The growing family of two-dimensional (2D) materials 1-3 can be used to assemble van der Waals heterostructures with a wide range of properties 4-6 . Of particular interest are tunnelling heterostructures 7-9 , which have been used to study the electronic states both in the tunnelling barrier and in the emitter and collector contacts 10,11 . Recently, 2D ferromagnets have been studied theoretically 12-15 and experimentally 16-18 . Here we investigate electron tunnelling through a thin (2-6 layers) ferromagnetic CrBr 3 barrier. For devices with non-magnetic barriers, conservation of momentum can be relaxed by phonon-assisted tunnelling 8,19-21 or by tunnelling through localised states 8,21,22 . In the case of our ferromagnetic barrier the dominant tunnelling mechanisms are the emission of magnons 18 at low temperatures or scattering of electrons on localised magnetic excitations above the Curie temperature. Magnetoresistance in the graphene electrodes further suggests induced spin-orbit coupling and proximity exchange via the ferromagnetic barrier. Tunnelling with magnon emission offers the possibility of spin-injection, as has been previously demonstrated with other ferromagnetic barriers 23,24 . S1. Device fabrication S2. Temperature dependence of differential dI/dV b conductance on magnetic field for devices with different thickness of CrBr 3 S3. Quantum capacitance of Gr/CrBr 3 /Gr devices S4. Calculation of magnon density of states S5. Scattering rates

We observe a series of sharp resonant features in the differential conductance of graphene-hexagonal boron nitride-graphene tunnel transistors over a wide range of bias voltages between 10 and 200 mV. We attribute them to electron tunneling assisted by the emission of phonons of well-defined energy. The bias voltages at which they occur are insensitive to the applied gate voltage and hence independent of the carrier densities in the graphene electrodes, so plasmonic effects can be ruled out. The phonon energies corresponding to the resonances are compared with the lattice dispersion curves of graphene-boron nitride heterostructures and are close to peaks in the single phonon density of states.

Chirality is a fundamental property of electrons with the relativistic spectrum found in graphene and topological insulators. It plays a crucial role in relativistic phenomena, such as Klein tunneling, but it is difficult to visualize directly. Here, we report the direct observation and manipulation of chirality and pseudospin polarization in the tunneling of electrons between two almost perfectly aligned graphene crystals. We use a strong in-plane magnetic field as a tool to resolve the contributions of the chiral electronic states that have a phase difference between the two components of their vector wave function. Our experiments not only shed light on chirality, but also demonstrate a technique for preparing graphene's Dirac electrons in a particular quantum chiral state in a selected valley.