Magnetoresistance ratio of a point-like contact with a 1 nm wide domain wall at different MFP asymmetries

Abstract

This work presents a unified theoretical framework for spin-resolved electron transport in magnetic point contacts (PCs) in nanoscale dimensions. This work advances existing research by presenting a model which seamlessly transitions between Sharvin ballistic and Maxwell-Holm diffusive limits across the wide range of relevant contact sizes without incorporating empirical fitting factors. We analyzed the magnetoresistance (MR) of magnetic PCs formed with two ferromagnetic monodomains that may have parallel and antiparallel magnetization alignment, forming a constrained domain wall approximately 1.0 nm wide. The calculated MR exhibits strong dependence on scaling parameter (normalized contact radius), ratios of spin-dependent mean free paths, and Fermi wave-vectors. Furthermore, the calculated MR exhibits physically meaningful behavior over a wide range of spin-asymmetry parameters. In most regimes, the MR decreases with increasing normalized point-contact radius, becoming negative at some conditions. These results demonstrate that nanoscaled magnetic PCs have great efficiency in terms of magnetoresistnace change and promising for application due to their simplicity.

Figures (2)

• Figure 1: The schematic view of a PC with a chemical potential drop, depicted by a dashed red curve. The contact area is shown within a dotted rectangle. An electron with an initial $p_{F,\alpha }^L$ and trajectory angle $\theta_{L,\alpha }$ transmits through orifice, resulting in a $p_{F,\alpha }^R$ and $\theta_{R,\alpha}$.
• Figure 2: Dependence of MR ratio on the normalized contact radius for different MFP asymmetry: a) $R_{ \downarrow }^{L} =l_{\downarrow}^{L}/l_{\uparrow}^{L} = 5.0$, $R_{R \downarrow }^{L} =l_{\downarrow}^{L}/l_{\downarrow}^{R}= 1.0;$ b) $R_{ \downarrow }^{L} = 2.0$, $R_{R \downarrow }^{L} = 1.0;$ c) $R_{ \downarrow }^{L} = 1.0$, $R_{R \downarrow }^{L} = 1.0,$ and d) $R_{ \downarrow }^{L} = 5.0$, $R_{R \downarrow }^{L} = 3.0$, where $R_{\downarrow }^{R} =l_{\downarrow}^{R}/l_{\uparrow}^{R}= 5.0, 2.0, 1.0, 0.5, \text{and}~0.2$ nm is set for curve 1 to curve 5, respectively, for each panel. For example, assuming $l_{\uparrow}^{L}=3.0~\text{nm}$, then $a=0.3$ - $54.0$ nm, and case (a): $l_{\downarrow}^{L}=l_{\downarrow}^{R}=15.0~\text{nm}$, $l_{\uparrow }^{R} =l_{\downarrow}^{R}/R_{\downarrow}^{R}= 3.0, 7.5, 15.0, 30.0, 75.0$ nm; case (b): $l_{\downarrow}^{L}=l_{\downarrow}^{R}=6.0~\text{nm}$, $l_{\uparrow }^{R} = 1.2, 3.0, 6.0, 12.0, 30.0$ nm; case (c): $l_{\downarrow}^{L}=l_{\downarrow}^{R}=3.0~\text{nm}$, $l_{\uparrow }^{R} = 0.6, 1.5, 3.0, 6.0, 15.0$ nm; and case (d): $l_{\downarrow}^{L}=15.0~\text{nm}$, $l_{\downarrow}^{R}=5.0~\text{nm}$, $l_{\uparrow }^{R} = 1.0, 2.5, 5.0, 10.0, 25.0$ nm for curve 1 to curve 5, respectively.