Crystal structure and magnetic properties of the $5d$ transition metal oxides $A\mathrm{Os}{\mathrm{O}}_4\left(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}\right)$

We synthesized the $5d^1$ transition-metal oxides $A\mathrm{Os}{\mathrm{O}}_4\left(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}\right)$ by solid-state reaction, and performed structure determination and magnetic and heat capacity measurements. It was found that they crystallize in a scheelite ($A=\mathrm{K}$ and Rb) or a quasischeelite structure ($A=\mathrm{Cs}$) comprising distorted diamond lattices of septivalent Os ($d^1$) ions tetrahedrally coordinated by four oxide ions without local inversion symmetry; hence an antisymmetric spin-orbit coupling is expected in the crystals. The K and Rb compounds have Weiss temperatures of $\theta =-66$ and $-18\mathrm{K}$, effective magnetic moments of ${\mu }_{\mathrm{eff}}=1.44$ and $1.45{\mu }_{\mathrm{B}}/\mathrm{Os}$, and antiferromagnetic transition temperatures of $T_{\mathrm{N}}=36.9$ and 21.0 K, respectively. In contrast, the Cs compound has $\theta =12\mathrm{K}$ and ${\mu }_{\mathrm{eff}}=0.8{\mu }_{\mathrm{B}}/\mathrm{Os}$ without magnetic transition above 2 K, instead exhibiting a first-order structural transition at $T_{\mathrm{s}}=152.5\mathrm{K}$. The decline of the Os moment from $1.73{\mu }_{\mathrm{B}}/\mathrm{Os}$ for the simple $d^1$ spin, particularly for Cs, is likely to originate from the antiparallel orbital moment, although the spin-orbit coupling is generally quenched in the low-lying $e$ orbitals.

Figure 1

Powder-x-ray-diffraction patterns of ${\mathrm{KOsO}}_4$ (upper) and ${\mathrm{CsOsO}}_4$ (lower) with $\mathrm{Cu}\text{−}K\alpha$ radiation at 300 K. The plots correspond to the observed (red crosses), calculated (black line), difference profiles (blue line), and positions of Bragg peaks (green tick marks).

Figure 2

Crystal structures of ${\mathrm{KOsO}}_4$ (a) and ${\mathrm{CsOsO}}_4$ (b). Each Os atom is surrounded tetrahedrally by four oxide atoms. The distorted diamond networks made of Os atoms are drawn with sticks. The Os-Os, Os-O, and O-O distances in angstrom are written for ${\mathrm{KOsO}}_4$ (c), ${\mathrm{RbOsO}}_4$ (d), and ${\mathrm{CsOsO}}_4$ (e). The diamond lattices are represented with broken lines for K and Rb, while for ${\mathrm{CsOsO}}_4$, the short and long Os-Os distances are represented by thick and thin broken lines, respectively. The $\alpha \text{–}\sigma$ listed on the ${\mathrm{OsO}}_4$ tetrahedron are the O-Os-O bond angles, whose values are given in the text.

Figure 3

Temperature dependence of magnetic susceptibility down to 2 K obtained under a magnetic field of 1 T for ${\mathrm{KOsO}}_4$ (red) and ${\mathrm{RbOsO}}_4$ (blue). A molar unit corresponds to one formula unit of $A\mathrm{Os}{\mathrm{O}}_4$. Broad humps appear near 60 and 30 K for $A=\mathrm{K}$ and Rb, followed by antiferromagnetic orders at $T_{\mathrm{N}}=37.2$ and 21.2 K, respectively (indicated by arrows). The broken lines represent the calculated susceptibilities based on a high-temperature series expansion on $S=1/2$ diamond-lattice Heisenberg antiferromagnetic model [26]. The inset shows enlargements of magnetic susceptibility for $A=\mathrm{K}$ and Rb around $T_{\mathrm{N}}$.

Figure 4

Temperature dependence of heat capacity divided by temperature, $C/T$, for ${\mathrm{KOsO}}_4$ (a) and ${\mathrm{RbOsO}}_4$ (b). A molar unit corresponds to one formula unit of $A\mathrm{Os}{\mathrm{O}}_4$. As references of lattice contributions, the $C$/$T$ of nonmagnetic ${\mathrm{KReO}}_4$ and ${\mathrm{RbReO}}_4$ are plotted with broken lines in (a) and (b), respectively. Sharp peaks indicative of antiferromagnetic ordering appear at $T_{\mathrm{N}}=36.9$ and 21.0 K for ${\mathrm{KOsO}}_4$ and ${\mathrm{RbOsO}}_4$, respectively.

Figure 5

Temperature dependence of magnetic heat capacity, $C_{\mathrm{mag}}$, and magnetic entropy, $S_{\mathrm{mag}}$, for ${\mathrm{KOsO}}_4$ (a) and ${\mathrm{RbOsO}}_4$ (b). A molar unit corresponds to one formula unit of $A\mathrm{Os}{\mathrm{O}}_4$. Assuming the humps to be of Schottky type in $C_{\mathrm{mag}}$, the excitation gaps are estimated to be ${\mathrm{\Delta }}_{\mathrm{t}}=289\left(6\right)\mathrm{K}$ for K and ${\mathrm{\Delta }}_{\mathrm{t}}=230\left(13\right)\mathrm{K}$ for Rb, as drawn by the black solid lines.

Figure 6

(a) Temperature dependence of magnetic susceptibility and inverse magnetic susceptibility measured at 1 T for ${\mathrm{CsOsO}}_4$. The molar unit corresponds to one formula unit of ${\mathrm{CsOsO}}_4$. A weak anomaly appears at $T_{\mathrm{s}}=152.5\mathrm{K}$, where the inverse susceptibility changes in gradient. (b) Magnetic susceptibility near $T_{\mathrm{s}}$. (c) Heat capacity divided by temperature, $C/T$, for ${\mathrm{CsOsO}}_4$, featuring a jump at $T_{\mathrm{s}}=154.8\mathrm{K}$ with a change in entropy of $\mathrm{\Delta }S=0.41\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$, determined from the approximate base line (broken line).

Figure 7

(a) Synchrotron powder-x-ray diffraction pattern for ${\mathrm{CsOsO}}_4$ at 170 K (red solid line) and 130 K (blue solid line) at wavelength of $\lambda =0.689278\AA$. (b) A large structural change at $T_{\mathrm{s}}=154.8\mathrm{K}$ is seen in temperature dependence of the lattice constants $a$ (red circle), $b$ (blue upward triangle), $c$ (green square), and $\gamma$ (purple downward triangle), and $V$ (black diamond). Subscripts “o” and “m” denote orthorhombic and monoclinic crystal systems, respectively.