With a multitude of different phases and quantum critical points, heavy fermion materials should reign supreme as the prototype for competing order, a major contemporary theme in condensed matter physics. One key feature that differentiates the types of magnetic phases and critical points is the presence or absence of Kondo screening. This singlet formation is dramatically manifested in the Fermi surface, which may or may not include atomic f-orbital electron states. To provide a theoretical basis for the different types of magnetism, we have carried out asymptotically exact studies of the Kondo lattice model inside both the antiferromagnetic and ferromagnetic phases. A fundamental aspect of the approach is to map the magnetic Hamiltonian for the f-orbitals onto a quantum nonlinear sigma model (QNLsigmaM). The Kondo interaction results in an effective coupling between the QNLsigmaM fields and the conduction electrons. Renormalization group analyses show that the Fermi surface in the corresponding ordered states is small (not incorporating the f-orbitals) for both the ferromagnetic and antiferromagnetic cases. These results are of relevance to a number of materials, including YbRh2Si2 and CeRu2Ge2, where experimental measurements of magnetotransport and de Haas van Alphen effects have supplied evidence for small Fermi surface phases. The implications of our results for heavy fermion quantum critical points will also be discussed
