Magnetic order, transport and infrared optical properties in the $A$CrO${}_3$ system ($A$ $=$ Ca, Sr, and Pb)

The crystal structure and magnetic structure of the chromate series $A$CrO${}_3$ ($A$ $=$ Ca, Sr, Pb) where Cr exhibits the unusual Cr${}^{4+}$ oxidation state have been studied by comprehensive diffraction experiments. In addition we present a detailed analysis of the infrared optical properties of polycrystalline CaCrO${}_3$ which is found to be metallic along all crystallographic directions. CaCrO${}_3$ forms the rare case of a three-dimensional antiferromagnetic and metallic transition-metal oxide in which the occurrence of magnetic ordering is closely coupled to a flattening of the lattice. The same $C$-type magnetic order is also found in the Sr material and again is coupled to a structural distortion associated with lattice flattening. However, in SrCrO${}_3$ only a part of the sample transforms into the antiferromagnetic distorted phase. In contrast to CaCrO${}_3$ and SrCrO${}_3$, PbCrO${}_3$ clearly is insulating with a significantly larger unit-cell volume and exhibits $G$-type magnetic order.

Figure 1

(a) Synchrotron x-ray diffraction pattern of CaCrO${}_3$ measured at 20 K; black circles: measured intensity $I_{\mathrm{obs}}$; line: Rietveld fit $I_{\mathrm{calc}}$; gray line: $I_{\mathrm{obs}}-I_{\mathrm{calc}}-I_{\mathrm{offset}}$. (b)–(d) Lattice parameters $a$, $b$, and $c$ of CaCrO${}_3$. (e) Unit-cell volume $V$. (f) Orthorhombic splitting $\varepsilon =(a-b)/(a+b)$. (g) Pseudocubic lattice parameter $a_{\mathrm{cub}}=a/\sqrt{2}$, $b_{\mathrm{cub}}=b/\sqrt{2}$, and $c_{\mathrm{cub}}=c/2$; circles: synchrotron x-ray data; open triangles: neutron data.

Figure 2

(a) Powder-neutron diffraction pattern of CaCrO${}_3$ measured at the SPODI (at 5 K); circles: measured data; line: Rietveld fit; dark gray line: $I_{\mathrm{obs}}-I_{\mathrm{calc}}-I_{\mathrm{offset}}$; black/gray bars: nuclear/magnetic Bragg peak positions. (b) Tilt and rotational angles of the CrO${}_6$ octahedron. (c) Ratio of the O2-O2 bond lengths (gray) and ratio of the basal Cr-O2 distances. (d) Cr-O distances. (b)–(d) Open circles: single-crystal x-ray data; triangles: neutron data. (Lines are guides to the eye.)

Figure 3

(a) Neutron scattering intensity of CaCrO${}_3$ as a function of temperature and 2$\Theta$ measured on D20. (b) Two strongest magnetic peaks together with three different lines for the three fit models for $C_x$-, $C_y$-, and $C_z$-type AFM order (blue dotted, red solid, and green dashed) as measured at 1.7 K on D20; gray bars: magnetic Bragg peak positions. (c) Temperature dependence of the $C_y$-type AFM moment; black circles: D20 measurement; triangles: SPODI measurement.

Figure 4

(a) Electrical resistivity of CaCrO${}_3$ as a function of temperature and inverse temperature (inset). The second inset indicates a nominal activation energy $\Delta$. Arrows indicate either the magnetic ordering temperature (vertical) or measurements on cooling or heating. (b) Magnetic susceptibility of CaCrO${}_3$.

Figure 5

Infrared reflectivity $R\left(\omega \right)$ of polycrystalline CaCrO${}_3$ at different temperatures.

Figure 6

The optical conductivity ${\sigma }_1\left(\omega \right)$ in the infrared range as derived from a Kramers-Kronig analysis of $R\left(\omega \right)$ under the assumption that $\sigma \left(\omega \right)$ is isotropic and $\lambda \ll L_g$. Inset: phonon frequency range. The dashed line indicates the lower frequency limit of our experimental data of $R\left(\omega \right)$.

Figure 7

Optical conductivity ${\sigma }_1\left(\omega \right)$ of CaCrO${}_3$ at 25, 125, and 400 meV and the extrapolated value ${\sigma }_1^{\mathit{DC}}(\omega =0)$ as a function of temperature.

Figure 8

Comparison of (a) the reflectance and the optical conductivity (b) within the $ab$ plane and (c) parallel to the $c$ axis for different parameter sets for the Orenstein model.

Figure 9

Comparison between the effective medium model (red long-dashed line) and the results of the isotropic analysis (green short-dashed line). (a) Reflectance, (b) optical conductivity. The optical conductivity of the effective medium model is determined by Eq. (6). The only significant difference arises below about 10 meV.

Figure 10

(a)–(c) Powder-neutron diffraction patterns of SrCrO${}_3$ measured at 3 K (black circles), 35 K (cyan dashed line), and 95 K (red dotted line) at the D1A diffractometer ($\lambda$ = 1.3897Å; sample B). (d)–(e) Powder-neutron diffraction pattern measured at 3 K (black circles) and 100 K (red dotted line) at the SPODI diffractometer ($\lambda =1.548$ Å; sample A). The green solid lines are Rietveld fits; the blue dash-dotted line is a fit for a $C_{x/y}$-type AFM structure which is compared to the $C_z$-type AFM structure (green solid line); the upper and lower bars in parts(b) and (d) denote the Bragg positions of the cubic and tetragonalphases, respectively; the bars in parts (c) and (e) denote themagnetic Bragg peaks.

Figure 11

Temperature dependence of the lattice parameters in the three chromates CaCrO3, SrCrO3, and PbCrO3, their unit-cell volumes, and the normalized values for the lattice parameters and cell volumes are plotted as a function of temperature. The symbols are consistent for all four panels and refer to the respective compound.

Figure 12

Magnetic susceptibility of the SrCrO${}_3$ sample measured at 0.1 T in a superconducting quantum interference device (SQUID) magnetometer (sample B).

Figure 13

Temperature dependence of the electrical resistivity in the three chromates studied; for PbCrO${}_3$ the low-temperature resistivity exceeds the accessible experimental range.

Figure 14

(a) Lattice parameter $a$ of PbCrO${}_3$. (b) Powder-neutron diffraction pattern measured at 1.5 K (G4.1 diffractometer); black circles: measured intensities $I_{\mathrm{obs}}$ at 1.5 K; green solid line: Rietveld fit $I_{\mathrm{calc}}$; blue upper and magenta lower bars: positions of structural and magnetic Bragg peaks; red (gray) squares: measured intensities at 250 K.