# Publications

## Proposal of a micromagnetic standard problem for ferromagnetic resonance simulations

ArXiv arXiv (2016)

AA Baker, M Beg, G Ashton, M Albert, D Chernyshenko, W Wang, S Zhang, M-A Bisotti, M Franchin, CL Lu, R Stamps, T Hesjedal, H Fangohr

Nowadays, micromagnetic simulations are a common tool for studying a wide range of different magnetic phenomena, including the ferromagnetic resonance. A technique for evaluating reliability and validity of different micromagnetic simulation tools is the simulation of proposed standard problems. We propose a new standard problem by providing a detailed specification and analysis of a sufficiently simple problem. By analyzing the magnetization dynamics in a thin permalloy square sample, triggered by a well defined excitation, we obtain the ferromagnetic resonance spectrum and identify the resonance modes via Fourier transform. Simulations are performed using both finite difference and finite element numerical methods, with OOMMF and Nmag simulators, respectively. We report the effects of initial conditions and simulation parameters on the character of the observed resonance modes for this standard problem. We provide detailed instructions and code to assist in using the results for evaluation of new simulator tools, and to help with numerical calculation of ferromagnetic resonance spectra and modes in general.

## Proposal of a micromagnetic standard problem for ferromagnetic resonance simulations

Journal of Magnetism and Magnetic Materials Elsevier 421 (2016) 428-439

AA Baker, M Beg, G Ashton, M Albert, D Chernyshenko, W Wang, S Zhang, M-A Bisotti, M Franchin, CL Hu, R Stamps, T Hesjedal, H Fangohr

Nowadays, micromagnetic simulations are a common tool for studying a wide range of different magnetic phenomena, including the ferromagnetic resonance. A technique for evaluating reliability and validity of different micromagnetic simulation tools is the simulation of proposed standard problems. We propose a new standard problem by providing a detailed specification and analysis of a sufficiently simple problem. By analyzing the magnetization dynamics in a thin permalloy square sample, triggered by a well defined excitation, we obtain the ferromagnetic resonance spectrum and identify the resonance modes via Fourier transform. Simulations are performed using both finite difference and finite element numerical methods, with OOMMF and Nmag simulators, respectively. We report the effects of initial conditions and simulation parameters on the character of the observed resonance modes for this standard problem. We provide detailed instructions and code to assist in using the results for evaluation of new simulator tools, and to help with numerical calculation of ferromagnetic resonance spectra and modes in general.

## Anisotropic absorption of pure spin currents

Physical Review Letters American Physical Society 116 (2016) 047201

A Baker, AI Figueroa, CJ Love, SA Cavill, T Hesjedal, G van der Laan

Spin transfer in magnetic multilayers offers the possibility of ultra-fast, low-power device operation. We report a study of spin pumping in spin valves, demonstrating that a strong anisotropy of spin pumping from the source layer can be induced by an angular dependence of the total Gilbert damping parameter, a, in the spin sink layer. Using lab- and synchrotron-based ferromagnetic resonance, we show that an in-plane variation of damping in a crystalline leads to an anisotropic a in a polycrystalline . This anisotropy is suppressed above the spin diffusion length in Cr, which is found to be 8 nm, and is independent of static exchange coupling in the spin valve. These results offer a valuable insight into the transmission and absorption of spin currents, and a mechanism by which enhanced spin torques and angular control may be realized for next-generation spintronic devices.

## Engineering helimagnetism in MnSi thin films

AIP Advances American Institute of Physics 6 (2016) 015217

S Zhang, R Chalasani, AA Baker, N-J Steinke, AI Figueroa, A Kohn, G van der Laan, T Hesjedal

Magnetic skyrmion materials have the great advantage of a robust topological magnetic structure, which makes them stable against the superparamagnetic effect and therefore a candidate for the next-generation of spintronic memory devices. Bulk MnSi, with an ordering temperature of 29.5 K, is a typical skyrmion system with a propagation vector periodicity of ∼18 nm. One crucial prerequisite for any kind of application, however, is the observation and precise control of skyrmions in thin films at room-temperature. Strain in epitaxial MnSi thin films is known to raise the transition temperature to 43 K. Here we show, using magnetometry and x-ray spectroscopy, that the transition temperature can be raised further through proximity coupling to a ferromagnetic layer. Similarly, the external field required to stabilize the helimagnetic phase is lowered. Transmission electron microscopy with element-sensitive detection is used to explore the structural origin of ferromagnetism in these Mn-doped substrates. Our work suggests that an artificial pinning layer, not limited to the MnSi/Si system, may enable room temperature, zero-field skyrmion thin-film systems, thereby opening the door to device applications.

## Atomic level structural and chemical analysis of Cr-doped Bi₂Se₃

Scientific Reports Nature Publishing Group 6 (2016) 26549

A Ghasemi, D Kepaptsoglou, LJ Collins-McIntyre, Q Ramasse, T Hesjedal, VK Lazarov

We present a study of the structure and chemical composition of the Cr-doped 3D topological insulator Bi2Se3. Single-crystalline thin films were grown by molecular beam epitaxy on Al2O3 (0001), and their structural and chemical properties determined on an atomic level by aberration-corrected scanning transmission electron microscopy and electron energy loss spectroscopy. A regular quintuple layer stacking of the Bi2Se3 film is found, with the exception of the first several atomic layers in the initial growth. The spectroscopy data give direct evidence that Cr is preferentially substituting for Bi in the Bi2Se3 host. We also show that Cr has a tendency to segregate at internal grain boundaries of the Bi2Se3 film.

## Organic Transistors: Universal Magnetic Hall Circuit Based on Paired Spin Heterostructures (Adv. Electron. Mater. 6/2015)

S Zhang, AA Baker, JY Zhang, G Yu, S Wang, T Hesjedal

## High resolution STEM study of dy-doped Bi2Te3 thin films

Microscopy and Microanalysis Cambridge University Press 22 (2016) 1516-1517

V Srot, P Schoenherr, B Bussmann, SE Harrison, PA van Aken, T Hesjedal

Breaking the time-reversal symmetry (TRS) in three-dimensional (3D) topological insulators (TIs) is essential for unlocking exotic physical states and exploring potential device application. Doping of the prototypical 3D-TI Bi2Te3 with transition metal ions can lead to ferromagnetic ordering at low temperatures. Here we report the study of incorporation of dysprosium (Dy) into Bi2Te3 with the intent to achieve higher ferromagnetic ordering temperatures and higher magnetic moments.

## Modulated spin helicity stabilized by incommensurate orbital density waves in a quadruple perovskite manganite

Physical Review B American Physical Society 93 (2016) 180403-

RD Johnson, DD Khalyavin, P Manuel, A Bombardi, C Martin, LC Chapon, P Radaelli

Through a combination of neutron diffraction and Landau theory we describe the spin ordering in the ground state of the quadruple perovskite manganite CaMn7O12 - a magnetic multiferroic supporting an incommensurate orbital density wave that onsets above the magnetic ordering temperature, TN1 = 90 K. The multi-k magnetic structure in the ground state was found to be a nearly-constant-moment helix with modulated spin helicity, which oscillates in phase with the orbital occupancies on the Mn3+ sites via trilinear magneto-orbital coupling. Our phenomenological model also shows that, above TN2 = 48 K, the primary magnetic order parameter is locked into the orbital wave by an admixture of helical and collinear spin density wave structures. Furthermore, our model naturally explains the lack of a sharp dielectric anomaly at TN1 and the unusual temperature dependence of the electrical polarisation.

## Structural, electronic, and magnetic investigation of magnetic ordering in MBE-grown CrxSb2−xTe3 thin films

Europhysics Letters European Physical Society (2016)

LJ Collins-McIntyre, LB Duffy, A Singh, N-J Steinke, CJ Kinane, TR Charlton, A Pushp, AJ Kellock, SSP Parkin, SN Holmes, CHW Barnes, G van der Laan, S Langridge, T Hesjedal

We report the structural, electronic, and magnetic study of Cr-doped Sb2Te3 thin films grown by a two-step deposition process using molecular-beam epitaxy (MBE). The samples were investigated using a variety of complementary techniques, namely, x-ray diffraction (XRD), atomic force microscopy, SQUID magnetometry, magneto-transport, and polarized neutron reflectometry (PNR). It is found that the samples retain good crystalline order up to a doping level of x = 0:42 (in CrxSb2 xTe3), above which degradation of the crystal structure is observed by XRD. Fits to the recorded XRD spectra indicate a general reduction in c-axis lattice parameter as a function of doping, consistent with substitutional doping with an ion of smaller ionic radius. The samples show soft ferromagnetic behavior with the easy axis of magnetization being out-of-plane. The saturation magnetization is dependent on the doping level, and reaches from ~2 μB to almost 3 μB per Cr ion. The transition temperature (Tc) depends strongly on the Cr concentration and is found to increase with doping concentration. For the highest achievable doping level for phase-pure films of x = 0:42, a Tc of 125 K was determined. Electric transport measurements find surface-dominated transport below ~10 K. The magnetic properties extracted from anomalous Hall effect data are in excellent agreement with the magnetometry data. PNR studies indicate a uniform magnetization profile throughout the film, with no indication of enhanced magnetic order towards the sample surface.

## Transverse field muon-spin rotation measurement of the topological anomaly in a thin film of MnSi

Physical Review B: Condensed Matter and Materials Physics American Physical Society 93 (2016) 140412(R)

T Lancaster, F Xiao, Z Salman, IO Thomas, SJ Blundell, F Pratt, SJ Clark, T Prokscha, A Suter, SL Zhang, AA Baker, T Hesjedal

We present the results of transverse-field muon-spin rotation measurements on an epitaxially grown 40-nm-thick film of MnSi on Si(111) in the region of the field-temperature phase diagram where a skyrmion phase has been observed in the bulk. We identify changes in the quasistatic magnetic field distribution sampled by the muon, along with evidence for magnetic transitions around T≈40 and 30 K. Our results suggest that the cone phase is not the only magnetic texture realized in film samples for out-of-plane fields.

## Magnetic ordering in Ho-doped Bi2Te3 topological insulator thin films

Physica Status Solidi: Rapid Research Letters Wiley 10 (2016) 467–470-

AI Figueroa, SE Harrison, LJ Collins-McIntyre, G van der Laan, T Hesjedal

We investigate the magnetic properties of Ho-doped Bi2Te3 thin films grown by molecular beam epitaxy. Analysis of the polarized x-ray absorption spectra at the Ho M5 absorption edge gives an effective 4f magnetic moment which is ~45% of the Hund's rule ground state value. X-ray magnetic circular dichroism (XMCD) shows no significant anisotropy, which suggests that the reduced spin moment is not due to the crystal field effects, but rather the presence of non-magnetic or antiferromagnetic Ho sites. Extrapolating the temperature dependence of the XMCD measured in total electron yield and fluorescence yield mode in a field of 7 T gives a Curie-Weiss temperature of \theta_CW ~ -30 K, which suggests antiferromagnetic ordering, in contrast to the paramagnetic behavior observed with SQUID magnetometry. From the anomaly of the XMCD signal at low temperatures, a Neel temperature TN between 10 K and 25 K is estimated.

## Free-standing millimetre-long Bi2Te3 sub-micron belts catalyzed by TiO2 nanoparticles

Nanoscale Research Letters SpringerOpen 11 (2016) 308

P Schoenherr, F Zhang, D Kojda, RU Mitdank, M Albrecht, SF Fischer, T Hesjedal

Physical vapour deposition (PVD) is used to grow millimetre-long Bi2 Te3 sub-micron belts catalysed by TiO2 nanoparticles. The catalytic efficiency of TiO2 nanoparticles for the nanostructure growth is compared with the catalyst-free growth employing scanning electron microscopy. The catalyst-coated and catalyst-free substrates are arranged side-by-side, and overgrown at the same time, to assure identical growth conditions in the PVD furnace. It is found that the catalyst enhances the yield of the belts. Very long belts were achieved with a growth rate of 28 nm/min. A ∼1-mm-long belt with a rectangular cross-section was obtained after 8 h of growth. The thickness and width were determined by atomic force microscopy, and their ratio is ∼1:10. The chemical composition was determined to be stoichiometric Bi2Te3 using energy-dispersive X-ray spectroscopy. Temperature-dependent conductivity measurements show a characteristic increase of the conductivity at low temperatures. The room temperature conductivity of 0.20×1^5 S⋅m^−1 indicates an excellent sample quality.

## Resonant elastic x-ray scattering from the skyrmion lattice in Cu₂OSeO₃

Physical Review B - Condensed Matter and Materials Physics American Physical Society 93 (2016) 214420-

S Zhang, A Bauer, H Berger, C Pfleiderer, G van der Laan, T Hesjedal

We report the study of the skyrmion state near the surface of Cu₂OSeO₃ using soft resonant elastic x-ray scattering (REXS) at the Cu L₃ edge. Within the lateral sampling area of 200 × 200 µm², we found a long-range-ordered skyrmion lattice phase as well as the formation of skyrmion domains via the multiple splitting of the diffraction spots. In a recent REXS study of the skyrmion phase of Cu₂OSeO₃ [Phys. Rev. Lett. 112, 167202 (2014)], Langner et al. reported a double-splitting which they interpret as arising from the moiré pattern of two superposed skyrmion sublattices, originating from the two inequivalent Cu sites. However, we find no energy splitting of the Cu peak in xray absorption measurements, which is to be expected considering the system in more detail. We show that the experimental data reported by Langner et al. does not support their interpretation and discuss alternative origins of the peak splitting. In particular, we find that for magnetic field directions deviating from the major cubic axes, a multidomain skyrmion lattice state is obtained, which consistently explains the splitting of the magnetic spots into two—and more—peaks.

## Oxidation effects in rare earth doped topological insulator thin films

Scientific Reports Nature Publishing Group 6 (2016)

AI Figueroa, G van der Laan, SE Harrison, G Cibin, T Hesjedal

The breaking of time-reversal symmetry (TRS) in topological insulators is a prerequisite for unlocking their exotic properties and for observing the quantum anomalous Hall effect (QAHE). The incorporation of dopants which exhibit magnetic long-range order is the most promising approach for TRS-breaking. REBiTe3, wherein 50% of the Bi is substitutionally replaced by a RE atom (RE=Gd, Dy, and Ho), is a predicted QAHE system. Despite the low solubility of REs in bulk crystals of a few %, highly doped thin films have been demonstrated, which are free of secondary phases and of high crystalline quality. Here we study the effects of exposure to atmosphere of rare rarth-doped Bi2(Se,Te)3 thin films using x-ray absorption spectroscopy. We demonstrate that these RE dopants are all trivalent and effectively substitute for Bi3+ in the Bi2(Se,Te)3 matrix. We find an unexpected high degree of sample oxidation for the most highly doped samples, which is not restricted to the surface of the films. In the low doping limit, the RE-doped films mostly show surface oxidation, which can be prevented by surface passivation, encapsulation, or in-situ cleaving to recover the topological surface state.

## On the temperature dependence of spin pumping in ferromagnet–topological insulator–ferromagnet spin valves

Results in Physics Elsevier 6 (2016) 293-294

AA Baker, AI Figueroa, G van der Laan, T Hesjedal

Topological insulators (TIs) have a large potential for spintronics devices owing to their spinpolarized, counter-propagating surface states. Recently, we have investigated spin pumping in a ferromagnet-TI-ferromagnet structure at room temperature. Here, we present the temperature-dependent measurement of spin pumping down to 10 K, which shows no variation with temperature.

## Incommensurate counterrotating magnetic order stabilized by Kitaev interactions in the layered honeycomb $α$-Li$_2$IrO$_3$

Physical Review B American Physical Society 93 (2016) 195158

S Williams, RD Johnson, F Freund, S Choi, A Jesche, I Kimchi, S Manni, A Bombardi, P Manuel, P Gegenwart, R Coldea

The layered honeycomb magnet α-Li2IrO3 has been theoretically proposed as a candidate to display unconventional magnetic behaviour associated with Kitaev interactions between spin-orbit entangled jeff = 1=2 magnetic moments on a honeycomb lattice. Here we report single crystal magnetic resonant x-ray diffraction combined with powder magnetic neutron diffraction to reveal an incommensurate magnetic order in the honeycomb layers with Ir magnetic moments counterrotating on nearest-neighbor sites. This unexpected type of magnetic structure for a honeycomb magnet cannot be explained by a spin Hamiltonian with dominant isotropic (Heisenberg) couplings. The magnetic structure shares many key features with the magnetic order in the structural polytypes β-and γ-Li2IrO3, understood theoretically to be stabilized by dominant Kitaev interactions between Ir moments located on the vertices of three-dimensional hyperhoneycomb and stripyhoneycomb lattices, respectively. Based on this analogy and a theoretical soft-spin analysis of magnetic ground states for candidate spin Hamiltonians, we propose that Kitaev interactions also dominate in α-Li2IrO3, indicative of universal Kitaev physics across all three members of the harmonic honeycomb family of Li2IrO3 polytypes.

## Multidomain Skyrmion Lattice State in Cu₂OSeO₃

Nano Letters American Chemical Society 16 (2016) 3285–3291-

SL Zhang, A Bauer, DM Burn, P Milde, E Neuber, LM Eng, H Berger, C Pfleiderer, G van der Laan, T Hesjedal

Magnetic skyrmions in chiral magnets are nanoscale, topologically-protected magnetization swirls that are promising candidates for spintronics memory carriers. Therefore, observing and manipulating the skyrmion state on the surface level of the materials are of great importance for future applications. Here, we report a controlled way of creating a multidomain skyrmion state near the surface of a Cu₂OSeO₃ single crystal, observed by soft resonant elastic x-ray scattering. This technique is an ideal tool to probe the magnetic order at the L₃ edge of 3d metal compounds giving a depth sensitivity of ~50 nm. The single-domain sixfold-symmetric skyrmion lattice can be broken up into domains overcoming the propagation directions imposed by the cubic anisotropy by applying the magnetic field in directions deviating from the major cubic axes. Our findings open the door to a new way to manipulate and engineer the skyrmion state locally on the surface, or on the level of individual skyrmions, which will enable applications in the future.

## The Magneto-Hall Difference and the Planar Extraordinary Hall Balance

AIP Advances American Institute of Physics (2016)

T Hesjedal, SL Zhang

The extraordinary Hall balance (EHB) is a general device concept that harnesses the net extraordinary Hall effect (EHE) arising from two independent magnetic layers, which are electrically in parallel. Different EHB behavior can be achieved by tuning the strength and type of interlayer coupling, i.e., ferromagnetic or antiferromagnetic of varying strength, allowing for logic and memory applications. The physics of the EHE in such a multilayered systems, especially the interface-induced effect, will be discussed. A discrepancy between the magnetization and the Hall effect, called the magneto-Hall difference (MHD) is found, which is not expected in conventional EHE systems. By taking advantage of the MHD effect, and by optimizing the materials structure, magnetoresistance ratios in excess of 40,000% can be achieved at room-temperature. We present a new design, the planar EHB, which has the potential to achieve significantly larger magnetoresistance ratios.

## Monoclinic crystal structure of α−RuCl3 and the zigzag antiferromagnetic ground state

Physical Review B American Physical Society 92 (2015) 235119-

R Johnson, SC Williams, AA Haghighirad, J Singleton, V Zapf, P Manuel, II Mazin, Y Li, HO Jeschke, R Valenti, R Coldea

The layered honeycomb magnet alpha-RuCl3 has been proposed as a candidate to realize a Kitaev spin model with strongly frustrated, bond-dependent, anisotropic interactions between spin-orbit entangled jeff=1/2 Ru4+ magnetic moments. Here we report a detailed study of the three-dimensional crystal structure using x-ray diffraction on untwinned crystals combined with structural relaxation calculations. We consider several models for the stacking of honeycomb layers and find evidence for a crystal structure with a monoclinic unit cell corresponding to a stacking of layers with a unidirectional in-plane offset, with occasional in-plane sliding stacking faults, in contrast with the currently-assumed trigonal 3-layer stacking periodicity. We report electronic band structure calculations for the monoclinic structure, which find support for the applicability of the jeff=1/2 picture once spin orbit coupling and electron correlations are included. We propose that differences in the magnitude of anisotropic exchange along symmetry inequivalent bonds in the monoclinic cell could provide a natural mechanism to explain the spin gap observed in powder inelastic neutron scattering, in contrast to spin models based on the three-fold symmetric trigonal structure, which predict a gapless spectrum within linear spin wave theory. Our susceptibility measurements on both powders and stacked crystals, as well as neutron powder diffraction show a single magnetic transition at TN ~ 13K. The analysis of the neutron data provides evidence for zigzag magnetic order in the honeycomb layers with an antiferromagnetic stacking between layers. Magnetization measurements on stacked single crystals in pulsed field up to 60T show a single transition around 8T for in-plane fields followed by a gradual, asymptotic approach to magnetization saturation, as characteristic of strongly anisotropic exchange interactions.

## Study of Ho-doped Bi2Te3 topological insulator thin films

Applied Physics Letters American Institute of Physics 107 (2015) 1-1

SE Harrison, LJ Collins-McIntyre, S Zhang, AA Baker, AI Figueroa, AJ Kellock, A Pushp, YL Chen, SSP Parkin, JS Harris, G van der Laan, T Hesjedal

Breaking time-reversal symmetry through magnetic doping of topological insulators has been identified as a key strategy for unlocking exotic physical states. Here, we report the growth of Bi2Te3 thin films doped with the highest magnetic moment element Ho. Diffraction studies demonstrate high quality films for up to 21% Ho incorporation. Superconducting quantum interference device magnetometry reveals paramagnetism down to 2 K with an effective magnetic moment of ~mu_B/Ho. Angle-resolved photoemission spectroscopy shows that the topological surface state remains intact with Ho doping, consistent with the material’s paramagnetic state. The large saturation moment achieved makes these films useful for incorporation into heterostructures, whereby magnetic order can be introduced via interfacial coupling.