  Magnonics is a rapidly growing field, attracting much attention for its
potential applications in data transport and processing. Many individual
magnonic devices have been proposed and realized in laboratories. However, an
integrated magnonic circuit with several separate magnonic elements has yet not
been reported due to the lack of a magnonic amplifier to compensate for
transport and processing losses. The magnon transistor reported in [Nat.
Commun. 5, 4700, (2014)] could only achieve a gain of 1.8, which is
insufficient in many practical cases. Here, we use the stimulated three-magnon
splitting phenomenon to numerically propose a concept of magnon transistor in
which the energy of the gate magnons at 14.6 GHz is directly pumped into the
energy of the source magnons at 4.2 GHz, thus achieving the gain of 9. The
structure is based on the 100 nm wide YIG nano-waveguides, a directional
coupler is used to mix the source and gate magnons, and a dual-band magnonic
crystal is used to filter out the gate and idler magnons at 10.4 GHz frequency.
The magnon transistor preserves the phase of the signal and the design allows
integration into a magnon circuit.
