Rapid development of magnetic nanotechnologies calls for experimental techniques capable of providing magnetic information with subnanometre spatial resolution. Available probes of magnetism either detect only surface properties, such as spin-polarized scanning tunnelling microscopy, magnetic force microscopy or spin-polarized low-energy electron microscopy, or they are bulk probes with limited spatial resolution or quantitativeness, such as X-ray magnetic circular dichroism or classical electron magnetic circular dichroism (EMCD). Atomic resolution EMCD methods have been proposed, although not yet experimentally realized. Here, we demonstrate an EMCD technique with an atomic size electron probe utilizing a probe-corrected scanning transmission electron microscope in its standard operation mode. The crucial element of the method is a ramp in the phase of the electron beam wavefunction, introduced by a controlled beam displacement. We detect EMCD signals with atomic-plane resolution, thereby bringing near-atomic resolution magnetic circular dichroism spectroscopy to hundreds of laboratories worldwide.
We examine the validity of the rotating wave approximation (RWA) in non-adiabatic holonomic single-qubit gates [New J. Phys. 14, 103035 (2012)]. We demonstrate that the adoption of RWA may lead to a sharp decline in fidelity for rapid gate implementation and small energy separation between the excited and computational states. The validity of the RWA in the recent experimental realization [Nature (London) 496, 482 (2013)] of non-adiabatic holonomic quantum computation for a superconducting qubit is examined.PACS numbers: 03.65. Vf, 03.67.Lx, 85.25.Cp Holonomic quantum computation (HQC) is the idea of using non-Abelian geometric phases to implement robust quantum gates [1]. By using adiabatic holonomies, HQC becomes tolerant to errors caused by fluctuations of the slowly changing control parameters. On the other hand, dissipation may have detrimental effects on the gates, leading to the need of performing the gate operations as fast as possible by using non-adiabatic holonomies. Nonadiabatic strategies have been shown [2] to be effective to minimize this error source. However, a shortening of the run time may in turn lead to other errors that can lower the gate fidelity and therefore put a limitation on the speed of holonomic gate operations. Here, we examine how the validity of the rotating wave approximation (RWA) depends on the run time and energy structure of the three level Λ setting used to implement non-adiabatic non-Abelian geometric gates first proposed in Ref. [3] and experimentally demonstrated in Refs. [4,5].The speed of quantum gate operations is generally limited by unwanted effects that become more pronounced when the run time is decreased. One such effect is related to the quasi-monochromatic approximation [6] that breaks down for short pulses, causing population of energy levels outside the computational subspace [7,8]. Another speed-limiting feature is the RWA, which is expected to break down when the run time of the gate becomes too short. This leads to a situation where the Rabi flopping is accompanied by faster fidelity reducing oscillations [9]; an effect that can be suppressed by embedding the qubit in an off-resonant Λ system [10]. We quantify the validity of the RWA by computing the fidelity of the ideal RWA-based non-adiabatic holonomic single-qubit gate operations with respect to numerical solutions of the exact Schrödinger equation.The Λ system consists of states |0 and |1 coupled to the auxiliary excited state |e via a pair of oscillating electric field pulses E j (t) = j g j (t) cos(ω j t), j = 0, 1, g j (t) being envelope functions describing the pulse shape and duration. The polarization j (t) is chosen so as to allow for the j ↔ e transition only. The Hamiltonian of the system readsĤ(t) =Ĥ 0 +μ · [E 0 (t) + E 1 (t)], wherê H 0 = −f e0 |0 0| − f e1 |1 1| is the bare Hamiltonian (by putting the energy of the excited state to zero) andμ is the electric dipole operator. By tuning the oscillation frequencies ω j on resonance with the bare transition frequencies f ej , the Hamiltonia...
Although magnetism originates at the atomic scale, the existing spectroscopic techniques sensitive to magnetic signals only produce spectra with spatial resolution on a larger scale. However, recently, it has been theoretically argued that atomic size electron probes with customized phase distributions can detect magnetic circular dichroism. Here, we report a direct experimental real-space detection of magnetic circular dichroism in aberration-corrected scanning transmission electron microscopy (STEM). Using an atomic size-aberrated electron probe with a customized phase distribution, we reveal the checkerboard antiferromagnetic ordering of Mn moments in LaMnAsO by observing a dichroic signal in the Mn L-edge. The novel experimental setup presented here, which can easily be implemented in aberration-corrected STEM, opens new paths for probing dichroic signals in materials with unprecedented spatial resolution.
While the performance of magnetic tunnel junctions based on metal/oxide interfaces is determined by hybridization, charge transfer, and magnetic properties at the interface, there are currently only limited experimental techniques with sufficient spatial resolution to directly observe these effects simultaneously in real-space. In this letter, we demonstrate an experimental method based on Electron Magnetic Circular Dichroism (EMCD) that will allow researchers to simultaneously map magnetic transitions and valency in real-space over interfacial cross-sections with sub-nanometer spatial resolution. We apply this method to an Fe/MgO bilayer system, observing a significant enhancement in the orbital to spin moment ratio that is strongly localized to the interfacial region. Through the use of first-principles calculations, multivariate statistical analysis, and Electron Energy-Loss Spectroscopy (EELS), we explore the extent to which this enhancement can be attributed to emergent magnetism due to structural confinement at the interface. We conclude that this method has the potential to directly visualize spin and orbital moments at buried interfaces in magnetic systems with unprecedented spatial resolution.
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