Artificial Spin Ice: Thermal Relaxation and Emergent Magnetic Monopoles in Arrays of Frustrated Nanomagnets
Figure 1: Direct observation of thermal relaxation in artificial square ice . While undergoing thermal relaxation from an energetically excited state (a), the system passes through two distinct regimes, namely a string regime (a)-(d), with isolated strings of reversed island moments increasing in length and number, followed by a domain regime (e)-(g). In the domain regime there are many ground state domains of opposite chirality, with some expanding while others shrink until the whole array is in a fully ordered single-domain ground state configuration (h).Artificial spin ice systems, consisting of dipolar coupled single-domain nanomagnets arranged in two-dimensional geometries, have drawn increasing interest from the research community as they provide a possibility to investigate the effects of geometrical frustration in real space and time using appropriate imaging techniques. With electron beam lithography, one can fine tune the structure of the system in terms of nanomagnet size, lattice geometry and lattice periodicity. The system behaviour in response to an external stimulus can then be investigated with different microscopy techniques.
Thus far, the main research focus was directed towards investigations of two geometries, namely artificial square ice and artificial kagome spin ice [1-7]. Artificial square ice was first introduced as a two-dimensional analogue to pyrochlore spin ice, where the role of the Ising spins is mimicked by the magnetic moments of elongated nanomagnets, whose shape anisotropy fixes their moment direction.
Figure 2: Thermal relaxation of a single-ring artificial kagome spin ice structure . Starting from two different high-energy states B1 and B2, the system will end up in one of two degenerate ground state configurations, A1 or A2, which depends on the pathway chosen within its energy landscape (blue arrows).Our initial research on artificial spin ice concentrated on field-driven experiments [6,7,8-10]. Employing x-ray photoemission electron microscopy (PEEM) to resolve the exact arrangement of the nanomagnet moments, we investigated the possibility to achieve with demagnetization procedures the low-energy configurations in the building blocks of artificial kagome ice , and we observed the creation and propagate of emergent magnetic monopoles in extended arrays [7,9,10].
Most recently our main goal has been to fabricate artificial spin ice structures that exhibit fluctuating magnetic moments at experimentally accessible temperatures in order to access their true thermodynamics. This was achieved either by patterning Permalloy (Ni80Fe20) wedge films [2,4,5] or -doped Pd(Fe) films [3,11]. In artificial square ice, we were able to follow in real time a thermally-driven relaxation process from an initial high energy configuration of the magnetic moments to a ground state configuration  (see Fig. 1). In building blocks of artificial kagome ice, our simple thermal annealing procedure, that involves a moderate heating above the nanomagnet blocking temperatures (TB = 320-330 K), proved to be highly effective in achieving the low-energy configurations [4,5] (see Fig. 2 and Movie below). However, with increasing systems size, it becomes more and more difficult to access the predicted ground state configurations , a fact that makes artificial kagome spin ice an ideal system to explore optimized annealing procedures both experimentally and theoretically.
- L. J. Heyderman and R. L. Stamps, Artificial ferroic systems: novel functionality from structure, interactions and dynamics. J Phys: Condens Matter 25, 363201 (2013).
- A. Farhan, P. M. Derlet, A. Kleibert, A. Balan, R. V. Chopdekar, M. Wyss, J. Perron, A. Scholl, F. Nolting, L. J. Heyderman, Direct Observation of Thermal Relaxation in Artificial Spin Ice. Phys Rev Lett 111, 057204 (2013).
- V. Kapaklis, U. B. Arnalds, A. Farhan, R. V. Chopdekar, A. Balan, A. Scholl, L. J. Heyderman, B. Hjorvarsson, Thermal fluctuations in artificial spin ice. Nat Nano 9, 514-519 (2014).
- A. Farhan, P. M. Derlet, A. Kleibert, A. Balan, R. V. Chopdekar, M. Wyss, L. Anghinolfi, F. Nolting, L. J. Heyderman, Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems. Nat Phys 9, 375-382 (2013).
- A. Farhan, A. Kleibert, P. M. Derlet, L. Anghinolfi, A. Balan, R. V. Chopdekar, M. Wyss, S. Gliga, F. Nolting, L. J. Heyderman, Thermally induced magnetic relaxation in building blocks of artificial kagome spin ice. Phys Rev B 89, 214405 (2014).
- E. Mengotti, L. J. Heyderman, A. Fraile Rodriguez, A. Bisig, L. Le Guyader, F. Nolting, H. B. Braun, Building blocks of an artificial kagome spin ice: Photoemission electron microscopy of arrays of ferromagnetic islands. Phys Rev B 78, 144402 (2008).
- E. Mengotti, L. J. Heyderman, A. F. Rodriguez, F. Nolting, R. V. Hugli, H. B. Braun, Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice. Nat Phys 7, 68-74 (2011).
- R. V. Chopdekar, G. Duff, R. V. Hugli, E. Mengotti, D. A. Zanin, L. J. Heyderman, H. B. Braun, Controlling vortex chirality in hexagonal building blocks of artificial spin ice. New J Phys 15, 125033 (2013).
- R. V. Hugli, G. Duff, B. O'Conchuir, E. Mengotti, L. J. Heyderman, A. F. Rodriguez, F. Nolting, H. B. Braun, Emergent magnetic monopoles, disorder, and avalanches in artificial kagome spin ice (invited). J Appl Phys 111, 07e103 (2012).
- R. V. Hugli, G. Duff, B. O'Conchuir, E. Mengotti, A. F. Rodriguez, F. Nolting, L. J. Heyderman, H. B. Braun, Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles. Philos T R Soc A 370, 5767-5782 (2012).
- U. B. Arnalds, A. Farhan, R. V. Chopdekar, V. Kapaklis, A. Balan, E. T. Papaioannou, M. Ahlberg, F. Nolting, L. J. Heyderman, B. Hjorvarsson, Thermalized ground state of artificial kagome spin ice building blocks. Appl Phys Lett 101, 112404 (2012).