Spin current generation in organic antiferromagnets

Abstract

Spin current-a flow of electron spins without a charge current-is an ideal information carrier free from Joule heating for electronic devices. The celebrated spin Hall effect, which arises from the relativistic spin-orbit coupling, enables us to generate and detect spin currents in inorganic materials and semiconductors, taking advantage of their constituent heavy atoms. In contrast, organic materials consisting of molecules with light elements have been believed to be unsuited for spin current generation. Here we show that a class of organic antiferromagnets with checker-plate type molecular arrangements can serve as a spin current generator by applying a thermal gradient or an electric field, even with vanishing spin-orbit coupling. Our findings provide another route to create a spin current distinct from the conventional spin Hall effect and open a new field of spintronics based on organic magnets having advantages of small spin scattering and long lifetime.

Fig. 1

Schematic illustrations of the spin current generation. a Flows of up- and down-spin magnons (electrons) and spin current driven by a thermal gradient (an electric field) in the AFM state. The red and blue ellipses represent the two kinds of molecular dimers, forming a checker-plate-type lattice. The arrows in the dimers represent the localized spin moments. b Field-angle dependence of the spin current generation (green arrows) driven by a thermal gradient or an electric field (gray arrows)

Fig. 2

Schematic illustration of the lattice structure of $\kappa$-Cl and the energy bands. a Molecular arrangement in the two-dimensional conducting layer. The red and blue circles represent the two kinds of ET dimers, termed $A$ and $B$, respectively, in the unit cell. The green line denotes the glide plane perpendicular to the $xy$ plane. b Network of the dominant electron transfer bonds, $\mathrm{a}$ (orange bold line), $\mathrm{b}$ (dotted line), $\mathrm{p}$ (solid line), and $\mathrm{q}$ (broken line). The gray circles represent the ET molecules, and the red and blue ellipses show the $A$ and $B$ dimers, respectively. The arrows represent the local spin moments in the AFM phase. We note that another glide plane exists when considering the layer stacking, but it does not affect our discussions. c Energy band dispersion composed of the frontier orbitals of ET molecules in the PM metallic phase with the transfer integrals $\left(t_{\mathrm{a}},t_{\mathrm{p}},t_{\mathrm{q}},t_{\mathrm{b}}\right)=\left(-0.207,-0.102,0.043,-0.067\right)$ eV (green solid line) and that of the single-band picture in the large dimerization limit (broken line). The average electron number in the unit cell is $6$ and the Fermi energy ${\epsilon }_{\mathrm{f}}$ is shown. d Energy band dispersion in the AFM insulating phase with the intra-molecular Coulomb interaction $U=1$ eV, within the self-consistent mean-field theory. e Contour map of the spin splitting subtracting the down-spin energy from the up-spin energy of the top band in d in the first Brillouin zone. The trajectory shows the symmetric lines in c and d

Fig. 3

Spatial anisotropy of inter-dimer transfer integrals. a, b Effective transfer integrals between the central dimer ($A$ in a and $B$ in b) and the surrounding ones, obtained from the second-order perturbation processes with respect to the bonding-antibonding orbital hybridizations, in the PM phase. c–f Effective transfer integrals calculated likewise for up- (c, d) and down-spin (e, f) electrons in the AFM phase (the local magnetic moment is about $0.168\hslash$). The areas of the red (blue) shaded circles represent the amplitudes of positive (negative) transfer integrals. The amplitudes are shown in the circles in unit of meV

Fig. 4

Effective NNN exchange interactions, magnon dispersions, and heat-spin current conversion in the AFM insulating state. a Real-space distribution of the NN exchange interactions $J$ (solid lines) and $J^{\prime }$ (broken lines) between $A$ and $B$ dimers (left panel) and those of the NNN exchange interactions $K$ (purple solid lines) and $K^{\prime }$ (purple broken lines) between $A$ dimers (middle panel) and $B$ dimers (right panel). b, $t_{\mathrm{q}}$ dependences of $K$ and $K^{\prime }$ at $U=1$ eV. The red arrow represents the value of $t_{\mathrm{q}}$ in $\kappa$-Cl. c Magnon dispersions at $\left(J,J^{\prime },K,K^{\prime }\right)=\left(80,20,2,0\right)$ meV within the linear spin-wave theory. The inset shows a contour map of the spin splitting between the up- and down-spin magnons in the first Brillouin zone. d $\left(T,K\right)$ dependences of the spin current conductivity under a thermal gradient, ${\chi }_{xy}^{\mathrm{SQ}}$. The other exchange interactions and the damping factor are $\left(J,J^{\prime },K^{\prime },\eta \right)$ = $\left(80,20,0,1\right)$ meV. e $K$ dependences of the heat-spin current conversion rate $\alpha \left(=\mid 2J{\chi }_{xy}^{\mathrm{SQ}}∕\hslash {\kappa }_{yy}\mid \right)$ at $k_{\mathrm{B}}T=0.5$ meV and $1$ meV, where ${\kappa }_{yy}$ is the thermal conductivity along the $y$-axis. The red arrow represents the value of $K$ in $\kappa$-Cl

Fig. 5

Charge-spin current conversion in the electron-doped AFM metallic state. a $\left(U,n\right)$ dependences of the spin current conductivity to an electric field, ${\chi }_{xy}^{\mathrm{SC}}$. The broken line represents the phase boundary between the PM and AFM metallic phases, and the blue thick line shows the AFM insulating phase at three-quarter filling. The damping factor is $\gamma =1$ meV. The insets show the Fermi surface structures of up-spin (red) and down-spin (blue) electrons at $\left(U,n\right)=\left(1\mathrm{eV},6.1\right)$ and $\left(1\mathrm{eV},6.4\right)$. The gray shaded areas denote the occupied states. b $n$ dependences of the charge-spin current conversion rate $\beta \left(=\mid 2e{\chi }_{yx}^{\mathrm{SC}}∕\hslash {\sigma }_{xx}\mid \right)$, $\mid {\chi }_{yx}^{\mathrm{SC}}\mid$, and the diagonal electrical conductivity ${\sigma }_{xx}$ at $U=1$ eV