Orbital-selective magnetism in the spin-ladder iron selenides Ba${}_{1-x}$K${}_x$Fe${}_2$Se${}_3$

Here we show that the 2.80(8)${\mu }_{\mathrm{B}}$ Fe${}^{-1}$ block antiferromagnetic order of BaFe${}_2$Se${}_3$ transforms into stripe antiferromagnetic order in KFe${}_2$Se${}_3$ with a decrease in moment to 2.1(1)${\mu }_{\mathrm{B}}$ Fe${}^{-1}$. This reduction is larger than expected from the change in electron count from Ba${}^{2+}$ to K${}^{+}$, and occurs with the loss of the displacements of Fe atoms from ideal positions in the ladders, as found by neutron pair distribution function analysis. Intermediate compositions remain insulating, and magnetic susceptibility measurements show a suppression of magnetic order and probable formation of a spin glass. Together, these results imply an orbital-dependent selection of magnetic versus bonded behavior, driven by relative bandwidths and fillings.

Figure 1

Schematic of KFe${}_2$Se${}_3$ (space group Cmcm) showing (a) stacking of [Fe${}_2$Se${}_3$] ladders and (b) the perspective perpendicular to the plane of the ladders.

Figure 2

(a) Normalized electrical resistivity on polycrystalline pellets of Ba${}_{1-x}$K${}_x$Fe${}_2$Se${}_3$ highlighting one-dimensional variable range hopping behavior. (b) The temperature dependences of the magnetic susceptibilities illustrate the initial suppression of magnetic order (indicated by arrows) with increasing $x$, followed by a reappearance of antiferromagnetic order.

Figure 3

(a) NPD data (black circles) of KFe${}_2$Se${}_3$ and Rietveld refinement of the best magnetic structure. (b) Tem-perature-dependent NPD data illustrate the growth of the magnetic Bragg peaks on cooling. The magnetic moment saturates at 2.1(1)${\mu }_{\mathrm{B}}$ Fe${}^{-1}$. (c) Schematic of the stripe magnetic structure of KFe${}_2$Se${}_3$ compared to the block magnetic structure of BaFe${}_2$Se${}_3$ (Ref. 20).

Figure 4

(a) PDFs of KFe${}_2$Se${}_3$ at $T$ = 5, 100, and 300 K (black circles) with fits to the crystallographic Cmcm structure. (b) Representations of a single ladder illustrate the changes in local structure and magnetism with substitution of the $A$ site in $A$Fe${}_2$Se${}_3$.

Figure 5

Phase diagram of Ba${}_{1-x}$K${}_x$Fe${}_2$Se${}_3$. (a) As $x$ increases, block antiferromagnetic order (AFM-B) is suppressed, but for $x$ ≥ 0.9, stripe antiferromagnetic order (AFM-S) appears. (b) The average Fe-Fe distance at 300 K steadily increases (open circles), while the Fe-Fe displacements, determined by Rietveld (long, solid diamonds; short, solid triangles) and PDF analysis of KFe${}_2$Se${}_3$ (solid squares), vanish. Concomitantly, a linear increase in $\left[{\left(k_{\mathrm{B}}{T}_0\right)}^{-1}\right]$ is consistent with the addition of hopping carriers. Above $x$ > 0.7, a downturn indicates either a reduction in the number of, or an increase in localization of, carriers. (c) Orbital selective magnetism in Ba${}_{1-x}$K${}_x$Fe${}_2$Se${}_3$: BaFe${}_2$Se${}_3$ has four half-filled $d$ bands, three narrow and one dispersed. While on-site repulsion ($U$) gaps the narrow bands, the dispersed band is gapped by a density wave. In KFe${}_2$Se${}_3$, depopulation reduces the effect of $U$ on one of the narrow bands, resulting in its switch to nonmagnetic behavior.