The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelectric and magneto-optic applications. In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin-Wagner theorem; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and composition engineering, or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine CrGeTe atomic layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temperature (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 tesla). This result is in contrast to the insensitivity of the transition temperature to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocrystalline anisotropy, opening up a large spin-wave excitation gap. We explain the observed phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temperature is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. CrGeTe is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviours, opening the door to exploring new applications such as ultra-compact spintronics.

Polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed non-zero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3 He-A.PACS numbers: 74.25. Gz,74.70.Pq,74.25.Ha,78.20.Ls Soon after the discovery of the layered-perovskite superconductor Sr 2 RuO 4 [1], it was predicted to be an oddparity superconductor [2,3]. Subsequently, a large body of experimental results in support of odd-parity superconductivity has been obtained [4], with the most recent one being a phase-sensitive measurement [5]. The symmetry of the superconducting state is related simply to the relative orbital angular momentum of the electrons in each Cooper pair. Odd parity corresponds to odd orbital angular momentum and symmetric spin-triplet pairing. While a priori the angular momentum state can be p (i.e. L = 1), f ( i.e. L = 3), or even higher order [6,7], theoretical analyses of superconductivity in Sr 2 RuO 4 favor the p-wave order parameter symmetry [2,8]. There are many allowed p-wave states that satisfy the cylindrical Fermi surface for a tetragonal crystal which is the case of Sr 2 RuO 4 (see e.g. table IV in [4]). Some of these states break time-reversal symmetry (TRS), since the condensate has an overall magnetic moment because of either the spin or orbital (or both) parts of the pair wave function. While an ideal sample will not exhibit a net magnetic moment, surfaces and defects at which the Meissner screening of the TRS-breaking moment is not perfect can result in a small magnetic signal [7]. Indeed, muon spin relaxation (µSR) measurements on good quality single crystals of Sr 2 RuO 4 showed excess relaxation that spontaneously appear at the superconducting transition temperature. The exponential nature of the increased relaxation suggested that its source is a broad distribution of internal fields, of strength ∼ 0.5 Oe, from a dilute array of sources [9,10]. While TRS breaking is not the only explanation for the µSR observations, it was accepted as the most likely one [4]. However, since the existence of TRS breaking has considerable implications for understanding the superconductivity of Sr 2 RuO 4 , establishing the existence of this effect, and in particular in the bulk without relying on imperfections and defects is of utmost importance. The challenge is therefore to couple to the TRS-breaking part of the order parameter to demonstrate the effect unambiguously.In this paper we show results of polar Kerr effect (PKE) measurements on high quality single crystals of Sr 2 RuO 4 . In these measurements we are searching for an effect analogous to the magneto-optic Kerr effect (MOKE) which would cause a rotation of the direction of polarization of the reflected linearly polarized light normally incident to the superconducting planes. PKE is sensitive to TRS breaking since it measures the existenc...

A propagating Majorana mode Although Majorana fermions remain elusive as elementary particles, their solid-state analogs have been observed in hybrid semiconductor-superconductor nanowires. In a nanowire setting, the Majorana states are localized at the ends of the wire. He et al. built a two-dimensional heterostructure in which a one-dimensional Majorana mode is predicted to run along the sample edge (see the Perspective by Pribiag). The heterostructure consisted of a quantum anomalous Hall insulator (QAHI) bar contacted by a superconductor. The authors used an external magnetic field as a “knob” to tune into a regime where a Majorana mode was propagating along the edge of the QAHI bar covered by the superconductor. A signature of this propagation—half-quantized conductance—was then observed in transport experiments. Science , this issue p. 294 ; see also p. 252

The polar Kerr effect in the high-T c superconductor YBa 2 Cu 3 O 6x was measured at zero magnetic field with high precision using a cyogenic Sagnac fiber interferometer. We observed nonzero Kerr rotations of order 1 rad appearing near the pseudogap temperature T and marking what appears to be a true phase transition. Anomalous magnetic behavior in magnetic-field training of the effect suggests that time reversal symmetry is already broken above room temperature. , large compared to the superconducting (SC) transition temperature, T c . Two major classes of theories have been introduced in an attempt to describe the pseudogap state: One in which the pseudogap temperature T represents a crossover into a state with preformed pairs with a d wave gap symmetry [6,7], and another in which T marks a true transition into a phase with broken symmetry that ends at a quantum critical point, typically inside the superconducting dome. While at low doping this phase may compete with superconductvity, it might provide fluctuations that are responsible for the enhanced transition temperature near its quantum critical point (e.g., as in Ref. [8] In this Letter, we report high resolution optical Kerreffect measurements on YBa 2 Cu 3 O 6x crystals with various hole concentrations p. (p is, in turn, a monotonic function of the oxygen concentration x, and it also depends on oxygen ordering in the chains [12].) We identify a sharp phase transition at a temperature T s p, below which there is a nonzero Kerr angle, indicating the existence of a phase with broken time reversal symmetry (TRS). Both the magnitude and hole concentration dependence of T s are in close correspondence with those of the pseudogap crossover temperature, T , which has been identified in other physical quantities. In particular, as shown in Fig. 1, T s is substantially larger than the superconducting T c in underdoped materials, but drops rapidly with increasing hole concentration, so that it is smaller than T c in a near optimally doped crystal and extrapolates to zero at a putative quantum critical point under the superconducting dome. The magnitude of the Kerr rotation in YBa 2 Cu 3 O 6x (YBCO) is smaller by 4 orders of magnitude than that observed in other itinerant ferromagnetic oxides [13,14], and the temperature dependence is ''superlinear'' near T c , FIG. 1 (color online). The onset of the Kerr-effect signal, T s (circles), and T c (red squares) for the YBa 2 Cu 3 O 6x samples reported in this Letter. Also shown are T c p (from [12]) and T N p (from [22]).

Strongly correlated electron systems show many exotic properties such as unconventional superconductity, quantum criticality, and Kondo insulating behavior. In addition, the Kondo insulator SmB 6 has been predicted theoretically to be a 3D topological insulator with a metallic surface state. We report here transport measurements on doped SmB 6 , which show that ~3% magnetic and non-magnetic dopants in SmB 6 exhibit clearly contrasting behavior, evidence that the metallic surface state is only destroyed when time reversal symmetry is broken. We find as well a quantum percolation limit of impurity concentration which transforms the topological insulator into a conventional band insulator by forming impurity band.Our careful thickness dependence results show that SmB 6 is the first demonstrated perfect 3D topological insulator with virtually zero residual bulk conductivity.

A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations. The surface transport, however, remains difficult to isolate from the bulk conduction in most existing TI crystals (particularly Bi2Se3, Bi2Te3 and Sb2Te3) due to impurity caused bulk conduction. We report in large crystals of topological Kondo insulator (TKI) candidate material SmB6 the thickness-independent surface Hall effects and non-local transport, which persist after various surface perturbations. These results serve as proof that at low temperatures SmB6 has a metallic surface that surrounds an insulating bulk, paving the way for transport studies of the surface state in this proposed TKI material.

This article reviews recent theoretical and experimental work on a new class of topological material-topological Kondo insulators, which develop through the interplay of strong correlations and spin-orbit interactions. The history of Kondo insulators is reviewed along with the theoretical models used to describe these heavy fermion compounds. The Fu-Kane method of topological classification of insulators is used to show that hybridization between the conduction electrons and localized f electrons in these systems gives rise to interaction-induced topological insulating behavior. Finally, some recent experimental results are discussed, which appear to confirm the theoretical prediction of the topological insulating behavior in samarium hexaboride, where the long-standing puzzle of the residual low-temperature conductivity has been shown to originate from robust surface states

Ultrathin films of the itinerant ferromagnet SrRuO 3 were studied using the transport and magneto-optic polar Kerr effect. We find that below 4 monolayers, the films become insulating and their magnetic character changes as they loose their simple ferromagnetic behavior. We observe a strong reduction in the magnetic moment which for 3 monolayers and below lies in the plane of the film. Exchange-bias behavior is observed below the critical thickness and may point to induced antiferromagnetism in contact with ferromagnetic regions.