  We investigated Sr$_3$Ru$_2$O$_7$, a quantum critical metal that shows a
metamagnetic quantum phase transition and electronic nematicity, through
density functional calculations. These predict a ferromagnetic ground state in
contrast to the experimentally observed paramagnetism, raising the question of
competing magnetic states and associated fluctuations that may suppress
magnetic order. We did a search to identify such low energy
antiferromagnetically ordered metastable states. We find that the lowest energy
antiferromagnetic state has a striped order. This corresponds to the E-type
order that has been shown to be induced by Mn alloying. We also note
significant transport anisotropy in this E-type ordered state. These results
are discussed in relation to experimental observations.
