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Systematic Effective Field Theory Investigation of Spiral Phases in Hole-Doped Antiferromagnets on the Honeycomb Lattice

Motivated by possible applications to the antiferromagnetic precursor of the high-temperature superconductor Na$_x$CoO$_2\cdot$yH$_2$O, we use a systematic low-energy effective field theory for magnons and holes to study different phases of doped antiferromagnets on the honeycomb lattice. The effective action contains a leading single-derivative term, similar to the Shraiman-Siggia term in the square lattice case, which gives rise to spirals in the staggered magnetization. Depending on the values of the low-energy parameters, either a homogeneous phase with four or a spiral phase with two filled hole pockets is energetically favored. Unlike in the square lattice case, at leading order the effective action has an accidental continuous spatial rotation symmetry. Consequently, the spiral may point in any direction and is not necessarily aligned with a lattice direction.