Domain-wall magnetoresistance of Co nanowires

Using density functional theory implemented within a tight-binding linear muffin-tin orbital method we perform calculations of electronic, magnetic, and transport properties of ferromagnetic free-standing fcc Co wires with diameters up to 1.5 nm. We show that finite-size effects play an important role in these nanowires resulting in oscillatory behavior of electronic charge and the magnetization as a function of the wire thickness, and a nonmonotonic behavior of spin-dependent quantized conductance. We calculate the magnetoresistance (MR) of a domain wall (DW) modeled by a spin-spiral region of finite width sandwiched between two semi-infinite Co wire leads. We find that the DW MR decreases very rapidly, on the scale of a few interatomic layers, with the increasing DW width. The largest MR value of about 250% is predicted for an abrupt DW in the monatomic wire. We show that, for some energy values, the density of states and the conductance may be nonzero only in one spin channel, making the MR for the abrupt DW infinitely large. We also demonstrate that for the abrupt DW a large MR may occur due to the hybridization between two spin subbands across the DW interface. We do not find, however, such a behavior at the Fermi energy for the Co wires considered.

Figure 1

Cross section of the $5\times 4$ wire representing a periodically repeated super cell of two fcc (001) layers with five (white) and four (gray) Co atoms in each layer.

Figure 2

(a) Density of states for monatomic Co wire for majority- (the top panel) and minority- (the bottom panel) spin electrons as a function of energy. The dotted curve is the $s\text{−}p$ partial DOS scaled up by a factor of 10 to make it visible. (b) Conductance of a ferromagnetic wire as a function of energy for majority- and minority-spin channels. (c) Conductance of the abrupt DW as a function of energy. The Fermi energy is denoted by the dashed vertical line.

Figure 3

Domain-wall magnetoresistance as function of the domain-wall width $d_{\mathrm{DW}}$ in units of the interlayer separation, for a monatomic (triangles), $2\times 2$ (squares), and $5\times 4$ (circles) wires.

Figure 4

Transmission coefficient (solid line) and magnetoresistance (dashed line) of an abrupt DW between two half-metallic electrodes with the magnetization direction rotated by angle $\theta$ as predicted by a one-dimensional single-band tight-binding model in a narrow band limit. Note that the MR is defined here by $\mathrm{MR}=({\Gamma }_0-{\Gamma }_{\mathrm{DW}})∕{\Gamma }_0$ so that the maximum MR value is equal to unity.

Figure 5

(a) Density of states for $2\times 2$ Co wire for majority- (the top panel) and minority- (the bottom panel) spin electrons as a function of energy. (b) Conductance of a ferromagnetic wire as a function of energy for majority- and minority-spin channels. (c) Conductance for the abrupt DW configuration as a function of energy. The vertical arrow shows the energy at which the conductance through the abrupt DW is strongly suppressed.

Figure 6

Results of a two-band tight-binding model: (a) Density of states for minority- (the top panel) and majority- (the bottom panel) spin electrons as a function of energy. (b) Conductance for minority- and majority-spin channels as a function of energy. (c) Conductance for the abrupt DW as a function of energy.