61] S. Koohpayeh, D. Fort, and J. Abell, Progress in Crystal Growth and Characterization of Materials 54, 121 (2008).
[62] S. Mugiraneza and A. M. Hallas, Communications Physics 5, 95 (2022).
[63] K. Dey, S. Sauerland, J. Werner, Y. Skourski, M. Abdel-Hafiez, R. Bag, S. Singh, and R. Klingeler, Physical Review B 101, 195122 (2020).
[64] P. Debye, Annalen der Physik 344, 789 (1912).
[65] R. Baierlein, Thermal physics (Cambridge University Press, 1999).
[66] H. Kikuchi, M. Ozeki, N. Kurita, S. Asai, T. J. Williams, T. Hong, and T. Masuda, Journal of the Physical Society of Japan 94, 024703 (2025).
[67] A. R. Denton and N. W. Ashcroft, Physical review A 43, 3161 (1991).
[68] M. Hoffmann , K. Dey, J. Werner, R. Bag, J. Kaiser, H. Wadepohl,Y. Skourski, M. Abdel-Hafiez, S. Singh, Physical Review B 104, 014429 (2021).
[69] J.-Q. Yan, S. Okamoto, Y. Wu, Q. Zheng, H. Zhou, H. Cao, and M. A. McGuire, Physical Review Materials 3, 074405 (2019).