${\mathrm{YRuO}}_3$: A quantum weak ferromagnet

The perovskite ${\mathrm{YRuO}}_3$ containing low-spin $d^5{\mathrm{Ru}}^{3+}$ has a Pnma orthorhombic structure with elongated ${\mathrm{RuO}}_6$ octahedra evidencing orbital order and is insulating to low temperatures with a band gap of 70 meV. Canted antiferromagnetic ${\mathrm{Ru}}^{3+}$ spin order is observed below $T_{\mathrm{C}}=97\mathrm{K}$, and magnetization plateaus that emerge below 62 K reveal a quantum weak ferromagnetic state where 1/8 of the spins are reversed, reflecting extreme single-ion anisotropy resulting from the strong spin-orbit coupling of the $d^5{\mathrm{Ru}}^{3+}$ ion. Dynamic effects of the reversed spins give rise to an unusual negative AC susceptibility response, and a partial freezing of this motion occurs at 27 K.

Figure 1

(a) The Pnma unit cell of ${\mathrm{YRuO}}_3$ with Y, Ru, and O depicted in orange, red, and black, respectively. Elongated Ru-O bonds are shown in green and display the cooperative Jahn-Teller distortion arising from orbital ordering. Red arrows show the $G$-type antiferromagnetic structure order of ${\mathrm{Ru}}^{3+}$ moments below 97 K. $a$ and $c$ axes are shown, and $b$ is perpendicular to their plane. (b) Calculated isosurfaces (at $0.02/\mathrm{boh}{\mathrm{r}}^3$) of magnetization density reveal orbital ordering in ${\mathrm{YRuO}}_3$. The structure is drawn as a $\surd 2\times 1\times \surd 2$ supercell of the Pnma structure projected on the (010) plane, and shows ordering of Ru $d_{xy}$ (spin-up) and $d_{yx}$ (spin-down) orbitals, colored green and red, respectively. Red and light-blue atoms denote O and Ru.

Figure 2

Zero-field-cooled/field-cooled magnetic susceptibilities (black/red) of ${\mathrm{YRuO}}_3$ under a magnetic field of 0.1 T showing the magnetic ordering transition at $T_{\mathrm{C}}=97\mathrm{K}$. Inset shows neutron powder diffraction patterns at 1.7 and 120 K. Red star identifies the magnetic peak from spin order in ${\mathrm{YRuO}}_3$; black star marks a spin-ordering peak from the ${\mathrm{Y}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ impurity.

Figure 3

Magnetization-field hysteresis loops for ${\mathrm{YRuO}}_3$ with loops between 2 and 50 K and between 50 and 90 K separated for clarity. Insets show low-field data. The saturated weak magnetization $M_{\mathrm{w}}$ and the ¾$M_{\mathrm{w}}$ quantum weak ferromagnetic features are labeled. $M_{\mathrm{w}}$ is linearly extrapolated from the high-field magnetization to $H=0$ as shown and the ¾$M_{\mathrm{w}}$ line is drawn parallel to the $M_{\mathrm{w}}$ line with $M=¾M_{\mathrm{w}}$ at $H=0$.

Figure 4

Model for the ¾$M_{\mathrm{w}}$ quantum weak ferromagnetic state observed in ${\mathrm{YRuO}}_3$. Moments lie parallel to two symmetry-related easy axes resulting from tilting of octahedra. The vertical spin components (parallel to the crystallographic $c$ axis) are coupled antiferromagnetically and weak ferromagnetic (wF) components that arise from DM coupling are ordered in the horizontal ($b$-axis) direction as shown by the lower blue arrows. The ¾$M_{\mathrm{w}}$ state results from inversion of all moments in every eighth plane, as indicated by the red boxes, so that moments remain parallel to their easy axes while reversing their wF direction.

Figure 5

(a) Real $\left({\chi }^{\prime }\right)$ and imaginary $\left({\chi }^{″}\right)$ parts of the AC susceptibility of ${\mathrm{YRuO}}_3$ measured at frequencies from 100 Hz to 10 kHz between 2 and 110 K with an AC field amplitude of 1.5 mT. The magnetic ordering transition of ${\mathrm{YRuO}}_3$ is seen at 97 K, and a smaller peak at 86 K corresponds to the antiferromagnetic ordering transition of the impurity pyrochlore phase ${\mathrm{Y}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ [13, 14]. (b) Plot of log(relaxation time) against inverse temperature. The Vogel-Fulcher fit over the 30–55 K range is shown and the vertical arrow marks the 27 K transition in spin dynamics. Inset shows the fitted low- $\left({\chi }_{\mathrm{T}}\right)$ and high- $\left({\chi }_{\mathrm{S}}\right)$ frequency limits of AC susceptibility.