We have previously found experimental evidence for several quantum phenomena in oxygen-ion implanted of hydrogenated graphite: ferromagnetism, antiferromagnetism, paramagentism, triplet superconductivity, Andreev states, Little-Parks oscillations, Lamb shift, Casimir effect, colossal magnetoresistance, and topologically-protected flat-energy bands [1-6]. Triplet superconductivity results in the formation of Josephson junctions, thus with potential of being used for spintronics applications in the critical area of quantum computing. In this paper, we are showing new experimental evidence for the formation of two-dimensional (2D) spin waves in oxygen-ion enriched and in hydrogenated highly oriented pyrolytic graphite. The temperature evolution of the remanent magnetization Mrem(T) data confirms the formation of spin waves that follow the 2D Heisenberg model with a weak uniaxial anisotropy. In addition, the step-like features also found in the temperature dependence of the electrical resistivity between insulating and metallic states suggest several outstanding possibilities, such as a structural transition, triplet superconductivity, and chiral properties.