Deconstructing magnetization noise: Degeneracies, phases, and mobile fractionalized excitations in tetris artificial spin ice.

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.

Artificial Magnetic Tripod Ice.

We study the collective behavior of interacting arrays of nanomagnetic tripods. These objects have six discrete moment states, in contrast to the usual two states of an Ising-like moment. Our experimental data demonstrate that triangular lattice arrays form a "tripod ice" that exhibits charge ordering among the effective vertex magnetic charges, in direct analogy to artificial kagome spin ice. The results indicate that the interacting tripods have effective moments that act as emergent local variables, with strong connections to the well-studied Potts and clock models. In addition, the tripod moments display a tendency toward a nearest neighbor alignment in our thermalized samples that separates this system from kagome spin ice. Our results open a path toward the study of the collective behavior of nonbinary moments that is unavailable in other physical systems.

Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic.

Materials that exhibit simultaneous order in their electric and magnetic ground states hold promise for use in next-generation memory devices in which electric fields control magnetism. Such materials are exceedingly rare, however, owing to competing requirements for displacive ferroelectricity and magnetism. Despite the recent identification of several new multiferroic materials and magnetoelectric coupling mechanisms, known single-phase multiferroics remain limited by antiferromagnetic or weak ferromagnetic alignments, by a lack of coupling between the order parameters, or by having properties that emerge only well below room temperature, precluding device applications. Here we present a methodology for constructing single-phase multiferroic materials in which ferroelectricity and strong magnetic ordering are coupled near room temperature. Starting with hexagonal LuFeO3-the geometric ferroelectric with the greatest known planar rumpling-we introduce individual monolayers of FeO during growth to construct formula-unit-thick syntactic layers of ferrimagnetic LuFe2O4 (refs 17, 18) within the LuFeO3 matrix, that is, (LuFeO3)m/(LuFe2O4)1 superlattices. The severe rumpling imposed by the neighbouring LuFeO3 drives the ferrimagnetic LuFe2O4 into a simultaneously ferroelectric state, while also reducing the LuFe2O4 spin frustration. This increases the magnetic transition temperature substantially-from 240 kelvin for LuFe2O4 (ref. 18) to 281 kelvin for (LuFeO3)9/(LuFe2O4)1. Moreover, the ferroelectric order couples to the ferrimagnetism, enabling direct electric-field control of magnetism at 200 kelvin. Our results demonstrate a design methodology for creating higher-temperature magnetoelectric multiferroics by exploiting a combination of geometric frustration, lattice distortions and epitaxial engineering.

Field-Tunable Interactions and Frustration in Underlayer-Mediated Artificial Spin Ice.

Artificial spin ice systems have opened experimental windows into a range of model magnetic systems through the control of interactions among nanomagnet moments. This control has previously been enabled by altering the nanomagnet size and the geometry of their placement. Here we demonstrate that the interactions in artificial spin ice can be further controlled by including a soft ferromagnetic underlayer below the moments. Such a substrate also breaks the symmetry in the array when magnetized, introducing a directional component to the correlations. Using spatially resolved magneto-optical Kerr effect microscopy to image the demagnetized ground states, we show that the correlation of the demagnetized states depends on the direction of the underlayer magnetization. Further, the relative interaction strength of nearest and next-nearest neighbors varies significantly with the array geometry. We exploit this feature to induce frustration in an inherently unfrustrated square lattice geometry, demonstrating new possibilities for effective geometries in two-dimensional nanomagnetic systems.

Crystallites of magnetic charges in artificial spin ice.

Artificial spin ice is a class of lithographically created arrays of interacting ferromagnetic nanometre-scale islands. It was introduced to investigate many-body phenomena related to frustration and disorder in a material that could be tailored to precise specifications and imaged directly. Because of the large magnetic energy scales of these nanoscale islands, it has so far been impossible to thermally anneal artificial spin ice into desired thermodynamic ensembles; nearly all studies of artificial spin ice have either treated it as a granular material activated by alternating fields or focused on the as-grown state of the arrays. This limitation has prevented experimental investigation of novel phases that can emerge from the nominal ground states of frustrated lattices. For example, artificial kagome spin ice, in which the islands are arranged on the edges of a hexagonal net, is predicted to support states with monopolar charge order at entropies below that of the previously observed pseudo-ice manifold. Here we demonstrate a method for thermalizing artificial spin ices with square and kagome lattices by heating above the Curie temperature of the constituent material. In this manner, artificial square spin ice achieves unprecedented thermal ordering of the moments. In artificial kagome spin ice, we observe incipient crystallization of the magnetic charges embedded in pseudo-ice, with crystallites of magnetic charges whose size can be controlled by tuning the lattice constant. We find excellent agreement between experimental data and Monte Carlo simulations of emergent charge-charge interactions.

A strong ferroelectric ferromagnet created by means of spin-lattice coupling.

Ferroelectric ferromagnets are exceedingly rare, fundamentally interesting multiferroic materials that could give rise to new technologies in which the low power and high speed of field-effect electronics are combined with the permanence and routability of voltage-controlled ferromagnetism. Furthermore, the properties of the few compounds that simultaneously exhibit these phenomena are insignificant in comparison with those of useful ferroelectrics or ferromagnets: their spontaneous polarizations or magnetizations are smaller by a factor of 1,000 or more. The same holds for magnetic- or electric-field-induced multiferroics. Owing to the weak properties of single-phase multiferroics, composite and multilayer approaches involving strain-coupled piezoelectric and magnetostrictive components are the closest to application today. Recently, however, a new route to ferroelectric ferromagnets was proposed by which magnetically ordered insulators that are neither ferroelectric nor ferromagnetic are transformed into ferroelectric ferromagnets using a single control parameter, strain. The system targeted, EuTiO(3), was predicted to exhibit strong ferromagnetism (spontaneous magnetization, approximately 7 Bohr magnetons per Eu) and strong ferroelectricity (spontaneous polarization, approximately 10 microC cm(-2)) simultaneously under large biaxial compressive strain. These values are orders of magnitude higher than those of any known ferroelectric ferromagnet and rival the best materials that are solely ferroelectric or ferromagnetic. Hindered by the absence of an appropriate substrate to provide the desired compression we turned to tensile strain. Here we show both experimentally and theoretically the emergence of a multiferroic state under biaxial tension with the unexpected benefit that even lower strains are required, thereby allowing thicker high-quality crystalline films. This realization of a strong ferromagnetic ferroelectric points the way to high-temperature manifestations of this spin-lattice coupling mechanism. Our work demonstrates that a single experimental parameter, strain, simultaneously controls multiple order parameters and is a viable alternative tuning parameter to composition for creating multiferroics.

Magnetic structure and ordering of multiferroic hexagonal LuFeO_{3}.

We report on the magnetic structure and ordering of hexagonal LuFeO_{3} films of variable thickness grown by molecular-beam epitaxy on YSZ (111) and Al_{2}O_{3} (0001) substrates. These crystalline films exhibit long-range structural uniformity dominated by the polar P6_{3}cm phase, which is responsible for the paraelectric to ferroelectric transition that occurs above 1000 K. Using bulk magnetometry and neutron diffraction, we find that the system orders into a ferromagnetically canted antiferromagnetic state via a single transition below 155 K regardless of film thickness, which is substantially lower than that previously reported in hexagonal LuFeO_{3} films. The symmetry of the magnetic structure in the ferroelectric state implies that this material is a strong candidate for linear magnetoelectric coupling and control of the ferromagnetic moment directly by an electric field.

Topological kinetic crossover in a nanomagnet array.

Ergodic kinetics, which are critical to equilibrium thermodynamics, can be constrained by a system's topology. We studied a model nanomagnetic array in which such constraints visibly affect the behavior of the magnetic moments. In this system, magnetic excitations connect into thermally active one-dimensional strings whose motion can be imaged in real time. At high temperatures, our data showed the merging, breaking, and reconnecting of strings, resulting in the system transitioning between topologically distinct configurations. Below a crossover temperature, the string motion is dominated by simple changes in length and shape. In this low-temperature regime, the system is energetically stable because of its inability to explore all possible topological configurations. This kinetic crossover suggests a generalizable conception of topologically broken ergodicity and limited equilibration.

Perpendicular magnetization and generic realization of the Ising model in artificial spin ice.

We have studied frustrated kagome arrays and unfrustrated honeycomb arrays of magnetostatically interacting single-domain ferromagnetic islands with magnetization normal to the plane. The measured pairwise spin correlations of both lattices can be reproduced by models based solely on nearest-neighbor correlations. The kagome array has qualitatively different magnetostatics but identical lattice topology to previously studied artificial spin ice systems composed of in-plane moments. The two systems show striking similarities in the development of moment pair correlations, demonstrating a universality in artificial spin ice behavior independent of specific realization in a particular material system.

Ignoring your neighbors: moment correlations dominated by indirect or distant interactions in an ordered nanomagnet array.

We have studied the moment correlations within triangular lattice arrays of single-domain coaligned nanoscale ferromagnetic islands. Independent variation of lattice spacing along and perpendicular to the island axis tunes the magnetostatic interactions between islands through a broad range of relative strengths. For certain lattice parameters, the sign of the correlations between near-neighbor island moments is opposite to that favored by the pairwise interaction. This finding, supported by analysis of the total correlation in terms of direct and convoluted indirect contributions across multiple pairwise interactions, indicates that indirect interactions and/or those mediated by further neighbors can be tuned to be dominant, with implications for the wide range of systems composed of interacting nanomagnets.

Purification and magnetic interrogation of hybrid Au-Fe3O4 and FePt-Fe3O4 nanoparticles.

Purifying heterodimers: differential magnetic catch and release separation is used to purify two important hybrid nanocrystal systems, Au-Fe(3)O(4) and FePt-Fe(3)O(4). The purified samples have substantially different magnetic properties compared to the as-synthesized materials: the magnetization values are more accurate and magnetic polydispersity is identified in morphologically similar hybrid nanoparticles.

String Phase in an Artificial Spin Ice.

One-dimensional strings of local excitations are a fascinating feature of the physical behavior of strongly correlated topological quantum matter. Here we study strings of local excitations in a classical system of interacting nanomagnets, the Santa Fe Ice geometry of artificial spin ice. We measured the moment configuration of the nanomagnets, both after annealing near the ferromagnetic Curie point and in a thermally dynamic state. While the Santa Fe Ice lattice structure is complex, we demonstrate that its disordered magnetic state is naturally described within a framework of emergent strings. We show experimentally that the string length follows a simple Boltzmann distribution with an energy scale that is associated with the system's magnetic interactions and is consistent with theoretical predictions. The results demonstrate that string descriptions and associated topological characteristics are not unique to quantum models but can also provide a simplifying description of complex classical systems with non-trivial frustration.

Effective temperature in an interacting vertex system: theory and experiment on artificial spin ice.

Frustrated arrays of interacting single-domain nanomagnets provide important model systems for statistical mechanics, as they map closely onto well-studied vertex models and are amenable to direct imaging and custom engineering. Although these systems are manifestly athermal, we demonstrate that an effective temperature, controlled by an external magnetic drive, describes their microstates and therefore their full statistical properties.

Stress propagation: getting to the bottom of a granular medium.

Penetration by an object through a dense granular medium (for example, by a finger pushing slowly into the sand on a beach) presents an interesting physics problem that is closely related to issues of practical importance in soil science. Here we measure the penetration-resistance force for an object approaching the solid bottom boundary of a granular sample--analogous to the finger approaching a flat rock buried in the beach. We find that the penetration resistance near the boundary increases exponentially, which demonstrates the existence of an intrinsic length scale to the 'jamming' caused by a locally applied stress.

Chemical synthesis of air-stable manganese nanoparticles.

Elemental manganese has a complex crystal structure and unusual magnetic properties, making it an intriguing target for exploration in nanocrystalline form. However, because of its oxophilicity and the difficulty in reducing soluble metal salts to elemental Mn using the most common solution-phase reducing agents, it has been challenging to synthesize and stabilize elemental Mn nanoparticles using solution chemistry methods. Here we report the chemical synthesis of alpha-Mn nanoparticles using n-butyllithium as a reducing agent. The nanoparticles have been characterized by powder XRD, TEM, electron diffraction, infrared spectroscopy (DRIFT), XPS, and SQUID magnetometry. An amorphous manganese oxide layer bound by oleate ligands helps to render the nanoparticles air-stable. The oxide-coated alpha-Mn nanoparticles are paramagnetic.

Room-temperature chemical synthesis of shape-controlled indium nanoparticles.

Shape-controlled metal nanoparticles are of interest because of their wide range of properties that are useful for applications that include optics, electronics, magnetism, and catalysis. Indium metal is an attractive target for nanoparticle synthesis because it is superconducting, plasmonically active, and is a component in low-melting solders and solid-state lubricants. Indium nanoparticles are typically synthesized using harsh physical or chemical techniques, and rigorous shape control is difficult. Here we present a simple and robust kinetically controlled process for synthesizing shape-controlled indium nanoparticles. By controlling the rate of dropwise addition of a solution of NaBH4 in tetraethylene glycol to an alcoholic solution of InCl3 and poly(vinyl pyrrolidone), indium nanoparticles are formed with shapes that include high aspect ratio nanowires and uniform octahedra and truncated octahedra. The zero-dimensional indium nanoparticles exhibit an SPR band centered around 400 nm, and all morphologies are superconducting (Tc = 3.4 K) with higher critical fields than bulk indium.

Epitaxial growth of highly-crystalline spinel ferrite thin films on perovskite substrates for all-oxide devices.

The potential growth modes for epitaxial growth of Fe3O4 on SrTiO3 (001) are investigated through control of the energetics of the pulsed-laser deposition growth process (via substrate temperature and laser fluence). We find that Fe3O4 grows epitaxially in three distinct growth modes: 2D-like, island, and 3D-to-2D, the last of which is characterized by films that begin growth in an island growth mode before progressing to a 2D growth mode. Films grown in the 2D-like and 3D-to-2D growth modes are atomically flat and partially strained, while films grown in the island growth mode are terminated in islands and fully relaxed. We find that the optimal structural, transport, and magnetic properties are obtained for films grown on the 2D-like/3D-to-2D growth regime boundary. The viability for including such thin films in perovskite-based all-oxide devices is demonstrated by growing a Fe3O4/La0.7Sr0.3MnO3 spin valve epitaxially on SrTiO3.