Magnetic-field-induced ferroelectric states in centrosymmetric $R_2\mathrm{BaCu}{\mathrm{O}}_5$ ($R=\mathrm{Dy}$ and Ho)

The linear magnetoelectric effect and multiferroicity phenomena occur independently due to breaking inversion symmetry below the magnetically ordered state of either transition metal or rare-earth ions. Here, we report the occurrence of a linear magnetoelectric effect and magnetic field-induced ferromagnetism and ferroelectricity below $T_{\mathrm{N}}^R$ in the orthorhombic green phases $R_2\mathrm{BaCu}{\mathrm{O}}_5$ ($R=\mathrm{Dy}$ and Ho). They undergo a long-range antiferromagnetic ordering of ${\mathrm{Cu}}^{2+}$ ($T_{\mathrm{N}}^{\mathrm{Cu}}=18.5$ and 17.5 K) and $R^{3+}$ ions ($T_{\mathrm{N}}^{\mathrm{Dy}}=10.7\mathrm{K}$ and $T_{\mathrm{N}}^{\mathrm{Ho}}=8\mathrm{K}$). The neutron diffraction study reveals that these compounds undergo a first-order magnetic transition from the high-temperature centrosymmetric antiferromagnetic phase ($P_{\mathrm{b}}{112}_1/n$) to the low-temperature noncentrosymmetric phases $Pn{m}^{\prime }a$ (Dy) and $P{112}_1^{\prime }/a$ (Ho), which allow linear magnetoelectric coupling. This is consistent with field-induced electric polarization, below $T_{\mathrm{N}}^R$, which varies linearly up to ∼1.2 T. Above a critical field $\left(H_{\mathrm{c}}>1.2\mathrm{T}\right)$, both compounds exhibit metamagnetic transitions with magnetization close to the saturation value $M_s \sim 10.1{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ (Dy) and $\sim 11.8{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ (Ho) at 7 T. Above the metamagnetic transition, a new polar state appears with large electric polarization, indicating field-induced ferroelectricity. We discuss the important role of $4f\text{−}3d$ coupling in determining the ground state magnetic structure responsible for the magnetoelectric coupling in both compounds.

Figure 1

(a) Crystal structure of ${\mathrm{Dy}}_2\mathrm{BaCu}{\mathrm{O}}_5$ at 25 K. (b) ${\mathrm{Dy}}_2{\mathrm{O}}_{11}$ blocks are formed by triangular face-shared $\mathrm{Dy}{\mathrm{O}}_7$ polyhedrons. (c) Inequivalent Dy sites with Dy-O-Cu bond angles.

Figure 2

(a) and (d) Left axis: Temperature-dependent DC magnetization measured under 100 Oe in field-cooled (FC) condition. Right axis: Specific heat measured under zero magnetic field. (b) and (e) DC magnetization measured under different magnetic fields. (c) and (f) Isothermal $M$($H$) curves for ${\mathrm{Dy}}_2\mathrm{BaCu}{\mathrm{O}}_5$ and ${\mathrm{Ho}}_2\mathrm{BaCu}{\mathrm{O}}_5$, respectively. Insets show $\mathit{dM}/\mathit{dH}$ vs H.

Figure 3

(a) and (b) Temperature-dependent dielectric constant and corresponding loss measured under different magnetic fields and frequency $f=50\mathrm{kHz}$, respectively. (c) $T$ dependence of pyrocurrent recorded for different magnetic fields with the poling electric field $E=+8.96\mathrm{kV}/\mathrm{cm}$. (d) Polarization is obtained by integrating the pyrocurrent with respect to time. The inset shows magnetic field-dependent polarization. (e) Switching of polarization by changing the direction of the poling electric field measured under 1 and 5 T magnetic fields. (f) Direct current (DC) bias at 1 T, measured in $E\perp H$ for ${\mathrm{Dy}}_2\mathrm{BaCu}{\mathrm{O}}_5$.

Figure 4

(a) and (b) Dielectric constant against temperature measured with frequency $f=50\mathrm{kHz}$ under different magnetic fields and corresponding loss, respectively. (c) and (d) $T-H$-dependent pyrocurrent and electric polarization. (e) The obtained DC bias signal under different magnetic fields. (f) Switching of polarization at 1 and 5 T, for ${\mathrm{Ho}}_2\mathrm{BaCu}{\mathrm{O}}_5$.

Figure 5

Magnetic field dependent (a) derivative of magnetization obtained from $M$ vs $H$ curve at 2 K. (b) Relative dielectric constant measured at $f=50\mathrm{kHz}$. (c) Magnetoelectric current recorded after poling the ${\mathrm{Ho}}_2\mathrm{BaCu}{\mathrm{O}}_5$ sample under electric and magnetic fields. (d) Electric polarization is obtained by integrating the magnetoelectric current.

Figure 6

Magnetoelectric current measured against the magnetic field for both compounds. Left panel: ${\mathrm{Dy}}_2\mathrm{BaCu}{\mathrm{O}}_5$. Right panel: ${\mathrm{Ho}}_2\mathrm{BaCu}{\mathrm{O}}_5$.

Figure 7

Representation of magnetic structure of ${\mathrm{Dy}}_2\mathrm{BaCu}{\mathrm{O}}_5$ at (a) 13 K and (b) 1.5 K (orange = Dy1, purple = Dy2, and blue = Cu). The magnetic moments of Dy1 and Cu atoms for 13 K and Cu for 1.5 K have been multiplied by 2 for display purposes.

Figure 8

The ordered magnetic moments and their components for Dy1, Dy2, and Cu as a function of temperature for ${\mathrm{Dy}}_2\mathrm{BaCu}{\mathrm{O}}_5$.

Figure 9

Representation of the magnetic structures of ${\mathrm{Ho}}_2\mathrm{BaCu}{\mathrm{O}}_5$ at (a) $T$ = 12.0 K (WISH) and (b) 2.3 K (D1B). The magnetic moments of Ho1 and Cu atoms at 12 K and Cu at 2.3 K have been multiplied by 2 for display purposes.

Figure 10

Magnetic moments and their components for atoms Ho1, Ho2, and Cu as a function of temperature for ${\mathrm{Ho}}_2\mathrm{BaCu}{\mathrm{O}}_5$. The refinements have been performed with no contribution of ${\mathrm{mGM}}_3^{-}$ (no $y$ components). In the region of ${\mathbf{k}}_{\mathrm{C}1} \left(T>8\mathrm{K}\right)$, there are single sites (Ho1_1, Ho2_1, and Cu_1), and in the region of two propagation vectors ${\mathbf{k}}_{\mathrm{C}1}+{\mathbf{k}}_{\mathrm{C}2} \left(T<8\mathrm{K}\right)$, the sites of magnetic atoms split into two inequivalent positions (Ho1_1, Ho1_2, Ho2_1, Ho2_2, Cu_1, Cu_2).

Figure 11

Scheme of the H-T phase diagram for $R_2\mathrm{BaCu}{\mathrm{O}}_5$ ($R=\mathrm{Dy}$ and Ho) along with the magnetic structures of ${\mathrm{Dy}}_2\mathrm{BaCu}{\mathrm{O}}_5$ in two phases are shown.