Origin of the enhanced ferroelectricity in multiferroic $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$

In orthorhombic $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ single crystals, $\mathrm{S}{\mathrm{m}}^{3+}$ crystal-field (CF) excitations are studied by infrared transmission as a function of temperature and under applied magnetic field up to 10 T. These measurements are complemented with the study of Raman-active phonon frequency shifts as a function of temperature between 300 and 5 K. The frequencies of all ${}^{6}H_j$ crystal-field levels of $\mathrm{S}{\mathrm{m}}^{3+}$ were determined as well as those of ${}^{6}F_j$. At high temperatures, the evolutions of $\mathrm{S}{\mathrm{m}}^{3+}$ CF excitations exhibit anomalies around the characteristic temperatures, $T^{*}\sim 60\mathrm{K}$ and $T^{\mathrm{S}}\sim 120\mathrm{K}$ and reflect the thermal disorder induced by splitting of the Sm–O bonds in $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ that contribute to the frequency and linewidth phonon shifting. At low temperatures, the degeneracy of the ground-state Kramers doublet is lifted (${\mathrm{\Delta }}_0\sim 36\mathrm{c}{\mathrm{m}}^{-1}$) due to the $\mathrm{S}{\mathrm{m}}^{3+}-\mathrm{M}{\mathrm{n}}^{3+}$ interaction in the ferroelectric phase and strongly enhanced below $T_{\mathrm{C}}\sim 26\mathrm{K}$. The Sm-Mn exchange interaction $J_6$ is determined and compared to that of Gd-Mn interaction in $\mathrm{GdM}{\mathrm{n}}_2{\mathrm{O}}_5$. The Sm magnetic moment $m_{\mathrm{Sm}}\left(T\right)$ and the Sm contribution to the magnetic susceptibility are also evaluated from ${\mathrm{\Delta }}_0\left(T\right)$, indicating that the Sm-Mn interaction is strongly implicated in the magnetic and the ferroelectric orderings below $\sim 26\mathrm{K}$. The study of the $\mathrm{S}{\mathrm{m}}^{3+}$ CF excitations as a function of magnetic field reveals twinning in $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$. This twinning could affect its electric polarization behavior versus magnetic field.

Figure 1

Temperature dependence of the Raman spectra of $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ in $x\left(y^{\prime }{z}^{\prime }\right)x$ and $x$($zz$)$x$ (at 5 K) configurations.

Figure 2

Thermal evolution of the Raman frequency of the $213\mathrm{c}{\mathrm{m}}^{-1}$ (a), $615\mathrm{c}{\mathrm{m}}^{-1}$ (b), $624\mathrm{c}{\mathrm{m}}^{-1}$ (c), $667\mathrm{c}{\mathrm{m}}^{-1}$ (d), and $691\mathrm{c}{\mathrm{m}}^{-1}$ (e) modes and the normalized integrated intensity (b) of the $691\mathrm{c}{\mathrm{m}}^{-1}$ mode in $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$. Dotted lines correspond to the anharmonic behavior. The dashed lines indicate the characteristic temperatures $T_{\mathrm{C}}, T_{\mathrm{N}}, T^{*}$, and $T^{\mathrm{S}}$ defined in the text.

Figure 3

Transmission spectra of $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ as a function of temperature (a), at 4.5, 30, and 100 K, and under applied magnetic field (b) at 0, 5, and 10 T (at 4.2 K).

Figure 4

Absorbance spectra of $\mathrm{S}{\mathrm{m}}^{3+} {}^{6}H_{5/2}\to {}^{6}H_{9/2}$ and ${}^{6}H_{5/2}\to {}^{6}H_{11/2}$ CF transitions as a function of temperature, between 100 and 4.5 K in $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$.

Figure 5

(a) Variation of the splitting ${\mathrm{\Delta }}_0\left(T\right)$ as a function of temperature. (b) Normalized data of the electric polarization Ps and the splitting ${\mathrm{\Delta }}_0\left(T\right)$ with respect to their values at 4.5 K. (c) Temperature dependence of $m_{\mathrm{Sm}}\left(T\right)/m_{\mathrm{Sm}}\left(0\right)$ calculated from ${\mathrm{\Delta }}_0\left(T\right)$ using Eq. (2) and compared to its direct measurements by neutron diffraction.

Figure 6

(a) Magnetic susceptibility of $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ along the $a, b$, and $c$ directions. (b) Samarium contribution to the magnetic susceptibility of $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ calculated according to Eq. (3). (c) Isothermal magnetization curves of $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ at 2 K for $H$ parallel to $a$- and $c$ axes.

Figure 7

Magnetic-field dependence of the $\mathrm{S}{\mathrm{m}}^{3+} {}^{6}H_{5/2}\to {}^{6}H_{9/2}$ and ${}^{6}H_{5/2}\to {}^{6}H_{11/2}$ CF transitions in $\mathrm{SmM}{\mathrm{n}}_2{\mathrm{O}}_5$ at 4.2 K.