Unusual ferrimagnetism in ${\mathrm{Ca}{\mathrm{Fe}}_2\mathrm{O}}_4$

Incomplete cancellation of collinear antiparallel spins gives rise to ferrimagnetism. Even if the oppositely polarized spins are owing to the equal number of a single magnetic element having the same valence state, in principle, a ferrimagnetic state can still arise from the crystallographic inequivalence of the host ions. However, experimental identification of such a state as “ferrimagnetic” is not straightforward because of the often tiny magnitude expected for $M$ and the requirement for a sophisticated technique to differentiate similar magnetic sites. We report a synchrotron-based resonant x-ray investigation at the Fe $L_{2,3}$ edges on an epitaxial film of $\mathrm{Ca}{\mathrm{Fe}}_2{\mathrm{O}}_4$, which exhibits two magnetic phases with similar energies. We find that while one phase of $\mathrm{Ca}{\mathrm{Fe}}_2{\mathrm{O}}_4$ is antiferromagnetic, the other one is ferrimagnetic with an antiparallel arrangement of an equal number of spins between two distinct crystallographic sites with very similar local coordination environments. Our results further indicate two distinct origins of an overall minute $M$; one is intrinsic, from distinct ${\mathrm{Fe}}^{3+}$ sites, and the other one is extrinsic, arising from defective ${\mathrm{Fe}}^{2+}$ likely forming weakly coupled ferrimagnetic clusters. These two origins are uncorrelated and have very different coercive fields. Hence, this work provides a direct experimental demonstration of ferrimagnetism solely due to crystallographic inequivalence of the ${\mathrm{Fe}}^{3+}$ as the origin of the weak $M$ of $\mathrm{Ca}{\mathrm{Fe}}_2{\mathrm{O}}_4$.

Figure 1

Magnetic structures of $\mathrm{Ca}{\mathrm{Fe}}_2{\mathrm{O}}_4$ in (a) the $A$ phase and (b) the $B$ phase, where orange and blue spheres represent ${\mathrm{Fe}}^{3+}$ having a magnetic moment pointing to $+\mathbf{b}$ and $-\mathbf{b}$, respectively, and (c) its phase sequence for powder samples (up) [9] and for single-crystal samples (down) [8]. A number written on the spheres denotes the Fe sites, either Fe1 or Fe2. (a) and (b) were drawn by vesta [31].

Figure 2

(a) Schematic representation of the $\mathrm{Ca}{\mathrm{Fe}}_2{\mathrm{O}}_4$ film orientation grown on a $\mathrm{Ti}{\mathrm{O}}_2$ substrate, adapted from Ref. [10]. There are different crystallographic domains present, and the surface normal is either [001] or [302] oriented. Experimental setup for (b) REXS and (c) XMCD measurements. The (001) reflection appears around $\sim {55}^{\circ }$ of $\theta$ at the Fe $L_3$ edge. For the XMCD measurements, we employed grazing incidence of x rays around ${30}^{\circ }$, enabling us to examine magnetization along [010].

Figure 3

(a) REXS profiles of the (001) reflection with the Laue oscillations due to the finite sample thickness, taken at various temperatures. (b) Temperature dependence of (001) integrated intensities, and (c) photon-energy dependence while maintaining the diffraction condition for the (001) reflection at various temperatures. (a) and (b) were taken at the photon energy of 710.8 eV.

Figure 4

Two-dimensional maps of (001) intensities taken at (a) 40, (b) 100, (c) 150, and (d) 200 K, with the photon energy of 710.25 eV. Intensities are normalized by those of the 200 K data at (e) 40, (f) 100, and (g) 150 K. These maps were taken in the region surrounded by a white box in (h). Black areas in (a)–(g) lie outside of the sample, and gray dashed lines indicate the sample outline, which has been cut at the bottom-right corner for better recognition of sample orientation.

Figure 5

(a) XAS and (b) XMCD taken at 30 K (red) and 150 K (black). XAS is obtained as the sum of two data with opposite helicity of circular polarization $\left(C+/C-\right)$ and is normalized to its highest peak, whereas XMCD is obtained as the difference between $C+$ and $C-$.

Figure 6

History dependence of XMCD spectra taken at 150 K after zero-field cooling (ZFC) directly from room temperature (green) compared with the XMCD at 150 K after ZFC to 2 K, magnetic cycling (±6 T), and warming in $+6$ T (black). The black data are the same as Figs. 5 and 7.

Figure 7

XMCD spectra taken at (a) 30 K and 6 T, and (b) 150 K and 6 T, which are reproduced by two contributions from different ${\mathrm{Fe}}^{3+}$ sites except for the minor feature at low energy, as found in (c) and (d). Broken curves correspond to calculated respective contributions to the spectra while a red curve corresponds to the sum of the contributions. (e) Sketch representing the growth of the $A$ phase and resultant decrease in total magnetization.

Figure 8

Magnetic-field dependence of the XMCD signals at (a) 150 and (b) 30 K. Hysteresis curve for ${\mathrm{Fe}}^{3+}$ (1) and ${\mathrm{Fe}}^{3+}$ (2) at (c) 30 and (d) 150 K obtained from fits with calculated spectra to (a) and (b).