Observation of magnetic order in multiferroic ${\mathrm{SmMn}}_2{\mathrm{O}}_5$ studied by resonant x-ray magnetic scattering

We report a resonant x-ray magnetic scattering study of multiferroic ${\mathrm{SmMn}}_2{\mathrm{O}}_5$, for which the microscopic magnetic properties have not yet been revealed. Dielectric measurements indicated that ferroelectric phase transitions occur around $T_{\mathrm{C}1}\simeq 34$ K and $T_{\mathrm{C}2}\simeq 28$ K. Resonant x-ray magnetic scattering was observed at both the Sm $L{}_{\text{I}\text{I}\text{I}}$ and Mn $K$ edges in the ferroelectric phase below $T_{\mathrm{C}2}$. The Sm and Mn magnetic moments align antiferromagnetically with a magnetic propagation wave vector ${\mathrm{q}}_{\mathrm{M}}=(1/2,0,0)$, and the ferroelectric transition coincides with the antiferromagnetic transition. The azimuthal dependence of the resonant magnetic signals confirmed that the Sm and Mn magnetic moments have a dominant $c$-axis component, which is quite unique because Mn moments have a dominant $a$-axis component in other $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ $(R=\text{rare earth},\text{Y},\text{Bi})$ compounds. We propose a magnetic structure with the magnetic space group $P_{2a}b{2}_{1}m$, which allows electric polarization along the $b$ axis in the ferroelectric phase.

Figure 1

Crystal structure of $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ at room temperature, projected (a) in the $ab$ plane and (b) in the $ac$ plane, as visualized by vesta [11]. $J_1\sim J_5$ shows representative magnetic interactions between neighboring Mn ions.

Figure 2

Scattering geometry at $\psi ={90}^{\circ }$, where the $c^{*}$ axis is perpendicular to the scattering plane and parallel to the $z_2$ axis. ${\mathrm{k}}_{\mathrm{i}}$ and ${\mathrm{k}}_{\mathrm{f}}$ are wave vector of incident and scattered x rays, respectively. Scattering vector is defined as $\mathrm{Q}={\mathrm{k}}_{\mathrm{f}}-{\mathrm{k}}_{\mathrm{i}}$.

Figure 3

(a) Energy dependence of the (5.5 0 0) signals around the Sm $L{}_{\text{I}\text{I}\text{I}}$ edge at $\psi ={90}^{\circ }$ and $T=4$ K. (b) $\theta \text{−}2\theta$ profiles around the (5.5 0 0) position at $T=4$ K. The incident x rays were $\pi$-polarized.

Figure 4

(a) Energy scans at $\mathrm{Q}=(5.5,0,0)$ (filled circles) and at $\mathrm{Q}=(5.45,0,0)$ (open circles) around the Mn $K$ edge, taken at $\psi ={90}^{\circ }$ and at $T=4$ K. The two dashed lines indicate $E=6.554$ and 6.5585 keV, respectively. The incident x rays were $\pi$-polarized. (b) Difference in intensity between signals at $\mathrm{Q}=(5.5,0,0)$ and at $\mathrm{Q}=(5.45,0,0)$. $\theta \text{−}2\theta$ profiles around the (5.5 0 0) position (c) at $E=6.5585$ keV (on-resonance) and (d) at $E=6.554$ keV (off-resonance).

Figure 5

Temperature dependence of (a) scattering intensities observed around the Sm $L{}_{\text{I}\text{I}\text{I}}$ edge (filled circles) and the Mn $K$ edge (open circles), and (b) the propagation wave vector ${\mathrm{q}}_{\mathrm{M}}=(q_x,0,0)$. The incident x rays were $\pi$-polarized. The temperature dependence of (c) the magnetic susceptibility and (d) the dielectric constant (red line) and the electric polarization (black line) along the $b$ axis.

Figure 6

Energy scans (a) around the Sm $L{}_{\text{I}\text{I}\text{I}}$ edge at $\mathrm{Q}=(5.5,0,0)$ and (b) around the Mn $K$ edge at $\mathrm{Q}=(5.5,0,0)$ (filled circles) and at $\mathrm{Q}=(5.51,-0.01,-0.01)$ (open circles), taken at $\psi =0^{\circ }$ and $T\simeq 5$ K. The incident x rays were $\sigma$-polarized. (c) Difference in intensity between the signals at $\mathrm{Q}=(5.5,0,0)$ and at $\mathrm{Q}=(5.51,-0.01,-0.01)$ around the Mn $K$ edge, with a fitting line added.

Figure 7

Azimuthal dependence of resonant scattering observed at $\mathrm{Q}=(5.5,0,0)$ around the Sm $L{}_{\text{I}\text{I}\text{I}}$ (filled circles) and Mn $K$ edges (open circles). The incident x rays were $\sigma$-polarized for both absorption edges. The intensities at the Sm $L{}_{\text{I}\text{I}\text{I}}$ and Mn $K$ edges were normalized by the integrated intensity of the (4 0 0) Bragg peak. Signals coming from the Sm and Mn magnetic moments both disappeared at $\psi ={90}^{\circ }$ when the $c^{*}$ axis was perpendicular to scattering plane. The red line shows the calculated values for the $\sigma \text{−}{\pi }^{\prime }$ process in Eq. (1), assuming that the magnetic moments had only a $c$-axis component.

Figure 8

Dielectric and magnetic phase diagram of ${\mathrm{SmMn}}_2{\mathrm{O}}_5$. The phase transition temperatures were determined to be $T_{\mathrm{N}1}\simeq 44$ K, $T_{\mathrm{N}2}(=T_{\mathrm{C}1})\simeq 34$ K, $T_{\mathrm{N}3}\simeq 28$ K, $T_{\mathrm{C}2}\simeq 28$ K, and $T_{\mathrm{CM}}\simeq 26$ K.

Figure 9

Magnetic structure with ${\mathrm{q}}_{\mathrm{M}}=(1/2,0,0)$, assuming that the Sm and Mn magnetic moments each have only a $c$-axis component and the magnetic space group is $P_{2a}b{2}_{1}m$, projected (a) in the $ab$ plane and (b) in the $ac$ plane. The $m,a^{\prime },2_1$, and $2_1^{\prime }$ elements are situated at $z=0$ and $z=1/2$, and the $b,b^{\prime },2_1$, and $2_1^{\prime }$ elements are located at $x=1/4$ and $3/4$.