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Center for Nonlinear Studies |
Magnetism has provided a fertile testbed for physical models, such as the Heisenberg and Ising models. Most of these investigations have focused on solid materials and relate to their atomic properties such as the atomic magnetic moments and their interactions. Recently, advances in nanotechnology have enabled the controlled patterning of nano-sized magnetic particles, which can be arranged in extended lattices. Tailoring the geometry and the magnetic material of these lattices, the magnetic interactions and magnetization reversal energy barriers can be tuned. This enables interesting interaction schemes to be examined on adjustable length and energy scales. As a result such nano-magnetic systems represent an ideal playground for the study of physical model systems, being facilitated by direct magnetic imaging techniques. One particularly interesting case is that of systems exhibiting frustration, where competing interactions cannot be simultaneously satisfied. This results in a degeneracy of the ground state and intricate thermodynamic properties. An archetypical frustrated physical system, is water ice [1]. Similar physics can be mirrored in nano-magnetic arrays, by tuning the arrangement of neighboring magnetic islands, referred to as artificial spin ice, where an ensemble of dipolar coupled lithographically fabricated single-domain islands are arranged on frustrated lattices [2]. The phase space of these systems comprises an extensive manifold of ground states and magnetically charged vertex state excitations [3]. The thermal creation of these charges and the investigation of their dynamics is a highly desirable objective for the exploration of effects related to magnetic charge propagation and manipulation. However, until recently the energy scales associated with excitations have been thermally inaccessible, inhibiting ergodicity and rendering the study of magnetic fluctuations and dynamics challenging [4, 5]. Here we demonstrate how the energy landscape of extended artificial spin ice systems can be shaped by the design of the lattice geometry and choice of magnetic material. Using Photo-Electron Emission Microscopy (PEEM) employing x-ray magnetic circular dichroism (XMCD), we show that the extent of thermal ground state ordering is affected by the strength of dipolar interactions, and by monitoring the abundance of different vertex states we identify a transition from a frozen state to one in which the system is capable of exploring its energy landscape utilizing thermal fluctuations. This work provides a route for the control of the density of magnetic monopole charges and their interactions in extended artificial spin ice systems.
[1] L. Pauling, The structure and entropy of ice and of other crystals with some randomness of atomic arrangement, Journal of the American Chemical Society 57, 2680–2684 (1935).
[2] R. F. Wang, C. Nisoli, R. S. Freitas, J. Li, W. McConville, B. J. Cooley, M. S. Lund, N. Samarth, C. Leighton, V. H. Crespi, and P. Schiffer, Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands, Nature 439, 303–306 (2006).
[3] J. P. Morgan, A. Stein, S. Langridge, and C. H. Marrows, Thermal ground-state ordering and elementary excitations in artificial magnetic square ice, Nature Physics 7, 75–79 (2011).
[4] V. Kapaklis, U. B. Arnalds, A. Harman-Clarke, E. T. Papaioannou, M. Karimipour, P. Korelis, A. Taroni, P. C. W. Holdsworth, S. T. Bramwell, and B. Hj¨ orvarsson, Melting artificial spin ice, New Journal of Physics 14, 035009 (2012).
[5] A. Farhan, P. M. Derlet, A. Kleibert, A. Balan, R. V. Chopdekar, M. Wyss, L. Anghinolfi, F. Nolting, and L. J. Heyderman, Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems, Nature Physics 9, 375–382 (2013).
[6] A. Farhan, P. M. Derlet, A. Kleibert, A. Balan, R. V. Chopdekar, M. Wyss, J. Perron, A. Scholl, F. Nolting, and L. J. Heyderman, Direct Observation of Thermal Relaxation in Artificial Spin Ice, Physical Review Letters 111, 057204 (2013).
Host: Cristiano Nisoli