Interface states in CoFe${}_2$O${}_4$ spin-filter tunnel junctions

Spin-filter tunneling is a promising way to generate highly spin-polarized current, a key component for spintronics applications. In this paper we explore the tunneling conductance across the spin-filter material CoFe${}_2$O${}_4$ interfaced with Au electrodes, a geometry which provides nearly perfect lattice matching at the CoFe${}_2$O${}_4$/Au(001) interface. Using density functional theory calculations we demonstrate that interface states play a decisive role in controlling the transport spin polarization in this tunnel junction. For a realistic CoFe${}_2$O${}_4$ barrier thickness, we predict a tunneling spin polarization of about $-60\%$. We show that this value is lower than what is expected based solely on considerations of the spin-polarized band structure of CoFe${}_2$O${}_4$, and therefore that these interface states can play a detrimental role. We argue that this is a rather general feature of ferrimagnetic ferrites and could make an important impact on spin-filter tunneling applications.

Figure 1

(a) Structural model for the Au/CFO/Au tunnel junction. The magnetic moment direction in each layer is indicated by the arrows. LDOS of (b) bulk CFO, (c) interfacial and (d) middle CFO layers of the Au/CFO/Au tunnel junction, and (e) the surface layer of a standalone (001) CFO slab. The green line represents octahedral Co, the red line octahedral Fe, the blue line tetrahedral Fe, the yellow line O, and the black line total LDOS. The majority- and minority-spin LDOS are displayed in the upper and lower panels, respectively. The vertical dashed lines denote the Fermi energy.

Figure 2

Spin-dependent complex band structure of CFO for ${\mathbf{k}}_{\parallel }=0$ in the Γ→$Z$ direction for majority spin (left panel) and minority spin (right panel). The middle panel shows real bands (black, majority; red, minority spin) for the same direction. The complex bands are connected to the real bands and inherit their symmetry properties. The curvature for complex and real bands is the same at the connecting points due to the analytic properties of the energy dispersion function $E$($k_z$). The dashed green line indicates the position of the Fermi level in the Au/CFO/Au tunnel junction.

Figure 3

(a)–(c) ${\mathbf{k}}_{\parallel }$-resolved majority-spin LDOS (arbitrary units) at (a) $E_F$, (b) $E_F$ $+$ 0.2 eV, and (c) $E_F$ $+$ 0.4 eV for the surface atomic layer in the standalone (001) CFO slab. (d) Integrated LDOS, Δ$n$, in real space for the surface layer of the (001) CFO slab from $E_F$ to $E_F$ $+$ 0.4 eV. Color indicates the density on a plane cutting through the surface Co atoms and the shaded surfaces correspond to a constant density Δ$n$ $=$ 0.05 Å${}^{-3}$.

Figure 4

${\mathbf{k}}_{\parallel }$-resolved majority-spin LDOS (arbitrary units) at the Fermi energy for (a) interfacial and (b) middle CFO layers in a Au/CFO/Au tunnel junction.

Figure 5

${\mathbf{k}}_{\parallel }$-resolved transmission at $E_F$ for (a) majority-spin channels and (b) minority-spin channels of the Au/CFO/Au tunnel junction. The lowest decay rate κ of the (c) majority-spin and (d) minority-spin evanescent states of bulk CFO as a function of ${\mathbf{k}}_{\parallel }$ in the 2D BZ at VBM $+$ 0.4 eV.