Enhanced ferrimagnetism in auxetic ${\text{NiFe}}_2{\text{O}}_4$ in the crossover to the ultrathin-film limit

We investigate the sensitive interplay between magnetic, electronic, and structural properties in the ferrimagnetic oxide ${\text{NiFe}}_2{\text{O}}_4$. Emphasis is placed on the impact of reduced dimensionality in the crossover from bulk-like to ultrathin films. We observed an enhanced saturation magnetization $M_S$ for ultrathin ${\text{NiFe}}_2{\text{O}}_4$ films on ${\text{Nb-SrTiO}}_3$ (001) substrates that co-occurs with a reduced out-of-plane lattice constant under compressive in-plane epitaxial strain. We found a bulk-like cationic coordination of the inverse spinel lattice independent of the ${\text{NiFe}}_2{\text{O}}_4$ film thickness, thus ruling out a cationic inversion that nominally could account for an enhanced $M_S$. Moreover, our study instead uncovers a reduction of the unit cell volume, i.e., an auxetic behavior in ultrathin ${\text{NiFe}}_2{\text{O}}_4$ films.

Figure 1

Schematic representation of the inverse spinel lattice of ${\mathrm{NiFe}}_2{\mathrm{O}}_4$: ${\mathrm{Fe}}^{3+}$ cations (red) are distributed equally across tetra- ($T_d$) and octahedral ($O_h$) lattice sites, while ${\mathrm{Ni}}^{2+}$ cations (green) occupy $O_h$ sites. An antiferromagnetic coupling between the $T_d$ and $O_h$ sites compensates the magnetic moments of the ${\mathrm{Fe}}^{3+}$ cations, which is why only the ${\mathrm{Ni}}^{2+}$ cations account for the net macroscopic magnetization of 2 ${\mu }_B$/f.u. (where f.u. denotes formula units).

Figure 2

$\theta \text{−}2\theta$ scans of the ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ (004) reflection for varying film thickness. The out-of-plane lattice constant $a_{\mathrm{oop}}$ decreases below the bulk value for ultrathin films (see inset).

Figure 3

Details of the in-plane $M\text{−}H$ hysteresis loops of ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ on ${\text{SrTiO}}_3$ (001) recorded at $T=5$ K with a maximum applied field of up to 36 kOe. The inset shows the saturation magnetization $M_S$ as a function of ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ film thickness.

Figure 4

HAXPES spectra of ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ films with varying film thickness recorded at a photon energy of $h\nu =4$ keV. (a) Ni $2p$ core level spectra and references for one monolayer NiO and NiO bulk [30]. (b) Fe $2p$ core level spectra in comparison to model spectra taken from Ref. [31].

Figure 5

XANES spectra of (a) the Ni K edge and (b) the Fe K edge from ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ films with varying film thickness. For comparison a Fe $K$ edge spectrum of zinc ferrite, which exhibits the normal spinel structure, is plotted (reproduced from Ref. [34]). The inset in (b) shows the integrated spectral weight of the Fe K edge pre-edge feature in dependence of the film thickness, where the dotted line represents the bulk value.

Figure 6

Experimental XMCD spectrum from the Fe $L_{2,3}$ edge of the 2-nm-thick ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ film and the corresponding fit. The resulting lattice site occupancy for various film thicknesses is depicted in the inset.