Tuning the Néel Temperature of Hexagonal Ferrites by Structural Distortion

To tune the magnetic properties of hexagonal ferrites, a family of magnetoelectric multiferroic materials, by atomic-scale structural engineering, we studied the effect of structural distortion on the magnetic ordering temperature ($T_N$) in these materials. Using the symmetry analysis, we show that unlike most antiferromagnetic rare-earth transition-metal perovskites, a larger structural distortion leads to a higher $T_N$ in hexagonal ferrites and manganites, because the $K_3$ structural distortion induces the three-dimensional magnetic ordering, which is forbidden in the undistorted structure by symmetry. We also revealed a near-linear relation between $T_N$ and the tolerance factor and a power-law relation between $T_N$ and the $K_3$ distortion amplitude. Following the analysis, a record-high $T_N$ (185 K) among hexagonal ferrites was predicted in hexagonal ${\mathrm{ScFeO}}_3$ and experimentally verified in epitaxially stabilized films. These results add to the paradigm of spin-lattice coupling in antiferromagnetic oxides and suggests further tunability of hexagonal ferrites if more lattice distortion can be achieved.

Figure 1

(a) Atomic structure of $h\text{−}R{\mathrm{FeO}}_3$ depicted by a hexagonal unit cell. The arrows through the Fe atoms indicate the spins. The arrows from the atoms indicate the atomic displacements of the $K_3$ lattice distortion. The table indicates the hexagonal stacking. (b) The geometric arrangement of Fe atoms in the $z=0$ and $z=c/2$ layers. The arrows through the Fe atoms indicate the spins. The atom ${\mathrm{Fe}}_0$ is highlighted by its ${\mathrm{FeO}}_5$ trigonal bipyramid to depict the local symmetry. (c) $\log \{T_N/[S(S+1)]/K\}$ as a function of $\log (Q_{K_3})$. Inset: $T_N/[S(S+1)]$ as a function of the tolerance factor. The dashed line is a linear fit to the data. The data are from the literature (see text).

Figure 2

Structural and magnetic characterizations of $h$-${\mathrm{ScFeO}}_3(001)/{\mathrm{Al}}_2{\mathrm{O}}_3$ films. (a) $\theta /2\theta$ x-ray (1.789 Å) diffraction. (b) and (c) are the RHEED diffraction patterns measured when the electron beam are along the (1-10) and (100) directions respectively. (d) X-ray absorption spectra measured at the Fe $L$ edges using $s$ (in plane) and $p$ (out of plane) linearly polarized x-ray beams. (e) A slice of the reciprocal space of $h$-${\mathrm{ScFeO}}_3$ at $L=1$ measured using neutron diffraction at CORELLI (see text). (f) Temperature dependence of the neutron diffraction intensities of the (101) and (114) peaks measured at CORELLI and HB3A. (g) Temperature dependence of the magnetization per formula unit (f.u.) measured during warming after field cool (10 kOe) and zero field cool using 100 Oe and 500 Oe. (h) Magnetization-field hysteresis loop measured at 100 K. The magnetic field is along the film normal direction.

Figure 3

(a) The dependence of $T_N$ and $T_N/S(S+1)$ on the tolerance factor. The dashed line is a guide to the eye. (b) The magnetization from the canting of Fe spins ($M_{\text{Fe}}$) as a function of the in-plane lattice constant. Except for $h$-${\mathrm{YbFeO}}_3$ and $h$-${\mathrm{ScFeO}}_3$ in (a) and $h$-${\mathrm{ScFeO}}_3$ in (b), the data are from the literature (see text).