Origin of spin-glass-like magnetic anomaly in the superconducting and multiferroic spin ladder ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$

The spin ladder system ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ presents puzzling magnetic behaviors, such as a spin-glass-like phase below $\sim 50$ K. In this paper, an exchange bias effect with a large vertical shift in the field-cooled hysteresis loop is observed below 50 K. We also evidence the existence of uncompensated spins by susceptibility, magnetic remanence, and hysteresis loop measurements. The thermoremanent and isothermoremanent magnetization curves evidence a two-dimensional diluted antiferromagnet (DAFF) nature. Moreover, a nanometer-sized layered structure is observed by scanning electron microscope (SEM) and confirmed by scanning transmission electron microscope (STEM) coupled with electron energy loss spectroscopy (EELS). The discovery of exchange bias in antiferromagnetic ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ crystals adds a new dimension to the research of its superconducting and multiferroic properties.

Figure 1

(a) Temperature dependence of dc magnetization for ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$. The magnetic field of 10 kOe is applied along the $a, b$, and $c$ axes. The open and close circles represent the curves after ZFC and FC, respectively. (b) Time dependence of the remanent magnetization measured immediately after the field setting to zero. The inset shows the case of ${\mathrm{La}}_{1.96}{\mathrm{Sr}}_{0.04}\mathrm{Cu}{0}_4$ which displays a spin-glass behavior below 7 K [32].

Figure 2

(a) Hysteresis loops for the applying field along $a$ at 5 K after ZFC and FC. [(b) and (c)] Hysteresis loops for the applying field along $b$ and $c$, respectively. The cooling field is 10 kOe for the FC measurement.

Figure 3

(a) TRM and IRM vs $H_{\mathrm{FC}}$ of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ at 5 K. The red line is the fitting to the power law, $TRM\propto H^{v_{\text{H}}}$. The inset shows how the filed changed with temperature during the measurement of TRM and IRM. (b) Temperature dependence of the vertical shift after FC. (c) The vertical shift as a function of cooling field $H_{\mathrm{FC}}$ at 5 K. The red line is a linear fitting of the data. (d) Temperature dependence of coercivity in the hysteresis loops after ZFC and FC, respectively. The data is from the same measurements of (b). The red line is a guide for the eyes.

Figure 4

[(a) and (b)] SEM images of $bc$ and $ab$ planes, respectively.

Figure 5

(a) Low-magnification HAADF-STEM image of the ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ crystal along the $a-b$ plane. (b) High-magnification HAADF-STEM image presenting a typical planar fault. (c) Atomically resolved HAADF-STEM image of the ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ structure supported with an atomic model for guiding the reader. The red, green, and blue balls represent Fe, Se, and Ba, respectively. (d) HAADF-STEM image including the region of interest, i.e., highlighted by the red rectangle, where the EELS hyper-spectral acquisition was performed across a nanometer-scale planar fault. [(e) and (f)] Elemental reconstructed maps from Ba-$M_5$ and Fe-$L_3$ edges, respectively, probed across the planar fault and (h) the corresponding “false” color map combining both Ba (red) and Fe (cyan) components. (g) Relative Ba and Fe composition profiles extracted from the map (h) and summed along the b direction, parallel to the planar fault.

Figure 6

[(a)–(c)] ZFC and FC hysteresis loops of crystal (along $a$), powder1, and powder2 measured at 5 K. [(d)–(f)]Temperature dependence of ZFC and FC magnetization curves under 10 kOe for crystal (along $a$), powder1, and powder2. The insets of (e) and (f) show the SEM images of powder1 and powder2, respectively.