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Nematic antiferromagnetic states in bulk FeSe

We revisit bulk FeSe through the systematic first-principles electronic structure calculations. We find that there are a series of staggered $n$-mer antiferromagnetic (AFM) states with corresponding energies below that of the collinear AFM state which is the ground state for the parent compounds of most iron-based superconductors. Here the staggered $n$-mer ($n$ any integer $>1$) means that a set of $n$ adjacent spins parallel on a line along $b$-axis with spins in antiparallel between $n$-mers and along $a$-axis. Among them, the lowest energy states are quasi-degenerate staggered dimer and staggered trimer AFM states as well as their any staggered combinations. Thus, to have the largest entropy to minimize the free energy at low temperature, the most favorable state is such a quasi-one-dimensional antiferromagnet in which along $b$-axis a variety of $n$-mers, mostly dimers and trimers, are randomly antiparallel aligned while along $a$-axis spins are antiparallel aligned, i.e. actually a nematic paramagnet. This finding accounts well for the absence of long-range magnetic order in bulk FeSe and meanwhile indicates the dominant stripe spin fluctuation and the nematicity as spin-driven.