PHYSICAL REVIEW B 97, 224428 (2018) Stabilizing skyrmions by nonuniform strain in ferromagnetic thin films without a magnetic field Yinuo Shi and Jie Wang * Department of Engineering Mechanics & Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Zheda Road 38, Hangzhou 310027, China (Received 23 April 2018; revised manuscript received 16 June 2018; published 28 June 2018) Magnetic skyrmions with topologically protected spin textures have recently attracted much attention due to their fascinating properties and potential application in advanced spintronics devices. For ferromagnetic thin films, skyrmions usually appear only in the presence of magnetic field. The stabilization of skyrmions in the absence of magnetic field remains an important challenge. Here, using a real-space phase field model based on Ginzburg-Landau theory, we demonstrate that a nonuniform strain can stabilize skyrmions in the FeGa thin film without a magnetic field. The phase field simulations show that the FeGa thin film exhibits a metastable skyrmion phase in the absence of magnetic field when a nonuniform strain with a cosine profile is applied. It is found that the metastable skyrmions can be transformed into a helical phase if a localized magnetic field or pulse of spin-polarized current is applied, resulting in the coexistence of skyrmion and helical phases in the ferromagnetic thin films. Furthermore, the skyrmion and helical phases can remain dynamically stable during the motion driven by a spin-polarized current. The coexistence of skyrmion and helical phases in the ferromagnetic thin films without magnetic field has potential application in skyrmion-based spintronic devices. DOI: 10.1103/PhysRevB.97.224428 I. INTRODUCTION Magnetic skyrmions are nanometer-sized chiral spin texture found in B20-type chiral magnets such as FeGe [1,2], MnSi [3], and Fe 1-x Co x Si [4]. The formation of skyrmions is mainly attributed to the competition between the exchange interaction and Dzyaloshinskii-Moriya interaction (DMI) [5]. The DMI arises from inversion symmetry breaking in magnetic materials with a noncentrosymmetric lattice or in magnetic multilayers, which can result in a rich variety of chiral magnetization configurations, including the helical, conical, and skyrmions magnetization configurations [6]. Due to their unusual physical properties, such as topological Hall effects [7] and current- driven skyrmion motion [8,9], skyrmions have attracted exten- sive attention for the potential application in the high-density data storage [10] and novel functional devices [11]. The formation and stability of skyrmions are crucial for the applications of skyrmions in different spintronic devices. In the absence of magnetic field, the ground state of most chiral magnets is helical phase and the spontaneous skyrmions phase is unstable [5]. Recent theoretical [12] and experimental [3,13] results show that the skyrmions phase can only be stabilized in a limited region of applied magnetic field and temperature. For ferromagnetic thin film [2] or ultrathin film [14] materials, though the skyrmions phase can be stabilized in a larger region of magnetic field and temperature, the ground state of spontaneous skyrmions without an external magnetic field can only be stabilized by special methods, such as laterally confined geometries [15], pinning by defects [16], or using spatially divergent current-induced spin-orbit torque [17], which is difficult to be realized in practical application of skyrmions. * jw@zju.edu.cn Due to the magnetoelastic coupling effect of ferromagnetic materials, strain is an important and promising degree of free- dom to modulate skyrmions. Recently, many works have been done on the mechanical control of skyrmions. For example, Butenko et al. [18] have found that the effect of distortion can stabilize skyrmions phase in a broad range of applied fields. Nii et al. [19] have succeeded in creating and annihilating a skyrmion crystal through a mechanical stress. Shibata et al. [20] have observed very large anisotropic deformations of skyrmions induced by uniaxial strains, which indicates a large strain-induced anisotropy in DMI. Koretsune et al. [21] have demonstrated that the value of DMI coefficient, which controls the stability and size of skyrmions, can be controlled as a function of the external strain. Wang et al. [22] have explored the uniaxial strain modulation of topological phase transition in ferromagnetic thin films by using a phase field model, in which the ferromagnetic-to-skyrmion and skyrmion-to-helical phase transitions take place sequentially as a uniaxial tensile strain increases under specific magnetic fields. In the above- mentioned mechanical control of skyrmions, however, only a uniform strain or stress has been employed and thus an external magnetic field is needed to stabilize the skyrmions. In the present work, through a phase field model based on Ginzburg-Landau theory, we investigate the possibility of stabilizing the skyrmions by applying nonuniform strain at zero external magnetic fields. The applied nonuniform strain is designed with a cosine distribution, which is similar to the nonuniform deformation of skyrmions. The phase field simulations show that the FeGa thin films subjected to the nonuniform strain exhibit a metastable skyrmion phase in the absence of magnetic field. By applying a localized magnetic field or pulse of spin-polarized current, skyrmions phase can be locally transformed to helical phase, resulting in the coex- istence of skyrmion and helical phases in the ferromagnetic 2469-9950/2018/97(22)/224428(6) 224428-1 ©2018 American Physical Society