Perovskite-based two-dimensional ferromagnet Sr<sub>2</sub>RuO<sub>4</sub> monolayer

Zhang Jun-Ting; Ji Ke; Xie Yu; Li Chao

doi:10.7498/aps.73.20241042

Abstract

At present, the research on two-dimensional (2D) ferromagnets is mainly concentrated on van der Waals materials, while the successful preparation of strain-free freestanding 2D perovskite films provides a great opportunity for designing 2D ferromagnets beyond van der Waals materials. Perovskite oxide SrRuO₃, a typical perovskite itinerant ferromagnet, has broad application prospects in many fields. In this work, the lattice dynamics, ground-state structure, electronic and magnetic properties of its perovskite monolayer with formula Sr₂RuO₄, as well as the effect of external electric field, are studied by combining first-principles calculation, symmetry analysis and Monte Carlo simulation. The influence of the Hubbard parameter U is also revealed. The results indicate that the ground-state structure under all U values presents the structural phase (space group P4/mbm) generated by octahedral rotation distortion. Similar to the SrRuO₃ bulk, Sr₂RuO₄ has a monolayer ground-state phase that exhibits ferromagnetism, which is independent of the U value and thus robust. Density functional theory calculation using Hubbard parameter U predicts the ground-state phase of the monolayer to be a ferromagnetic half metal with an out-of-plane easy-magnetization axis, while excluding that the U parameter predicts the ground-state phase to be a ferromagnetic metallic state. The ferromagnetism mainly originates from the strong ferromagnetic exchange interaction between the nearest neighbor spin pairs. The simulated Curie temperature of the Sr₂RuO₄ monolayer is 177 K, which is close to the value (150 K) of its bulk phase. The out-of-plane electric field does not change the ground-state structure nor ferromagnetism of the Sr₂RuO₄ monolayer, but can significantly modulate its electronic property and magnetic property. When an external electric field exceeding 0.3 V/Å is applied, the system undergoes a transition from a ferromagnetic half-metal state to a ferromagnetic metallic state. This work indicates the potential application of Sr₂RuO₄ monolayer in low-dimensional spintrnic devices, and provides a reference for developing perovskite-based 2D ferromagnets and realizing the control of 2D magnetism by electric field.

Keywords:

Authors and contacts

School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China

Corresponding author: Zhang Jun-Ting, juntingzhang@cumt.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12374097, 11974418).

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References

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[2]	Gong C, Zhang X 2019 Science 363 706 Google Scholar
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图 1 Sr₂RuO₄单层原型相的(a)晶体结构和(b)声子谱

Figure 1. (a) Schematic crystal structure and (b) phonon spectrum of the prototype phase of Sr₂RuO₄ monolayer.

DownLoad: Full-Size Img PowerPoint

图 2 Sr₂RuO₄单层每种晶格畸变模式的能量随模式幅度的变化, 涉及(a) 旋转(R)和倾斜(T), 以及(b) JT₁和JT₂扭曲模式. 插图为四种晶格扭曲模式的示意图, 其中弯曲的箭头代表八面体转动方向, 而直箭头表示阴离子位移方向

Figure 2. Energy variation of each distortion mode with the mode amplitude for the Sr₂RuO₄ monolayer, involves (a) rotation (R) and tilt (T), and (b) JT₁ and JT₂ modes. The illustration shows four lattice distortion modes, where the curved arrows represent the direction of octahedral rotation and the straight arrows indicate the direction of anion displacement

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图 3 Sr₂RuO₄单层基态相的(a) 晶体结构, (b) 声子谱, (c) 300 K 下的第一性分子动力学模拟

Figure 3. Crystal structure (a), phonon spectrum (b), and first-principles molecular dynamics simulation (at 300 K) (c) of the ground-state phase of Sr₂RuO₄ monolayer.

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图 4 Sr₂RuO₄单层基态相在不同U值下的上自旋和下自旋投影能带结构　(a) $ U_{{\mathrm{eff}}} = 1.2 $ eV; (b) $ U_{{\mathrm{eff}}} = 2 $ eV; (c) $ U_{{\mathrm{eff}}} = 0 $ eV

Figure 4. Projected up and down spin band structures of the ground-state phase of Sr₂RuO₄ monolayer at different U values: (a) $ U_{{\mathrm{eff}}} = 1.2 $ eV; (b) $ U_{{\mathrm{eff}}} = 2 $ eV; (c) $ U_{{\mathrm{eff}}} = 0 $ eV.

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图 5 (a) 不同反铁磁序的示意图和相对能量(相对于铁磁相), 以及$ U_{{\mathrm{eff}}} = 1.2 $ eV 时计算的(b)不同自旋面的磁各向异性能量曲线和 (c) 蒙特卡罗模拟的磁化和比热曲线

Figure 5. (a) Schematic of different antiferromagnetic orders and their relative energy (to ferromagnetic order) for the ground-state phase. (b) Energy curves of magnetic anisotropy for different spin planes, and (c) magnetization and specific heat curves in Monte Carlo simulation calculated at $ U_{{\mathrm{eff}}} = 1.2 $ eV.

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图 6 (a)上自旋带隙和磁矩及(b)磁交换相互作用、磁各向异性常数、居里温度随电场强度的变化

Figure 6. (a) Variation of the up-spin band gap and magnetic moment, and (b) magnetic exchange interaction, magnetic anisotropy constant and Curie temperature with the electric-field intensity.

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表 1 Sr₂RuO₄单层不同晶格畸变模式及其各种组合所产生的结构相的对称性和不同U值下的相对能量, 其中基态相的能量被设置为0. 符号“—”表示对应的结构相不稳定, 即经过结构优化后转变为其他结构相

Table 1. Symmetry and the relative energy at different U values of structural phases resulting from different distortion modes and their various combinations for the Sr₂RuO₄ monolayer. Energy of the ground-state phase is set to 0. The symbol “—” represents that the corresponding structural phase is unstable, that is, it is transformed into another structural phases after structural optimization.

Distortion modes	Space group	$ \Delta E $/(meV·f.u.^–1)
Distortion modes	Space group	$ U_{{\mathrm{eff}}} = 0 $	$ U_{{\mathrm{eff}}} = 0.5 $	$ U_{{\mathrm{eff}}} = 1.2 $	$ U_{{\mathrm{eff}}} = 1.5 $	$ U_{{\mathrm{eff}}} = 2 $
$ {\mathrm{Para}} $	$ P4/mmm $	154	172	225	227	214
${\mathrm{ R}}(M_2^+) $	$ P4/mbm $	0	0	0	0	0
$ {\mathrm{T}}(a, 0)(M_5^+) $	$ Pmna $	—	—	228	225	214
$ {\mathrm{T}}(a, a)(M_5^+) $	$ Cmma $	—	—	227	224	212
$ {\mathrm{JT}}_1(M_3^+) $	$ P4/mbm $	—	—	—	—	—
$ {\mathrm{JT}}_2(M_4^+) $	$ P4/mmm $	—	—	—	—	—
$ {\mathrm{R}} \oplus {\mathrm{JT}}_1 $	$ Pbam $	—	—	—	—	—
$ {\mathrm{R}} \oplus {\mathrm{JT_2}} $	$ P4/m $	—	—	—	—	—
$ {\mathrm{R}} \oplus {\mathrm{T}}(a, 0) $	$ P2_1/c $	—	—	—	—	—
$ {\mathrm{R}} \oplus {\mathrm{T}}(a, a) $	$ C2/m $	—	—	—	—	—
$ {\mathrm{T}}(a, 0) \oplus {\mathrm{JT}}_1 $	$ P2_1/c $	—	—	—	—	—
$ {\mathrm{T}}(a, 0) \oplus {\mathrm{JT_2}} $	$ P2/m $	—	—	—	—	—
$ {\mathrm{T}}(a, a) \oplus{\mathrm{ JT}}_1 $	$ C2/m $	—	—	—	—	—
$ {\mathrm{T}}(a, a) \oplus {\mathrm{JT}}_2 $	$ C2/m $	—	—	—	—	—
$ {\mathrm{R}} \oplus {\mathrm{T}}(a, 0) \oplus {\mathrm{JT}}_1 $	$ P2_1/c $	—	—	—	—	—
${\mathrm{ R}} \oplus {\mathrm{T}}(a, 0) \oplus {\mathrm{JT}}_2 $	$ P\bar{1} $	—	—	—	—	—
$ {\mathrm{R}} \oplus{\mathrm{ T}}(a, a) \oplus {\mathrm{JT}}_1 $	$ P\bar{1} $	—	—	—	—	—
$ {\mathrm{R}} \oplus {\mathrm{T}}(a, a) \oplus {\mathrm{JT}}_2 $	$ P\bar{1} $	—	—	—	—	—

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表 2 不同U值下计算的最近邻($ J_1 $)和次近邻($ J_2 $)磁交换作用参量, 磁各向异性常数(K), 磁矩(M)及居里温度($ T_{\mathrm{C }}$)

Table 2. Nearest neighbor ($ J_1 $) and next nearest neighbor ($ J_2 $) magnetic exchange interaction parameters, magnetic anisotropy constant (K), magnetic moment (M) and Curie temperature ($ T_{\mathrm{C}} $) calculated at different U values.

$ U_{{\mathrm{eff}}} $/eV	$ J_1 $/meV	$ J_2 $/meV	K/meV	M/$ \mu_{\mathrm{B}} $	$ T_{\mathrm{C}} $/K
0	11.48	–1.35	1.57	0.73	81
0.5	15.39	1.73	1.11	0.96	111
1.2	25.34	–2.41	1.83	1.43	177
1.5	31.18	–3.90	1.70	1.44	195
2	38.38	–8.53	1.81	1.47	202

DownLoad: CSV

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[1]	Burch K S, Mandrus D, Park J G 2018 Nature 563 47 Google Scholar
[2]	Gong C, Zhang X 2019 Science 363 706 Google Scholar
[3]	肖寒, 弭孟娟, 王以林 2021 70 127503 Google Scholar Xiao H, Mi M J, Wang Y L 2021 Acta Phys. Sin. 70 127503 Google Scholar
[4]	Gong C, Li L, Li Z, Ji H, Stern A, Xia Y, Cao T, Bao W, Wang C, Wang Y, Qiu Z Q, Cava R J, Louie S G, Xia J, Zhang X 2017 Nature 546 265 Google Scholar
[5]	Huang B, Clark G, Navarro-Moratalla E, Klein D R, Cheng R, Seyler K L, Zhong D, Schmidgall E, McGuire M A, Cobden D H, Yao W, Xiao D, Jarillo-Herrero P, Xu X 2017 Nature 546 270 Google Scholar
[6]	Song T C, Cai X H, Tu M W Y, Zhang X, Huang B, Wilson N P, Seyler K L, Zhu L, Taniguchi T, Watanabe K, McGuire M A, Cobden D H, Xiao D, Yao W, Xu X D 2018 Science 360 1214 Google Scholar
[7]	Klein D R, MacNeill D, Lado J L, Soriano D, Navarro-Moratalla E, Watanabe K, Taniguchi T, Manni S, Canfield P, Fernández-Rossier J, Jarillo-Herrero P 2018 Science 360 1218 Google Scholar
[8]	Kim H H, Yang B, Patel T, Sfigakis F, Li C, Tian S, Lei H, Tsen A W 2018 Nano Lett. 18 4885 Google Scholar
[9]	Wang Z, Zhang T Y, Ding M, et al. 2018 Nat. Nanotechnol. 13 554 Google Scholar
[10]	Jiang X, Liu Q X, Xing J P, Liu N S, Guo Y, Liu Z F, Zhao J J 2021 Appl. Phys. Rev. 8 031305 Google Scholar
[11]	Dagotto E, Hotta T, Moreo A 2001 Phys. Rep. 344 1 Google Scholar
[12]	Dagotto E 2005 Science 309 257 Google Scholar
[13]	Eerenstein W, Mathur N D, Scott J F 2006 Nature 442 759 Google Scholar
[14]	Hong S S, Yu J H, Lu D, Marshall A F, Hikita Y, Cui Y, Hwang H Y 2017 Sci. Adv. 3 eaao5173 Google Scholar
[15]	Ji D X, Cai S H, Paudel T R, Sun H Y, Zhang C C, Han L, Wei Y F, Zang Y P, Gu M, Zhang Y, Gao W P, Huyan H X, Guo W, Wu D, Gu Z B, Tsymbal E Y, Wang P, Nie Y F, Pan X Q 2019 Nature 570 87 Google Scholar
[16]	Lu J, Luo W, Feng J, Xiang H 2018 Nano Lett. 18 595 Google Scholar
[17]	Zhang J T, Shen X F, Wang Y C, Ji C, Zhou Y, Wang J L, Huang F Z, Lu X M 2020 Phys. Rev. Lett. 125 017601 Google Scholar
[18]	Zhang J T, Zhou Y, Wang F, Shen X F, Wang J L, Lu X M 2022 Phys. Rev. Lett. 129 117603 Google Scholar
[19]	Zhou Y, Dong S, Shan C X, Ji K, Zhang J T 2022 Phys. Rev. B 105 075408 Google Scholar
[20]	Shen X F, Wang F, Lu X M, Zhang J T 2023 Nano Lett. 23 735 Google Scholar
[21]	Ji K, Wu Z, Shen X, Wang J, Zhang J 2023 Phys. Rev. B 107 134431 Google Scholar
[22]	Gertjan K, Lior K, Wolter S, Guus R, Steven D J, Chang-Beom E, A B D H, R B M 2012 Rev. Mod. Phys. 84 253 Google Scholar
[23]	Anwar M S, Lee S R, Ishiguro R, Sugimoto Y, Tano Y, Kang S J, Shin Y J, Yonezawa S, Manske D, Takayanagi H, Noh T W, Maeno Y 2016 Nat. Commun. 7 13220 Google Scholar
[24]	Li W, Liao L, Deng C G, Lebudi C, Liu J C, Wang S X, Yi D, Wang L F, Li J F, Li Q 2024 Nano Lett. 24 5010 Google Scholar
[25]	Ohnishi T, Takada K 2011 Appl. Phys. Express 4 025501 Google Scholar
[26]	Wakabayashi Y K, Kaneta-Takada S, Krockenberger Y, Taniyasu Y, Yamamoto H 2021 ACS Appl. Electron. Mater. 3 2712 Google Scholar
[27]	Kresse G, Hafner J 1993 Phys. Rev. B 47 558(R Google Scholar
[28]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[29]	Perdew J P, Ruzsinszky A, Csonka G I, Vydrov O A, Scuseria G E, Constantin L A, Zhou X, Burke K 2009 Phys. Rev. Lett. 102 039902 Google Scholar
[30]	Şaşıoğlu E, Friedrich C, Blügel S 2011 Phys. Rev. B 83 121101 Google Scholar
[31]	Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J, Sutton A P 1998 Phys. Rev. B 57 1505 Google Scholar
[32]	Kulik H J, Cococcioni M, Scherlis D A, Marzari N 2006 Phys. Rev. Lett. 97 103001 Google Scholar
[33]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[34]	Campbell B J, Stokes H T, Tanner D E, Hatch D M 2006 J. Appl. Crystallogr. 39 607 Google Scholar
[35]	Gonze X, Lee C 1997 Phys. Rev. B 55 10355 Google Scholar
[36]	Togo A, Tanaka I 2015 Scr. Mater. 108 1 Google Scholar
[37]	Marshall A F, Klein L, Dodge J S, Ahn C H, Reiner J W, Mieville L, Antagonazza L, Kapitulnik A, Geballe T H, Beasley M R 1999 J. Appl. Phys. 85 4131 Google Scholar
[38]	Wang F, Zhou Y, Shen X F, Dong S, Zhang J T 2023 Phys. Rev. Appl. 20 064011 Google Scholar

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Perovskite-based two-dimensional ferromagnet Sr₂RuO₄ monolayer

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Perovskite-based two-dimensional ferromagnet Sr2RuO4 monolayer

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Perovskite-based two-dimensional ferromagnet Sr₂RuO₄ monolayer