Magnetic switching of ferroelectric domains at room temperature in multiferroic PZTFT

Single-phase magnetoelectric multiferroics are ferroelectric materials that display some form of magnetism. In addition, magnetic and ferroelectric order parameters are not independent of one another. Thus, the application of either an electric or magnetic field simultaneously alters both the electrical dipole configuration and the magnetic state of the material. The technological possibilities that could arise from magnetoelectric multiferroics are considerable and a range of functional devices has already been envisioned. Realising these devices, however, requires coupling effects to be significant and to occur at room temperature. Although such characteristics can be created in piezoelectric-magnetostrictive composites, to date they have only been weakly evident in single-phase multiferroics. Here in a newly discovered room temperature multiferroic, we demonstrate significant room temperature coupling by monitoring changes in ferroelectric domain patterns induced by magnetic fields. An order of magnitude estimate of the effective coupling coefficient suggests a value of ~1 × 10-7 sm-1.

Improved description of chemical barriers with generalized gradient approximations (GGAs) and meta-GGAs

The performance of exchange and correlation (xc) functionals of the generalized gradient approximation (GGA) type and of the meta-GGA type in the calculation of chemical reactions is related to topological features of the electron density which, in turn, are connected to the orbital structure of chemical bonds within the Kohn-Sham (KS) theory. Seventeen GGA and meta-GGA xc functionals are assessed for 15 hydrogen abstraction reactions and 3 symmetrical S(N)2 reactions. Systems that are problematic for standard GGAs characteristically have enhanced values of the dimensionless gradient argument s(sigma)(2) with local maxima in the bonding region. The origin of this topological feature is the occupation of valence KS orbitals with an antibonding or essentially nonbonding character. The local enhancement of s(sigma)(2) yields too negative exchange-correlation energies with standard GGAs for the transition state of the S(N)2 reaction, which leads to the reduced calculated reaction barriers. The unwarranted localization of the effective xc hole of the standard GGAs, i.e., the nondynamical correlation that is built into them but is spurious in this case, wields its effect by their s(sigma)(2) dependence. Barriers are improved for xc functionals with the exchange functional OPTX as x component, which has a modified dependence on s(sigma)(2). Standard GGAs also underestimate the barriers for the hydrogen abstraction reactions. In this case the barriers are improved by correlation functionals, such as the Laplacian-dependent (LAP3) functional, which has a modified dependence on the Coulomb correlation of the opposite- and like-spin electrons. The best overall performance is established for the combination OLAP3 of OPTX and LAP3.

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn-Sham orbitals: Application to dissociating H-2

The standard local density approximation and generalized gradient approximations fail to properly describe the dissociation of an electron pair bond, yielding large errors (on the order of 50 kcal/mol) at long bond distances. To remedy this failure, a self-consistent Kohn-Sham (KS) method is proposed with the exchange-correlation (xc) energy and potential depending on both occupied and virtual KS orbitals. The xc energy functional of Buijse and Baerends [Mol. Phys. 100, 401 (2002); Phys. Rev. Lett. 87, 133004 (2001)] is employed, which, based on an ansatz for the xc-hole amplitude, is able to reproduce the important dynamical and nondynamical effects of Coulomb correlation through the efficient use of virtual orbitals. Self-consistent calculations require the corresponding xc potential to be obtained, to which end the optimized effective potential (OEP) method is used within the common energy denominator approximation for the static orbital Green's function. The problem of the asymptotic divergence of the xc potential of the OEP when a finite number of virtual orbitals is used is addressed. The self-consistent calculations reproduce very well the entire H-2 potential curve, describing correctly the gradual buildup of strong left-right correlation in stretched H-2. (C) 2003 American Institute of Physics.

On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential (BP-GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability alpha, the Cauchy coefficient S-4, and the static average hyperpolarizability beta. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr (BLYP), and Becke-Perdew (BP) characteristically underestimate contributions to alpha and S-4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N-2 molecule shows, that both SAOP and BP-GRAC yield reliable energies omega(i) and oscillator strengths f(i) of individual excitations, so that they reproduce well the spectral structure of alpha and S-4.(C) 2002 American Institute of Physics.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn-Sham (KS) exchange potential v(xsigma)(CEDA) is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. v(xsigma)(CEDA) is an explicit functional of the occupied KS orbitals, which has the Slater v(Ssigma) and response v(respsigma)(CEDA) potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities \psi(isigma)\(2), as well as "off-diagonal" ones from the occupied-occupied orbital products psi(isigma)psi(j(not equal1)sigma). Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies epsilon(isigma) are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-epsilon(isigma) values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of v(xsigma)(CEDA) appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H-n over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential. (C) 2002 American Institute of Physics.

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to the standard approximate Kohn-Sham exchange-correlation (xc) potentials are considered with the aim to improve the excitation energies (especially for higher excitations) calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection (GRAC) of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends (LB) are seamlessly connected to the (shifted) xc potential of Becke and Perdew (BP) with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N-2, CO, CH2O, C2H4, C5NH5, C6H6, Li-2, Na-2, K-2. The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of (model) orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine "local" density functional with an analytical representation. (C) 2001 American Institute of Physics.

Magnetic properties of copper hexadecaphthalocyanine (F16CuPc) thin films and powders

The structural and magnetic properties of F16CuPc thin films and powder, including x-ray diffraction (XRD), superconducting quantum interference device (SQUID) magnetometry, and theoretical modelling of exchange interactions are reported. Analysis of XRD from films, with thickness ranging between 100 and 160 nm, deposited onto Kapton and a perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) interlayer shows that the stacking angle (defined in the text) of the film is independent of the thickness, but that the texture is modified by both film thickness and substrate chemistry. The SQUID measurements suggest that all samples are paramagnetic, a result that is confirmed by our theoretical modelling including density functional theory calculations of one-dimensional molecular chains and Green's function perturbation theory calculations for a molecular dimer. By investigating theoretically a range of different geometries, we predict that the maximum possible exchange interaction between F16CuPc molecules is twice as large as that in unfluorinated copper-phthalocyanine (CuPc). This difference arises from the smaller intermolecular spacing in F16CuPc. Our density functional theory calculation for isolated F16CuPc molecule also shows that the energy levels of Kohn-Sham orbitals are rigidly shifted similar to 1 eV lower in F16CuPc compared to CuPc without a significant modification of the intramolecular spin physics, and that therefore the two molecules provide a suitable platform for independently varying magnetism and charge transport. 

Simulations of magnetic microstructure in thin film elements used for programmable motion of magnetic particles

The results of two-dimensional micromagnetic modeling of magnetization patterns in Permalloy ellipses under the influence of rotating constant-amplitude magnetic fields are discussed. Ellipses of two different lateral sizes have been studied, 0.5m x 1.5m and 1m x 3m. The amplitude of the rotating magnetic field was varied between simulations with the condition that it must be large enough to saturate or nearly saturate the ellipse with the field applied along the long axis of the ellipse. For the smaller ellipse size it is found that the magnetization pattern forms an S state and the direction of the net magnetization lags behind the direction of the applied field. At a critical angle of the rotating magnetic field the direction of the magnetization switches by a large angle to a new S state. Both the critical angle and the angle interval of the switch depend on field amplitude. For this new state, it is instead the applied field direction that lags behind the magnetization direction. The transient magnetization patterns correspond to multi-domain patterns including two vortices, but this state never exists for the equilibrated magnetization patterns. The behavior of the larger ellipse in rotating field is different. With the field applied along the long-axis of the ellipse, the magnetization of the ellipse is nearly saturated with a vortex close to each apex of the ellipse. As the field is rotated, this magnetization pattern remains and the net-magnetization direction lags behind the direction of the field until for a certain angle of the applied field an equilibrium multi-domain state is created. Comparisons are made with corresponding experimental results obtained by performing in-field magnetic force microscopy on Permalloy ellipses.

Chemical tuning of the interlayer magnetic coupling in TlCo2Se2-xSx

The system TlCo2Se2-xSx has been thoroughly investigated by neutron powder diffraction and SQUID magnetometry. TlCo2Se2-xSx is a layered tetragonal structure containing atomic cobalt layers separated by a distance of 6.4 angstrom in the sulphide and 6.8 angstrom in the selenide. The solid solubility of isovalent selenium and sulphur atoms in the structure makes it possible to continuously vary the interlayer distance and thereby tune the magnetic coupling between the Co-layers. At low temperatures, the Co-atoms are ferromagnetically ordered within the layers and magnetic moments lie in the ab-plane. However, these Co-moments form a helical magnetic structure that prevails for 0 <= x <= 1.5 with a gradual decrease of the angle between adjacent Co-layers from 122 degrees to 39 degrees. For x >= 1.75, a collinear ferromagnetic structure is stable. The relationship between the coupling angle and the Co-interlayer separation shows an almost linear behaviour. The helical phase contains no net spontaneous magnetic moment up to TlCo2SeS, where a small net magnetic moment appears that increases until the ferromagnetic structure is found for 1.75 <= x <= 2.0. (C) 2005 Elsevier B.V. All rights reserved.

Cycloidal magnetic order in the compound IrMnSi

A new compound, IrMnSi, has been synthesized, and its crystal structure and magnetic properties have been investigated by means of neutron powder diffraction, magnetization measurements, and first-principles theory. The crystal structure is found to be of the TiNiSi type (ordered Co2P, space group Pnma). The Mn-projected electronic states are situated at the Fermi level, giving rise to metallic binding, whereas a certain degree of covalent character is observed for the chemical bond between the It and Si atoms. A cycloidal, i.e., noncollinear, magnetic structure was observed below 460 K, with the propagation vector q=[0,0,0.4530(5)] at 10 K. The magnetism is dominated by large moments on the Mn sites, 3.8 mu(B)/atom from neutron diffraction. First-principles theory reproduces the propagation vector of the experimental magnetic structure as well as the angles between the Mn moments. The calculations further result in a magnetic moment of 3.21 mu(B) for the Mn atoms, whereas the Ir and Si moments are negligible, in agreement with observations. A calculation that more directly incorporates electron-electron interactions improves the agreement between the theoretical and experimental magnetic moments. A band mechanism is suggested to explain the observed magnetic order.

Micromagnetic studies of Fe/Co ellipses with competing anisotropy contributions

The effects of competing magneto-crystalline and shape anisotropies on magnetization reversal were studied in situ in arrays of sub-micron Fe/Co ellipses of compositions Fe2/Co6 and Fe8/Co3 with magnetic force microscopy (MFM). A simple model assigning magnetization values to the different types of domain structures observed in the MFM images was used to estimate the field dependence of the total magnetization of a sample. The agreement with macroscopic magnetization measurements is discussed. 

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.

Crystal structure and magnetic properties of the new phase Mn3IrSi

A new phase in the ternary Ir-Mn-Si system has been synthesised. From powder neutron diffraction data the crystal structure was determined to be of the AlAu4 type and to be described in the cubic space group P2(1)3 with the unit cell a = 6.4973(3) Angstrom. Susceptibility measurements using a SQUID-magnetometer showed a transition typical of anti ferromagnetism, with T-N = 210 K. Low temperature antiferromagnetic order is confirmed by extra peaks in neutron diffractograms recorded at 10 and 80 K. (C) 2004 Elsevier B.V. All rights reserved.

Stripe domain structure in epitaxial (001) BiFeO3 thin films on orthorhombic TbScO3 substrate

We have analyzed the ferroelastic and ferroelectric domain structure of high crystalline quality (001) BiFeO3 films on orthorhombic (110) TbScO3 substrates. Two domains were present in stripes separated by (010) vertical boundaries, with spontaneous polarizations in adjacent domains rotated by 109 degrees. The striped morphology was caused by nucleation of only two ferroelastic domains on the low symmetry GdFeO3-type substrate. Domain engineering through substrate symmetry is an important finding for rhombohedral ferroelectric epitaxial thin films. The stripe pattern with vertical walls may be useful for extracting domain wall contributions to magnetism and electrical transport properties of BiFeO3 materials.

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.