Underlying mechanism for exchange bias in single-molecule magnetic junctions

Magnetic proximity has been observed in a variety of solid-state magnetic devices, but has been less discussed at the molecular scale. In this study, the magnetotransport calculation is carried out using the generalized Landau-Lifshitz-Gilbert (LLG) equation combined with density functional theory (DFT) and our self-developed junpy calculated spin-torque effect. Except for the current driven spin torque, which is a promising approach for magnetization switch in magnetic random access memory, the equilibrium fieldlike spin torque also plays a crucial role in the strain-controlled exchange bias with current-controlled magnetic coercivity in single-molecule magnetic junctions. The tight-binding model is further employed to clarify the critical role of the interfacial spin filter effect arising from the hybridization between the linker and Co apex. These multidisciplinary DFT+junpy+LLG results may provide important and practical implications in the dual control of magnetic proximity and magnetization switching in molecular spintronics at low temperature, either by tensile strain or via smaller applied current density of the order of $\mathrm{MA}/{\mathrm{cm}}^2$.

Figure 1

(a) Junction geometry of the dissociated Co/BDA(BDT)/Co SMMJ with NH (S) linker is expressed in a two-probe device. $\widehat{\mathbf{p}}$ and $\widehat{\mathbf{m}}$ are the unit vectors of magnetization of the left (fixed) and right (free) Co nanowires and linkers, respectively. $\widehat{\mathbf{p}}$ is fixed along the $z$ direction, while $\widehat{\mathbf{m}}$ is freely rotated by an angle $\theta$ around the $y$ axis with respect to the $z$ axis to form a noncollinear magnetic configuration. (b) Schematic of macrospin assumption with in-plane external magnetic field, ${\mathbf{H}}_{\mathbf{ext}}$, and net damplike ${\mathbf{T}}_{\parallel }$ (STT) and fieldlike ${\mathbf{T}}_{\perp }$ (FLST) components of spin torque acting on the magnetization of the right Co.

Figure 2

Angle dependence of the DFT+junpy calculated equilibrium FLST field, $H_{\text{damp}}^{\left(0\right)}sin\theta$, without an applied current for (a) Co/BDA/Co and (b) Co/BDT/Co SMMJs under various tensile strains ($\epsilon$). The insets are the schematic plots of $H_{\text{damp}}^{\left(0\right)}$ and $H_k$ in unstrained (a) BDA and BDT cases when $\theta$ is below and above ${90}^{\circ }$, where $H_k$ is the cohesive field of the right Co electrode. The DFT+junpy+LLG calculated magnetization hysteresis curves ($m_z$-H) for (c) Co/BDA/Co and (d) Co/BDT/Co SMMJs under various tensile strains at zero temperature. The gray shaded area represents the field region between $\pm {\mu }_0{H}_k$. The $H_{\text{C1}}$ ($H_{\text{C2}}$) is the threshold field required for P-to-AP (AP-to-P) magnetization switching, where P and AP denote the parallel ($\theta =0^{\circ })$ and antiparallel ($\theta ={180}^{\circ }$), respectively.

Figure 3

DFT-calculated spin-polarized transmission spectra (top) for (a) Co/BDA/Co and (b) Co/BDT/Co SMMJs in parallel ($\theta =0$) magnetic configuration under various tensile strains $\epsilon$, where $E_{\text{F}}=0.0$ eV denotes the Fermi energy. Schematic 1D-TB energy profiles of noncollinear $\mathrm{L}/\mathrm{IL}/\mathrm{Ben}/\mathrm{IR}\left(\theta \right)/\mathrm{R}(\theta$) (middle), and the angle dependence of TB+junpy calculated equilibrium FLST spin torque $T_{\perp }^{\left(0\right)}$ (bottom), for (c) Co/BDA/Co and (d) Co/BDT/Co SMMJs under various tensile strains. The notations of IL (IR) and Ben refer to the spin-polarized left (right) NH/S linker and central phenyl ring, respectively. The red and blue arrows denote the bottom of the spin-up and spin-down energy bands of left (L) and right (R) Co. Since the magnetization $\widehat{\mathbf{p}}$ in region L is fixed in the $+z$ direction, upon rotation of $\widehat{\mathbf{m}}$ along $\widehat{\mathbf{p}}$, the spin-up (spin-down) energy bands of region R acquire spin-down (spin-up) energy contributions. The red and the blue shaded areas denote the range of spin-polarized energy levels of the central IL/Ben/IR.

Figure 4

Top: Angle dependence of DFT+junpy calculated current-driven spin-torque fields, $H_{\text{damp}}^{\left(J\right)}sin\theta$, with writing current densities of $J=\pm 1.8\mathrm{MA}/{\mathrm{cm}}^2$ for (a) Co/BDA/Co and (b) Co/BDT/Co SMMJs under various tensile strains $\epsilon$. Bottom: Current dependence of DFT+junpy+LLG calculated ${\mu }_0{H}_{\text{C1}}$ and ${\mu }_0{H}_{\text{C2}}$ for (c) Co/BDA/Co and (d) Co/BDT/Co SMMJs under various tensile strains at zero temperature. The black vertical arrows and purple shaded areas represent the strain control and current control of the threshold fields, $H_{\text{C1}}$ and $H_{\text{C2}}$, respectively. The $H_{\text{C1}}$ ($H_{\text{C2}}$) is the threshold field required for P-to-AP (AP-to-P) magnetization switching.

Figure 5

Finite writing pulse phase diagrams for DFT+junpy+LLG calculated (a) Co/BDA/Co and (b) Co/BDT/Co SMMJs without strain at various temperatures ranging from 0 to 100 K. The time step is 10 ps, and the integration time is $0.1\mu \mathrm{s}$ in each field point. Each diagram is averaged with 10 identical simulations with different random noise.