An exchange gap in the Dirac surface states of a topological insulator (TI) is necessary for observing the predicted unique features such as the topological magnetoelectric effect as well as to confine Majorana fermions. We experimentally demonstrate proximity-induced ferromagnetism in a TI, combining a ferromagnetic insulator EuS layer with ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, without introducing defects. By magnetic and magnetotransport studies, including anomalous Hall effect and magnetoresistance measurements, we show the emergence of a ferromagnetic phase in TI, a step forward in unveiling their exotic properties.

Strain and charge co-mediated magnetoelectric coupling are expected in ultra-thin ferromagnetic/ferroelectric multiferroic heterostructures, which could lead to significantly enhanced magnetoelectric coupling. It is however challenging to observe the combined strain charge mediated magnetoelectric coupling and difficult in quantitatively distinguish these two magnetoelectric coupling mechanisms. We demonstrated in this work, the quantification of the coexistence of strain and surface charge mediated magnetoelectric coupling on ultra-thin Ni_0.79Fe_0.21/PMN-PT interface by using a Ni_0.79Fe_0.21/Cu/PMN-PT heterostructure with only strain-mediated magnetoelectric coupling as a control. The NiFe/PMN-PT heterostructure exhibited a high voltage induced effective magnetic field change of 375 Oe enhanced by the surface charge at the PMN-PT interface. Without the enhancement of the charge-mediated magnetoelectric effect by inserting a Cu layer at the PMN-PT interface, the electric field modification of effective magnetic field was 202 Oe. By distinguishing the magnetoelectric coupling mechanisms, a pure surface charge modification of magnetism shows a strong correlation to polarization of PMN-PT. A non-volatile effective magnetic field change of 104 Oe was observed at zero electric field originates from the different remnant polarization state of PMN-PT. The strain and charge co-mediated magnetoelectric coupling in ultra-thin magnetic/ferroelectric heterostructures could lead to power efficient and non-volatile magnetoelectric devices with enhanced magnetoelectric coupling.

In addition to the weak antilocalization cusp observed in the magnetoresistance (MR) of topological insulators at low temperatures and low magnetic fields, we find that the high-field MR in Bi₂Te₂Se is linear in field. At fields up to B = 14 T, the slope of this linear-like MR is nearly independent of temperature over the range T = 7 to 150 K. We find that the linear MR arises from the competition between a logarithmic phase coherence component and a quadratic component. The quantum phase coherence dominates up to high temperatures, where the coherence length remains longer than the mean free path of electrons.

A theoretical prediction by de Gennes suggests that the resistance in a $\mathrm{FI}/\mathrm{S}/\mathrm{FI}$ (where FI is a ferromagnetic insulator, and S is a superconductor) structure will depend on the magnetization direction of the two FI layers. We report a magnetotransport measurement in a $\mathrm{EuS}/\mathrm{Al}/\mathrm{EuS}$ structure, showing that an infinite magnetoresistance can be produced by tuning the internal exchange field at the $\mathrm{FI}/\mathrm{S}$ interface. This proximity effect at the interface can be suppressed by an ${\mathrm{Al}}_2{\mathrm{O}}_3$ barrier as thin as 0.3 nm, showing the extreme confinement of the interaction to the interface giving rise to the demonstrated phenomena.