Mechanism for Electrostatically Generated Magnetoresistance in Chiral Systems without Spin-Dependent Transport

Abstract

Significant attention has been drawn to electronic transport in chiral materials coupled to ferromagnets in the chirality-induced spin selectivity (CISS) effect. A large magnetoresistance (MR) is usually observed, which is widely interpreted to originate from spin (dependent) transport. However, there are severe discrepancies between the experimental results and the theoretical interpretations, most notably the apparent failure of the Onsager reciprocity relations in the linear response regime. We provide an alternative mechanism for the two terminal MR in chiral systems coupled to a ferromagnet. For this, we point out that it was observed experimentally that the electrostatic contact potential of chiral materials on a ferromagnet depends on the magnetization direction and chirality. The mechanism that we provide causes the transport barrier to be modified by the magnetization direction, already in equilibrium, in the absence of a bias current. This strongly alters the charge transport through and over the barrier, not requiring spin transport. This provides a mechanism that allows the linear response resistance to be sensitive to the magnetization direction and also explains the failure of the Onsager reciprocity relations. We propose experimental configurations to confirm our alternative mechanism for MR.

Keywords: chiral system; chirality-induced spin selectivity; equilibrium electrostatic potential; linear response; magnetoresistance; spin transport; spin valve effect.

Figure 1

(a) Elementary spin-dependent transmission and reflection model for a chiral system. The “favored” electron spin is transmitted, and the “unfavored” electron spin is reflected but has to spin-flip^, because directional spin transmission always requires a spin-flip reflection process to avoid spin currents in equilibrium. (b) A ferromagnet gives rise to spin-dependent transport, but this is fundamentally different because the preferred spin is set by the magnetization direction, not the propagation direction. (c) Energy level diagram of a chiral system contacted by a ferromagnet tip (FM Tip) and a metal substrate (NM) to illustrate the alternative origin for the MR. At the interface between the tip and the chiral system, a Schottky-like barrier is formed. The magnetization direction affects the contact potential Δ ψ_⇆ that is built up over a distance d. This then modifies the electrostatic potential profile of the chiral molecules.

Figure 2

(a) Calculated potential ψ(z) for a contact potential change of 50 mV. We use N_D = 10¹⁵ cm^–3 and ϵ_r = 5. The inserted graph shows the screening length λ as a function of the doping concentration on a semilogarithmic x-axis. (b) Energy level diagram of a chiral system in contact with a ferromagnet. When a bias is applied the (modified) transport can occur via three mechanisms: (1) thermionic emission, (2) tunneling through the barrier, and (3) transport within the screening length.

Figure 3

Effect of the potential profile modification with a spacer between the ferromagnetic substrate and the HOMO/LUMO band of the chiral system. (a) In most experiments that use a ferromagnet substrate, there is a gold (Au) layer between the ferromagnet and the chiral system. However, this is not significantly different from the case in which there is direct contact between the ferromagnet and the chiral system. (b) The potential profile of an oxide (Ox) tunnel barrier between the chiral system and the ferromagnet is also modified by the magnetization direction. Here, we ignore possible band bending of the HOMO/LUMO bands of the chiral system and show the potential profile only close to the ferromagnetic substrate, ignoring the normal metallic tip/substrate. (c) Proposed sample configuration with the chiral layer contacted by a gold-coated ferromagnet on one side and by a tunnel barrier on the other side. In this geometry, spin-dependent transport cannot generate an MR, but the contact potential modification can.

Figure 4

(a) Spin-dependent electron transmission model for electrons propagating from left-to-right though a chiral system coupled to a ferromagnet. The reversal of the magnetization does not affect the total charge current, and hence eq A2 does hold. Note that there are spin currents on both sides of the system which depend on the chirality and the magnetization direction but that the charge transport is unaffected by the magnetization direction. (b) This is fundamentally different from two connected ferromagnets and the magnetization of one of them being reversed.