Probing the role of ${\mathrm{Nd}}^{3+}$ ions in the weak multiferroic character of ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ by optical spectroscopies

Raman and infrared spectroscopies are used as local probes to study the dynamics of the Nd-O bonds in the weakly multiferroic ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ system. The temperature dependence of selected Raman excitations reveals the splitting of the Nd-O bonds in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$. The ${\mathrm{Nd}}^{3+}$ ion crystal field (CF) excitations in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ single crystals are studied by infrared transmission as a function of temperature, in the $1800-8000{\mathrm{cm}}^{-1}$ range, and under an applied magnetic field up to 11 T. The frequencies of all ${}^4{I}_j$ CF levels of ${\mathrm{Nd}}^{3+}$ are determined. We find that the degeneracy of the ground-state Kramers doublet is lifted (${\mathrm{\Delta }}_0\sim 7.5{\mathrm{cm}}^{-1}$) due to the ${\mathrm{Nd}}^{3+}\text{−}{\mathrm{Mn}}^{3+}$ interaction in the ferroelectric phase, below $T_C\sim 28\mathrm{K}$. The ${\mathrm{Nd}}^{3+}$ magnetic moment $m_{\mathrm{Nd}}\left(T\right)$ and its contribution to the magnetic susceptibility and the specific heat are evaluated from ${\mathrm{\Delta }}_0\left(T\right)$ indicating that the ${\mathrm{Nd}}^{3+}$ ions are involved in the magnetic and the ferroelectric ordering observed below $\sim 28\mathrm{K}$. The Zeeman splitting of the excited CF levels of the ${\mathrm{Nd}}^{3+}$ ions at low temperature is also analyzed.

Figure 1

The temperature dependence of the Raman spectra of ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ in the $x$($y^{\prime }{z}^{\prime }$)$x$. Inset: the Raman spectra of ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ at 5 K measured in the $x$($zz$)$x$ and $x$($yz$)$x$ configurations.

Figure 2

Temperature dependence of the Raman frequency (a), the normalized integrated intensity (b) and the FWHM (c) of the 214, 601, 622, 653, and $681{\mathrm{cm}}^{-1}$ modes in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$. The dotted lines correspond to the expected anharmonic behavior. The characteristic temperatures $T_{\mathrm{C}}$, $T_{\mathrm{N}}$, $T^{*}$, and $T^{\mathrm{S}}$ are defined in the text.

Figure 3

(a) Temperature dependence of the magnetic susceptibility M/H of a ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ single crystal measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions with an applied magnetic field of 500 Oe along the $a$ and the $c$ axis. Inset: The Curie-Weiss fitting of their inverse susceptibility as a function of temperature. (b) and (c) present the derivative of χ along the $c$ and the $a$ axis, respectively. (d) Isothermal $M\left(H\right)$ curves measured along the $a$ axis (for 2 and 8 K) and the $c$ axis (for 2 K). Inset: The derivative of $M\left(H\right)$ curve measured along the $c$ axis.

Figure 4

(a) Transmission spectra of ${\mathrm{Nd}}^{3+}{}^4{I}_{9/2}{\to }^4{I}_{11/2}$, ${}^4{I}_{13/2}$, and ${}^4{I}_{15/2}$ CF transitions in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ at 4.5 K. (b) The temperature dependence of the ${\mathrm{Nd}}^{3+}{I}_{9/2}\to I_{13/2}$ CF transitions in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$. * indicates a saturated excitation.

Figure 5

Magnetic field dependence of the ${\mathrm{Nd}}^{3+}{I}_{9/2}\to I_{11/2}$ (a), $I_{9/2}\to I_{13/2}$ (b), and $I_{9/2}\to I_{15/2}$ (b) CF transitions in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ at 4.2 K. * indicate saturated excitations.

Figure 6

(a) The temperature dependence of the absorption bands ($\sim 3920{\mathrm{cm}}^{-1}$) for the $f\text{−}f$ transitions of ${\mathrm{Nd}}^{3+}$ in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$. (b) and (c) present the temperature dependence of the frequency and the FWHM of the $3920{\mathrm{cm}}^{-1}$ CF excitation between 275 and 30 K, respectively. (d) presents a schematic of the splitting of the ${\mathrm{Nd}}^{3+}$ ground-state and excited level of the Kramers doublet. Arrows show the observed absorption lines.

Figure 7

Absorbance maps of ${\mathrm{Nd}}^{3+}{I}_{\mathbf{9}/\mathbf{2}}\to I_{\mathbf{13}/\mathbf{2}}$ CF transitions as a function of temperature (a), between 45 and 4.5 K, and magnetic field (b), where the empty white squares indicate the CF frequency levels of the ${}^4{I}_{\mathbf{13}/\mathbf{2}}$ multiplet. * indicates a saturated excitation. The notations PM, PE, ICM, CM, and FE are used to represent paramagnetic, paraelectric, incommensurate magnetic, commensurate magnetic, and ferroelectric states.

Figure 8

(a) The variation of the splitting ${\mathrm{\Delta }}_0\left(T\right)$ as a function of temperature. (b) The temperature dependence of $m_{\mathrm{Nd}}\left(T\right)/m_{\mathrm{Nd}}\left(0\right)$ calculated from ${\mathrm{\Delta }}_0\left(T\right)$ using Eq. (1). (c) and (d) represent the neodymium contribution to the magnetic susceptibility and the specific heat of ${\mathrm{NdMn}}_2{\mathrm{O}}_5$, calculated according to Eqs. (2) and (3) (blue filled circles) and compared with direct measurements (red filled circles) of magnetic susceptibility ($\mathrm{H}\parallel \mathrm{a}$) and the specific heat (taken from the Ref. [17]). Inset: difference in susceptibility ${\chi }_{\mathrm{NdMn}2\mathrm{O}5}\left(T\right)-{\chi }_{\mathrm{Nd}}\left(T\right)$ corresponding to the Mn contribution to the magnetic susceptibility.