Toroidal quantum states in molecular spin-frustrated triangular nanomagnets with weak spin-orbit coupling: Applications to molecular spintronics

Abstract

We theoretically investigate the ground-state spin texture and spin transport properties of triangular rings with on-site spins ${S}_{q}=\frac{1}{2}\phantom{\rule{0.28em}{0ex}}(q=1--3)$. In the limit of strong antiferromagnetic exchange coupling and weak spin-orbit coupling, we find it is possible to prepare a noncollinear degenerate ground state with a zero magnetic moment and a nonzero toroidal moment $\mathbf{\ensuremath{\tau}}=g{\ensuremath{\mu}}_{B}{\ensuremath{\sum}}_{q}{\mathbf{r}}_{q}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{q}$, aligned along the ${C}_{3}$-symmetry axis. These pure toroidal states can be prepared: (i) within the fourfold degenerate spin-frustrated ground state even without any spin-orbit coupling; (ii) within the ground Kramers doublet resulting from weak spin-orbit splitting of the fourfold degenerate frustrated manifold via Dzyaloshinskii-Moriya antiferromagnetic exchange coupling. We also investigate the relationship between toroidal states and chiral spin states, characterized by the eigenvalues of the scalar spin chirality operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\chi}}=\frac{4}{\sqrt{3}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{S}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{S}}}_{2}\ifmmode\times\else\texttimes\fi{}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{S}}}_{3}$, and find that, since $[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{\ensuremath{\tau}}},\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\chi}}]\ensuremath{\ne}0$, it is not possible to prepare states that are both toroidal and chiral simultaneously. Finally, by setting up a quantum transport model in the Coulomb blockade regime, we find that a spin current injected through a spin-polarized source electrode into the triangle is partially reversed upon scattering with the molecular toroidal states. This spin-switching effect is, in fact, a signature of molecular spin-transfer torque, which can be harnessed to modify the nonequilibrium populations of the $+\ensuremath{\tau}$- and $\ensuremath{-}\ensuremath{\tau}$-toroidal states, thus, to induce a net toroidal magnetization in the device using a spin current.