Effects of the lattice distortion on the magnetic order in rare-earth nickelates

The low-temperature magnetic order in the rare-earth nickelates is a subject of vigorous debate in the literature. Recent work emphasized the primary role of the electron-phonon coupling for the metal-insulator transition in the nickelates, and suggested that lattice distortions are the driver of the transition, leading to the observed charge order. However, to our knowledge there has been little work on the impact of lattice distortions on the magnetic order, in particular whether distortions favour some orders over others. In this thesis, we study the magnetic order in the nickelates at zero temperature, and investigate whether the breathing-mode lattice distortions select a preferred ground state. An effective two-band Hubbard model for the nickelates is constructed and coupled to the lattice distortions with an on-site Holstein-like term. The distortions are treated semiclassically. Using the Hartree-Fock approximation, we obtain the magnetic phase diagram, then turn on the coupling to the lattice to observe its impact on the various phases. Our model reproduces the earlier work showing the stronger charge disproportionation and insulating behaviour in the phase space due to increased coupling to the lattice. Furthermore, we find numerous 4-site magnetic orders that are self-consistent within the model, including all of the main suggestions in the literature (states such as ↑↑↓↓,↑→↓← and ⇑0⇓0). However, in this model a magnetic order can only couple to the lattice distortions if there is nonzero charge disproportionation. As a result, we find that coupling to the lattice distortions broadly favours the ⇑0⇓0 order in large sectors of the parameter space. Finally, we considered the impact of longer range hopping on the magnetic order: we find that the shape of the density of states, rather than overall bandwidth, primarily determines the magnetic ground state. A van Hove singularity arises even for small 2nd-nearest hopping amplitudes, which results in robust ferromagnetism across most of the phase diagram in a Stoner-like fashion. On the contrary, even small 4th-nearest amplitudes decrease the Fermi level density of states, resulting in ballooning of the metallic phase despite a barely renormalized bandwidth.Science, Faculty ofPhysics and Astronomy, Department ofGraduat