Reply to: Bias-induced electrostatic magnetoresistance in ferromagnet/chiral systems

replying to S. Tirion & B. van Wees Nature Communications https://doi.org/10.1038/s41467-025-65680-5 (2025)

Recently, we proposed a magnetochiral charge pumping theory¹ to explain the unusual magnetoresistance (MR) in chirality-induced spin selectivity (CISS) experiments. Our theory includes two essential steps. First, the coexistence of chirality, magnetism and dissipation (due to current flow) leads to a non-Hermitian skin effect at the ferromagnet-chiral molecule interface. As a nonequilibrium phenomenon, the skin effect requires finite current but does not depend on the direction of current. Next, the skin effect leads to charge trapping inside the insulating molecules, which is a nonadiabatic process. While the charge trapping or detrapping is triggered by the current-induced skin effect, their persistence does not require the persistence of current. Even without current flow, the trapped charge has a long lifetime and remains stable inside the molecular layer which is effectively a dielectric layer. Here, resistance of such a dielectric layer changes dramatically upon charge trapping/detrapping (see Fig. 1), insensitive to the bias direction. Therefore, CISS MR bypasses the constraint of Onsager’s reciprocal relation, different from the electric magnetochiral anisotropy (EMCA).

Fig. 1: The potential profile for a CISS device with charge trapping.

a The charge trapping center (localized defect) is indicated by the dashed red circle in the molecular layer. If the electron is trapped there, it remains a metastable state even at zero bias (V_bias), like a nonvolatile memory device. Such a memory effect cannot be captured by the charge accumulation model in ref. ². Red and blue lines represent the potential of trapped and un-trapped states, respectively. b, c The charge trapping significantly modifies the tunneling barrier across the insulating molecular layer at finite bias. For example, the electron tunneling barrier is always higher in the electron trapped case, intendent from the bias direction. d Illustration of the CISS resistance (R) hysteresis between charge trapped and detrapped states, as a memory switched by the magnetic field (B).

However, Tirion and van Wees argued² that the current-induced MR should be to bias-dependent according to their model, where the charge accumulation continually changes the potential and leads to a bias-linear MR. This scenario commonly applies for ordinary semiconductor devices, where the charge at the interface (referred to as node in ref. ²) transiently reaches balance with two electrodes. The interface chemical potential always lies between chemical potentials of the two electrodes. As they showed, such a charge accumulation (called by Tirion and van Wees) leads to bias-linear MR (or EMCA) rather than CISS MR. However, we should point out that this adiabatic charge accumulation model cannot account for the nonadiabatic charge trapping scenario proposed by our work.

In the following, we refer to their model as the charge accumulation in the node and our model as the charge trapping in trapping centers of the molecular layer. We illustrate the charge trapping center as a local potential well inside the molecular layer for a CISS device in Fig. 1. When this center traps an electron, the overall tunneling barrier will increase due to the Coulomb interaction. The charge trapping is qualitatively different from the charge accumulation in several aspects. (i) The charge trapping is induced by the skin effect related to current and occurs nonadiabatically after turning on current flow, but it remains a metastable state in the absence of current or bias. In contrast, the charge accumulation is induced and maintained by the current. Thus, charge trapping is nonvolatile while the charge accumulation is volatile. (ii) Different from accumulated charge, the trapped charge has a long lifetime and does not leak into electrodes because the trapped electron is confined by a potential in the insulator and effectively isolated from metallic reservoirs. Here, the charge trapping state is not in thermodynamic equilibrium but a metastable state, distinct from the charge accumulation case where node and electrodes maintain connection and balance. (iii) Physically, the charge accumulation occurs usually at the interface between the metal and the semiconductor layer while the charge trapping happens at defects or impurities within the insulating layer. Therefore, Tirion and van Wees’ model cannot describe such a nonvolatile metastable state for charge trapping because it does not include the nonadiabatic dynamics.

Furthermore, the charge trapping in our theory is like the charge trapping effect in charge trapping memories in solid devices^3,4 and organic semiconductors⁵ and in the gate oxide of a metal-oxide-semiconductor field-effect transistor (MOSFET)^6,7,8, where charge trapping occurs at localized defects inside an insulating dielectric layer. The metastable charge storage is induced by a gate voltage but remains robust after removing the voltage, to realize a memory. In ref. ¹, we pointed out that carrier trapping is a commonly observed phenomenon in molecular junction transport. In our model, the trapped charge is built up by current via the skin effect and remains robust in the absence of current. Here, the skin effect plays a similar role to gate voltage in the charge trap memory or MOSFET. The trapped charge results in significant potential change, independent from the direction of current.

As we showed in our previous work¹, merely the non-Hermitian skin effect, which occurs at the ferromagnetic-molecule interface, leads to MR of EMCA. Thus, we explicitly pointed out EMCA serves as the transport signature of the skin effect while the skin effect represents the spectroscopic manifestation of the system out of equilibrium. The charge accumulation model, which occurs also at the ferromagnet-molecule interface (called node in ref. ²), by Tirion and van Wees is another equivalent explanation of EMCA but fails to capture the charge trapping—the second key factor in our theory.

To summarize, we proposed that CISS MR is caused by the memory effect of charge trapping, driven by the skin effect at nonequilibrium phase. Tirion and van Wees discussed a bias-induced and bias-maintained MR by a model of charge accumulation at the interface. Their model could not reproduce CISS MR because it does not include the charge trapping effect, representing a typical failure when interpreting CISS transport from a conventional theory. In our work¹, the charge trapping or detrapping is bias-triggered but not bias-maintained because charge trapping has a nonvolatile memory (Fig. 1d), resulting in the MR independent from the bias direction.