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The magnetic and electronic phase diagram of a model for thequasi-one-dimensional alkali metal iron selenide compound Na$_2$FeSe$_2$ ispresented. The novelty of this material is that the valence of iron isFe$^{2+}$ contrary to most other iron-chain compounds with valence Fe$^{3+}$.Using first-principles techniques, we developed a three-orbital tight-bindingmodel that reproduces the {\it ab initio} band structure near the Fermi level.Including Hubbard and Hund couplings and studying the model via the densitymatrix renormalization group and Lanczos methods, we constructed the groundstate phase diagram. A robust region where the block state $\uparrow \uparrow\downarrow \downarrow \uparrow \uparrow \downarrow \downarrow$ is stabilizedwas unveiled. The analog state in iron ladders, employing 2$\times$2ferromagnetic blocks, is by now well-established, but in chains a blockmagnetic order has not been observed yet in real materials. The phase diagramalso contains a large region of canonical staggered spin order $\uparrow\downarrow \uparrow \downarrow \uparrow \downarrow \uparrow$ at very largeHubbard repulsion. At the block to staggered transition region, a novel phaseis stabilized with a mixture of both states: an inhomogeneous orbital-selectivecharge density wave with the exotic spin configuration $\uparrow \uparrow\downarrow \uparrow \downarrow \downarrow \uparrow \downarrow$. Our predictionsfor Na$_2$FeSe$_2$ may guide crystal growers and neutron scatteringexperimentalists towards the realization of block states in one-dimensionaliron-selenide chain materials.

Prediction of exotic magnetic states in the alkali metal quasi-one-dimensional iron selenide compound Na$_2$FeSe$_2$