Disorder driven maximum in the magnetoresistance of spin polaron systems

TL;DR

This work investigates how structural disorder and electron–spin coupling in a minimal two-dimensional Heisenberg–Kondo framework generate spin-polaron states near $T_c$ and produce large magnetoresistance. Using Langevin spin dynamics and exact diagonalization of the electronic sector, the authors map resistivity, DOS, and mobility-edge behavior across impurity strength $V$ and coupling $J'$, revealing an optimal disorder $V_{opt}\approx 2t$ that maximizes MR at finite field and temperature. They show that MR can approach ${\sim}90\%$ in 2D when polaron formation is thermally enhanced and field-driven metallization occurs, whereas too little or too much disorder suppresses this effect. The results yield a magnetoresistance map in the $(V,J')$ plane and offer a framework to interpret MR in low-carrier-density local-moment magnets, such as EuO and GdN, via disorder-controlled polaron physics and mobility-edge shifts.

Abstract

Ferromagnetic polarons are self trapped states of an electron in a locally spin polarised environment. They occur close to the magnetic $T_c$ in low carrier density local moment magnets when the electron-spin coupling is comparable to the hopping scale. In non disordered systems the primary signatures are a modest non-monotonicity in the temperature dependent resistivity $ρ(T)$, and a magnetoresistance that can be $\sim 20-30 \%$ at $T_c$, at fields that, in energy units, are $\sim 0.01 k_BT_c$. We find that structural disorder, in the form of pinning centers, promotes polaron formation, hugely increases the resistivity peak at $T_c$, and can enhance the magnetoresistance to $\sim 80\%$. The change in magnetoresistance with disorder is, however, non-monotonic. Too much disorder just creates an Anderson insulator - with the resistivity unresponsive to the magnetisation. This paper establishes the optimum disorder for maximising the magnetoresistance, suggests the physical process behind the unusual disorder dependence, and provides a magnetoresistance map - in terms of coupling and disorder - that locates some of the existing magnetic semiconductors within this framework.

Figures (6)

• Figure 1: The zero field resistivity $\rho(T)$. (a) The resistivity at $V=0$ and three finite values of $V$. Note the maxima-minima structure in $\rho(T)$ and the increasing insulating behavior at low and high temperature as $V$ increases. (b) The 'cross term' $\rho_{cr}(T)$ (see text) normalised by $\rho(T)$. This captures the enhancement due to the coupling of structural and magnetic effects. This function grows initially with increasing $V$, and drops after $V = 2t$.
• Figure 2: Density of states at zero field. Panels (a)-(d) show the DOS for $V/t=0,1,2,3$, respectively, for three values of $T/T_c$ (marked in panel (a)). Other panels follow the same colour code. At $V=0$ there is essentially featureless at all $T$, with the finite size fluctuations smoothing out with $T$. At $V/t=1,2$ we see a depression (pseudogap) appearing around $\omega \sim \mu$ with increasing $T$. At $V=3t$ there is a prominent depression already at $T=0$ and it becomes somewhat broader at persists to the highest $T$. We are approaching a regime where the DOS is 'gapped' and essentially $T$ independent.
• Figure 3: Magnetoresistance. (a) The MR, defined as $(\rho(T,0) - \rho(T,h))/\rho(T,0)$ at $T=T_c$ and $h/t = 0.001,0.003,0.01$ shown for varying $V$. The MR expectedly increases with increasing $h$, but has an unusual $V$ dependence. The moderate MR, $\sim 10-20\%$ at $V=0$ increases to a maximum $\sim 60-70\%$ at $V \sim 2t$, and then falls off. (b) The high temperature, high field, MR - $(\Delta \rho/\rho)_{\infty}$ - where $\rho$ is the resistivity is the background of the structural disorder and random spins, and the suppression corresponds to a fully spin-polarised background. This calculation does not involve any magnetic annealing. We want to highlight that this quantity is a reasonable proxy for the finite $T$, finite $h$ MR both in terms of magnitude and $V$ dependence.
• Figure 4: Field dependence of the density of states. The panels (a)-(d) show the DOS at $T=T_c$ for $h/t=0.001,0.003,0.01$ and $V/t=0,1,2,3$. (a) At $V=0$ the DOS is essentially featureless and insensitive to $h$. (b)-(c) The modest dip at $\omega \sim \mu$ at $h=0$ is smoothed out with increasing $h$. For $V=2t$ the low $h$ dip is more prominent than at $V=t$. (d) The prominent suppression in the DOS near $\mu$ at $T_c$ is hardly affected by application of the field.
• Figure 5: Location of the mobility edge $\epsilon_c$ with respect to the chemical potential. The mobility edge is calculated via an estimate of the inverse participation ratio (IPR) of the electronic states on the annealed backgrounds. (a) Shows the temperature dependence of $\epsilon_c - \mu$ at $h=0$ for $V/t = 0,1,2,3$. For $V/t=0,1$ the mobility edge approaches $\mu$ from below, comes closest for $T \sim T_c$, but never crosses. The states are always delocalised. At $V=2t$ it crosses near $T = T_c$ and drops back again. For $V=3t$$\epsilon_c - \mu > 0$ for all $T$, the states at the chemical potential are always localised. (b) This tracks the field dependence of $\epsilon_c - \mu$ staying at $T=T_c$. The applied field expectedly drives the mobility edge downwards since it weakens localisation. From the data we see that at $V=2t$ a weak field can push $\epsilon_c$ from above $\mu$ to below $\mu$, crudely causing an 'insulator-metal transition'. Something similar happens at $V=3t$ as well, but at much larger field. At even larger $V$ the insulating state will persist at arbitrarily large $h$.