Lorentz TEM investigation of the switching behavior in artificial spin ice building blocks

Frustration – the inability to simultaneously satisfy all interactions – occurs in a wide range of systems including neural networks, water ice and magnetic systems. An example of the latter is the so called spin-ice in pyrochlore materials [1] which have attracted a lot of interest not least due to the emergence of magnetic monopole defects when the ‘ice rules’ governing the local ordering breaks down [2]. However it is not possible to directly measure the frustrated property – the direction of the magnetic moments – in such spin ice systems with current experimental techniques. This problem can be solved by instead studying artificial spin-ice systems where the molecular magnetic moments are replaced by nanoscale ferromagnetic islands [3-8]. Two different arrangements of the ferromagnetic islands have been shown to exhibit spin ice behaviour: a square lattice maintaining four moments at each vertex [3,8] and the Kagome lattice which has only three moments per vertex but equivalent interactions between them [4-7]. Magnetic monopole defects have been observed in both types of lattices [7-8]. One of the challenges when studying these artificial spin-ice systems is that it is difficult to arrive at the fully demagnetised ground-state [6-8].
Here we present a study of the switching behaviour of building blocks of the Kagome lattice influenced by the termination of the lattice. Ferromagnetic islands of nominal size 1000 nm by 100 nm were fabricated in five island blocks using electron-beam lithography and lift-off techniques of evaporated 18 nm Permalloy (Ni80Fe20) films. Each block consists of a central island with four arms terminated by a different number and placement of ‘injection pads’, see Figure 1. The islands are single domain and magnetised along their long axis. The structures were grown on a 50 nm thick electron transparent silicon nitride membrane to allow TEM observation, which was back-coated with a 5 nm film of Au to prevent charge build-up during the TEM experiments.
To study the switching behaviour the sample was subjected to a magnetic field strong enough to magnetise all the blocks in one direction, see Figure 1. Each block obeys the Kagome lattice ‘ice-rules’ of “2-in, 1-out” or “1-in, 2-out” in this fully magnetised state. Fresnel mode Lorentz TEM images of the sample were then recorded as a magnetic field of increasing magnitude was applied in the opposite direction. While the Fresnel mode is normally used to image magnetic domain structures [9] for these types of samples it is possible to deduce the direction of the magnetisation from the Lorentz contrast [5]. All images were recorded at the same over-focus judged to give good Lorentz contrast.
The magnetisation was found to switch at different magnitudes of the applied field for nominally identical blocks. However, trends could still be identified: all the blocks with any injection pads, regardless of placement and number, switched the direction of the magnetisation of their central island at significantly smaller magnitudes of the applied magnetic field than the blocks without injection pads. It can therefore be concluded that the addition of an injection pad lowers the energy barrier to switching the connected island, acting as a nucleation site for monopole defects. In these five island blocks the defects immediately propagate through to the other side, but in a larger lattice the monopoles could potentially become trapped at a vertex and observed [10].
References

[1] M J Harris et al, Phys Rev Lett 79 (1997) p.2554.
[2] C Castelnovo, R Moessner and S L Sondhi, Nature 451 (2008) p. 42.
[3] R F Wang et al, Nature 439 (2006) 303.
[4] M Tanaka et al, Phys Rev B 73 (2006) 052411.
[5] Y Qi, T Brintlinger and J Cumings, Phys Rev B 77 (2008) 094418.
[6] E Mengotti et al, Phys Rev B 78 (2008) 144402.
[7] S Ladak et al, Nature Phys 6 (2010) 359.
[8] C Phatak et al, Phys Rev B 83 (2011) 174431.
[9] J N Chapman, J Phys D 17 (1984) 623.
[10] The authors gratefully acknowledge funding from the EPSRC under grant number EP/D063329/1.

Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

Nonlinear dynamics of multidimensional electrostatic excitations in nonthermal plasmas

Electrostatic solitary waves in plasmas are the focus of many current studies of localized electrostatic disturbances in both laboratory and astrophysical plasmas. Motivated by recent experimental observations, in which electrostatic solitary structures were detected in laser-plasma experiments, we have undertaken an investigation of the nonlinear dynamics of plasma evolving in two dimensions, in the presence of excess superthermal background electrons. We investigate the effect of a magnetic field on weakly nonlinear ion-acoustic waves. Deviation from the Maxwellian distribution is effectively modelled by the kappa model. A linear dispersion relation is derived, and a decrease in frequency and phase speed in both parallel and perpendicular modes can be seen, which is due to excess superthermal electrons, and which is stronger in the upper mode, and hardly noticeable in the lower (acoustic) mode. We show that ion-acoustic solitary waves can be generated during the nonlinear evolution of a plasma fluid, and their nonlinear propagation is governed by a Zakharov-Kuznetsov (ZK) type equation. A multiple scales perturbation technique is used to derive the ZK equation. Shock excitations can be produced if we allow for dissipation in the model, resulting in a Zakharov-Kuznetsov Burgers type equation. Different types of shock solutions and solitary waves are obtained, depending on the relation between the system parameters, and the effect of these on electrostatic shock structures is investigated numerically. A parametric investigation is conducted into the role of plasma nonthermality and magnetic field strength. © 2013 IOP Publishing Ltd.

Tuning non-Markovianity by spin-dynamics control

We study the interplay between forgetful and memory-keeping evolution enforced on a two-level system by a multi-spin environment whose elements are coupled to local bosonic baths. Contrarily to the expectation that any non-Markovian effect would be buried by the forgetful mechanism induced by the spin-bath coupling, one can actually induce a full Markovian-to-non-Markovian transition of the two-level system's dynamics, controllable by parameters such as the mismatch between the energy of the two-level system and of the spin environment. For a symmetric coupling, the amount of non-Markovianity surprisingly grows with the number of decoherence channels. DOI: 10.1103/PhysRevA.87.022317

Spin-wave modes in Ni nanorod arrays studied by Brillouin light scattering

Dynamic magnetic properties of arrays of Ni nanorods with a low aspect ratio have been investigated. It has been shown that the spectra of spin-wave resonances localized on nanorods with a low aspect ratio typically feature the presence of zones with high density of states resulting in a characteristic two-peak pattern of Stokes and anti-Stokes lines of magneto-optical (MO) Brillouin light scattering with pronounced Stokes–anti-Stokes (S-AS) asymmetry. A simple theoretical model based on the analysis of the elliptic character of the polarization of the optical wave interacting with a dipole magnetostatic wave has been proposed. It has been shown that the S-AS asymmetry is due entirely to the asymmetry of the MO interaction efficiency with respect to time reversal of the magnetic precession in a magnon.

The internal structure of asteroid (25143) Itokawa as revealed by detection of YORP spin-up *’**

Context. Near-Earth asteroid (25143) Itokawa was visited by the Hayabusa spacecraft in 2005, resulting in a highly detailed shape and surface topography model. This model has led to several predictions for the expected radiative torques on this asteroid, suggesting that its spin rate should be decelerating. Aims. To detect changes in rotation rate that may be due to YORP-induced radiative torques, which in turn may be used to investigate the interior structure of the asteroid. Methods. Through an observational survey spanning 2001 to 2013 we obtained rotational lightcurve data at various times over the last five close Earth-approaches of the asteroid. We applied a polyhedron-shape-modelling technique to assess the spin-state of the asteroid and its long term evolution. We also applied a detailed thermophysical analysis to the shape model determined from the Hayabusa spacecraft. Results. We have successfully measured an acceleration in Itokawa's spin rate of dω/dt = (3.54 ± 0.38) × 10 rad day, equivalent to a decrease of its rotation period of ~45 ms year. From the thermophysical analysis we find that the centre-of-mass for Itokawa must be shifted by ~21 m along the long-axis of the asteroid to reconcile the observed YORP strength with theory. Conclusions. This can be explained if Itokawa is composed of two separate bodies with very different bulk densities of 1750 ± 110 kg m and 2850 ± 500 kg m, and was formed from the merger of two separate bodies, either in the aftermath of a catastrophic disruption of a larger differentiated body, or from the collapse of a binary system. We therefore demonstrate that an observational measurement of radiative torques, when combined with a detailed shape model, can provide insight into the interior structure of an asteroid. Futhermore, this is the first measurement of density inhomogeneity within an asteroidal body, that reveals significant internal structure variation. A specialised spacecraft is normally required for this.

Structural Capital of University Spin-Out Firms: The Moderating Role of University Incubators

University incubators (UI) are generally believed to be important in the successful commercialisation of university spin-outs (USO) with over half of all UK Universities having established an on-campus UI. In this chapter we examine the value of UIs in the spin-out process, focusing on the structural networks of USOs located in a UI as compared to USOs in a University with no access to a UI. Our primary research question is therefore: to what extent does the structural network of USOs with access to an on-campus UI differ from USOs without? The research therefore con-tributes to a growing critique of the effectiveness of UIs in commercialis-ing academic research and the recognition of positive direct and indirect externalities from participation in networks. Through network mapping of all USOs from two research intensive universities, we profile and ana-lyse the formal and informal network ties of USOs to various partners in-ternal and external to the host university. Through interviews we also consider how these networks enhance the resources and capabilities of USOs. Our findings highlight significant differences, with USOs located in a UI having more informal but fewer formal ties, both to other USOs as well as within the host University. In contrast, location in an incuba-tor was not found to affect the extent and nature of ties with external or-ganisations. Reasons for these differences are examined through inter-views with the USOs and point to various factors including the proactive brokering role of incubator and university staff, university bureaucracy, the hidden networks of executive board members across USOs, university equity investment policy and complementary technologies.

Distillable entanglement and area laws in spin and harmonic-oscillator systems

We address the presence of nondistillable (bound) entanglement in natural many-body systems. In particular, we consider standard harmonic and spin-1/2 chains, at thermal equilibrium and characterized by few interaction parameters. The existence of bound entanglement is addressed by calculating explicitly the negativity of entanglement for different partitions. This allows us to individuate a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We discuss how the appearance of bound entanglement can be linked to entanglement-area laws, typical of these systems. Various types of interactions are explored, showing that the presence of bound entanglement is an intrinsic feature of these systems. In the harmonic case, we analytically prove that thermal bound entanglement persists for systems composed by an arbitrary number of particles. Our results strongly suggest the existence of bound entangled states in the macroscopic limit also for spin-1/2 systems.

Effective cutting of a quantum spin chain by bond impurities

Spin chains are promising media for short-haul quantum communication. Their usefulness is manifested in all those situations where stationary information carriers are involved. In the majority of the communication schemes relying on quantum spin chains, the latter are assumed to be finite in length, with well-addressable end-chain spins. In this paper we propose that such a configuration could actually be achieved by a mechanism that is able to effectively cut a spin ring through the insertion of bond defects. We then show how suitable physical quantities can be identified as figures of merit for the effectiveness of the cut. We find that, even for modest strengths of the bond defect, a ring is effectively cut at the defect site. In turn, this has important effects on the amount of correlations shared by the spins across the resulting chain, which we study by means of a scattering-based mechanism of a clear physical interpretation. © 2013 American Physical Society.

Quantum annealing of an ising spin-glass by Green's function Monte Carlo

We present an implementation of quantum annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin glass in transverse field. In particular, we study whether or not such a method is more effective than the path-integral Monte Carlo- (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wave functions, as the key point of the algorithm. We performed GFMC-QA runs using such a Boltzmann-type trial wave function, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wave functions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.

Probing spin-orbit-interaction-induced electron dynamics in the carbon atom by multiphoton ionization

We use R-matrix theory with time dependence (RMT) to investigate multiphoton ionization of ground-state atomic carbon with initial orbital magnetic quantum number M_L=0 and M_L=1 at a laser wavelength of 390 nm and peak intensity of 10(14) W/cm(2). Significant differences in ionization yield and ejected-electron momentum distribution are observed between the two values for M_L. We use our theoretical results to model how the spin-orbit interaction affects electron emission along the laser polarization axis. Under the assumption that an initial C atom is prepared at zero time delay with M_L=0, the dynamics with respect to time delay of an ionizing probe pulse modeled by using RMT theory is found to be in good agreement with available experimental data.

Direct Detection of YORP Spin-up on Asteroid (25143) Itokawa and Implications for its Internal Structure

Near-Earth asteroid (25143) Itokawa was visited by the Hayabusa spacecraft in 2005, resulting in a highly detailed surface shape and topography model. This model has led to several predictions for the expected radiative torques on this asteroid, suggesting that its spin rate should be decelerating. Through an observational survey spanning 2001 to 2013 we have successfully measured an acceleration in its spin rate of dω/dt = 3.54 (± 0.38) × 10^(-8) rad day^(-2), equivalent to a decrease of its rotation period of ~ 45 ms year^(-1). Using the shape model determined from the Hayabusa spacecraft, we applied a detailed thermophysical analysis, to reconcile the predicted YORP strength with that observed. We find that the center-of-mass for Itokawa must be shifted by ~20 m along the long-axis of the asteroid to reconcile observations with theory. This can be explained if Itokawa is composed of two separate bodies with very different bulk densities of 1740 ± 110 kg m^(-3) and 2730 ± 440 kg m^(-3), and was formed from the merger of two separate bodies, consistent with the collapse of a binary system or the re-accumulation of material from a catastrophic collisional disruption. We demonstrate that an observational measurement of radiative torques, when combined with a detailed shape model, can provide insight into the interior structure of an asteroid.

Dynamics of the entanglement spectrum in spin chains

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.