Ultrafast magnon transistor at room temperature

We study sequential tunneling of magnetic excitations in nonitinerant systems through triangular molecular magnets. It is known that the quantum state of these molecular magnets can be controlled by application of an electric or a magnetic field. Here, we use this fact to control the flow of a pure magnetization current through the molecular magnet by electric or magnetic means. This allows us to design a system that behaves as a magnon transistor. We show how to combine three magnon transistors to form a nand gate, and give several possible realizations of the latter, one of which could function at room temperature using transistors with an 11 ns switching time.

Figure 1

(a),(b) Pictorial representation of a single purely magnetic spin transistor, including Heisenberg parameters of the subsystems and the different magnetic and electric fields. The field $B_0$ is applied to both spin reservoirs (here shown as 1D AF spin chains) and the molecular magnet, the magnetic field $\Delta B\left(t\right)$ is applied only to the left reservoir, and the fields $E^{\prime }$ and $B^{\prime }$ are applied only to the molecular magnet. The left reservoir acts as source -terminal of the transistor, the molecular magnet as gate, and the right reservoir as drain (see inset). (c),(d) Excitation spectrum corresponding to the Hamiltonian in Eq. (2). In (c) we choose $g_M{\mu }_{B}B=D_M=1$, and in (d) we put $D_M=5$ and $E^{\prime }=0$.

Figure 2

(a),(b) ${\log }_{10}\left(I_S\right)$ versus $\Delta B$ for different values of the magnetic field $B$, for 1D AF reservoirs with different Luttinger liquid parameters $K$. Due to the gapless nature of the spinons, we can always set $B=B_0$ and $B^{\prime }=0$ when considering AF reservoirs. (c) ${\log }_{10}\left(I_S\right)$ versus $\Delta B$ for different values of the magnetic field $B$, for 1D FM reservoirs. Here, $B_0=1$ $\mu$T and $B^{\prime }\approx B$. (d),(e) ${\log }_{10}\left(I_S\right)$ versus $\Delta B$ for different values of $d{E}^{\prime }$, for AF reservoirs with different Luttinger liquid parameters $K$. We assumed $D_M/k_B=0.6$ K and $B_0=150$ mT. (f) ${\log }_{10}\left(I_S\right)$ versus $\Delta B$ for different values of $d{E}^{\prime }$, for the FM system. Here, $B_0=1$ $\mu$T and $B^{\prime }=150$ mT. We assumed $D_M/k_B=0.6$ K. (g) Illustration of the alternative switching mechanism for FM reservoirs. When the level splitting of the molecular magnet is smaller than the minimum energy of a magnon in the lead, the system is in the insulating phase. Again, $B_0=1$ $\mu$T. The plots (a)–(g) are for parameters $J/k_B=100$ K, $T=10$ mK, and $J_1^{\prime }/k_B=J_2^{\prime }/k_B=0.05$ K (see text). For the FM plots, $S=1$. In (d)–(f) we have assumed that the left (right) reservoir is coupled to spin 2(3) in the molecular magnet with strength $J_{1\left(2\right)}^{\prime }$. This setup is beneficial, since in this way both reservoirs decouple from the molecular magnet for $d{E}^{\prime }\gg D_M$. (h) $I_S$ versus $\Delta B$ for different values of $d{E}^{\prime }$ for the AF system, at an experimentally accessible temperature. Parameters are $J/k_B=100$ K, $J^{\prime }/k_B=2$ K, $D_M/k_B=0.3$ K, $B=75$ mT, and $T=1$ K.

Figure 3

(a) Proposed setup to measure the switching effect due to the spin-electric effect. The setup consists of a single-layer crystal of triangular magnets, of dimension 0.2 $\times$ 0.2 $\mu$m. The crystal contains $\sim 4\times {10}^4$ molecules, given a lattice constant of 1 nm. The crystal is weakly exchange coupled to a bulk collection of AF 1D spin chains, such as is realized in SrCuO${}_2$ (Ref. 40) or Cs${}_2$CoCl${}_4$ (Ref. 41). Assuming the lattice constant is commensurate with that of the crystal, the setup contains $\sim 4\times {10}^4$ parallel transistors. The $\sim {10}^3$ molecules at the edge can be accessed electrically by an array of STM tips. Using our previous estimate for $d$ and the values from the text, fields between ${10}^8$ and ${10}^4$ V m${}^{-1}$ are required to switch between insulating and conducting states. (b) Combining three transistors into a single nand gate. (c) Proposed setup to enhance the magnetic field due to the accumulated magnons. The role of the perforated superconductor is to increase the density of magnetic field lines due to the magnetic field ${\mathbf{B}}_{\mathrm{mag}}$ and thereby increase the magnetic field acting on the molecular magnet. The crystal of molecular magnets is placed directly above the hole in the superconductor. We denote by $f$ the portion of the total flux directly on the surface of the magnet that can be enhanced into the area of the molecular magnets. $a_x$ and $a_y$ (not shown) are the dimensions of the hole of the superconductor, which should equal those of the crystal of molecular magnets.