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Abstract
We report Xray resonant magnetic scattering studies of a Permalloy artificial square ice nanomagnet array, focussing on the fielddriven evolution of the sum Σ and difference Δ signals of left and right handed circularly polarized synchrotron Xrays at different lateral positions in reciprocal space Q _{ x }. We used Xrays tuned to the Fe L_{3} resonance energy, with the scattering plane aligned along a principal symmetry axis of the array. Details of the specular Δ hysteresis curve are discussed, following the system magnetization from an initial demagnetized state. The periodic structure gives rise to distinct peaks at inplane reciprocal Bragg positions, as shown by fitting Σ(Q _{ x }) to a model based on a simple unit cell structure. Diffraction orderdependent hysteresis in Δ is observed, indicative of the reordering of magnetization on the system's two interpenetrating sublattices, which markedly deviates from an ideal Ising picture under strong applied fields.
We would like to thank Raymond Fan for useful discussions. This work was supported by the UK EPSRC and the STFC Centre for Materials Physics and Chemistry. The research was carried out in part at the Center for Functional Nanomaterials and the National Synchrotron Light Source, Brookhaven National Laboratory, which are supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DEAC0298CH10886.
I. INTRODUCTION
II. METHODS
III. RESULTS
A. Specular Virgin Hysteresis Loop
B. Magnetic Rocking Curve
C. Offspecular Hysteresis Loops
IV. CONCLUSIONS
Key Topics
 Xray scattering
 17.0
 Magnetic hysteresis
 12.0
 Magnetic islands
 12.0
 Ice
 8.0
 Soft Xrays
 6.0
Figures
(a) Scanning electron microscopy image of an artificial square ice. Nominally, elements are L = (264.5 ± 0.2) nm by w = (104.8 ± 0.3) nm in area, fabricated from a Permalloy layer of 26 nm thickness, with a lattice constant of a = 500 nm. The scale bar indicates a length of 500 nm as defined by the microscope. A structural unit cell (UC) is boxed. (b) The scattering geometry used, with reference to the defined Cartesian coordinate axes. xz is defined as the scattering plane, with z normal to the sample surface. xy is the sample plane. Q is the wave vector transfer, the difference between scattered and incident Xray wave vector respectively, as discussed in the text. The structural unit cell is also boxed. A simple model of the ideal structural unit cell is shown inset, with island 1 and 2 shown as white and grey rectangles respectively. Note, for ease of calculation, the UC is positioned to cut elements in half lengthwise with elements overlapping the UC boundary, as per Eq. (2). Magnetic field H was applied in the xdirection.
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(a) Scanning electron microscopy image of an artificial square ice. Nominally, elements are L = (264.5 ± 0.2) nm by w = (104.8 ± 0.3) nm in area, fabricated from a Permalloy layer of 26 nm thickness, with a lattice constant of a = 500 nm. The scale bar indicates a length of 500 nm as defined by the microscope. A structural unit cell (UC) is boxed. (b) The scattering geometry used, with reference to the defined Cartesian coordinate axes. xz is defined as the scattering plane, with z normal to the sample surface. xy is the sample plane. Q is the wave vector transfer, the difference between scattered and incident Xray wave vector respectively, as discussed in the text. The structural unit cell is also boxed. A simple model of the ideal structural unit cell is shown inset, with island 1 and 2 shown as white and grey rectangles respectively. Note, for ease of calculation, the UC is positioned to cut elements in half lengthwise with elements overlapping the UC boundary, as per Eq. (2). Magnetic field H was applied in the xdirection.
Specular hysteresis of the Δ signal for 2θ = 16°, measured with the PD. Beginning from an initial asfabricated state of M _{ x } = 0, Δ^{0 +}(H) (circles) follows polarization of the system into a saturated state at H = +1.5 kOe, which is maintained up to +2 kOe. Δ^{+−} (squares) and Δ^{−+} (triangles) then follow a main hysteresis loop between ±2 kOe.
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Specular hysteresis of the Δ signal for 2θ = 16°, measured with the PD. Beginning from an initial asfabricated state of M _{ x } = 0, Δ^{0 +}(H) (circles) follows polarization of the system into a saturated state at H = +1.5 kOe, which is maintained up to +2 kOe. Δ^{+−} (squares) and Δ^{−+} (triangles) then follow a main hysteresis loop between ±2 kOe.
Inplane Q _{ x } rocking scans along a principal square ice axis, measured with the APD at 2θ = 11.66°, with H held at +100 Oe following a large polarizing field of −2 kOe. Σ(Q _{ x }) (circles) is found to possess a Hindependent background with Bragg peaks at positions Q _{ x } = 2n _{ x }π/a for diffraction orders n _{ x }, which are wellfit to a simple model (solid line) based on the unit cell shown in Fig. 1 and Eqs (1) to (3), as described in the text. Fitting returns L = 247.1 nm, w = 86.4 nm and a = 516.6 nm. The polarized magnetic state, also with period a, results in coincident peaks in Δ(Q _{ x }) (squares). The halforder features observed, indicated by arrows, are attributed to weak harmonic contamination from the monochromator.
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Inplane Q _{ x } rocking scans along a principal square ice axis, measured with the APD at 2θ = 11.66°, with H held at +100 Oe following a large polarizing field of −2 kOe. Σ(Q _{ x }) (circles) is found to possess a Hindependent background with Bragg peaks at positions Q _{ x } = 2n _{ x }π/a for diffraction orders n _{ x }, which are wellfit to a simple model (solid line) based on the unit cell shown in Fig. 1 and Eqs (1) to (3), as described in the text. Fitting returns L = 247.1 nm, w = 86.4 nm and a = 516.6 nm. The polarized magnetic state, also with period a, results in coincident peaks in Δ(Q _{ x }) (squares). The halforder features observed, indicated by arrows, are attributed to weak harmonic contamination from the monochromator.
Hysteresis of normalized signal at increasing diffraction orders, n _{ x } = 0 to + 4, measured with the APD at 2θ = 11.66°. The curves appear as superpositions of easylike and hardlike hysteresis loops, related to the two orthogonal sublattices of the system. Error bars are calculated as the standard error from nine repeated normalized curves at a given diffraction order.
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Hysteresis of normalized signal at increasing diffraction orders, n _{ x } = 0 to + 4, measured with the APD at 2θ = 11.66°. The curves appear as superpositions of easylike and hardlike hysteresis loops, related to the two orthogonal sublattices of the system. Error bars are calculated as the standard error from nine repeated normalized curves at a given diffraction order.
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Abstract
We report Xray resonant magnetic scattering studies of a Permalloy artificial square ice nanomagnet array, focussing on the fielddriven evolution of the sum Σ and difference Δ signals of left and right handed circularly polarized synchrotron Xrays at different lateral positions in reciprocal space Q _{ x }. We used Xrays tuned to the Fe L_{3} resonance energy, with the scattering plane aligned along a principal symmetry axis of the array. Details of the specular Δ hysteresis curve are discussed, following the system magnetization from an initial demagnetized state. The periodic structure gives rise to distinct peaks at inplane reciprocal Bragg positions, as shown by fitting Σ(Q _{ x }) to a model based on a simple unit cell structure. Diffraction orderdependent hysteresis in Δ is observed, indicative of the reordering of magnetization on the system's two interpenetrating sublattices, which markedly deviates from an ideal Ising picture under strong applied fields.
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