Evidence of multiferroicity in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$

Recently, $R{\text{Mn}}_2{\text{O}}_5$ ($R=\text{rare}$ earth, $\text{Bi}, \text{Y}$) type multiferroics have drawn considerable attention, because of magnetically induced ferroelectricity along with an extremely large magnetoelectric coupling. Here, we present a detailed study on ${\text{NdMn}}_2{\text{O}}_5$ which is a crucial composition between the nonferroelectric ${\text{PrMn}}_2{\text{O}}_5$ and ferroelectric ${\text{SmMn}}_2{\text{O}}_5$. We report the results of heat capacity, magnetization, dielectric permittivity, and electric polarization measurements along with an accurate description of the structural and microscopic magnetic properties obtained from high resolution x-ray and neutron diffraction studies. We show that ${\text{NdMn}}_2{\text{O}}_5$ is ferroelectric, although the magnitude of polarization is much weaker than that of the other multiferroic members. The direction of the polarization is along the crystallographic $b$ axis and its magnitude can be tuned with the application of a magnetic field. Moreover, unlike the other multiferroic members of this series, ferroelectricity in ${\text{NdMn}}_2{\text{O}}_5$ emerges in an incommensurate magnetic state. The present study also provides evidence in support of the influence of the rare-earth size on the magnetoelectric phase diagram.

Figure 1

(a) A perspective view of the crystal structure of $R{\text{Mn}}_2{\text{O}}_5$. Magnetic exchange interactions ($J_i$) (b) in the $(a,b)$ plane and (c) along the $c$ direction. (d) A magnified representation of ${\text{Mn}}^{4+}{\text{O}}_6$ octahedron and ${\text{Mn}}^{3+}{\text{O}}_5$ square pyramid.

Figure 2

Thermal variation of the heat capacity ($C_p$) over temperature ($T$) for the platelike and (inset) needlelike crystals.

Figure 3

(a) Temperature ($T$) dependence of magnetization ($M$) for the powder sample measured in zero field cooled heating (ZFCH), field cooled cooling (FCC), and field cooled heating (FCH) protocols with an applied magnetic field of 100 Oe. Inset: Curie-Weiss fitting of the inverse susceptibility data as a function of temperature. (b) ZFCH $M\left(T\right)$ data of the powder sample emphasizing the anomaly at $T_{3P}$. Inset: $M\left(H\right)$ curves measured at 32 and 45 K. (c) Low field region of the $M\left(H\right)$ curves to show the hysteresis effect. (d) Zero field cooled $M\left(T\right)$ data of the platelike crystal measured along three different crystallographic axes with a field of 1 kOe. (e) $M\left(T\right)$ data along the $a$ direction for the same type of crystal emphasizing the magnetic transition. Inset: Curie-Weiss fitting of the inverse susceptibility data as a function of temperature.

Figure 4

Temperature dependence of the real part of dielectric permittivity (${\epsilon }^{\prime }$) for both (a) powder and (b) platelike crystal (along $b$). The inset of (a) shows the presence of thermal hysteresis in ${\epsilon }^{\prime }$ of the powder sample. The thermal variation of the imaginary part of the dielectric permittivity (${\epsilon }^{\prime \prime }$) for the platelike crystal measured at 100 kHz along the $b$ axis is depicted in the inset of (b). The background is unknown and has not been subtracted from the measured dielectric data. Thermal variations of the pyroelectric current are shown for the (c) powder and (d) platelike crystal (along $b$). For the crystal, data have been shown for measurements performed in zero magnetic field as well as with a field of 90 kOe. Electric polarization ($P$) of the powder sample as a function of $T$ measured in zero magnetic field is shown in (e), whereas (f) depicts the temperature variation of $P$ along the $b$ direction for the platelike crystal measured in zero magnetic field as well as with a field of 90 kOe.

Figure 5

Powder x-ray diffraction patterns recorded at 35 K (represented along with Rietveld refinement) and 3 K using synchrotron based radiation at the CRISTAL beam line (Soleil, France).

Figure 6

Color mapping of the NPD patterns collected between 30 and 2 K. The white, red, and green arrows indicate the magnetic reflections corresponding to $q_1$ (also $q_2$), $q_{\text{CM}}$, and $3q_1$ propagation vectors, respectively.

Figure 7

(a) Single-crystal neutron diffraction at 15 K by scanning along the $c^{*}$ direction to show the presence of magnetic reflection associated with two close but different propagation wave vectors $q_1$ and $q_2$. Solid lines are fits to the peaks with two Gaussian functions along with a background term. (b) Thermal variation of the integrated intensities of various magnetic reflections obtained from NPD. Here, solid lines have been used as a guide to the eye.

Figure 8

Magnetic and electric phase diagram of ${\text{NdMn}}_2{\text{O}}_5$ powder. Here, PM, ICM, CM, PE, and FE are abbreviated forms used to denote paramagnetic, incommensurate magnetic, commensurate magnetic, paraelectric, and ferroelectric states, respectively. The magnetic wave vectors ($q_1, q_2$, and $q_{\text{CM}}$) corresponding to each magnetic phase have been mentioned in parentheses.

Figure 9

(a) Rietveld refinement (experimental data: red squares; calculated profile: black solid line; allowed nuclear reflections: blue vertical marks; allowed magnetic reflections: green vertical marks) of the NPD data recorded at 15 K in the ICM2 phase. The difference between the experimental and the calculated profiles is depicted at the bottom of the graph. The inset depicts the magnetic structure as obtained from the refinement of the NPD data.