Checkerboard to stripe charge ordering transition in TbBaFe${}_2$O${}_5$

A combined neutron and x-ray diffraction study of TbBaFe${}_2$O${}_5$ reveals a rare checkerboard to charge ordering transition. TbBaFe${}_2$O${}_5$ is a mixed valent compound where Fe${}^{2+}$/Fe${}^{3+}$ ions are known to arrange into a stripe charge ordered state below $T_V=291$ K that consists of alternating Fe${}^{2+}$/Fe${}^{3+}$ stripes in the basal plane running along the $\mathit{b}$ direction. Our measurements reveal that the stripe charge ordering is preceded by a checkerboard charge ordered phase between $T_V<T<T^{*}=308$ K. The checkerboard ordering is stabilized by intersite Coulomb interactions which give way to a stripe state stabilized by orbital ordering.

Figure 1

Charge and spin ordering structures for the stripe CO phase for $T<T_V$ (left), checkerboard CO phase for $T_V<T<T^{*}$ (center), and mixed valent phase $T^{*}<T<T_N$ (right) in both the a-b and b-c crystallographic planes. Triangles and squares correspond to different nominally Fe ionic valences in the square pyramidal coordination; Fe${}^{2+}$ (green), Fe${}^{3+}$ (brown), and Fe${}^{2.5+}$ (blue). Arrows denote the magnetic moment of the respective ions.

Figure 2

Temperature dependence of heat capacity (a), resistivity (b), and magnetization (c) upon warming and cooling. (Heat capacity measurements upon cooling were performed only around $T_V$). Resistivity measurements were taken along the in- and out-of-plane directions. Magnetization measurements were taken with a 1 kG applied field both parallel and perpendicular to the $\mathit{c}$ direction.

Figure 3

Neutron scattering measurements taken (a)–(b) between $T_N$ and $T^{*}$ showing the AFM ordering in the mixed valent phase at $\mathit{\tau }$${}_{\text{G2}}$, (c)–(d) between $T^{*}$ and $T_V$ showing three characteristic propagation vectors in the “premonitory” phase; $\mathit{\tau }$${}_{\text{G2}}$, q${}_{\text{checker}}$, and ${\mathit{\tau }}^{*}$, and (e)–(f) below $T_V$ showing $\mathit{\tau }$${}_{\text{G1}}$ and q${}_{\text{stripe}}$ propagation vectors characterizing the stripe CO state. The error bars indicate a statistical error of one standard deviation.

Figure 4

X-ray diffraction data below $T$${}_V$ in (a) the ($H$0$L$) plane showing q${}_{\text{stripe}}$ and (c) the (HHL) plane below $T_V$ showing no superlattice reflections. Between $T^{*}$ and $T_V$, panel (b) shows the disappearance of stripe ordering in the ($H$0$L$) plane, and panel (d) the appearance of checkerboard CO peaks at q${}_{\text{checker}}$ in the (HHL) plane.

Figure 5

Various charge and magnetic order parameters measured with neutron (filled circles) and x-ray scattering (open circles). At $T_V=291$ K the appearance of stripe order associated with ${\mathbf{q}}_{\text{stripe}}=(1/2,0,1)$ (d) results in switching of the mixed-valent magnetic structure from ${\mathit{\tau }}_{\text{G2}}=(1/2,1/2,1/2)$ (a) to ${\mathit{\tau }}_{\text{G1}}=(1/2,1/2,1)$ (c). The phase between $T_V<T<T^{*}=308$ K is characterized by checkerboard charge ordering at ${\mathbf{q}}_{\text{checker}}=(1/2,1/2,1)$ in (c) and an associated moment modulation along the $\mathit{c}$ direction in (b) with ${\mathit{\tau }}^{*}=(0,0,1/2)$. Note the transition to a log intensity scale in the upper part of panel (c). Scattering intensity error bars which represent statistical errors of one standard deviation are included but are smaller than symbols.