Extended reciprocal space observation of artificial spin ice with x-ray resonant magnetic scattering

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Extended reciprocal space observation of artificial spin ice with x-ray resonant magnetic scattering

J. Perron, L. Anghinolfi, B. Tudu, N. Jaouen, J.-M. Tonnerre, M. Sacchi, F. Nolting, J. Lüning, and L. J. Heyderman

Phys. Rev. B 88, 214424 – Published 23 December 2013

Abstract

Soft x-ray resonant magnetic scattering is an element-sensitive technique that enables the characterization of the magnetic properties of a wide variety of systems. Here we apply this technique to study lithographically produced artificial spin ice, a particular class of magnetically frustrated systems comprising arrays of nanomagnets. Using a CCD detector we can access a large fraction of the reciprocal space at once, allowing us to easily distinguish the signatures of the magnetic ground-state ordering. Comparing the dichroic signal at the position of the Bragg peaks with model calculations based on the kinematical theory of x-ray diffraction, we are able to determine the number of reversed moments as a function of applied magnetic field for each of the two sublattices. This study demonstrates the benefit of having direct access to a significant fraction of the reciprocal space, and opens the way towards more sophisticated x-ray based experiments on artificial spin ice such as scattering of coherent x-ray beams to explore the dynamics of thermally activated systems.

Received 23 October 2013

DOI:https://doi.org/10.1103/PhysRevB.88.214424

Authors & Affiliations

J. Perron^1,2,3,4, L. Anghinolfi^3,4,*, B. Tudu^1,2,†, N. Jaouen⁵, J.-M. Tonnerre^6,7, M. Sacchi^5,8,9, F. Nolting⁴, J. Lüning^1,2, and L. J. Heyderman^3,4

¹Sorbonne Universités, UPMC Univ Paris 06, UMR 7614, LCPMR, 75005 Paris, France
²CNRS, UMR 7614, LCPMR, 75005 Paris, France
³Laboratory for Mesoscopic Systems, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
⁴Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
⁵Synchrotron SOLEIL, 91192 Gif-sur-Yvette, France
⁶Université Grenoble Alpes, Institut Néel, 38042 Grenoble, France
⁷CNRS, Institut Néel, 38042 Grenoble, France
⁸Sorbonne Universités, UPMC Univ Paris 06, UMR 7588, INSP, 75005 Paris, France
⁹CNRS, UMR 7588, INSP, 75005 Paris, France

^*luca.anghinolfi@psi.ch
^†Current address: Department of Physics, Jadavpur University, 700032 Kolkata, India.

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Vol. 88, Iss. 21 — 1 December 2013

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Images

Figure 1
(a) SEM picture of part of the $2 \times 2$ mm $^{2}$ array of artificial square ice built from Permalloy nanomagnets of $230 nm \times 80 nm \times 20$ nm (length $\times$ width $\times$ thickness). Inset: Illustration of the cylindrical approximation used to analytically represent the individual nanomagnets. The cylinders have height $h$ and elliptical cross section with semiaxes $a$ and $b$ . (b) Experimental scattering setup. The sample surface is parallel to the $x − y$ plane, with the direction of the incident x-ray beam and applied magnetic field, $H$ , along $y$ . The angle of incidence is $θ = 8^{\circ}$ .
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Figure 2
Scattering from as-grown artificial square ice. (a) Schematic of the sample geometry. The dashed box indicates the structural unit cell, containing two nanomagnets with different orientations. The corresponding two sublattices $S_{1}$ and $S_{2}$ are highlighted in gray and white, respectively. The red arrows represent the lattice vectors and the red dots indicate the square lattice, which has periodicity $a$ . (b) Experimental scattering pattern recorded off resonance (690 eV), containing structural information only. The first order Bragg peaks are indicated with a dashed box. The position of the specular reflection, which has been suppressed using a beam stop, is indicated with a dashed ellipse. (c) Schematic of the magnetic ground state, consisting of alternating rows of nanomagnets (highlighted in gray and white) with magnetic moments pointing towards opposite directions. The magnetic unit cell is indicated with the dashed box. (d) Experimental scattering pattern recorded at the Fe $L_{3}$ edge (706.8 eV), including both structural and magnetic information. The Bragg peaks highlighted in red are of pure magnetic origin and are a signature of long range ground-state ordering of the nanomagnet moments. The dashed box indicates the same first order Bragg peaks as in (b). (e) Schematic of a state at remanence following saturation. (f) Scattering pattern recorded at the Fe $L_{3}$ edge (706.8 eV) at remanence (zero field) after applying a magnetic field of 0.1 T.
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Figure 3
XMCD contrast at different Bragg peaks at remanence as a function of applied field. (a) Scattering pattern with the peaks considered, labeled $P_{1}$ to $P_{4}$ ( $S P$ indicates the specular reflection). (b) Schematic of the sample misalignment with respect to the applied field direction. The angle between the field direction and the nanomagnet long axis is bigger in the sublattice $S_{1}$ (indicated with $φ_{1}$ ) than in $S_{2}$ (indicated with $φ_{2}$ ). (c) XMCD contrast at the first order peaks $P_{1}$ and $P_{2}$ . The two loops have different coercive fields, $H_{P_{1}} = 475$ Oe and $H_{P_{2}} = 455$ Oe, respectively. (d) XMCD contrast at the second order peaks $P_{3}$ and $P_{4}$ . Here, the two curves are identical within the experimental error and the coercive field is $H_{P_{3}} = H_{P_{4}} = 468$ Oe.
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Figure 4
Comparison between experimental and numerical dichroic scattering patterns. Figures (a) and (c) have been measured at applied magnetic fields of 480 Oe and $- 472$ Oe, respectively. The corresponding calculated best-fit patterns are shown in (b) and (d).
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