Magnetic diffuse scattering in artificial kagome spin ice

Editors' Suggestion

Magnetic diffuse scattering in artificial kagome spin ice

Oles Sendetskyi, Luca Anghinolfi, Valerio Scagnoli, Gunnar Möller, Naëmi Leo, Aurora Alberca, Joachim Kohlbrecher, Jan Lüning, Urs Staub, and Laura Jane Heyderman

Phys. Rev. B 93, 224413 – Published 13 June 2016

Abstract

The study of magnetic correlations in dipolar-coupled nanomagnet systems with synchrotron x-ray scattering provides a means to uncover emergent phenomena and exotic phases, in particular in systems with thermally active magnetic moments. From the diffuse signal of soft x-ray resonant magnetic scattering, we have measured magnetic correlations in a highly dynamic artificial kagome spin ice with sub-70-nm Permalloy nanomagnets. On comparing experimental scattering patterns with Monte Carlo simulations based on a needle-dipole model, we conclude that kagome ice I phase correlations exist in our experimental system even in the presence of moment fluctuations, which is analogous to bulk spin ice and spin liquid behavior. In addition, we describe the emergence of quasi-pinch-points in the magnetic diffuse scattering in the kagome ice I phase. These quasi-pinch-points bear similarities to the fully developed pinch points with singularities of a magnetic Coulomb phase, and continually evolve into the latter on lowering the temperature. The possibility to measure magnetic diffuse scattering with soft x rays opens the way to study magnetic correlations in a variety of nanomagnetic systems.

Received 11 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.224413

Physics Subject Headings (PhySH)

Dipolar interaction Superparamagnetism

2-dimensional systems Magnetic systems Nanostructures

Kagome lattice Spin ice X-ray diffuse scattering X-ray resonant magnetic scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Oles Sendetskyi^1,2, Luca Anghinolfi^1,2,3, Valerio Scagnoli^1,2, Gunnar Möller^4,*, Naëmi Leo^1,2, Aurora Alberca⁵, Joachim Kohlbrecher³, Jan Lüning^6,7, Urs Staub⁵, and Laura Jane Heyderman^1,2,†

¹Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland
²Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
³Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
⁴TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
⁵Swiss Light Source, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
⁶Sorbonne Universités, UPMC Université de Paris 06, UMR 7614, LCPMR, 75005 Paris, France
⁷CNRS, UMR 7614, LCPMR, 75005 Paris, France

^*Present address: School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom; G.Moller@kent.ac.uk
^†laura.heyderman@psi.ch

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 93, Iss. 22 — 1 June 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Scanning electron microscopy image of our artificial kagome spin ice sample with sub-70-nm nanomagnets. A magnified image of a single kagome ring is given in the inset with the lattice and nanomagnet dimensions in nm. (b) Schematic illustration of the nanomagnets on the kagome lattice with the structural unit cell marked in pink, which belongs to the $p 6 m m$ plane group. $a_{1}, a_{2}$ , and $a_{3}$ are the structural lattice unit vectors. Thin gray lines represent mirror planes and serve as a guide for the eye. The experimental scattering plane is parallel to the crystallographic direction $〈 1 \bar{2} 1 〉$ indicated by the black arrow. There are three nanomagnets per unit cell, indicated by the three nanomagnets shaded in black.
Reuse & Permissions
Figure 2
Experimental geometry for x-ray resonant magnetic scattering with circularly polarized $C_{+}$ synchrotron x rays. $k_{i}, θ_{i}$ are the incident x-ray wave vector and angle, and $k_{f}, θ_{f}$ are the final wave vector and angle. $q_{z}$ and $q_{x}$ are the momentum transfers along the $z$ and $x$ directions, respectively. The orientation of the nanomagnets relative to the scattering plane is shown schematically in the inset.
Reuse & Permissions
Figure 3
Zero-field-cooled and field-cooled magnetization (ZFC/FC) measurements of our artificial kagome spin ice sample performed with a SQUID magnetometer using an external magnetic field of 10 Oe. The blocking temperature $T_{b} = 160$ K is indicated with an arrow. The standard errors are smaller than the data markers.
Reuse & Permissions
Figure 4
Comparison between experimental and calculated magnetic diffuse scattering patterns in reflection geometry. (a) Magnetic scattering pattern measured at 200 K, obtained from the difference between the on-resonance and off-resonance patterns at 708 eV and 690 eV, respectively. (b) Numerical calculation of the resonant magnetic scattering from Monte Carlo configurations in the kagome ice I phase. (c) Magnetic scattering pattern measured at 280 K, obtained from the difference between the on-resonance and off-resonance patterns at 708 eV and 690 eV, respectively. (d) Numerical calculation of the resonant magnetic scattering from Monte Carlo configurations in the paramagnetic phase. Only the magnetic scattering contribution was simulated. The scattering plane was oriented along the $〈 1 \bar{2} 1 〉$ crystallographic direction [see Figs. 1 and 2]. Each experimental pattern is an average over eleven measurements. The dark blue broad stripes on the experimental patterns are the shadows of the aluminum mask, which covers the Bragg peaks and specular reflection. The arcs of closely packed reflections in the experimental patterns arise due to the contamination from higher-order harmonics of the undulator.
Reuse & Permissions
Figure 5
Numerical calculation of the structure factor (top row) and resonant magnetic scattering in transmission geometry (bottom row). Only the magnetic contribution is shown as predicted from Monte Carlo simulations. Data for the paramagnetic [(a), (b)] and kagome ice I phase [(c), (d)] are based on the same set of Monte Carlo configurations that we used for comparison with the experimental results shown in Fig. 4. For the kagome ice II phase [(e), (f)] the representative configurations were also taken from our Monte Carlo simulations. Note that magnetic pinch points appear at the same positions as the structural peaks (not shown), e.g., at ( $01 \bar{1}$ ), ( $10 \bar{1}$ ), ( $1 \bar{1} 0$ ), ( $0 \bar{1} 1$ ), ( $\bar{1} 01$ ), and ( $\bar{1} 10$ ). Insets in the lower row are the intensity profiles of the pinch point at the ( $\bar{1} 10$ ) position.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics