When a three-dimensional (3D) ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall condu
ctance. The recent realization of this phenomenon - the quantum anomalous Hall effect - provides a conceptually new platform for studies of edge-state transport, distinct from the more extensively studied integer and fractional quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt driven crossover from predominantly edge state transport to diffusive transport in Cr-doped (Bi,Sb)2Te3 thin films, as the system transitions from a quantum anomalous Hall insulator to a gapless, ferromagnetic topological insulator. The crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain using the Landauer-Buttiker formalism. Our methodology provides a powerful means of quantifying edge state contributions to transport in temperature and chemical potential regimes far from perfect quantization.
The breaking of time-reversal symmetry by ferromagnetism is predicted to yield profound changes to the electronic surface states of a topological insulator. Here, we report on a concerted set of structural, magnetic, electrical and spectroscopic meas
urements of MBS thin films wherein photoemission and x-ray magnetic circular dichroism studies have recently shown surface ferromagnetism in the temperature range 15 K $leq T leq 100$ K, accompanied by a suppressed density of surface states at the Dirac point. Secondary ion mass spectroscopy and scanning tunneling microscopy reveal an inhomogeneous distribution of Mn atoms, with a tendency to segregate towards the sample surface. Magnetometry and anisotropic magnetoresistance measurements are insensitive to the high temperature ferromagnetism seen in surface studies, revealing instead a low temperature ferromagnetic phase at $T lesssim 5$ K. The absence of both a magneto-optical Kerr effect and anomalous Hall effect suggests that this low temperature ferromagnetism is unlikely to be a homogeneous bulk phase but likely originates in nanoscale near-surface regions of the bulk where magnetic atoms segregate during sample growth. Although the samples are not ideal, with both bulk and surface contributions to electron transport, we measure a magnetoconductance whose behavior is qualitatively consistent with predictions that the opening of a gap in the Dirac spectrum drives quantum corrections to the conductance in topological insulators from the symplectic to the orthogonal class.
We report a magneto-optical Kerr effect study of the collective magnetic response of artificial square spin ice, a lithographically-defined array of single-domain ferromagnetic islands. We find that the anisotropic inter-island interactions lead to a
non-monotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.
We report magnetization and magetoresistance measurements in hybrid ferromagnetic metal/semiconductor heterostructures comprised of MnAs/(Ga,Mn)As bilayers. Our measurements show that the (metallic) MnAs and (semiconducting) (Ga,Mn)As layers are exch
ange coupled, re- sulting in an exchange biasing of the magnetically softer (Ga,Mn)As layer that weakens with layer thickness. Magnetoresistance measurements in the current-perpendicular-to-the-plane geometry show a spin valve effect in these self-exchange biased bilayers. Similar measurements in MnAs/p- GaAs/(Ga,Mn)As trilayers show that the exchange coupling diminishes with spatial separation between the layers.
