Electrical and Thermal Control of Magnetic Exchange Interactions

We investigate the far-from-equilibrium nature of magnetic anisotropy and exchange interactions between molecular magnets embedded in a tunnel junction. By mapping to an effective spin model, these magnetic interactions can be divided into three types: isotropic Heisenberg, anisotropic Ising, and anisotropic Dzyaloshinski-Moriya contributions, which are attributed to the background nonequilibrium electronic structures. We further demonstrate that both the magnetic self- and exchange interactions can be controlled either electrically by gating and tuning the voltage bias, or thermally by adjusting the temperature bias. We show that the Heisenberg and Ising interactions scale linearly, while the Dzyaloshinski-Moriya interaction scales quadratically, with the molecule-lead coupling strength. The interactions scale linearly with the effective spin polarizations of the leads and the molecular coherence. Our results pave a way for smart control of magnetic exchange interactions at atomic and molecular levels.

Figure 1

Sketch of magnetic molecules embedded in a junction between magnetic leads. Electrons may tunnel between the electrodes and the localized levels ${ϵ}_n$, and between the levels. An electron residing in level $n$ interacts with the localized spin moment $S_n$. The setup may be achieved by, e.g., stacking molecules on top of each other on a surface or constructing a chain on an insulating surface, using scanning tunneling microscopy techniques.

Figure 2

Heisenberg exchange $J_{12}$ as function of (a) chemical potential $\mu$, (b) bias voltage $V$, and (c) temperature difference $\mathrm{\Delta }T=T_R-T_L$. The plots in (a) and (b) are offset for clarity, the system is gated ($\mu =-2\mathrm{meV}$) in (b), (c), while the colors refer to different spin polarizations ($p_L,p_R$) in the leads. The inset in (a) shows the electronically induced anisotropy fields $J_{1(2)}$ acting on the individual spins. Here, ${ϵ}_0=0$, ${\mathcal{T}}_c=3\mathrm{\Gamma }=v_1/5=v_2/5=1\mathrm{meV}$, and $T_L=1\mathrm{K}$.

Figure 3

Ising exchange $I_{12}$. The system is gated ($\mu =-2\mathrm{meV}$) in (b), (c), while other parameters are as in Fig. 2.

Figure 4

DM exchange $D_{12}$. The system is biased ($V=0.1\mathrm{mV}$) in (a) and gated ($\mu =-2\mathrm{meV}$) in (b), (c), while other parameters are as in Fig. 2.