Anisotropic Band-Split Magnetism in Magnetostrictive CoFe$_2$O$_4$

TL;DR

This work investigates the magnetoelastic origin of magnetostriction in the ferrimagnetic spinel $CoFe_{2}O_{4}$ by combining neutron diffraction and inelastic neutron scattering with theory. It finds a large magnon band splitting of about $\sim 60$ meV and a small uniaxial anisotropy gap of about $\sim 3$ meV, arising from strong inter-sublattice exchange and trigonal local distortions. The authors develop an averaged linear spin-wave model and an effective $S=1$ description that capture the two magnon branches and reveal how a ferrimagnetic molecular field locks moments to structural domain axes, favoring domain switching and enhancing magnetostriction. They also examine how site disorder and finite tetragonal distortions modulate the spectrum and discuss implications for spintronic devices and spin Seebeck effects.

Abstract

Single crystal spinel CoFe$_2$O$_4$ exhibits the largest room-temperature saturation magnetostriction among non-rare-earth compounds and a high Curie temperature ($T_c \sim 780$ K), properties that are critical to a wide range of industrial and medical applications. Neutron spectroscopy reveals a large band splitting ($\sim$ 60 meV) between two ferrimagnetic magnon branches, which is driven by site mixing between Co$^{2+}$ and Fe$^{3+}$ cations, and a significantly weaker magnetocrystalline anisotropy ($\sim$ 3 meV). Central to this behavior is the competition between extremely large mismatched molecular fields on the tetrahedral $A$-site and octahedral $B$-site sublattices and the single-ion anisotropy on the $B$-site. This creates a strong energetic anisotropy that locks the magnetic moment within each structural domain in place. As a result of these differing energy scales, switching structural domains is energetically favored over a global spin reorientation under applied magnetic fields, and this is what amplifies the magnetostrictive nature of CoFe$_2$O$_4$.

Figures (9)

• Figure 1: (a) View along [111] of the CoFe2O4 inverse spinel structure: space group $Fd\overline{3}m$ (227). The Co and Fe cations occupy tetrahedral $A$ and octahedral $B$ sites. (b) Two possible magnetic structures consistent with the neutron diffraction data. The red and grey colors represent the two distinct magnetic sublattices. (c-d) Neutron diffraction (DMC,PSI) patterns measured above (900 K) and below (1.6 K) the transition temperature $T_c \sim 780$ K. Solid red lines represent the Rietveld refinement using Fullprof software. rodriguez2001 The large dotted oval highlights the large change in the (111) Bragg peak intensity across $T_c$.
• Figure 2: (a) Temperature dependence (Smartlab, Edinburgh) of the lattice constant measured with x-ray diffraction. Note that all refinements were done using the cubic $Fd\overline{3}m$ space group. (b) Temperature dependence of the (111) Bragg peak integrated intensity, which is almost entirely magnetic, obtained from the DMC (PSI) neutron diffractometer (see Figs. 1 $c,d$). The onset of magnetic order coincides with a change in the curvature of the thermal expansion. (c) Rietveld refinement of the X-ray SmartLab data measured at 973 K.
• Figure 3: (a) Anisotropy gap at low energy measured on MERLIN. Data have been integrated $\pm 0.1$ r.l.u perpendicular to the slice direction. Intensities, $I$, given in arbitrary units. (b) Unsymmetrized constant-energy slice at $E = 40 \pm 2$ meV. (c) Constant-energy slices (integrated $\pm 2$ meV) through the symmetrized data measured with $E_i =75$ meV. (d) Spin-wave dispersion of the lower magnon mode measured on MERLIN, integrated $\pm 0.1$ r.l.u perpendicular to the slice direction. (e) Data from MAPS showing the upper magnon mode, integrated $\pm 0.1$ r.l.u perpendicular to the slice direction. $(\mathbf{Q},E)$ slices have been background subtracted.
• Figure 4: Evidence for anti-crossing of magnons near 75 meV. Gaussian-fitted dispersion peaks are overlaid and shown as crosses. A discontinuity in the dispersion curve is visible around $H =0.25$ r.l.u. Data have been integrated $\pm 0.1$ r.l.u perpendicular to the slice direction.
• Figure 5: Comparison of the fitted model convolved with a Lorentzian kernel with a full width at half maximum (FWHM) of 8 meV (right) with the MAPS data (left). Measured data have been integrated $\pm 0.1$ r.l.u perpendicular to the slice direction. Over-plotted in red is the dispersion of the model with an opacity proportional to the dynamical structure factor.