. † These authors contributed equally to this project. The existence of electronic symmetry breaking in the underdopedcuprates, and its disappearance with increased hole-density p, are now widely reported. However, the relationship between this transition and the momentumspace ( ⃗ -space) electronic structure underpinning the superconductivity has not been established. Here we visualize the ⃗ =0 (intra-unit-cell) and ⃗ ≠0 (density wave) broken-symmetry states simultaneously with the coherent ⃗ -space topology, for Bi2Sr2CaCu2O8+d samples spanning the phase diagram 0.06≤p≤0.23.We show that the electronic symmetry breaking tendencies weaken with increasing p and disappear close to pc=0.19. Concomitantly, the coherent ⃗ -space topology undergoes an abrupt transition, from arcs to closed contours, at the same pc. These data reveal that the ⃗ -space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point. 2The highest known superconducting critical temperature Tc (1-3) occurs atop the Tc(p) 'dome' of hole-doped cuprates (Fig. 1A). In addition to the superconductivity, electronic broken-symmetry states (4) have also been reported at low p in many such compounds. Wavevector ⃗ =0 (intra-unit-cell) symmetry breaking, typically of 90 orotational (C4) symmetry, is reported in YBa2Cu3O6+, . Finite wavevector ⃗ ≠0 (density wave) modulations breaking translational symmetry, long detected in underdoped 16), are now also reported in underdoped YBa2Cu3O6+, . Summarizing all such reports in Fig. 1A reveals some stimulating observations.First, although the ⃗ =0 and ⃗ ≠0 states are detected by widely disparate techniques and are distinct in terms of symmetry, they seem to follow approximately the same phasediagram trajectory (shaded band Fig. 1A) as if facets of a single phenomenon (26). The second implication is that a critical point (perhaps a quantum critical point) associated with these broken-symmetry states may be concealed beneath the Tc(p) dome.Numerous earlier studies reported sudden alterations in many electronic/magnetic characteristics near p=0.19 (2,3,27), but whether these phenomena are caused by electronic symmetry changes (28) at a critical point was unknown. 3In ⃗ -space, the hole-doped cuprates also exhibit an unexplained transition in electronic structure with increasing hole density. Open contours or "Fermi arcs" (29)(30)(31)(32) are reported at low p in all compounds studied, while at high p closed hole-like pockets surrounding ⃗ = (±1, ±1) / 0 are observed (33,34). One possibility is that such a transition could occur due to the disappearance of an electronic ordered state, with the resulting modifications to the Brillouin zone geometry altering the topology of the electronic bands (28). 4Our strategy is therefore a simultaneous examination of both the ⃗ -space 11,36) or at the Bragg wavevectors (11,26,35). But the complete doping dependence of these broken-symmetry signatures was unknown. 6To determine the ⃗ -space t...

The discovery of new phenomena in layered and nanostructured magnetic devices is driving rapid growth in nanomagnetics research. Resulting applications such as giant magnetoresistive field sensors and spin torque devices are fuelling advances in information and communications technology, magnetoelectronic sensing and biomedicine. There is an urgent need for high-resolution magnetic-imaging tools capable of characterizing these complex, often buried, nanoscale structures. Conventional ferromagnetic resonance (FMR) provides quantitative information about ferromagnetic materials and interacting multicomponent magnetic structures with spectroscopic precision and can distinguish components of complex bulk samples through their distinctive spectroscopic features. However, it lacks the sensitivity to probe nanoscale volumes and has no imaging capabilities. Here we demonstrate FMR imaging through spin-wave localization. Although the strong interactions in a ferromagnet favour the excitation of extended collective modes, we show that the intense, spatially confined magnetic field of the micromagnetic probe tip used in FMR force microscopy can be used to localize the FMR mode immediately beneath the probe. We demonstrate FMR modes localized within volumes having 200 nm lateral dimensions, and improvements of the approach may allow these dimensions to be decreased to tens of nanometres. Our study shows that this approach is capable of providing the microscopic detail required for the characterization of ferromagnets used in fields ranging from spintronics to biomagnetism. This method is applicable to buried and surface magnets, and, being a resonance technique, measures local internal fields and other magnetic properties with spectroscopic precision.

No abstract

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking timereversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr 0.08 (Bi 0.1 Sb 0.9 ) 1.92 Te 3 . Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship Δ(r) ∝ n(r) is confirmed throughout and exhibits an electron-dopant interaction energy J* = 145 meV·nm 2 . These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.ferromagnetic topological insulator | Dirac-mass gapmap | Dirac-mass disorder | magnetic dopant atoms T hat the surface states of 3D topological insulators (TIs) exhibit a "massless" Dirac spectrum EðkÞ = Zvk · σ with spinmomentum locking and protected by time-reversal symmetry is now firmly established. Opening a gap in this spectrum is key to the realization of several extraordinary new types of electronic phenomena. The prevalent approach to opening this "Dirac-mass gap" is to dope the materials with magnetic atoms (1-6). A plethora of new physics is then predicted, including σ xy = ±e 2 =h quantum anomalous Hall effects (QAHE) (7, 8), topological surface-state magneto-electric effects (9-12), related magneto-optical Kerr and Faraday rotations (10, 13, 14), axionic-like electrodynamics (15, 16), and even E-field induced magnetic monopoles (17,18). As yet, none of these phenomena except the QAHE (19-22) have been detected, and the QAHE itself is poorly understood because σ xy = ±e 2 =h is observed only at temperatures far below 1 K.Interactions between the TI surface electrons and the magnetic dopant atoms at random surface locations r i can be represented theoretically by a Hamiltonian of the type H DA = −J p P S i · sδðr − r i Þ. Here S i (s) is the spin of each dopant (surfacestate carrier) measured in units of Z, and J p is their exchangeinteraction energy scale. In the simple case of a homogenous ferromagnetic state with magnetization parallel to the surface normal z, the Hamiltonian becomes H = −J p n 0...

No abstract