Uncharacteristic phase separation trends with the ionic size in cobaltites

Using elastic neutron scattering on single crystals of ${\text{La}}_{1-x}{A}_x{\text{CoO}}_3$ ($A={\text{Ca}}^{2+}$, ${\text{Sr}}^{2+}$, and ${\text{Ba}}^{2+}$), we found the development of magnetic superstructures below the global magnetic transition to be strongly dependent on the size of the $A$-site dopant, $⟨r_A⟩$, in an unusual way. Upon reducing the $⟨r_A⟩$ (i.e., as with Ca doping), only a commensurate ferromagnetic cluster phase is evident. On expanding the $⟨r_A⟩$, the tendency toward coexistence of competing ferromagnetic and antiferromagnetic orders increases giving rise to an inhomogeneous ground state. The antiferromagnetic ordered state, initially incommensurate, continuously strengthens and becomes commensurate with long-range order and a characteristic cubic wave vector of ${\vec{Q}}_c=\left(0.25,0.25,0.25\right)$ with $x$. The two competing order parameters become comparable in magnitude indicative of the phase-separated nature of the cobalt perovskite system.

Figure 1

(Color online) The scans along $\left(h,h,h\right)$ shown for (a) $x=0.18$ were collected at TOPAN at the temperatures shown, and along $\left(h,h,1-\left|h\right|\right)$ for (b) 0.15, (c) 0.10, and (d) 0.03 of the Ba crystals, and 5 and 10% Ca shown in the inset of (d) were collected at SPINS at the temperatures shown in (b). Measurements above $T_{SG}$ are shown in red, while those performed below are shown in black. Broad satellite peaks are present in the low-temperature scans for $x=0.10$ and 0.15 (also for 0.06 but is not shown here) while they become Bragg-like for $x=0.18$. No satellite features are evident in the $x=0.03$ as well as in both of the Ca crystals as seen from the scans at 5 K shown in the inset of (d). The order parameters of the two magnetic signals, the satellite (green), and ferromagnetic (blue) components, are shown in (e) $x=0.18$, (f) 0.15, and (g) 0.10. The order parameter is rescaled to 0:1 by $\left(I\text{−}{I}_{\text{min}}\right)/I_{\text{max}}$. These are compared to FC ${\chi }_{bulk}$ at 1000 Oe for the $x=0.10$ and 0.15. In (e), FC and ZFC curves are shown for data collected at 100 Oe. The cusp observed in the ZFC curve coincides with the onset temperature of the satellite peaks. Shown in (h) is the integrated intensity which is proportional to the volume fraction as a function of temperature for the $x=0.10$ and compares well with ${\chi }_{bulk}$. Error bars represent $\pm 1$ sigma.

Figure 2

(Color online) Data for the Ba crystals as a function of hole concentration. (a) is a plot of the IC peak position, $\delta$, with $x\%$ which is compared to the $\delta$ dependence on $x\%$ obtained previously for Sr crystals. (b) is a plot of the order parameter for the two magnetic phases. (c) is a plot of the normalized satellite peak intensity, $I_{\text{IC}}$ and the (001) Bragg peak, $I_{\text{FMC}}$. The $I_{\text{IC}}$ was determined from the integrated peak area of a Lorentzian fit along the (111) direction through the IC peak while the FMC intensity was determined from the integrated peak area of a Lorentzian fit along the (00L) direction through (001). For the normalization by the nuclear Bragg peak, intensity from a longitudinal scan through the Bragg peak and a contribution due to the mosaic of the crystal from the scan along the transverse direction was taken into account. Also, since data were collected at two different energies at TOPAN and SPINS, a $\text{sin}{\left(2\theta \right)}_{magnetic}/\text{sin}{\left(2\theta \right)}_{nuclear}$ term needed to be applied for the satellite peaks to be properly scaled. This was not necessary for the FM peak. (d) is a plot of a comparison of the incommensurate, ${\xi }_{\text{IC}}$ and commensurate, ${\xi }_{\text{FMC}}$, correlation lengths. Note that $\xi$ is comparable in the two magnetic phases at all $x$ while the value of $80\text{Å}$ for the 18% is a lower bound since in the experimental setup of TOPAN, the peaks became resolution limited.

Figure 3

(Color online) The correlation length, $\xi$, as a function of $⟨r_A⟩$, determined for the two magnetic components in Ca, Sr, and Ba crystals of 5(6) and 10%. In determining $⟨r_A⟩$, the average $⟨A⟩$ site nine-coordinated radius was used using the appropriate concentration of ${\text{Co}}^{3+}/{\text{Co}}^{4+}$. At a constant hole concentration, ${\xi }_{\text{FMC}}$ is always larger in Ca than in Sr and Ba crystals. No second magnetic phase has been detected in Ca. At the same time, as $⟨r_A⟩$ increases, ${\xi }_{\text{FMC}}$ and ${\xi }_{\text{IC}}$ become comparable. The lines are guides to the eye. Also shown on the right panel are values of the magnetization from Ref. 30.