Multiferroic phase diagram of $E$-type $R{\mathrm{MnO}}_3$ films studied by neutron and x-ray diffraction

We present a generalized multiferroic phase diagram for orthorhombic $R{\mathrm{MnO}}_3\left(R=\mathrm{Gd}–\mathrm{Lu}\right)$ based on coherently grown thin films. The magnetic order was identified by neutron-diffraction and resonant soft x-ray scattering experiments. For large $R$-ions $\left(R=\mathrm{Gd}–\mathrm{Dy}\right)$, the transition temperature to a long-range ordered antiferromagnetic phase is only weakly dependent on the $R$-ion radius, but decreases monotonically with decreasing $R$-ion radius for films with $R=\mathrm{Ho}–\mathrm{Lu}$. The antiferromagnetic phase is characterized by an incommensurate order of the ${\mathrm{Mn}}^{3+}$ spins, which successively locks into a commensurate $E$-type state. These findings confirm a uniform multiferroic ground state independent of the $R$ ion and are in excellent agreement with predicted properties of strain-induced multiferroicity in these materials. In particular, strong variation of multiferroic properties in these epitaxial films compared to bulk highlights the tuning ability of strain.

Figure 1

Experimental geometry for RSXD using linearly polarized incident and scattered light. The scattering wave vector $\mathbf{Q}=(k^{{}^{\prime }}-k)$ is along the $b$ axis, where $k\left(k^{{}^{\prime }}\right)$ is the incoming (outgoing) wave vector of light.

Figure 2

Electron diffraction image of a 100 nm (010)-oriented o-${\mathrm{HoMnO}}_3$ film grown on (010) ${\mathrm{YAlO}}_3$. (a) Diffraction image of a section cut along the (001) in-plane direction. The rows of diffraction spots for the film and substrate are marked with arrows. (b) Diffraction image of a section cut along the (100) in-plane direction. The rows of diffraction spots for the film and substrate are marked with arrows.

Figure 3

Normalized peak intensity of $\left(0q1\right)$ reflection and magnetic modulation wave vector (inset) of (a) ${\mathrm{GdMnO}}_3$, (b) ${\mathrm{TbMnO}}_3$, (c) ${\mathrm{DyMnO}}_3$, (d) ${\mathrm{HoMnO}}_3$, (e) ${\mathrm{TmMnO}}_3$, and (f) ${\mathrm{YbMnO}}_3$. The solid lines are guide to eye and dotted lines (inset) mark the commensurate order at $q_{Mn}=0.5{\mathbf{b}}^{*}$.

Figure 4

Temperature-dependent appearance of the (0 1/2 2) reflection from the normalized peak intensity of ${\mathrm{TbMnO}}_3$. Inset: (0 1/2 2) reflections measured at $T\sim 4\mathrm{K}$ .

Figure 5

Plots showing $q$ scans for $\left(0q1\right)$ magnetic reflections at different temperatures of (a) ${\mathrm{TbMnO}}_3$, (b) ${\mathrm{DyMnO}}_3$, (c) ${\mathrm{HoMnO}}_3$, and (d) ${\mathrm{YbMnO}}_3$.

Figure 6

(a) Magnetic reflections $\left(0q1\right)$ of ${\mathrm{LuMnO}}_3$ measured at $T$ =14 K and 31 K, (b) temperature dependence of $\left(0q1\right)$ peak intensity showing the $T_{\text{N}}$ and (inset) magnetic susceptibility measurements showing $T_{\text{M}}$ from Ref. [25].

Figure 7

(a) Temperature dependence of the magnetic reflection $\left(0q0\right)$ of 10 nm (010)-oriented ${\mathrm{GdMnO}}_3$ film measured using RSXD diffraction. (b) Plot of the temperature-dependent integrated intensity and (inset) the magnetic modulation vector $\left(q\right)$ along the $b$ axis with lowering of temperature derived from the $\left(0q0\right)$ reflections.

Figure 8

Normalized capacitance $\mathrm{[}\mathrm{\Delta }C=\left(C\right(T\left)\text{−}C\right(50\mathrm{K}\left)\right)/C\left(50\mathrm{K}\right)]$ along the $a$ axis under applied magnetic field $\left({\mu }_{o}H\right)$ along the $a$ axis $\left({\mu }_{o}H\parallel P\right)$, and the $c$ axis $\left({\mu }_{o}H\perp P\right)$ for ${\mathrm{GdMnO}}_3$ in (a) and (b), respectively, and for ${\mathrm{LuMnO}}_3$ in (c) and (d), respectively.

Figure 9

Multiferroic phase diagram of $R{\mathrm{MnO}}_3$ showing the $R$ ion radius dependence of magnetic and electric transition temperatures. Values of $T_{\text{M}}$ and $T_{\text{FE}}$ are taken from Ref. [25]. Schematic image of the $E$-type magnetic order of Mn spins in $ab$ plane shown. The atoms are represented by blue (Lu), green (Mn), and red (O) spheres. Magnitude and direction of spin is drawn as a guide to the eye.