Chiral spin textures such as skyrmions are of interest to the field of spintronics for their potential use in future computing devices. Hall effect measurements are a simple and powerful method to probe the electronic and magnetic properties of materials. The topological Hall effect, which appears as anomalies in Hall resistance versus magnetic field measurements compared to magnetic measurements, has frequently been used to establish the occurrence of chiral spin textures. However, in addition to experimental issues, intrinsic electronic mechanisms combined with inhomogeneity in materials and at interfaces can lead to an inhomogeneous anomalous Hall effect which could be mistaken for a topological Hall signal. This review covers recent research using Hall effect measurements to probe chiral spin textures, focusing on SrRuO3 as a model system. The ambiguity between Hall effects due to topological sources has led to disagreement in the interpretation of experimental results and casts doubts on the effectiveness of these techniques for investigating chiral spin textures.
The ν = 0 quantum Hall state in graphene has attracted experimental [1][2][3][4][5][6][7][8][9][10][11] and theoretical [12][13][14][15][16][17][18] interest.Graphene supports four zero-energy Landau levels which are described by spin and valley degeneracies.These lead to a number of approximately degenerate symmetry-broken states 12,14 . Electron-electron and electron-phonon interactions break valley-symmetry and determine the ground state of the ν = 0 state. The consensus emerging from theory [16][17][18] and experiment 3,8,9,11 is that these interactions favour an antiferromagnetic insulating state which supports long-range spin-polarized edge transport 3,11 . Here we report a competition between canted antiferromagnetic and ferromagnetic quantum Hall states in graphene placed on a ferrimagnetic insulator Y3Fe5O12 (YIG), which induces a uniform magnetic exchange field in graphene of the order 60 T. The magnetic order and energy gap of the edge modes in graphene are tunable with an 8 T out-of-plane magnetic field at 2.7 K.A magnetic field parallel (B∥) to the plane of graphene can promote a ferromagnetic (F-) state 9 . In general, however a competition between antiferromagnetic (AF-) and F-states leads to a canted antiferromagnetic (CAF-) state in which the spins are tilted parallel (as preferred by the Zeeman field) and perpendicular (as preferred by the interactions that favour AF order) to the magnetic field, pointing in opposite directions in the two sublattices as schematically illustrated in Fig. 1. The CAF-state continuously interpolates between the AF-(θ = π/2) and F-states (θ = 0), where θ is the angle between the spins and magnetic field. In the AF-state, charged edge excitations are gapped, but the F-state supports gapless counterpropagating edge modes 15,17 . Therefore, in the CAF-state the energy gap of the edge modes is tunable with a magnetic field with a gap at θ = π/2 which vanishes at θ = 0 (Ref. 17), and a competition between the CAF-and F-states can be detected by transport measurements 9 . Although a tunable energy
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