Magnetic Structure and Ordering of Multiferroic Hexagonal ${\mathrm{LuFeO}}_3$

We report on the magnetic structure and ordering of hexagonal ${\mathrm{LuFeO}}_3$ films of variable thickness grown by molecular-beam epitaxy on YSZ (111) and ${\mathrm{Al}}_2{\mathrm{O}}_3$ (0001) substrates. These crystalline films exhibit long-range structural uniformity dominated by the polar $P{6}_{3}cm$ phase, which is responsible for the paraelectric to ferroelectric transition that occurs above 1000 K. Using bulk magnetometry and neutron diffraction, we find that the system orders into a ferromagnetically canted antiferromagnetic state via a single transition below 155 K regardless of film thickness, which is substantially lower than that previously reported in hexagonal ${\mathrm{LuFeO}}_3$ films. The symmetry of the magnetic structure in the ferroelectric state implies that this material is a strong candidate for linear magnetoelectric coupling and control of the ferromagnetic moment directly by an electric field.

Figure 1

Characterization of a 250 nm thick film of $h\text{−}{\mathrm{LuFeO}}_3$ on YSZ (YSZ-250 nm). (a) Schematic of the crystal structure of $h\text{−}{\mathrm{LuFeO}}_3$ with the $P{6}_{3}cm$ space group. (b) XRD at room temperature, with $h\text{−}{\mathrm{LuFeO}}_3$ $00l$ reflections labeled accordingly; substrate peaks are denoted by (*). (c) STEM image along the [110] direction highlighting the positions of the Lu-ions in the “up down down” pattern demonstrating the $P{6}_{3}cm$ structure. (d) Magnetization at 0.01 T under FC (closed circles) and ZFC (open circles) conditions. Inset: high temperature magnetization for magnetic fields 0.01, 0.05, and 0.1 T applied parallel to the $c$ axis.

Figure 2

Raman spectra of 200 nm thick $h\text{−}{\mathrm{LuFeO}}_3$ (YSZ-200 nm) measured at 10 K using both polarizations [14] demonstrating the Raman active phonon modes in the ferroelectric state of $h\text{−}{\mathrm{LuFeO}}_3$. Inset: Normalized Raman intensity of the $A_1$ mode (peak around $650{\mathrm{cm}}^{-1}$) as a function of temperature, solid line is a linear fit over the temperature region $400\mathrm{K}<\mathrm{T}<1050\mathrm{K}$.

Figure 3

Determination of the antiferromagnetic structure using neutron diffraction. The scattered intensity of the magnetic 101 and 100 reflections above and below $T_N$ and temperature dependence for the (a)–(c) YSZ-250 nm and (d)–(f) ${\mathrm{Al}}_2{\mathrm{O}}_3\text{−}200\mathrm{nm}$. (g)–(h) Intensity of the 101 reflection ${\mathrm{Al}}_2{\mathrm{O}}_3\text{−}70\mathrm{nm}$ and ${\mathrm{Al}}_2{\mathrm{O}}_3\text{−}20\mathrm{nm}$, respectively. (i) Temperature dependent intensity of the 101 reflection for films deposited on ${\mathrm{Al}}_2{\mathrm{O}}_3$. Solid lines in (c), (f), and (i) are fits with mean-field order parameter function, while others are Gaussian.

Figure 4

(a)–(d) Illustration of the four one-dimensional representations for $h\text{−}{\mathrm{LuFeO}}_3$. The magnetic structures below $T_R$ are shown in (e) and (f) and consist of combinations of the representations in (a)–(d). Labels in parenthesis refer to the equivalent notation used in Ref. [12], for example.