Spin Polarization in Transport Studies of Chirality-Induced Spin Selectivity

Abstract

Chirality-induced spin selectivity (CISS) is a recently discovered effect in which structural chirality can result in different conductivities for electrons with opposite spins. In the CISS community, the degree of spin polarization is commonly used to describe the efficiency of the spin filtering/polarizing process, as it represents the fraction of spins aligned along the chiral axis of chiral materials originating from non-spin-polarized currents. However, the methods of defining, calculating, and analyzing spin polarization have been inconsistent across various studies, hindering advances in this field. In this Perspective, we connect the relevant background and the definition of spin polarization, discuss its calculation in different contexts in the CISS, and propose a practical and meaningful figure of merit by quantitative analysis of magnetoresistance in CISS transport studies.

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

“…Using this model, it can be shown that, normalM normalR = I false↑ − I false↓ I false↑ + I false↓ = P F M P C h i r a l where I ↑ ↓ is the measured current with magnetization direction indicated by the subscript and P Chiral is the spin polarization of the chiral system. This clearly shows that the total MR can never exceed the polarization of the ferromagnet, even when we assume a perfect spin polarization of the chiral system ( P Chiral = 1), as was recently also pointed out by Liu and Weiss and others. Note that here the MR definition commonly used for CISS is applied, which is different from the conventional definition of the TMR ratio applied in the Julière model.…”

“…However, the measured MR is often directly interpreted in terms of the spin polarization of the transmitted electrons. It is crucial to distinguish the MR ,, generated by the entire circuit (chiral system + ferromagnet) from mechanisms that generate the spin-dependent electron transport in the chiral systems themselves. , In this work, we assume the presence of directional spin-dependent transmission and reflection in the chiral systems itself. However, despite this assumption, below, we identify five main problems with the common interpretation of the measured MR in terms of spin-dependent transport.…”

“…The reported MR for chiral systems coupled to a ferromagnet is typically above 50% and approaches 100% in a number of recent experimental results. , A conventional TMR spin valve consist of two ferromagnetic electrodes and operates based on spin-dependent tunneling for which the Julière model connects the spin polarization of the density of states of the ferromagnets, P FM , to the MR . Using this model, it can be shown that, where I ↑ ↓ is the measured current with magnetization direction indicated by the subscript and P Chiral is the spin polarization of the chiral system.…”

Chiral Induced Spin Selectivity

“…However, this treatment contrasts with classical definitions in which the spin polarization is formally given as the difference in populations for spin up and spin down electrons. 16,17 Thus, care must be taken when comparing findings between different measurement techniques.…”

“…For example, the CISS literature often defines polarizations as normalized anisotropies in electron currents or charge transfer rate constants, and these quantities can be convoluted with the spin density of states. However, this treatment contrasts with classical definitions in which the spin polarization is formally given as the difference in populations for spin up and spin down electrons. , Thus, care must be taken when comparing findings between different measurement techniques.…”