Ferromagnetic and ferroelectric $5d^1$ insulator ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$

Poly- and single-crystalline samples of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ have been successfully synthesized. ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ crystallizes in the noncentrosymmetric space group $P{6}_{3}cm$. ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ shows a ferromagnetic order below 5 K and a possible ferroelectric order below 150 K. A multiferroic state with both ferromagnetic and ferroelectric ordering is established, although the ferromagnetic and ferroelectric orders are not coupled. The experimental effective moment and the saturated magnetization for ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ are close to the spin-only value, indicating that the spin-orbit coupling does not play an important role, which is due to the large crystal field and spin splitting in ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$.

Figure 1

PXRD patterns and Rietveld fitting of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$. The inset shows a photograph of rodlike ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ crystals on a millimeter grid.

Figure 2

Crystal structure of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$.

Figure 3

Optical conductivity spectrum of the ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ single crystal at 300 K.

Figure 4

(a) Temperature dependence of FC magnetic susceptibility curves, $\chi \left(T\right)$, of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ single crystals. Inset shows corresponding ${\left(\chi -{\chi }_0\right)}^{\text{–}1}$ vs $T$ data. (b) Isothermal magnetization of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ single crystals at 2 K. Inset shows an enlarged view between –200 and 200 Oe.

Figure 5

Temperature-dependent specific heat of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$. Inset shows the magnetic contribution and the corresponding entropy.

Figure 6

The temperature dependence of the dielectric constant ε of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$. The inset shows the temperature dependence of dielectric loss.

Figure 7

(a) The temperature dependence of electric polarization of ${\mathrm{Ba}}_5{\left(\mathrm{Os}{\mathrm{O}}_5\right)}_3\mathrm{Cl}$ with different poling electric fields applied and (b) the corresponding pyroelectric data.

Figure 8

(a) Low-temperature pyroelectric data. (b) Low-temperature thermal expansion measured under varied magnetic fields.

Figure 9

Bulk band structure of GGA (a), GGA+FM $\left(U=2.7\right)$ (b), and GGA+FM+SOC (c). Spin-up and spin-down states are shown as red lines and blue dotted lines, respectively. (d) The schematic plot of splitting of five $d$ orbitals in this compound. The adopted Cartesian coordinates of the pyramid are shown. ${\mathrm{\Delta }}_1$ is the energy splitting of the lower three orbitals under the $C_{4v}$ symmetry of the pyramids (explicitly in its inset), ${\mathrm{\Delta }}_2$ is due to Zeeman coupling and Coulomb interaction $U$, and ${\mathrm{\Delta }}_{\mathrm{so}}$ is the energy change by spin-orbit coupling. $E_F$ denotes the Fermi level.