Evidence of Skyrmion-Tube Mediated Magnetization Reversal in Modulated Nanowires

Magnetic nanowires, conceived as individual building blocks for spintronic devices, constitute a well-suited model to design and study magnetization reversal processes, or to tackle fundamental questions, such as the presence of topologically protected magnetization textures under particular conditions. Recently, a skyrmion-tube mediated magnetization reversal process was theoretically reported in diameter modulated cylindrical nanowires. In these nanowires, a vortex nucleates at the end of the segments with larger diameter and propagates, resulting in a first switching of the nanowire core magnetization at small fields. In this work, we show experimental evidence of the so-called Bloch skyrmion-tubes, using advanced Magnetic Force Microscopy modes to image the magnetization reversal process of FeCoCu diameter modulated nanowires. By monitoring the magnetic state of the nanowire during applied field sweeping, a detected drop of magnetic signal at a given critical field unveils the presence of a skyrmion-tube, due to mutually compensating stray field components. That evidences the presence of a skyrmion-tube as an intermediate stage during the magnetization reversal, whose presence is related to the geometrical dimensions of the cylindrical segments

Spin configuration in isolated FeCoCu nanowires modulated in diameter

Cylindrical Fe28Co67Cu5 nanowires modulated in diameter between 22 and 35 nm are synthesized by electroplating into the nanopores of alumina membranes. High-sensitivity MFM imaging (with a detection noise of 1 µN m-1) reveals the presence of single-domain structures in remanence with strong contrast at the ends of the nanowires, as well as at the transition regions where the diameter is modulated. Micromagnetic simulations suggest that curling of the magnetization takes place at these transition sites, extending over 10–20 nm and giving rise to stray fields measurable with our MFM. An additional weaker contrast is imaged, which is interpreted to arise from inhomogeneities in the nanowire diameter

Direct observation of transverse and vortex metastable magnetic domains in cylindrical nanowires

We present experimental evidence of transverse magnetic domains, previously observed only in nanostrips, in CoNi cylindrical nanowires with designed crystal symmetry and tailored magnetic anisotropy. The transverse domains are found together with more conventional vortex domains along the same cylindrical nanowire, denoting a bistable system with similar energies. The surface and the inner magnetization distribution in both types of domains are analyzed by photoemission electron microscopy with x-ray magnetic circular dichroism contrast, and hysteresis loop in individual nanowires are measured by magneto-optical Kerr effect. These experimental data are understood and compared with complementary micromagnetic simulations

Entanglement entropy of non-unitary conformal field theory

Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as ceff(n+1)/2n log(L), where ceff=c-24Delta > 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Delta < 0 is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic, then there is an additional term proportional to $log(log(L)). These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models

Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks

We reconsider the computation of the entanglement entropy of two disjoint intervals in a (1+1) dimensional conformal field theory by conformal block expansion of the 4-point correlation function of twist fields. We show that accurate results may be obtained by taking into account several terms in the operator product expansion of twist fields and by iterating the Zamolodchikov recursion formula for each conformal block. We perform a detailed analysis for the Ising conformal field theory and for the free compactified boson. Each term in the conformal block expansion can be easily analytically continued and so this approach also provides a good approximation for the von Neumann entropy

Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

We study the temporal evolution of the entanglement Hamiltonian of an interval after a global quantum quench in free lattice models in one spatial dimension. In a harmonic chain we explore a quench of the frequency parameter. In a chain of free fermions at half filling we consider the evolution of the ground state of a fully dimerised chain through the homogeneous Hamiltonian. We focus on critical evolution Hamiltonians. The temporal evolutions of the gaps in the entanglement spectrum are analysed. The entanglement Hamiltonians in these models are characterised by matrices that provide also contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench