MFM imaging of micron-sized permalloy ellipses

The magnetic domain structure of micron-sized elliptic permalloy elements has been studied by magnetic force microscope (MFM) measurements, and has been compared to results from micromagnetic simulations. The elements all have the same aspect ratio, whereas the inter-elemental distance has been varied. Both the zero-field states and in field domain configurations have been studied. In zero-applied field, two different stable flux-closure states were found in both the MFM measurements and in the simulations. The different stable domain states occur as a result of minute differences in the local magnetic environment occurring during the demagnetization process. (C) 2004 Elsevier B.V. All rights reserved.

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.

Stability of 71 degrees stripe domains in epitaxial BiFeO3 films upon repeated electrical switching

The 71 degrees stripe domain patterns of epitaxial BiFeO3 thin films are frequently being explored to achieve new functional properties, dissimilar from the BiFeO3 bulk properties. We show that in-plane switching and out-of-plane switching of these domains behave very differently. In the in-plane configuration the domains are very stable, whereas in the out-of-plane configuration the domains change their size and patterns, depending on the applied switching voltage frequency.

Multiferroic PbZrxTi1-xO3/Fe3O4 epitaxial sub-micron sized structures

Large range well ordered epitaxial ferrimagnetic nominally Fe3O4 structures were fabricated by pulsed-laser deposition and embedded in ferroelectric PbZrxTi1-xO3 (x = 0.2, 0.52) epitaxial films. Magnetite dots were investigated by magnetic force microscopy and exhibited magnetic domain contrast at room temperature (RT). Embedding ferroelectric PbZrxTi1-xO3 layers exhibit remnant polarization values close to the values of single epitaxial layers. Transmission electron microscopy demonstrated the epitaxial growth of the composites and the formation of the ferrimagnetic and ferroelectric phases. Physical and structural properties of these composites recommend them for investigations of stress mediated magneto-electric coupling at room temperature. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3692583]

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

Current-driven magnetic rearrangements in spin-polarized point contacts

A method for investigating the dynamics of atomic magnetic moments in current-carrying magnetic point contacts under bias is presented. This combines the nonequilibrium Green's function (NEGF) method for evaluating the current and the charge density with a description of the dynamics of the magnetization in terms of quasistatic thermally activated transitions between stationary configurations. This method is then implemented in a tight-binding (TB) model with parameters chosen to simulate the main features of the electronic structures of magnetic transition metals. We investigate the domain wall (DW) migration in magnetic monoatomic chains sandwiched between magnetic leads, and for realistic parameters find that collinear arrangement of the magnetic moments of the chain is always favorable. Several stationary magnetic configurations are identified, corresponding to a different number of Bloch walls in the chain and to a different current. The relative stability of these configurations depends on the geometrical details of the junction and on the bias; however, we predict transitions between different configurations with activation barriers of the order of a few tens of meV. Since different magnetic configurations are associated with different resistances, this suggests an intrinsic random telegraph noise at microwave frequencies in the I-V curves of magnetic atomic point contacts at room temperature. Finally, we investigate whether or not current-induced torques are conservative.

Domain configuration of permalloy ellipses in a rotating magnetic field

The domain configuration of micron-sized permalloy ellipses was studied under the influence of an in-plane rotating magnetic field using magnetic force microscopy. The field amplitude was chosen such that when the field is applied parallel to the long axis of the ellipses they are saturated, but when the field is perpendicular to the long axis they exhibit multi-domain states. The rotation angle for nucleation and annihilation of domains was determined for different magnitudes of the applied magnetic field and for two different lateral sizes of ellipses, 6 Am x 2 Am and 3 Am x 1 Am. It was found that both nucleation and annihilation occur over a range of angles for both lateral sizes of ellipses. Saturated states are stable for a wider range of angles for larger values of the applied field.

Switching ferroelectric domain configurations using both electric and magnetic fields in Pb(Zr,Ti)O3–Pb(Fe,Ta)O3 single-crystal lamellae

Thin single-crystal lamellae cut from Pb(Zr,Ti)O3–Pb(Fe,Ta)O3 ceramic samples have been integrated into simple coplanar capacitor devices. The influence of applied electric and magnetic fields on ferroelectric domain configurations has been mapped, using piezoresponse force microscopy. The extent to which magnetic fields alter the ferroelectric domains was found to be strongly history dependent: after switching had been induced by applying electric fields, the susceptibility of the domains to change under a magnetic field (the effective magnetoelectric coupling parameter) was large. Such large, magnetic field-induced changes resulted in a remanent domain state very similar to the remanent state induced by an electric field. Subsequent magnetic field reversal induced more modest ferroelectric switching.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Mesoscale flux-closure domain formation in single-crystal BaTiO3

Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields, and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO3. Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO3 has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Shape-induced phase transition of domain patterns in ferroelectric platelets

Using a combination of experimental and computational techniques, changes in the domain structures seen infreestanding single-crystal platelets of BaTiO3 have been described in terms of a second-order phase transition.The transition is driven by the change in the length-to-width ratio of the platelet sidewalls and results in a symmetrybreaking of a complex, quadrant domain pattern. The phenomenon can be described by a Landau formalism inwhich (1) the order parameter is not the polarization but rather is the degree to which the domain pattern becomesoff-centered, and (2) the shape anisotropy of the platelet substitutes for temperature in the conventional Landauexpansion as the controlling thermodynamic variable. Bistability, in terms of the direction in which the domainpattern moves off center, coupled with the spontaneous macroscopic polarization and toroidal moment that resultfrom this off-centering, prompt the possibility of a new form of memory storage.

Bats use magnetite to detect the earth's magnetic field

While the role of magnetic cues for compass orientation has been confirmed in numerous animals, the mechanism of detection is still debated. Two hypotheses have been proposed, one based on a light dependent mechanism, apparently used by birds and another based on a "compass organelle" containing the iron oxide particles magnetite (Fe3O4). Bats have recently been shown to use magnetic cues for compass orientation but the method by which they detect the Earth's magnetic field remains unknown. Here we use the classic "Kalmijn-Blakemore" pulse re-magnetization experiment, whereby the polarity of cellular magnetite is reversed. The results demonstrate that the big brown bat Epteskus fuscus uses single domain magnetite to detect the Earths magnetic field and the response indicates a polarity based receptor. Polarity detection is a prerequisite for the use of magnetite as a compass and suggests that big brown bats use magnetite to detect the magnetic field as a compass. Our results indicate the possibility that sensory cells in bats contain freely rotating magnetite particles, which appears not to be the case in birds. It is crucial that the ultrastructure of the magnetite containing magnetoreceptors is described for our understanding of magnetoreception in animals.