Magnons : Spin-Waves in Magnetic Materials

The purpose of this essay is to develop the notion of emergent magnon excitations which appear in magnetic materials. In particular, we will discuss the so-called Holstein-Primakoff boson and Schwinger boson representations of spin-operators. This technique is powerful in that we can utilize the second quantization formalism discussed in class; however, we will find this approach places a constraint on the Hilbert space of the operators.[1] With the preceding formalism established, we will apply it to the Heisenberg model (a minimal model of a ferromagnet) and show that the low-energy quasiparticle excitations describing such a system are spin-waves.[2] We will conclude with a discussion of potential technologies which can exploit spinwave physics — a field known as magnonics.[3]