Electron-electron interaction in carbon-coated ferromagnetic nanowires

We have investigated the low temperature resistance behavior and the magnetoresistance of single-domain cobalt nanowires of various thicknesses ranging between $5\mathrm{nm}$ and $32\mathrm{nm}$ and wire widths ranging down to $32\mathrm{nm}$. The nanowires are coated with insulating carbon on three sides to prevent oxidation. Magnetic force microscopy investigations show that nanowires with widths below $800\mathrm{nm}$ are in a single-domain-like remanence state. The magnetoresistance is negative and is well explained by the anisotropic magnetoresistance (AMR). At low temperatures $T<30\mathrm{K}$ a logarithmic resistance increase is observed with decreasing temperature, which is consistently explained as originating from enhanced electron-electron interactions in two dimensions. Quantum corrections due to weak electron localization are not observed which is in contrast to recent theoretical predictions for two-dimensional ferromagnetic systems. However, the results are consistent with our earlier results obtained for platinum-capped and unprotected cobalt nanowires. A reduction of the wire width below about $400\mathrm{nm}$ yields a crossover behavior from two-dimensional to one-dimensional behavior with respect to the quantum corrections of the resistance.

Figure 1

(Color online) Magnetic force microscopy (MFM) images taken at remanence for two carbon-covered cobalt nanowires of different width but the same thickness of $20\mathrm{nm}$. Both wires were magnetically saturated prior to imaging within a magnetic field of $B=2\mathrm{T}$ applied longitudinally. While the upper wire $(w=2.16\mu \mathrm{m})$ is in a multidomainlike magnetic state at remanence, the narrow wire ($w=400\mathrm{nm}$, lower image) is in a single-domain-like state.

Figure 2

(Color online) Perpendicular magnetoresistance (MR) of a Co nanowire with width $w=225\mathrm{nm}$ covered with a $10\mathrm{nm}$ carbon layer. The MR continuously decreases until it reaches a saturation value of about –0.8% due to the anisotropic magnetoresistance (AMR). The absolute value of the resistance in a zero magnetic field is $R_0=10395\Omega$. The inset shows the perpendicular MR for a carbon-covered cobalt nanowire with a width of $35\mathrm{nm}$ measured at temperatures of $T=4.2\mathrm{K}$ and $T=240\mathrm{mK}$. Both measurements are identical and up to magnetic fields of $B=11\mathrm{T}$; no other contribution other than the AMR effect is observed.

Figure 3

(Color online) Resistance of a cobalt wire with a thickness of $20\mathrm{nm}$ and a width of $5.2\mu \mathrm{m}$ as a function of the logarithm of the temperature for various magnetic fields applied perpendicular to the substrate plane. While the slope of the different curves remains constant the absolute values of the resistance decrease due to the AMR effect (note the break in the $R$ axis). The full line represents a fit according to the theory for enhanced electron-electron interactions in two dimensions (Refs. 33, 34).

Figure 4

(Color online) Logarithmic slope of the $R\left(\ln T\right)$ behavior, as determined over one decade of temperature, as a function of a magnetic field applied in the $z$ direction for two Co wires with different widths as indicated. No magnetic field dependence of $\Delta G\left(10\right)$ is observed, proving that this resistance contribution results from electron-electron interaction effects rather than from WEL effects. The error bar is of the order of the dot size.

Figure 5

(Color online) Resistance of a cobalt nanowire with a thickness of $20\mathrm{nm}$ and a width of $40\mathrm{nm}$ as a function of the logarithm of the temperature for various magnetic fields applied perpendicular to the substrate plane. The slope of the resistance versus temperature remains constant for various external magnetic fields up to $B=4\mathrm{T}$. The full line represents a fit according to the theory for enhanced electron-electron interactions in one dimension (Refs. 33, 34).

Figure 6

Slope $\Delta G\left(10\right)$ of the resistance increase for a variety of carbon-covered cobalt nanowires as a function of the wire width. The logarithmic scale of the abscissa was chosen for the sake of a better presentation. Starting from the two-dimensional limit of $\Delta G\left(10\right)\approx 2.75\times {10}^{-5}◻∕\Omega$ values of $\Delta G\left(10\right)$ continuously increase with decreasing wire width. The full line is only a guide for the eye.

Figure 7

Electronic diffusion constant $D$ as a function of the wire width as obtained from a fit of Eq. (2) to the resistance versus temperature. In the two-dimensional limit $D$ is given by $D=\frac{1}{3}{v}_F{l}_e=3.5\times {10}^{-3}{\mathrm{m}}^2∕\mathrm{s}$ where $v_F=1.5\times {10}^6\mathrm{m}∕\mathrm{s}$ is the Fermi velocity of cobalt and $l_e=7\mathrm{nm}$ the elastic mean free path (dashed line). The dotted line is a guide for the eye and indicates the decrease of $D$ with decreasing wire width $w$.

Figure 8

(Color online) Resistance of an iron nanowire with a thickness of $30\mathrm{nm}$ and a width of $2.16\mu \mathrm{m}$ as a function of the logarithm of the temperature for various magnetic fields applied perpendicular to the sample plane. The slope of the curves remains constant while the absolute resistance decreases due to AMR.