Session R50: Artificial Spin Ice and Honeycomb Structures

Temperature dependent magnetism and asymmetric current biasing in artificial honeycomb lattice

The artificial honeycomb lattice is evolving into a new research arena to explore a plethora of novel magnetism predicted to occur as functions of temperature: a long-range spin ice, a spin liquid, an entropy driven magnetic charge-ordered state due to spin chirality. At low temperatures, the spin correlation is expected to develop into a unique spin solid state with net zero entropy and magnetization for an ordered ensemble of magnetic moments. We have created macroscopic samples of artificial magnetic honeycomb lattices of Permalloy with connected ultra-small bonds, \textasciitilde 10 nm bar length, which have never before been possible. The equivalent energy of the resulting systems is 10K and is thus amenable to both temperature- and field-dependent exploration of novel magnetic phenomena. We have performed detailed magnetic and electrical measurements that demonstrate the temperature dependent evolution of the magnetic correlation that reaches the spin solid state at low temperature for the first time. The electrical data exhibits an asymmetric current bias at higher temperatures, analogous to the properties of a semiconductor diode. This unique finding can be utilized to create a magnetic transistor and provides a new platform for spintronic applications.   

Magnetic Correlation in rare-earth artificial honeycomb system

2D artificial honeycomb lattice provides new avenue for the exploration of novel phases of magnetism, such as charge ordered and spin ordered states due to the spin chirality of vortex-type magnetic configuration in the structure. Previous experiments in this pursuit are limited by the present fabrication technique, which results in large element size and small samples. Using a new approach of hierarchical nanofabrication technique, we have been able to fabricate macroscopic size artificial honeycomb lattice of rare-earth magnet (Nd) with ultra-small bond size (12 x 5 x 5 nm). Magnetic and electronic measurements on the newly fabricated honeycomb sample reveal temperature dependent evolution of magnetic correlation in the system. In an interesting observation, it is found that magnetic properties changes from paramagnetic to diamagnetic in low applied magnetic field measurements (\textless 50 Oe). The corresponding transition temperature increases as the applied field decreases. This observation is in complete contrast to the permalloy honeycomb lattice, where a tendency to the spin solid state was detected at low temperature. The experimental results, in conjunction with micromagnetic simulations and theoretical calculations, will be discussed in the talk.   

Determination of the spin dynamics and magnetic Dirac nodes in a Heisenberg honeycomb lattice

We examine the energy ground states for different magnetic ground states of honeycomb lattices. Using linear spin wave theory, we analyze the evolution between the nearest, next-nearest, and next-next-nearest superexchange couplings for each spin configuration and compare to the ferromagnetic case. Overall, a phase diagram is determined and illustrates the spontaneous energy states in terms of exchange coupling. Furthermore, we analytically evaluate the spin dynamics and critical anisotropies for the various states, and show the presence of Goldstone modes and, in some cases, magnetic Dirac nodes for different spin configurations and couplings.   

Magnon bands with non-trivial topology in an artificial square spin ice

Artificial square spin ices can be viewed as reconfigurable magnonic crystals in which the magnon band structure can be manipulated by re-arranging the equilibrium magnetic configuration of the magnetic islands[1,2]. Depositing the islands on a spin-orbit scatterer such as Ta or Pt, endows the islands with an interfacial Dzyalishinskii-Moriya interaction. Here, we show using a semi-analytical model that this leads to a non-trivial topology in the magnon band structure. We use micromagnetic simulations to obtain the equilibrium magnetic states and to validate the semi-analytical model for the magnon dispersions in the first Brillouin zone. Our results are amenable to experimental verification using lithography and micro-focused Brillouin light scattering. The emergence of non-trivial topologies in the magnon bands implies the existence of topologically protected edge bands. This potentially leads to new applications using magnons in information technology. 1. E. Iacocca, S. Gliga, R.L. Stamps, and O. Heinonen, Phys. Rev. B {\bf93}, 134420 (2016). 2. Y.-L. Wang et al., Science {\bf352}, 6288 (2016).   

Quantifying the effects of disorder on switching of perpendicular spin ice arrays

There is much contemporary interest in probing custom designed, frustrated systems such as artificial spin ice. To that end, we study arrays of lithographically patterned, single-domain Pt/Co multilayer islands. Due to the perpendicular anisotropy of these materials, we are able to use diffraction-limited magneto-optical Kerr effect microscopy to access the magnetic state in situ with an applied field. As we tune the interaction strength by adjusting the lattice spacing, we observe the switching field distribution broadening with increasing dipolar interactions. Using a simple mathematical analysis we extract the intrinsic disorder (the disorder that would be present without interactions) from these switching field distributions. We also characterize the intrinsic disorder by systematically removing neighbor effects from the switching field distribution. Understanding this disorder contribution as well as the interaction strength allows us to more accurately characterize the moment correlation. This project was funded by the US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Grant No. DE- SC0010778   

3D magnetic nanostructures grown by focused electron and ion beam induced deposition

Three-dimensional nanomagnetism is an emerging research area, where magnetic nanostructures extend along the whole space, presenting novel functionalities not limited to the substrate plane. The development of this field could have a revolutionary impact in fields such as electronics, the Internet of Things or bio-applications. In this contribution, I will show our recent work on 3D magnetic nanostructures grown by focused electron and ion beam induced deposition. This 3D nano-printing techniques, based on the local chemical vapor deposition of a gas via the interaction with electrons and ions, makes the fabrication of complex 3D magnetic nanostructures possible. First, I will show how by exploiting different growth regimes, suspended Cobalt nanowires with modulated diameter can be patterned, with potential as domain wall devices. Afterwards, I will show recent results where the synthesis of Iron-Gallium alloys can be exploited in the field of artificial multiferroics. Moreover, we are developing novel methodologies combining physical vapor deposition and 3D nano-printing, creating Permalloy 3D nanostrips with controllable widths and lengths up to a few microns. This approach has been extended to more complex geometries by exploiting advanced simulation growth techniques combining Monte Carlo and continuum model methods. Throughout the talk, I will show the methodology we are following to characterize 3D magnetic nanostructures, by combining magneto-optical Kerr effect, scanning probe microscopy and electron and X-R magnetic imaging, and I will highlight some of the challenges and opportunities when studying these structures.   

Magnetoresistance in Permalloy Connected Brickwork Artificial Spin Ice

Artificial spin ice refers to a two-dimensional array of elongated ferromagnetic elements in which frustrated lattice geometry induces novel magnetic behavior. Here we examine room-temperature magnetoresistance properties of connected permalloy (Ni$_{\mathrm{81}}$Fe$_{\mathrm{19}})$ brickwork artificial spin ice. Both the longitudinal and transverse magnetoresistance of the nanostructure demonstrate an angular sensitivity that has not been previously observed. The observed magnetoresistance behavior can be explained from micromagnetic modelling using an anisotropic magnetoresistance model (AMR). As part of this study, we find that the ground state of the connected brickwork artificial spin ice can be reproducibly created by a simple field sweep in a narrow range of angles, and manifests in the magnetotransport with a distinct signal. Supported by the US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under grant number DE-SC0010778. Work at the University of Minnesota was supported by the NSF MRSEC under award DMR-1420013, and DMR-1507048.   

Emergent thermal kinetic behavior of artificial spin ice

Artificial spin ice systems are two dimensional arrays of single-domain nanomagnets designed to study frustration phenomena. By careful choice of the geometry of the system, the lattices can have ground states with non-trivial degeneracy. We study the kinetics of such systems through photoemission electron microscopy (PEEM) measurements of the fluctuations of the individual nanomagnet moments, looking at excitations above the magnetic ground states of the systems and how those excitations are impacted by lattice geometry. Detailed analysis of different systems shows non-trivial kinetics that originate from different interaction patterns. The study indicates the important role of effective excitation in the near-ground-state kinetics of these frustrated systems. This work was funded by the US Department of Energy under grant number DE-SC0010778. The work of M.S. and K.D. was supported by DOE DE-FE0011194. Work at UMN was supported by the NSF MRSEC under DMR-1420013, and DMR-1507048. The work of C.N. was carried out under the auspices of the US Department of Energy at LANL under contract number DE-AC52-06NA253962. The ALS was supported by the US Department of Energy under contract number DE-AC02-05CH11231.   

Thermodynamics of Polaronic States in Artificial Spin Ice

Artificial spin ices represent a class of systems consisting of lithographically patterned nanomagnets arranged in two-dimensional geometries. They were initially introduced as a two-dimensional analogue to geometrically frustrated pyrochlore spin ice, and the most recent introduction of artificial spin ice systems with thermally activated moment fluctuations not only delivered the possibility to directly investigate geometrical frustration and emergent phenomena with real space imaging, but also paved the way to design and investigate new two-dimensional magnetic metamaterials, where material properties can be directly manipulated giving rise to properties that do not exist in nature. Here, taking advantage of cryogenic photoemission electron microscopy, and using the concept of emergent magnetic charges, we are able to directly visualize the creation and annihilation of screened emergent magnetic monopole defects in artificial spin ice. We observe that these polaronic states arise as intermediate states, separating an energetically excited out-of-equilibrium state and low-energy equilibrium configurations. They appear as a result of a local screening effect between emergent magnetic charge defects and their neighboring magnetic charges, thus forming a transient minimum, before the system approaches a global minimum with the least amount of emergent magnetic charge defects.   

The Role of Geometric Defects in Frustrated Artificial Spin Ice Systems

Artificial spin ice systems consist of small islands of magnetization arranged in a lattice to order to create frustrated states at the vertices where the islands meet. In square ice magnetic islands have been removed to create the Shatki and Tetris lattices which alter the degree of frustration. In this work we introduce and investigate the effects of randomly removing magnetic islands in hexagonal spin ice by implementing the Metropolis-Hastings Monte Carlo Method to find equilibrium states over a wide temperature range. The geometric defects remove frustration at some of the vertices impacting the transition between the various charge ordered phases which is evident by a change in the transition temperature observed in heat capacity calculations. The inclusion of geometric defects also impacts the magnetization reversal properties leading to interesting dynamical phenomena not observed in the complete array. The random removal of islands leads to several different types of defects; large loops are often formed which induce a long range ordering, and single magnets are sometimes attached at only one vertex which can oscillate between two states. The various types of defects and their implications to the equilibrium states and reversal dynamics are investigated.   

Magnetic field-induced splitting of Bragg peaks in resonant magnetic x-ray diffraction from square artificial spin ice

Artificial spin ice (ASI) is a class of periodic magnetic nanostructures that can display magnetic phenomena like that of natural spin ices, including analogs of magnetic monopoles. Based on the ice structure and field history, ASI systems can form a variety of energetically degenerate magnetic structures. When we probed the magnetic structure of a square ASI using spatially coherent Fe L$_3$ ($\approx$707eV) x-rays, we found that ASI Bragg peaks split when exposed to magnetic fields. This field-induced splitting is reversible: Bragg peaks display gaussian profiles in zero-field. We will present a scattering model, analogous to the theory of anti-phase domains in alloys, that reveals the magnetic structure of the square ASI necessary to create split Bragg peaks.   

Emergent glassy state in a disordered artificial spin ice

Artificial spin ice has enabled the study of exotic frustrated matter not directly accessible in nature. Recently a new type of artificial spin ice on the shakti lattice has been proposed and experimentally observed. Here we investigate the emergence of the shakti ice phase starting from the well studied square spin-ice array. Due to the lack of a true degeneracy among the various ice-rule vertices, the square ice array develops a long-range N\'eel type order at low temperatures. By introducing long island spin to the center of randomly selected plaquettes, we show that the spin N\'eel order is quickly destroyed when the density of the center islands reaches the site percolation threshold, giving rise to a glassy phase. Interestingly, further addition of the center islands pushes the system into a spin ice phase. While spins remain disordered in both the glass and ice states, these two phases are distinguished by different dynamical behaviors as we demonstrated through a finite-size study of the spin-glass susceptibility. Our work also suggests a new approach to study the interplay of long range order, spin glass, and spin ice.