Coexisting multiple order parameters in single-layer $\mathrm{LuMn}{\mathrm{O}}_3$ films

Magnetoelectric multiferroics hold great promise for electrical control of magnetism or magnetic control of ferroelectricity. However, single phase ferroelectric materials with a sizeable ferromagnetic magnetization are rare. Here, we demonstrate that a single-phase orthorhombic $\mathrm{LuMn}{\mathrm{O}}_3$ thin film features coexisting magnetic and ferroelectric orders. The temperature dependence of the different order parameters are presented with ferromagnetic order appearing below 100 K and thus at much higher temperatures than ferroelectricity or antiferromagnetism $(T_{\mathrm{N}},T_{\mathrm{FE}}\le 40\mathrm{K})$.

Figure 1

(a) Muon spin polarization vs time in zero field at 100, 75, 60, 45, and 10 K. The solid lines are fits to the measured data. (b) Temperature dependence of the normalized internal magnetic field $B_{\mathrm{int}}\left(T\right)/B_{\mathrm{int}}\left(5K\right)$ as derived from ZF-μSR muon spin relaxation measurements with low energy muons implanted with 4.1 keV into a 56-nm-thin (110) $\mathrm{LuMn}{\mathrm{O}}_3$ thin film. For comparison, the normalized magnetic moment $\mu \left(T\right)/\mu \left(2\mathrm{K}\right)$ vs $T$ is shown (blue triangle), with µ being proportional to the square root of the integrated neutron intensity. The black dashed lines for the FM and AFM phase are a guide to the eye but also indicate how the temperature dependence of a single order parameter could look like when both orders coexist.

Figure 2

(a) $q$-scans for the AFM ($0\approx 0.5$ 1) Bragg peak of a 400 nm (110) LMO film with an area of 8 × 10 mm measured at different temperatures. (b) Integrated neutron intensity vs temperature for the AFM $(0\approx q_{\mathrm{k}}1)$, $q_{\mathrm{k}}\approx 0.5(\mathrm{r}.\mathrm{l}.\mathrm{u}.)$ (red dots). The magnetic ordering wave vector is $q_{\mathrm{k}}=0.488$ at 1.6 K and $T_{\mathrm{N}}\approx 40\mathrm{K}$. The temperature dependence of $q_{\mathrm{k}}$ is extracted from the same data set (blue square). (c) Susceptibility vs temperature for a 56-nm-thin (110) $\mathrm{LuMn}{\mathrm{O}}_3$ thin film with $H=30\mathrm{mT}$ along $\left[1\overline{1}0\right]$. The AFM transition temperature $T_{\mathrm{N}}$ is $\approx 36\mathrm{K}$. (d) $M$($H$) loops measured at 5, 20, and 40 K for a 56-nm-thin (110) $\mathrm{LuMn}{\mathrm{O}}_3$ thin film with $H$ along $\left[1\overline{1}0\right]$.

Figure 3

(a) Optical photograph of interdigitated electrodes patterned on a (110) oriented $\mathrm{LuMn}{\mathrm{O}}_3$ thin film. The two patterns are aligned along the main in-plane crystallographic axis of the substrate. (b) Remnant electric polarization for a 200 nm (110) $\mathrm{LuMn}{\mathrm{O}}_3$ film. $P$ was measured along the $\left[1\overline{1}0\right]$ in-plane direction with $T_{\mathrm{FE}}\approx 35\mathrm{K}$. In the inset, a $P$($E$) loop measured along $\left[1\overline{1}0\right]$ at 10 K is shown.

Figure 4

Sketch of a ferroic triangle showing the relation and techniques with which the ferroic orders, FM, AFM, and FE, and their mutual coupling have been established. The experimental techniques written in black letters (polarized neutron reflectometry, PNR; resonant soft x-ray diffraction, SXRD; x-ray diffraction, XRD) to identify ferroic properties have been reported elsewhere [22, 24]. Magnetization, susceptibility, $\mu \mathrm{SR}$, neutron diffraction, and electrical polarization are reported in the text.