Intrinsic skyrmions in monolayer Janus magnets

Skyrmions are localized solitonic spin textures with protected topology, which are promising as information carriers in ultradense and energy-efficient logic and memory devices. Recently, magnetic skyrmions have been observed in magnetic thin films, and are stabilized by the extrinsic interfacial Dzyaloshinskii-Moriya interaction (DMI) and/or external magnetic fields. The specific effects in magnetic monolayer materials have not been thoroughly studied. Here, we investigate the intrinsic magnetic skyrmions in a family of monolayer Janus van der Waals magnets, MnSTe, MnSeTe, VSeTe, and MnSSe, by the first-principles calculations combined with the micromagnetic simulations. The monolayer Janus MnSTe, MnSeTe, and VSeTe with out-of-plane geometric asymmetry and strong spin-orbit coupling have a large intrinsic DMI, which could stabilize a sub-50-nm intrinsic skyrmions in monolayer MnSTe and MnSeTe at zero magnetic field. Whereas a monolayer VSeTe with an in-plane easy axis forms a magnetic domain rather than skyrmions. Moreover, the size and shape of skyrmions can be tuned by an external magnetic field. Therefore, our work motivates a vista for seeking intrinsic skyrmions in atomic-scale magnets.

Figure 1

Atomic structures of pristine and Janus TMDs: (a) Top and side view of pristine TMDs, (b) Top and side view of Janus TMDs. Green $X$ and pink $X^{\prime }$ balls represent different chalcogen atoms (S, Se, and Te), while the red ball denotes the Mn atom. (c) The spin-polarized band structure of MnSTe. The spin-up and spin-down bands are indicated by black solid lines and red dashed lines, respectively. The Fermi level is set to zero and is represented by a blue dotted line. (d) The spin-polarized charge density of MnSTe. The spin-up and spin-down charge are indicated by yellow and blue isosurfaces, respectively. The collinear spin orientation on Mn and S/Te is shown in the enlarged panel (e) Schematic diagram of the Zener double-exchange mechanism for MnSTe.

Figure 2

(a) Left-hand and right-hand spin-spiral configurations used to calculate the DMI and $\mathrm{\Delta }{E}_{\mathrm{SOC}}$ of Janus TMDs. (b) The calculated microscopic DMI $d_{\parallel }$, (c) the micromagnetic DMI $D$, and (d) atomic resolved localization of the associated SOC energy $\mathrm{\Delta }{E}_{\mathrm{SOC}}$, defined as the difference of SOC energies between left-hand and right-hand spin-spiral configurations.

Figure 3

Magnetization distribution for the relaxed states at zero magnetic field in Janus MnSTe (a),(b) and VSeTe (c),(d). (a) skyrmion profile in the $xy$ plane, (b) out-of-plane magnetization component $m_z$ for the line profiles across the center of the skyrmions $(y=0)$ for monolayer MnSTe. Magnetic domains profile of VSeTe in the (c) $xy$ plane and (d) out-of-plane magnetization component $m_z$ for the line profiles across magnetic domains wall along $y=0$. The color scale for $m_z$ is inserted and arrows represent the in-plane component.

Figure 4

The evolution of the size and shape of skyrmions as a function of the external magnetic field for MnSTe.

Figure 5

The calculated phonon dispersion of monolayer Janus TMDs along the high symmetry path of the Brillioun zone: (a) MnSSe, (b) MnSTe, and (c) MnSeTe. The absence of imaginary frequency confirms that monolayer Janus TMDs are energetically stable.

Figure 6

The simulated STM image of (a) the pristine $\mathrm{MnS}{\mathrm{e}}_2$ and (b) Janus MnSeTe supercells under a bias voltage of 0.2 V.

Figure 7

The spin-polarized band structure of Janus TMDs: (a) MnSSe, (b) MnSTe, (c) MnSeTe, and (d) VSeTe. The spin-up and spin-down bands are indicated by black solid lines and red dashed lines, respectively. The Fermi level is set to zero and is represented by a blue dotted line. The spin-polarized charge density of Janus TMDs: (e) MnSSe, (f) MnSTe, (g) MnSeTe, and (h) VSeTe. The spin-up and spin-down charge are indicated by yellow and blue isosurfaces, respectively.

Figure 8

The spin-polarized band structure of pristine 1T TMDs: (a) $\mathrm{Mn}{\mathrm{S}}_2$, (b) $\mathrm{MnS}{\mathrm{e}}_2$, (c) $\mathrm{MnT}{\mathrm{e}}_2$, and (d) $\mathrm{VS}{\mathrm{e}}_2$. The spin-up and spin-down bands are indicated by black solid lines and red dashed lines, respectively. The Fermi level is set to zero and represented by a blue dotted line. The Fermi level touches the energy band for all the pristine 1T TMDs with large spin splitting, indicating that monolayer pristine 1T TMDs are magnetic material.

Figure 9

The band structure of Janus TMDs with SOC: (a) MnSSe, (b) MnSTe, (c) MnSeTe, and (d) VSeTe.

Figure 10

The spin-polarized band structure of Janus TMDs MnSTe with (a) $U_{\mathrm{eff}}=0\mathrm{eV}$, (b) $U_{\mathrm{eff}}=1\mathrm{eV}$, (c) $U_{\mathrm{eff}}=2\mathrm{eV}$, (d) $U_{\mathrm{eff}}=3\mathrm{eV}$, (e) $U_{\mathrm{eff}}=4\mathrm{eV}$, (f) $U_{\mathrm{eff}}=5\mathrm{eV}$. As can be seen, the selection of $U_{\mathrm{eff}}$ does not affect the metallic property.

Figure 11

(a) Magnetic domains profile in the $xy$ plane, (b) out-of-plane magnetization component $m_z$ and (c) in-plane magnetization component $m_x$ for the line profiles across magnetic domains wall along $y=0$ in MnSeTe. The color scale for $m_z$ is inserted and arrows represent the in-plane component.

Figure 12

The evolution of the size and shape of skyrmions as a function of positive external magnetic field for MnSeTe.

Figure 13

The evolution of the size and shape of skyrmions as a function of negative external magnetic field for MnSeTe.