Electronic Self-Organization in the Single-Layer Manganite ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_{1+x}{\mathrm{MnO}}_4$

We use neutron scattering to investigate the doping evolution of the magnetic correlations in the single-layer manganite ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_{1+x}{\mathrm{MnO}}_4$, away from the $x=0.5$ composition where the CE-type commensurate antiferromagnetic (AF) structure is stable. We find that short-range incommensurate spin correlations develop as the system is electron doped ($x<0.5$), which coexist with the CE-type AF order. This suggests that electron doping in this system induces an inhomogeneous electronic self-organization, where commensurate AF patches with $x=0.5$ are separated by electron-rich domain walls with short-range magnetic correlations. This behavior is strikingly different than for the perovskite ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$, where the long-range CE-type commensurate AF structure is stable over a wide range of electron or hole doping around $x=0.5$.

Figure 1

(a) Phase diagram of ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_{1+x}{\mathrm{MnO}}_4$. Solid symbols are from our measurements, open symbols from Ref. 15. $T_{\mathrm{CO}}$ denotes the transition temperature of CO-OO, $T_{\mathrm{ab}}$ and $T_N$ are the transition temperatures of 2D and 3D AF order. (b) Schematics of the experimental observations in reciprocal space. The pattern in lighter color originates from the $90°$ twinned domain. Orbital and spin configurations within the ${\mathrm{MnO}}_2$ plane that may explain the neutron results: (c) are diagonal and (d) horizontal domain walls, where extra electrons congregate. ${\mathrm{Mn}}^{4+}$ ions are denoted by black circles. The Jahn-Teller active ${\mathrm{Mn}}^{3+}$ ions have additional orbitals. The blue and red lines illustrate the ferromagnetic zigzag spin chains which are coupled antiferromagnetically. (e) Fourier transform of the spin configurations in (c) and (d) combined. Note the dominant spectral weight at ($1/4-\delta /\sqrt{2}$, $1/4-\delta /\sqrt{2}$) or ($3/4+\delta /\sqrt{2}$, $3/4+\delta /\sqrt{2}$) for the ${\mathrm{Mn}}^{3+}$ spins. (f) Experimentally observed doping dependence of incommensurability from both the ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Mn}}^{4+}$ sublattices.

Figure 2

Comparison of the low-$T$ magnetic scattering originating from the ${\mathrm{Mn}}^{3+}$ spins, for the $x=0.35$, $x=0.40$, and $x=0.45$ samples. The corresponding wave vector scans through the peaks, as indicated by the arrows, are presented in the lower panels. The data reveal that a separate ICM component develops as electrons are added from the $x=0.5$ point, which coexists with the $x=0.5$ AF order. The ICM scattering is short range, and separates further from the CM position and becomes broader as $x$ is reduced.

Figure 3

Comparison of the magnetic diffuse scattering originating from the ${\mathrm{Mn}}^{4+}$ spins at $T=10\mathrm{K}$ for the (a) $x=0.35$, (b) $x=0.40$, and (c) $x=0.45$ samples. Wave vector scans across the ICM and CM peaks are in the panels (d)–(f).

Figure 4

Wave vector scans of magnetic diffuse scattering from (a) ${\mathrm{Mn}}^{4+}$ and (b) ${\mathrm{Mn}}^{3+}$ sublattices of the $x=0.45$ sample at selected temperatures. Temperature dependence of the CM (red) and ICM (blue) peak intensities from the (c) ${\mathrm{Mn}}^{4+}$ and (d) ${\mathrm{Mn}}^{3+}$ sublattices for $x=0.35$, 0.40, and 0.45.