From measurements of fluctuation spectroscopy and weak nonlinear transport on the semimetallic ferromagnet EuB$_6$ we find direct 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 poorly conducting background. These different parts of the conducting network are probed separately by the noise spectroscopy/nonlinear transport and the conventional linear resistivity. We suggest a comprehensive and universal scenario for the MP percolation, which occurs at a critical magnetization either induced by ferromagnetic order at zero field or externally applied magnetic fields in the paramagentic region.
EuB$_6$ is a magnetic semiconductor in which defects introduce charge carriers into the conduction band with the Fermi energy varying with temperature and magnetic field. We present experimental and theoretical work on the electronic magnetotransport in single-crystalline EuB$_6$. Magnetization, magnetoresistance and Hall effect data were recorded at temperatures between 2 and 300 K and in magnetic fields up to 5.5 T. The negative magnetoresistance is well reproduced by a model in which the spin disorder scattering is reduced by the applied magnetic field. The Hall effect can be separated into an ordinary and an anomalous part. At 20 K the latter accounts for half of the observed Hall voltage, and its importance decreases rapidly with increasing temperature. As for Gd and its compounds, where the rare-earth ion adopts the same Hunds rule ground state as Eu$^{2+}$ in EuB$_{6}$, the standard antisymmetric scattering mechanisms underestimate the $size$ of this contribution by several orders of magnitude, while reproducing its $shape$ almost perfectly. Well below the bulk ferromagnetic ordering at $T_C$ = 12.5 K, a two-band model successfully describes the magnetotransport. Our description is consistent with published de Haas van Alphen, optical reflectivity, angular-resolved photoemission, and soft X-ray emission as well as absorption data, but requires a new interpretation for the gap feature deduced from the latter two experiments.
The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads to nontrivial topological states, such as topological insulators and Dirac semimetals. When the TRS is broken, the exchange field induces spin splitting of the bands. The inversion of a pair of spin-splitting subbands can generate more exotic topological states, such as quantum anomalous Hall insulators and magnetic Weyl semimetals. So far, such topological phase transitions driven by the TRS breaking have not been visualized. In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spin-splitting subbands at the TRI points of Brillouin zone in EuB$_6$, when a long-range ferromagnetic order is developed. The dramatic changes in the electronic structure result in a topological phase transition from a TRI ordinary insulator state to a TRS-broken topological semimetal (TSM) state. Remarkably, the magnetic TSM state has an ideal electronic structure, in which the band crossings are located at the Fermi level without any interference from other bands. Our findings not only reveal the topological phase transition driven by the TRS breaking, but also provide an excellent platform to explore novel physical behavior in the magnetic topological states of quantum matter.
From thermodynamic analysis we demonstrate that during metal-insulator transitions in pure matters, a nonequilibrium homogeneous state may be unstable against charge density modulations with certain wavelengths, and thus evolves to the equilibrium phase through transient electronic phase separation. This phase instability occurs as two inequalities between the first and the second derivatives of the free energy with respect to the order parameter are fulfilled. The dominant wavelength of the modulated phase is also derived. The computer simulation further confirms the theoretical derivation. Employing the pre-established phase-field model of VO$_2$, we show that this transient electronic phase separation may take place in VO$_2$ upon photoexcitation.
We have explored the magnetism in the non-geometrically frustrated spin-chain system $gamma$-CoV$_{2}$O$_{6}$ which possesses a complex magnetic exchange network. Our neutron diffraction patterns at low temperatures ($T$ $leqslant$ $T_{mathrm{N}}$ = 6.6 K) are best described by a model in which two magnetic phases coexist in a volume ratio 65(1) : 35(1), with each phase consisting of a single spin modulation. This model fits previous studies and our observations better than the model proposed by Lenertz $et$ $al$ in J. Phys. Chem. C 118, 13981 (2014), which consisted of one phase with two spin modulations. By decreasing the temperature from $T_{mathrm{N}}$, the minority phase of our model undergoes an incommensurate-commensurate lock-in transition at $T^{*}$ = 5.6 K. Based on these results, we propose that phase separation is an alternative approach for degeneracy-lifting in frustrated magnets.
Interest in many strongly spin-orbit coupled 5d-transition metal oxide insulators stems from mapping their electronic structures to a J=1/2 Mott phase. One of the hopes is to establish their Mott parent states and explore these systems potential of realizing novel electronic states upon carrier doping. However, once doped, little is understood regarding the role of their reduced Coulomb interaction U relative to their strongly correlated 3d-electron cousins. Here we show that, upon hole-doping a candidate J=1/2 Mott insulator, carriers remain localized within a nanoscale phase separated ground state. A percolative metal-insulator transition occurs with interplay between localized and itinerant regions, stabilizing an antiferromagnetic metallic phase beyond the critical region. Our results demonstrate a surprising parallel between doped 5d- and 3d-electron Mott systems and suggest either through the near degeneracy of nearby electronic phases or direct carrier localization that U is essential to the carrier response of this doped spin-orbit Mott insulator.