Double Exchange Model at Low Densities: Magnetic Polarons and Coulomb Suppressed Phase Separation

Abstract

We consider the double exchange model at very low densities. The conditions for the formation of self-trapped magnetic polarons are analyzed using an independent polaron model. The issue of phase separation in the low density region of the temperature-density phase diagram is discussed. We show how electrostatic and localization effects can lead to the substantial suppression of the phase separated regime. By examining connections between the resulting phase and the polaronic phase, we conclude that they reflect essentially the same physical situation of a ferromagnetic droplet containing one single electron. In the ultra diluted regime, we explore the possible stabilization of a Wigner crystal of magnetic polarons. Our results are compared with the experimental evidence for a polaronic phase in europium hexaboride (EuB6), and we are able to reproduce the experimental region of stability of the polaronic phase. We further demonstrate that phase-separation is a general feature expected in metallic ferromagnets whose bandwidth depends on the magnetization.

Enhanced ferromagnetism from electron-electron interactions in double-exchange-type models

“…In manganites it is well established that electronelectron interactions are at least as large as the Hund coupling, and may be the largest energy scale in the problem [1,[5][6][7]. The importance of interactions has also been stressed for DMS [8][9][10] and hexaborides [11]. The combination of disorder and electron-electron interactions may also play an important role in nanoscale electronic phase separation [12], which has been argued to be important for CMR in manganites [13].…”

Evolution of thermoelectric properties in EuxYb1−xB6 family

“…Indeed, both Raman scattering studies [26] and combined measurements of fluctuation spectroscopy as well as weak nonlinear transport [28] predict the formation of polarons in stoichiometric EuB 6 below 30-35 K. This result is also supported by thermal investigations [44], where the magnetic entropy crosses the line R • ln 8 corresponded to the 8 S 7/2 state of europium ion at ∼30 K. (Note that T pol shifts up to 39 K for the Eu 0.9 Yb 0.1 B 6 doped system [35]). Moreover the theoretical estimations proposed for EuB 6 in the framework of double exchange model [45] allowed the authors to reconstruct the diagram of polaronic stability as a function of electron density with bordering values T pol (n e ) ∼ 40-50 K. Thus, in our opinion there are two characteristic temperatures T pol and T * ≈ 2T pol describing different mechanisms of SRMO in the PM state of EuB 6 . Supplementing the scenario [24], in which only one point (T pol ) exists, we suppose that one more characteristic temperature T * indicating the growth the spin-fluctuations amplitude before the stabilization of polarons should be taken into account.…”

Inhomogeneous phases in a double-exchange magnet with long range Coulomb interactions

“…In addition to the macroscopic phase separation as described above, the double exchange-superexchange competition can also be resolved via an altogether different scenario (formation of magnetic polarons). When a single electron (or hole) is lodged into an antiferromagnetically ordered double-exchange magnet with zero chargecarriers, (x = 0), a free (self-trapped) magnetic polaron, or ferron 6,27,34,35,36,37,38 , is formed around it. It is essentially a microscopic FM region, containing one charge carrier, in an otherwise AFM system.…”