The nature of the emergent phase near a putative quantum critical point in the bilayer ruthenate Sr 3 Ru 2 O 7 has been a recent subject of intensive research. It has been suggested that this phase may possess electronic nematic order (ENO). In this work, we investigate the possibility of nematic domain formation in the emergent phase, using a phenomenological model of electrons with ENO and its coupling to lattice degrees of freedom. The resistivity due to the scattering off the domain walls is shown to closely follow the ENO parameter. Our results provide qualitative explanations for the dependence of the resistivity on external magnetic fields in Sr 3 Ru 2 O 7 . DOI: 10.1103/PhysRevLett.98.126407 PACS numbers: 71.27.+a, 63.20.Kr, 71.10.ÿw, 75.30.Kz Quantum critical behavior in metamagnetism represents the most unusual critical phenomenon in itinerant electron systems. It was shown in a series of remarkable experiments that the critical end point associated with the metamagnetic transition (MMT) can be driven to zero temperature in the bilayer ruthenate Sr 3 Ru 2 O 7 by changing the angle between the external magnetic field and the c axis of the material Later experiments on the ultrapure samples, however, have shown that the quantum critical end point is eventually avoided when the finite temperature critical point is pushed further down to zero temperature, and is replaced by two consecutive MMTs Currently there exist two competing proposals for the nature of this emergent phase. Binz et al. [8] proposed a phenomenological Ginzburg-Landau theory of magnetic Condon domains and suggested that the high resistivity may come from the scattering of electrons off the magnetic domains. Another proposal involves the formation of electronic nematic order (ENO) in the emergent phase; namely, the Fermi surface of the electrons spontaneously breaks the lattice rotational symmetry Very recently it has been reported that the high resistivity seen in the emergent phase is insensitive to demagnetization factor or shapes of the samples In this Letter, we offer a theory of the nematic domain formation and the resulting high resistivity in the emergent phase. The possibility of the nematic domains has not been studied theoretically even though such possibility was briefly discussed in the literature In search for a concise description, we start with an effective electronic Hamiltonian that captures the essential physics of ENO, namely, we consider the quadrupolar interaction between electrons In view of the magnetostriction data indicating a close relationship between the lattice and the emergent phase [5], we also consider the electron-lattice interaction. Since we are studying an effective Hamiltonian, we are only interested in general properties of this Hamiltonian and the precise values of the parameters should not be taken seriously. Remarkably this simplified model contains essential ingredients of the nematic domain formation and the resulting high resistivity. It is found that the electron-lattice interaction makes the formation of the nematic domains (at finite temperatures) much more likely by offering a large number of metastable domain configurations. Another key result of our work is that the magnetic field dependence of the resistivity in the nematic domain phase closely follows the field dependence of the ENO parame-PRL 98
