Thin films of topological insulator Bi2Se3 were deposited directly on insulating ferromagnetic EuS. Unusual negative magnetoresistance was observed near the zero field below the Curie temperature (TC), resembling the weak localization effect; whereas the usual positive magnetoresistance was recovered above TC. Such negative magnetoresistance was only observed for Bi2Se3 layers thinner than t ∼ 4nm, when its top and bottom surfaces are coupled. These results provide evidence for a proximity effect between a topological insulator and an insulating ferromagnet, laying the foundation for future realization of the half-integer quantized anomalous Hall effect in three-dimensional topological insulators.A topological insulator (TI) has a full energy gap in the bulk, and contains gapless surface states that cannot be destroyed by any non-magnetic impurities. Because of time reversal symmetry, the surface states cannot be back-scattered by non-magnetic impurities. 1,2 When a thin magnetic layer is applied on the surface, a full insulating gap is opened, and an electric charge close to the surface is predicted to induce an image magnetic monopole. 3,4 Probably the most extensively studied threedimensional TI (3D-TI) has been bismuth-selenide (Bi 2 Se 3 ), 5-7 exhibiting crystal structure that consists of atomic quintuple layers (QLs), with three QLs forming a unit cell. As made, uncompensated samples typically have a Fermi level above the Dirac point and intersecting the bulk conduction band. 8,9 In particular, low temperature transport measurements on ungated and uncompensated TI films show positive magnetoresistance (MR) at low magnetic fields and in a wide range of film thicknesses. [10][11][12] This was explained in terms of weak antilocalization (WAL) that results from spin-momentum locking on the surface state Dirac cone. 10,13 While the inability to account for the bulk bands (presumably because of their low mobility) has challenged this simple assignment, the discovery of weak localization (WL) effects at higher fields 12,14 and the ability to accurately separate quantum oscillation effects 15 in high-quality films may provide a first step towards a more comprehensive understanding of transport in these systems.By adopting topologically non-trivial Hamiltonians to describe these materials, various recent theories predict WL or negative MR near the zero field in a TI as a result of gap-opening at its surface state Dirac point. The negative MR may arise from the surface state when the Fermi level is sufficiently close to the top of the gap. 16 Alternatively, it can also be produced by bulk conduction and can only be observed when the surface conduction is sufficiently suppressed. 17,18 Such a phenomenon was reported in cases of gated ultra-thin Bi 2 Te 3 films 19 and magnetically doped Bi 2 Se 3 films. 20 To further elucidate the uniqueness of transport in the surface state of TI materials, and as an initial step towards realizing half-integer quantized anomalous Hall effect (QAHE) and other applications, we studied ...

Recent analysis has confirmed earlier general arguments that the Kerr response vanishes in any time-reversal invariant system which satisfies the Onsager relations. Thus, the widely cited relation between natural optical activity (gyrotropy) and the Kerr response, employed in Hosur et al, Phys. Rev. B 87, 115116 (2013), is incorrect. However, there is increasingly clear experimental evidence that, as argued in our paper, the onset of an observable Kerr signal in the cuprates reflects pointgroup symmetry rather than time-reversal symmetry breaking.Measurements of the rotation of the polarization of normal-incidence light upon reflection (Kerr effect) provide an extremely useful probe of any order which breaks time-reversal symmetry and all mirror symmetries, e.g. ferromagnetic order with a component of the moment perpendicular to the surface. However, arguments have been put forward that a combination of gyrotropy (handedness) and dissipation can lead to a Kerr response, even in the absence of time-reversal symmetry breaking. In Hosur et al. 1 we adopted these arguments and on this basis interpreted the onset of the Kerr effect below a welldefined, doping-dependent onset temperature in cuprate superconductors in terms of spontaneous generation of handedness induced by charge ordering. As outlined below, we are now persuaded by a review of the literature and by our own explicit calculations, that Kerr rotation is forbidden for a system subject to the combined constraints of linear response, thermal equilibrium, and time-reversal symmetry. We therefore wish to retract our suggestion that chiral charge density wave order, by itself, provides a basis for understanding the Kerr rotation observed in the cuprates.Assuming linear response, the Kerr effect can be inferred from the dielectric tensor of the material. It was a key element of the design of the Sagnac Interferometer employed 2-4 in the experiments in question, that it should reject all "non-reciprocal" effects. Reciprocity relations are implicit in linear response theory, which were used by Halperin 5 to demonstrate that the Kerr effect requires time-reversal symmetry breaking beyond simple dissipation. However, controversy existed before the Halperin paper 6-12 and continued to linger after it was published [13][14][15][16][17] .A source of the confusion can be traced to a subtlety in the boundary conditions on the electromagnetic field at the boundary between two media with different gyrotropic constants. Specifically, at the interface between two isotropic media, the requisite boundary conditions are:with α = 1/2, where ∆E , ∆B , and ∆γ are, respectively, the discontinuity in the parallel components of the electric and magnetic fields, and of the gyrotropy. The term proportional to ∆γ can be viewed as the contribution of an induced surface current, which for α = 1/2, but only for this value cancels the contributions of induced bulk currents to the Kerr effect. We will sketch below an analysis in one simple limit in which the value of α = 1/2 can be derived...

We prove an instance of the Reciprocity Theorem that demonstrates that Kerr rotation, also known as the magneto-optical Kerr effect, may only arise in materials that break microscopic time reversal symmetry. This argument applies in the linear response regime, and only fails for nonlinear effects. Recent measurements with a modified Sagnac Interferometer have found finite Kerr rotation in a variety of superconductors. The Sagnac Interferometer is a probe for nonreciprocity, so it must be that time reversal symmetry is broken in these materials.

The Sagnac Interferometer has historically been used for detecting non-reciprocal phenomena, such as rotation. We demonstrate an apparatus in which this technique is employed for high resolution measurements of the Magneto-Optical Polar Kerr effect-a direct indicator of magnetism. Previous designs have incorporated free-space components which are bulky and difficult to align. We improve upon this technique by using all fiber-optic coupled components and demonstrate operation at a new wavelength, 820 nm, with which we can achieve better than 1 µrad resolution. Mounting the system on a piezo-electric scanner allows us to acquire diffraction limited images with 1.5 µm spatial resolution. We also provide extensive discussion on the details and of the Sagnac Interferometer's construction.

High-quality thin films of the ferromagnetic insulator europium(II) sulfide (EuS) were fabricated by pulsed laser deposition on Al 2 O 3 (0001) and Si (100) substrates. A single orientation was obtained with the [100] planes parallel to the substrates, with atomic-scale smoothness indicates a near-ideal surface topography. The films exhibit uniform ferromagnetism below 15.9 K, with a substantial component of the magnetization perpendicular to the plane of the films. Optimization of the growth condition also yielded truly insulating films with immeasurably large resistance. This combination of magnetic and electric properties open the gate for novel devices that require a true ferromagnetic insulator.Over more than 50 years a wealth of new effects and properties have been discovered in binary lanthanide compounds. In particular, compounds of europium with elements of the sixth group (O,S,Se,Te) exhibit a rocksalt (NaCl)-type crystal structure with ordered magnetic states at low temperatures. As the lattice parameter increases from EuO to EuTe, a ferromagnetic ordered state of moments localized on Eu ions appear in EuO (T C ≈ 69 K) and in EuS (T C ≈ 16.7 K), 1,2 while EuSe and EuTe show collinear antiferromagnetic ordering with T N ≈ 4.2 K, T N ≈ 9.8 K respectively. 3,4 In these chalcogenide compounds, the S ground state of Eu 2+ ions and their simple face centered cubic (FCC) magnetic lattice facilitate testings of the Heisenberg model of ferromagnetism and theories of critical phenomena. 5-9 A variety of applications were proposed or implemented utilizing these magnetic semiconductors. 10-12 A class of magnetoelectric applications, such as π-Josephson junctions for quantum qubits 13-15 and recently proposed topological magnetoelectric effect associated with the surface state of topological insulators, 16-20 require fabrication of highquality insulating ferromagnet thin films with robust magnetic properties.Here we focus on EuS, which is a semiconductor with an indirect energy gap between the 4f 7 Eu states and the conduction band minimum at 300 K is 1.65 eV. [21][22][23] The lattice parameter of bulk crystals of EuS is a 0 = 5.967Å, with a ferromagnetic Curie temperature T C ≈ 16.7 K. When strained, the lattice constant change is accompanied by a change in Curie temperature, e.g. thin films of EuS grown on KCl show an increase in T C by as much as 2 K, due to compression induced by differential expana) Electronic mail: qiyang@stanford.edu sions of the film and substrate. 24 At the same time, very thin films will exhibit slightly lower T C due to dimensionality reduction. 25 However, although good electric insulation (ρ ∼ 10 4 Ω·cm) was obtained in high-quality single crystals, difficulties in material fabrication lead to disorder and unintentional doping, which may drastically reduce the resistivity to as low as ρ ∼ 10 −2 Ω·cm. 2,26 Such reduction in resistivity was found to be accompanied by increased Curie temperatures due to interactions between charge carriers and the Eu 2+ ions. 1,26-28 Particularly for t...