Magnetic dipole and higher pole interaction on a square lattice

Long-range order in quadrupolar systems on spherical surfaces

The interplay between curvature, confinement and ordering on curved manifolds, with anisotropic interactions between building blocks, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry and local positional order on orientational ordering in systems of long-range interacting point quadrupoles on a sphere in the zero temperature limit. Locally triangular spherical lattices show long-range ordered quadrupolar configurations only for specific symmetric lattices as strong geometric frustration prevents general global ordering. Conversely, the ground states on Caspar-Klug lattices are more diverse, with many different symmetries depending on the position of quadrupoles within the fundamental domain. We also show that by constraining the quadrupole tilts with respect to the surface normal, which models interactions with the substrate, and by considering general quadrupole tensors, we can manipulate the ground state configuration symmetry.

Magnetic dimer at a surface: Influence of gravity and external magnetic fields

The interaction of two dipolar hard spheres near a surface and under the influence of gravity and external perpendicular magnetic fields is investigated theoretically. The full ground-state phase diagram as a function of gravity and magnetic field strengths is established. A dimer (i.e., two touching beads) can only exist when the gravity and magnetic field strengths are simultaneously not too large. Thereby, upon increasing the magnetic field strength, three dimeric states emerge: a lying state (dimer axis parallel to the substrate), an inclined state (intermediate state between the lying and standing ones) and a standing state (dimer axis normal to the substrate). It is found that the orientation angles of the dimer axis and the dipole moment in the newly discovered inclined phase are related by a strikingly simple Snell-Descartes-like law. We argue that our findings can be experimentally verified in colloidal and granular systems.

Spatial and Temporal Correlations of XY Macro Spins

We use nano disk arrays with square and honeycomb symmetry to investigate magnetic phases and spin correlations of XY dipolar systems at the micro scale. Utilizing magnetization sensitive X-ray photoemission electron microscopy, we probe magnetic ground states and the "order-by-disorder" phenomenon predicted 30 years ago. We observe the antiferromagnetic striped ground state in square lattices, and 6-fold symmetric structures, including trigonal vortex lattices and disordered floating vortices, in the honeycomb lattice. The spin frustration in the honeycomb lattice causes a phase transition from a long-range ordered locked phase over a floating phase with quasi long-range order and indications of a Berezinskii-Thouless-Kosterlitz-like character, to the thermally excited paramagnetic state. Absent spatial correlation and quasi periodic switching of isolated vortices in the quasi long-range ordered phase suggest a degeneracy of the vortex circulation.

Collective magnetism in an artificial 2D XY spin system

Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations. When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a low-temperature ordered phase. However, the experimental realisation of such two-dimensional spin systems in crystalline materials is difficult since the dipolar coupling is usually much weaker than the exchange interaction. Here we realise two-dimensional magnetostatically coupled XY spin systems with nanoscale thermally active magnetic discs placed on square lattices. Using low-energy muon-spin relaxation and soft X-ray scattering, we observe correlated dynamics at the critical temperature and the emergence of static long-range order at low temperatures, which is compatible with theoretical predictions for dipolar-coupled XY spin systems. Furthermore, by modifying the sample design, we demonstrate the possibility to tune the collective magnetic behaviour in thermally active artificial spin systems with continuous degrees of freedom.

Spin waves across three-dimensional, close-packed nanoparticles

Inelastic neutron scattering is utilized to directly measure inter-nanoparticle spin waves, or magnons, which arise from the magnetic coupling between 8.4 nm ferrite nanoparticles that are self-assembled into a close-packed lattice, yet are physically separated by oleic acid surfactant. The resulting dispersion curve yields a physically-reasonable, non-negative energy gap only when the effective Q is reduced by the inter-particle spacing. This Q renormalization strongly indicates that the dispersion is a collective excitation between the nanoparticles, rather than originating from within individual nanoparticles. Additionally, the observed magnons are dispersive, respond to an applied magnetic field, and display the expected temperature-dependent Bose population factor. The experimental results are well explained by a limited parameter model which treats the three-dimensional ordered, magnetic nanoparticles as dipolar-coupled superspins.

The remanence ratio in CoFe2O4 nanoparticles with approximate single-domain sizes

Approximately single-domain-sized 9-, 13-, and 16-nm CoFe₂O₄ nanoparticles are synthesized using the thermal decomposition of a metal-organic salt. By means of dilution and reduction, the concentration, moment, and anisotropy of nanoparticles are changed and their influence on the magnetic properties is investigated. The relation of M _r/M _s ∝ 1/lgH _dip is observed, where M _r/M _s is the remanence ratio and H _dip is the maximum dipolar field. Especially, such relation is more accurate for the nanoparticle systems with higher concentration and higher moment, i.e., larger H _dip. The deviation from M _r/M _s ∝ 1/lgH _dip appearing at low temperatures can be attributed to the effects of surface spins for the single-phase CoFe₂O₄ nanoparticles and to the pinning effect of CoFe₂O₄ on CoFe₂ for the slightly reduced nanoparticles. Graphical Abstract Approximately single-domain-sized 9-, 13-, and 16-nm CoFe₂O₄ nanoparticles were synthesized and then the concentration, moment, and anisotropy of these NPs were changed. The correlation of M _r/M _s ∝ 1/lgH _dip was observed, independent of the size, concentration, moment, and anisotropy, and especially, such correlation is more accurate for the nanoparticle systems with higher concentration or moment, i.e., stronger dipolar interaction, which has not been reported before as far as we know.

Simultaneous effects of surface spins: rarely large coercivity, high remanence magnetization and jumps in the hysteresis loops observed in CoFe2O4 nanoparticles

Well-dispersed uniform cobalt ferrite nanoparticles were synthesized by thermal decomposition of a metal-organic salt in organic solvent with a high boiling point. Some of the nanoparticles were diluted in a SiO2 matrix and then the undiluted and diluted samples were characterized and their magnetic behavior explored. The undiluted and diluted samples exhibited maximum coercivity Hc of 23,817 and 15,056 Oe at 10 K, respectively, which are the highest values reported to date, and the corresponding ratios of remanence (Mr) to saturation (Ms) magnetization (Mr/Ms) were as high as 0.85 and 0.76, respectively. Interestingly, the magnetic properties of the samples changed at 200 K, which was observed in magnetic hysteresis M(H) loops and zero-field cooling curves as well as the temperature dependence of Hc, Mr/Ms, anisotropy, dipolar field, and the magnetic grain size. Below 200 K, both samples have large effective anisotropy, which arises from the surface spins, resulting in large Hc and Mr/Ms. Above 200 K, the effective anisotropy decreases because there is no contribution from surface spins, while the dipolar interaction increases, resulting in small Hc and Mr/Ms. Our results indicate that strong anisotropy and weak dipolar interaction tend to increase Hc and Mr/Ms, and also clarify that the jumps around H = 0 in M(H) loops can be attributed to the reorientation of surface spins. This work exposes the underlying mechanism in nanoscale magnetic systems, which should lead to improved magnetic performance.

Polarized neutron reflectivity from monolayers of self-assembled magnetic nanoparticles

We prepared monolayers of iron oxide nanoparticles via self-assembly on a bare silicon wafer and on a vanadium film sputter deposited onto a plane sapphire substrate. The magnetic configuration of nanoparticles in such a dense assembly was investigated by polarized neutron reflectivity. A theoretical model fit shows that the magnetic moments of nanoparticles form quasi domain-like configurations at remanence. This is attributed to the dipolar coupling amongst the nanoparticles.

Topologically protected magnetic helix for all-spin-based applications

The recent years have witnessed an emergence of the field of all-spin-based devices without any flow of charge. An ultimate goal of this scientific direction is the realization of the full spectrum of spin-based networks as in modern electronics. The concept of energy-storing elements, indispensable for those networks, are so far lacking. Analyzing analytically the size dependent properties of magnetic chains that are coupled via either exchange or long-range dipolar or Ruderman-Kittel-Kasuya-Yosida interactions, we discover a particularly simple law: magnetic configurations corresponding to helices with integer number of twists, which are commensurate with the chain's length, are energetically stable. This finding, supported by simulations and an experimentally benchmarked model, agrees with the study [R. Skomski et al., J. Appl. Phys. 111, 07E116 (2012)] showing that boundaries can topologically stabilize structures that are not stable otherwise. On that basis, an energy-storing element that uses spin at every stage of its operation is proposed.

Exploration of magnetic fluctuations in PdFe films

We investigated magnetic phase transitions, magnetic anisotropy, and magnetic domains in Pd1-xFex alloys with different Fe concentrations x = 2.2-7.2%. The Curie temperature depends linearly on the Fe concentration in the regime studied. The magnetization is dominantly in-plane with a small out-of-plane remanent contribution. Resonant magnetic small angle scattering with circularly polarized x-rays tuned to the L3 resonance edge of Fe revealed a small angle scattering ring corresponding to magnetic domain fluctuations on a length scale of 100 nm. These fluctuations are isotropically distributed in the film plane and appear to have an out-of-plane component. On increasing the transverse coherence of the incident beam, the scattering ring decomposes in a speckle pattern, indicative of magnetic correlations on a length scale smaller than the x-ray coherence length of about 4 μm.