Electronic phase separation due to magnetic polaron formation in the semimetallic ferromagnet EuB₆ — A weakly-nonlinear-transport study

Abstract

We report measurements of weakly nonlinear electronic transport, as measured by third-harmonic voltage generation V _3ω, in the low-carrier density semimetallic ferromagnet EuB₆, which exhibits an unusual magnetic ordering with two consecutive transitions at $T_{c_1 }$ = 15.6K and $T_{c_2 }$ = 12.5K. In contrast to the linear resistivity, the third-harmonic voltage is sensitive to the microgeometry of the electronic system. Our measurements provide evidence for magnetically-driven electronic phase separation consistent with the picture of percolation of magnetic polarons (MP), which form highly conducting magnetically ordered clusters in a paramagnetic and less conducting background. Upon cooling in zero magnetic field through the ferromagnetic transition, the dramatic drop in the linear resistivity at the upper transition $T_{c_1 }$ coincides with the onset of nonlinearity, and upon further cooling is followed by a pronounced peak in V _3ω at the lower transition $T_{c_2 }$. Likewise, in the paramagnetic regime, a drop of the material’s magnetoresistance R(H) precedes a magnetic-fieldinduced peak in nonlinear transport. A striking observation is a linear temperature dependence of V ^peak_3ω . We suggest a picture where at the upper transition $T_{c_1 }$ the coalescing MP form a conducting path giving rise to a strong decrease in the resistance. The MP formation sets in at around T* ∼ 35K below which these entities are isolated and strongly fluctuating, while growing in number. The MP then start to form links at $T_{c_1 }$, where percolative electronic transport is observed. The MP merge and start forming a continuum at the threshold $T_{c_2 }$. In the paramagnetic temperature regime $T_{c_1 }$ < T < T*, MP percolation is induced by a magnetic field, and the threshold accompanied by charge carrier delocalization occurs at a single critical magnetization.