PHYSICAL REVIEW B 105, 024414 (2022) Ferromagnetic and nonmagnetic 1T ′ charge density wave states in transition metal dichalcogenides: Physical mechanisms and charge doping induced reversible transition Kaiyun Chen , 1 Junkai Deng , 2 , * Dongxiao Kan, 1 Yuan Yan, 3 Qian Shi, 4 Wangtu Huo, 1 Mengshan Song, 1 Sen Yang, 4 , † and Jefferson Zhe Liu 3 , ‡ 1 Advanced Materials Research Central, Northwest Institute for Nonferrous Metal Research, Xi’an 710016, China 2 State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China 3 Department of Mechanical Engineering, The University of Melbourne, Parkville, VIC 3010, Australia 4 MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi’an Jiaotong University, Xi’an 710049, China (Received 11 November 2021; accepted 5 January 2022; published 13 January 2022) The charge density wave (CDW) states of two-dimensional transition metal dichalcogenides (TMDs) originate from intrinsic couplings between the electronic structures and lattice distortion, inducing interesting physical and chemical properties. The observed TMDs CDW states are mostly nonmagnetic (NM) but with a few ferromagnetic (FM) cases. Physical mechanisms for the formation of FM CDW remain elusive. In this paper, we used density functional theory calculations to study a set of TMDs with magnetic transition metal elements (e.g., V, Cr, and Mn). We found that the FM state can stem from the direct exchange to superexchange transition (e.g., CrX 2 ) or the M-M (M is the metal atom) dimerization (e.g., MnX 2 ). A crystal structure distortion index is proposed to distinguish the different formation mechanisms of FM CDW states. Interestingly, CrX 2 has both NM and FM CDW states, which is not observed in other TMDs materials. We found that charge (electron or hole) doping could modulate the different formation mechanisms and induce a phase transition between these two CDW states in CrS 2 , leading to significant actuation strain output (i.e., 12.17% and 5.93% along x and y directions, respectively) and drastic change of magnetism, which could enable some multifunctionality applications of TMD materials. DOI: 10.1103/PhysRevB.105.024414 I. INTRODUCTION The excellent electronic, magnetic, and chemical proper- ties of two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted extensive research, considering their great potential for next-generation electronic, optoelectronics, and electromechanical devices [1–5]. The various superior physical and chemical properties of the TMD family can be attributed to their chemical diversity and their multiple stable crystal structures. For example, the VI group Mo/W TMDs has the thermodynamically stable 2H phase as semiconduc- tors; meanwhile, these materials show metallic character after transits to 1T or 1T ′ phase through strain, charge doping, elec- tron beam radiation, alloying and many other methods [6–12]. These multiple properties in a single piece of TMD monolayer are the foundation for the lateral heterostructure designs in electronic and spintronic devices [13–15]. The low symmetry 1T ′ phase, observed in many TMDs, can be viewed as a distortion from the high-symmetry 1T phase. The periodic lattice distortion modulates the charge density and leads to the charge density wave (CDW) superstructures. These CDW states show fantastic proper- * junkai.deng@mail.xjtu.edu.cn † yangsen@mail.xjtu.edu.cn ‡ zhe.liu@unimelb.edu.au ties in experiments and theoretical studies, which expand the TMD applications to heterogeneous catalysis, supercon- ductor, ferromagnetism, superelasticity and shape memory effect [16–18]. At present, most of the reported 1T ′ CDW phases are nonmagnetic (NM). The prototypical examples are the well-known MoX 2 and WX 2 (X is the chalcogenide atoms). The formation of such NM-CDW phases has usu- ally been attributed to the Peierls distortion. The formation of zigzag M-M dimer chains in the 1T ′ phase stabilizes the distorted structure [2]. Based on the understanding, it has been demonstrated that charge doping could modulate the Perierls distortion to induce a reversible phase transition between the 1T ′ and 1T phase, leading to the superelasticity and shape memory effects [17]. In contrast, the reported 1T ′ FM-CDW phases are rare, e.g., 1T ′ CrX 2 [19,20]. The coupling of FM and CDW enables exciting properties that are not observed in the NM-CDW counterparts, e.g., the recently proposed strain-controlled 2D TMDs heterostructure-based spin valves [21]. However, the physical mechanisms for the formation remain elusive. Thus, there is a need to explore more 1T ′ FM-CDW phases and gain an in-depth understanding of their formation mechanisms to unleash their promising potentials in spintronics applications. In this work, we performed density functional theory (DFT) calculations for a set of TMD MX 2 materials with magnetic transition metal elements (i.e., M = V, Cr, and Mn and X = S, Se, and Te). We systematically study their crystal 2469-9950/2022/105(2)/024414(8) 024414-1 ©2022 American Physical Society