Hole-doping-induced melting of spin-state ordering in ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5+x}$

The layered perovskite cobaltite $R{\mathrm{BaCo}}_2{\mathrm{O}}_{5.5}$ ($R$: rare-earth elements) exhibits an abrupt temperature-induced metal-insulator transition (MIT) that has been attributed to spin-state ordering (SSO) of ${\mathrm{Co}}^{3+}$ ions. Here we investigate the hole-doping member of ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5+x}$ ($0\le x\le 0.24$) with multiple techniques. The analysis of crystal and magnetic structures by electron and neutron diffraction confirm the SSO in the insulating phase of undoped ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5}$, which is melted by increasing the temperature across the MIT. In addition, we discover that hole doping to ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5}$ also melts the SSO in conjunction with an insulator-metal transition. The experimental results from electron and neutron diffraction and soft-x-ray absorption spectroscopy (XAS) all lead to the conclusion that hole-doping-induced MIT occurs in the same manner as the temperature-induced MIT. Therefore, we propose a unified mechanism that dominates the temperature- and hole-doping-induced MIT in the ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5+x}$ system. Specifically, this mechanism involves symmetry breaking coupled with a SSO in the paramagnetic phase.

Figure 1

(a) $Pmmm(a_p\times 2a_p\times 2a_p)$ crystal unit cell with oxygen vacancy in the ${\mathrm{PrO}}_x$ layer leading to ordering along the $b$ axis. The crystal structure consists of two nonequivalent crystallographic Co sites: one pyramidal site Co(Pyr) and one octahedral site Co(Oct). (b) $Pmma(2a_p\times 2a_p\times 2a_p)$ crystal unit cell with four nonequivalent crystallographic Co sites labeled Co1(Pyr), Co2(Pyr), Co3(Oct), and Co4(Oct).

Figure 2

(a) Resistivity $\rho$ and inverse magnetic susceptibility ${\chi }^{-1}$ as a function of temperature for samples with $x=0$. The abrupt changes in $\rho$ and ${\chi }^{-1}$ at $T_{\text{MI}}$ mark the concurrence of the SST and MIT. The susceptibility was measured in the 100 Oe field after zero-field cooling (ZFC). The inset shows the isothermal magnetization as a function of magnetic field ($M-H$ curve) measured at 300 and 400 K, respectively, from which the paramagnetic behavior is made evident at both temperatures. So the MIT occurs in the paramagnetic phase. (b) Resistivity $\rho$ as a function of temperature for various hole-doping fractions $x$, which shows a sharp drop with increasing hole doping. The $x$ dependence of $\rho$ reveals a HDI-MIT at $x=0.12$. The anomalously low value in $\rho$ for $x=0.14$ above $\sim 200$ K is possibly due to the lower boundary resistance of polycrystalline grains compared with that in samples with other hole-doping fractions. This speculation can be verified by the resistivity as a function of $x$ in single crystals of ${\mathrm{GdBaCo}}_2{\mathrm{O}}_{5.5+x}$ [35].

Figure 3

(a) Integrated intensity as a function of temperature for magnetic reflections 111 and $11\frac{1}{2}$ indexed by the unit cell $(2a_p\times 2a_p\times 2a_p)$ from neutron powder diffraction. (b) Ferrimagnetic ($T_{N2}\le T\le T_{N1}$) structure of phase 1 and antiferromagnetic ($T\le T_{N2}$) structures of phase 2. Octahedra are in black and pyramids in blue.

Figure 4

(a) Crystal structure model, (b)–(d), (f) results of pulsed neutron powder diffraction, (e) electron diffraction and inverse magnetic susceptibility for ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5+x}$ (HDI-MIT). (a) The $P4/mmm(a_p\times a_p\times 2a_p)$ unit cell with the random distribution of oxygen vacancies in the ${\mathrm{PrO}}_x$ layer, leading to only one nonequivalent crystallographic Co site. (b) The diffraction pattern of the reflections 400 and 040, as well as the integrated intensity of reflection 131 (inset), which are indexed by the unit cell $(2a_p\times 2a_p\times 2a_p)$, as a function of hole-doping fractions $x$ at 300 K. The results suggest that the crystal structure transforms from the orthorhombic $Pmma(2a_p\times 2a_p\times 2a_p)$ to the orthorhombic $Pmmm(a_p\times 2a_p\times 2a_p)$ at $x=0.12$. (c) Comparison of the 200 reflection (left) with the 112 reflection (right) indexed by the tetragonal $(a_p\times a_p\times 2a_p)$ unit cell. The 200 reflection splits into two reflections, whereas the 112 reflection remains single in the framework of the orthorhombic $(a_p\times 2a_p\times 2a_p)$ unit cell. (d), (e) The superlattice reflections with respect to the $(a_p\times a_p\times 2a_p)$ unit cell observed in both neutron and electron diffraction patterns of $x=0.24$ sample at 300 K. (f) Magnetization (right axis) and integrated intensity (left axis) for the magnetic reflection $\frac{1}{2}11$ indexed by the unit cell $(a_p\times 2a_p\times 2a_p)$ as a function of temperature for $x=0.24$, marking the antiferromagnetic phase (AF phase) with $T_N=120$ K. The susceptibility was measured in the 100 Oe field after zero-field cooling (ZFC).

Figure 5

Inverse magnetic susceptibility ${\chi }^{-1}$ as a function of temperature for various hole-doping fractions $x$. The susceptibilities were measured in the 100 Oe field after zero-field cooling (ZFC). The slope increases in the paramagnetic phase (shaded region) with increasing $x$, corresponding to the $x$ dependence of effective magnetic moments ${\mu }_{\mathrm{eff}}$ at 300 K as obtained from a Curie–Weiss fit within the shaded region (see inset).

Figure 6

(a) Soft-x-ray absorption spectra (XAS) at oxygen $K$ edge for ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5}$ (TI-MIT) and (b) for ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5+x}$ (HDI-MIT). The intensities are normalized at about 539 eV after subtracting a small constant background. Upon decreasing either the temperature or hole-doping fraction, the threshold of the spectra shifts to the higher-energy side as shown by the arrow in the shaded region, indicating the common nature for both TI- and HDI-MITs.

Figure 7

Phase diagram of ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5+x}$ featuring the common nature for both the temperature- and hole-doping-induced MITs. The MITs are parametrized by $T_{\text{MI}}$ and $x_{\text{MI}}$, which are determined from the resistivity measurements [see Fig. 2]. The crystal structure transition temperatures $T_S$ and hole-doping fractions $x_S$ are determined by various diffraction technique probes [see Figs. 8 and 4, respectively]. $T_{SST}$ corresponds to the SST, which is identified by the change in the slope of the inverse susceptibility vs temperature [see Fig. 5]. $T_{N1}, T_{N2}$, and $T_N$, which are determined from magnetization measurements [see Fig. 5] and neutron-diffraction measurements [see Figs. 8 and 4], denote the magnetic-ordering transition temperature in the insulating phase and the poor-metallic phase, respectively. The schematic electronic structures are arranged in the form of a pseudocubic perovskite subcell with a Pr ion at body center. It represents the entire electronic structure because this subcell shares the CoO layer with that of the Ba-ion body center. The spin states of ${\mathrm{Co}}^{3+}$ ions are denoted by the occupancy of $e_g$ orbital, which clearly illustrates the SSO along the $a$ axis in the insulating phase. The pure spin state at each Co site may also be interpreted by the HS-LS mixed state with different ratios of HS to LS among the Co sites. The orbital orientations are inferred by comparing the individual $\mathrm{Co}–\mathrm{O}$ bond lengths along the $a, b, c$ axes. Thus, these orientations involve some uncertainty.

Figure 8

Results of (a) specific heat, (c) electron diffraction, and (b), (d)–(f) pulsed neutron powder diffraction for ${\mathrm{PrBaCo}}_2{\mathrm{O}}_{5.5}$ (TI-MIT). (a) Specific-heat curve in both heating and cooling process. The sharp peak and hysteresis between the heating and cooling processes indicate a first-order phase transition. (b) High-resolution neutron powder diffraction pattern, where the Bragg peaks are indexed by the $(2a_p\times 2a_p\times 2a_p)$ unit cell. The coexistence of two phases in the critical region is a clear indication of a first-order phase transition. (c) Electron diffraction pattern at 300 K, which shows a superlattice reflection along the $a$ axis with respect to the $(a_p\times 2a_p\times 2a_p)$ unit cell; i.e., the 011 reflection is the spot in the rectangle and the $\frac{1}{2}00$ reflection is the spot in the circle. We verified that no multiple scattering occurred during the measurement. (d) The superlattice reflections $\frac{3}{2}11, \frac{1}{2}31$, and $\frac{3}{2}01$ indexed by the $(a_p\times 2a_p\times 2a_p)$ unit cell observed by neutron powder diffraction at 300 K (below $T_{\text{MI}}$). (e) Magnitude of magnetic moment as a function of temperature for each Co site in phase 1, as determined from Rietveld refinement with the magnetic model in Fig. 3. The shaded region corresponds to the coexisting ferrimagnetic and antiferromagnetic structures. (f) Average $\mathrm{Co}–\mathrm{O}$ bond length $\langle d\rangle$ as a function of temperature for each Co site in the insulating phase (below $T_{\text{MI}}$) of the $Pmma$ structure and in the poor-metallic phase (above $T_{\text{MI}}$) of the $Pmmm$ structure. The shaded region corresponds to the coexisting structures [see panel (b)]. The red (black) curves stands for ${\mathrm{CoO}}_6$ octahedron (${\mathrm{CoO}}_5$ pyramid).