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Critical field and mobility for monopole drift motion. (a), The data points show the critical field, Bcrit = μ0Hcrit, for the onset of monopole motion for arrays of two different strengths of interaction, extracted from the fits in Fig. 4. The solid lines are the values from the modified Bean-Livingston theory. (b) The data points show the magnetic mobility μm extracted from the fits in Fig. 4, also plotted for each array. The solid lines are fits of Eq. 5 to the data. In both cases the solid symbols are for the a = 350 nm and the open symbols are for the a = 400 nm array.
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Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray...
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The interplay between topology and energy-hierarchy plays a vital role in the collective magnetic order in artificial ferroic systems. Here we investigate, experimentally, the effect of having one or two activation energies of interacting Ising-like magnetic islands -- mesospins -- in a thermalized, topologically frustrated artificial spin ice. The...
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... 10,15,16 As a result, the excitation occurring in square ASI is confined by strong string tension, resembling a pair of Nambu magnetic monopoles. [17][18][19][20][21][22][23] Recent advances in experimental techniques and nanofabrication have allowed the construction of three-dimensional ASI structures. [24][25][26][27] In this context, two sublattices of nanomagnets are vertically separated by a height offset h, populated by free magnetic monopoles at a critical height, h c . ...
Magnetic structure factor (MSF), calculated from ground state configuration previously obtained by Monte Carlo simulation in different rectangular artificial spin ices, is employed to investigate ground state degeneracy. Our analysis considers the importance of nanoislands size to the ratio between rectangle sides in the lattice parameters via a dumbbell model. Pinch points in MSF along with residual entropy, determined for a number of different rectangular lattices with disconnected nanoislands, point out the conditions for the emergency of a gauge field, through which magnetic monopoles interact effectively.
... have been investigated. These systems allow higher magnetic monopole mobility [8][9][10][11], because they present a non-energetic string connecting magnetic monopoles [12][13][14][15][16], resembling what has been called Dirac monopoles in natural crystals [17]. Some of the major issues that still need to be resolved are the difficulty of building a system ground state manifold with zero magnetic charges at vertices and a controlled method of selectively regulating magnetic charge mobility. ...
Artificial spin ices (ASI), containing magnetic monopole quasi-particles emerging at room temperature, have been investigated as a promising system to be applied in alternative low-power information technology devices. However, restrictions associated with the intrinsic energetic connections between opposing magnetic monopoles in conventional ASI need to be overcome to achieve this purpose. Here, photon-magnon scattering in nanomagnets is examined as an approach to locally activate the collective dynamics of interacting magnetic systems at the nanoscale. Low-power white and polarized light were employed as a new tool to manipulate magnetic monopole intensity, leading to tuning on the particles response to external magnetic field and spontaneous magnetization flipping without external field (thermodynamics). Our findings showing evidence of magnetic monopole plasma formation in a regular square ASI system are explained by an analytical model of photon-magnon conversion acting directly on the ASI nanomagnet dipole. Micromagnetic simulations based on the samples parameters and values obtained from the model present a very good qualitative correspondence between theory and observations for the investigated ASI system.
... We note that string-like cascades have been previously reported in square ASI [46,47] and unconnected honeycomb ASI systems [48,49], where they can be induced by quenched disorder. The connectivity of ASI structures is expected to have a strong impact on reversal dynamics during field protocols [50,51], which is dominated by the effects of the vertex type [52,53]. ...
... artificial spin ice | monopoles | noise | frustrated magnetism | fractionalized excitation While the existence of elementary magnetic monopoles remains hypothetical, spin (i.e., dipole) excitations in certain frustrated magnetic systems (1)(2)(3)(4) can fractionalize and separate into two delocalized "monopole-like" quasiparticles that each carry an effective magnetic charge (5)(6)(7)(8)(9)(10)(11)(12). These fractionalized excitations are topologically protected, can diffuse through the crystal lattice in thermal equilibrium, and can move in response to applied magnetic fields, motivating studies of "magnetricity" in analogy to electricity (13)(14)(15)(16)(17). ...
Direct detection of spontaneous spin fluctuations, or “magnetization noise,” is emerging as a powerful means of revealing and studying magnetic excitations in both natural and artificial frustrated magnets. Depending on the lattice and nature of the frustration, these excitations can often be described as fractionalized quasiparticles possessing an effective magnetic charge. Here, by combining ultrasensitive optical detection of thermodynamic magnetization noise with Monte Carlo simulations, we reveal emergent regimes of magnetic excitations in artificial “tetris ice.” A marked increase of the intrinsic noise at certain applied magnetic fields heralds the spontaneous proliferation of fractionalized excitations, which can diffuse independently, without cost in energy, along specific quasi-1D spin chains in the tetris ice lattice.
... Direct observation of such emergent quasiparticles at room temperature was subsequently accomplished by magnetic force microscopy [3], despite the predicted ground state obeying ice rule at each vertex has often escaped from observation in real samples. In ASI's such monopoles are nowadays termed Nambu-like monopoles [4,5], once they are connected by energetic strings, as it takes place with their high energy counterparts [6]. ...
Magnetic monopole unpairing as a function of external magnetic fields is presented as a fingerprint of this emergent quasiparticles freedom in a two-dimensional artificial spin ice system. Such freedom, required for example for further application in magnetricity, is only possible due to ground-state degeneracy, which causes a decreasing of the string energy in rectangular geometries, designed to allow highest equidistance among nano-magnets. We show by simulations that spin correlation in different rectangular artificial spin ices evolves from antiferromagnetic ordered magnetic structure to a ferromagnetic one, passing through an ice regime were pinch points related to Coulomb phase are observed. By measurements of magnetic force microscopy, we observe magnetic monopole creation, transport and annihilation in such systems with free monopoles created and transported throughout the sample without strings attached, as is commonly observed in conventional artificial spin ice systems.
... These effects are distinct from those caused by traditional extrinsic factors and are susceptible to the defect shape anisotropy because of the direct coupling at the defectlattice interface. It is reasonable to expect that other methods to manipulate the magnetic state could also utilize the defect-lattice coupling mechanism, e.g., by spin-polarized currents, microwave 19,52 or thermal excitation 36,51,[53][54][55] , or nanoscale field manipulation 56,57 . ...
Lithographically defined arrays of nanomagnets are well placed for application in areas such as probabilistic computing or reconfigurable magnonics due to their emergent collective dynamics and writable magnetic order. Among them are artificial spin ice (ASI), which are arrays of binary in-plane macrospins exhibiting geometric frustration at the vertex interfaces. Macrospin flips in the arrays create topologically protected magnetic charges, or emergent monopoles, which are bound to an antimonopole to conserve charge. In the absence of controllable pinning, it is difficult to manipulate individual monopoles in the array without also influencing other monopole excitations or the counter-monopole charge. Here, we tailor the local magnetic order of a classic ASI lattice by introducing a ferromagnetic defect with shape anisotropy into the array. This creates monopole injection sites at nucleation fields below the critical lattice switching field. Once formed, the high energy monopoles are fixed to the defect site and may controllably propagate through the lattice under stimulation. Defect programing of bound monopoles within the array allows fine control of the pathways of inverted macrospins. Such control is a necessary prerequisite for the realization of functional devices, e. g. reconfigurable waveguide in nanomagnonic applications.
... These include floating solid-state thin films for dynamically reconfigurable functional nanodevices [1], thin films undergoing all-optical switching phenomena for magnetic recording media [2], thin films undergoing magnetic phase transitions [3], and the exploitation of static and dynamic magnetic properties of Heusler alloy thin films towards their implementation in recording media [4,5]. Patterned magnetic thin films are a particular subgroup of interesting magnetic materials being developed for current and future technological applications, including the study of magnetic memories through patterned topological insulator materials [6], magnetic skyrmions [7], and artificially frustrated nanostructured systems [8,9]. ...
Antidot lattices made of magnetic thin films are good candidates to be employed in future magnetic recording media. In this manuscript we present a study on the effect of shape and field-induced magnetic anisotropies on the magnetization reversal of 10 nm and 50 nm thick permalloy antidot lattices. Rounded antidot square lattices were fabricated using a combination of electron beam evaporation and laser interference lithography, covering surfaces of a few cm2. We demonstrate that a magnetic anisotropy induced in the samples, as a consequence of an applied magnetic field during growth, competes with the shape anisotropy that dominates the response of the patterned thin films, and that the effect of the field-induced magnetic anisotropy scales with the thickness of the antidot thin films. Finally, we have quantified the anisotropy constant attributable to the uniaxial field-induced magnetic anisotropy in our antidot lattices. These findings are supported by micromagnetic simulations performed using MuMax3.
... While transient applied fields are often used in demagnetization protocols that help bring the ASI to its thermodynamic ground state [6][7][8][9][10] or are used to establish an initial out-of-equilibrium magnetic configuration (whose relaxation is subsequently monitored in zero field [11,12]), most experimental and theoretical ASI studies have been principally concerned with their geometry-or temperaturedependent magnetic properties in zero field. However, it is widely appreciated that an applied magnetic field B can provide an extremely important and versatile tuning parameter in ASIs [13][14][15][16][17][18][19]. Depending on its magnitude and direction, B can be used to drive phase transitions between different magnetic order parameters, or tune through equilibrium regimes where magnetic quasiparticle excitations (e.g., "magnetic monopoles") can readily form. ...
... Also shown are the energies of the type-III vertices, which have unbalanced three-in/one-out or three-out/onein arrangement and therefore possess an effective magnetic charge. As such, they can be considered as "monopole-like" quasiparticle excitations of the square ASI lattice whose static and dynamics properties were studied in detail in many earlier works [13][14][15][16][17][25][26][27][28][29] and whose crucial role in the equilibrium thermodynamics of square ASI will be discussed shortly. ...
... The temperature-dependent properties of ASIs at B = 0 were explored in many prior studies [12,17,18,[30][31][32][33][34][35][36][37]. As such, Fig. 2 highlights how temperature affects the full Bdependent maps of C m , noise, and long-range magnetic order. ...
Applied magnetic fields are an important tuning parameter for artificial spin ice (ASI) systems, as they candrive phase transitions between different magnetic ground states or tune through regimes with high populationsof emergent magnetic excitations (e.g., monopole-like quasiparticles). Here, using simulations supported byexperiments, we investigate the thermodynamic properties and magnetic phases of square and quadrupolar ASIas a function of applied in-plane magnetic fields. Monte Carlo simulations are used to generate field-dependentmaps of the magnetization, the magnetic specific heat, the thermodynamic magnetization fluctuations, andthe magnetic order parameters, all under equilibrium conditions. These maps reveal the diversity of magneticorderings and the phase transitions that occur in different regions of the phase diagrams of these ASIs, andare experimentally supported by magnetooptical measurements of the equilibrium “magnetization noise” inthermally active ASIs.
... While transient applied fields are often used in demagnetization protocols that help bring the ASI to its thermodynamic ground state [6][7][8][9][10], or are used to establish an initial out-of-equilibrium magnetic configuration (whose relaxation is subsequently monitored in zero field [11,12]), most experimental and theoretical ASI studies have been principally concerned with their geometry-or temperature-dependent magnetic properties in zero field. However, it is widely appreciated that an applied magnetic field B can provide an extremely important and versatile tuning parameter in ASIs [13][14][15][16][17][18][19]. Depending on its magnitude and direction, B can be used to drive phase transitions between different magnetic order parameters, or tune through equilibrium regimes where magnetic quasiparticle excitations (e.g., "magnetic monopoles") can readily form. ...
... Also shown are the energies of the type-III vertices, which have unbalanced 3-in/1-out or 3-out/1-in arrangement and therefore possess an effective magnetic charge. As such, they can be consid- ered as "monopole-like" quasiparticle excitations of the square ASI lattice, whose static and dynamics properties have been studied in detail in many earlier works [13][14][15][16][17][25][26][27][28][29], and whose crucial role in the equilibrium thermodynamics of square ASI will be discussed shortly. ...
... The temperature-dependent properties of ASIs at B=0 have been explored in many prior studies [12,17,18,[30][31][32][33][34][35][36][37]. As such, Fig. 2 highlights how temperature affects the full B-dependent maps of C m , noise, and long-range magnetic order. ...
Applied magnetic fields are an important tuning parameter for artificial spin ice (ASI) systems, as they can drive phase transitions between different magnetic ground states, or tune through regimes with high populations of emergent magnetic excitations (e.g., monopole-like quasiparticles). Here, using simulations supported by experiments, we investigate the thermodynamic properties and magnetic phases of square and quadrupolar ASI as a function of applied in-plane magnetic fields. Monte Carlo simulations are used to generate field-dependent maps of the magnetization, the magnetic specific heat, the thermodynamic magnetization fluctuations, and the magnetic order parameters, all under equilibrium conditions. These maps reveal the diversity of magnetic orderings and the phase transitions that occur in different regions of the phase diagrams of these ASIs, and are experimentally supported by magneto-optical measurements of the equilibrium "magnetization noise" in thermally-active ASIs.
... Such systems display a wide range of interesting behavior, including unusual ground states and magnetic-monopole-like excitations [12,13]. Avalanche-like phenomena have previously been examined in ASI arrays through studies of reversal behavior from one polarized state to another [14][15][16][17][18][19][20][21][22][23][24][25]. These included avalanche statistics and the relation of avalanche phenomena to the formation of monopole-antimonopole pairs. ...
... Specifically, we studied a rotated version of the canonical square ice system [see Fig. 1(a) [28] ], where each island was a single ferromagnetic domain with magnetization oriented along the long axis by shape anisotropy. Because of the rotation of our structure, the islands formed vertical columns [Figs 1(d),1(e)], with the island axes, and thus the magnetic moments, oriented at 45°from the column direction (similar to the geometry in Ref. [15,29]). Our square arrays had size L ¼ 70, 80, and 100, where L is the number of islands on each side of an array. ...
... The size of a cluster of flipped moments, S, can be defined as the total number of consecutive flipped moments along a column at a given H ext . Because we imaged in zero field at remanence, we did not examine the dynamics of the moment flipping process (which is expected to occur many orders of magnitude faster than MFM imaging) [15]. ...
We have measured magnetic-field-induced avalanches in a square artificial spin ice array of interacting nanomagnets. Starting from the ground state ordered configuration, we imaged the individual nanomagnet moments after each successive application of an incrementally increasing field. The statistics of the evolution of the moment configuration show good agreement with the canonical one-dimensional random field Ising model. We extract information about the microscopic structure of the arrays from our macroscopic measurements of their collective behavior, demonstrating a process that could be applied to other systems exhibiting avalanches.
