Spin Waves Revealed with X-Ray Vision

Spin Waves Revealed with X-Ray Vision
Christopher Crockett
Physics - Synopsis

Direct observation of coherent magnons with suboptical wavelengths in a single-crystalline ferrimagnetic insulator

J. Förster, J. Gräfe, J. Bailey, S. Finizio, N. Träger, F. Groß, S. Mayr, H. Stoll, C. Dubs, O. Surzhenko, N. Liebing, G. Woltersdorf, J. Raabe, M. Weigand, G. Schütz, and S. Wintz

Phys. Rev. B 100, 214416 (2019)

Schematics of the sample architecture and measurement setup. (a) Direct x-ray intensity image of the sample's transmission window. The central dark horizontal stripe is the antenna. (b) Single time frame of the time-resolved measurement with dynamical normalization that emphasizes the spin waves over the static background. Grayscale values represent the changes of the out-of-plane magnetization component. (c) Result of time-domain Fourier analysis, showing amplitude and phase of the waves in HSV (hue-saturation-value) color space (color code above the image).

Chirality-Dependent Transmission of SW through DW

Chirality-Dependent Transmission of Spin Waves through Domain Walls.
F. J. Buijnsters, Y. Ferreiros, A. Fasolino, and M. I. Katsnelson
Phys. Rev. Lett. 116, 147204 (2016)

Effect of the interfacial DMI on the magnetization profile $m\left(x\right)$ of a DW in a thin film with perpendicular anisotropy. (a) Away from the DW, magnetization points out of the film ($\hat{z}$ or $-\hat{z}$). Near the DW, the DMI creates an effective field $H_{\mathrm{DMI}}$ in the $-\hat{x}$ direction. Depending on the competition between the dipolar and DMI interactions, the equilibrium configurations circle, circle prime, star, star prime, and square, shown in (b)–(d), are possible. (b) Without DMI, the minimum-energy configurations (flux closure) are two equivalent Bloch DWs (circle, in dark colors, and circle prime, in light colors), whose in-plane orientations differ by 180°. (c) For intermediate DMI, the minimum-energy configurations are intermediate between Bloch and Néel. There are two equivalent minimum-energy states (star and star prime), whose in-plane orientations differ by approximately 90° for an appropriately tuned DMI strength $D$. (d) For strong DMI, a single minimum-energy configuration (square) exists: a Néel DW with magnetization in the center pointing in the $-\hat{x}$ direction.

SW excitation from pinned magnetic DWs

Tunable short-wavelength spin wave excitation from pinned magnetic domain walls.
Ben van de Viele, Sampo J. Hämäläinen, Pavel Baláž, Federico Montoncello & Sebastiaan van Dijken
Scientific Reports 6, 21330 (2016)

(a) Schematic of the ferroelectric-ferromagnetic bilayer structure. The polarization of the ferroelectric a1 and a2 domains is aligned along the elongated in-plane axis of the tetragonal BaTiO3 lattice and it rotates by 90 degrees at the domain boundaries. Via strain transfer and inverse magnetostriction, uniaxial anisotropy is induced in the ferromagnetic layer. The resulting ferromagnetic domain pattern fully correlates with the ferroelectric domain structure and magnetic domain walls are strongly pinned onto the ferroelectric domain boundaries by abrupt 90 degree rotations of magnetic anisotropy. (b) Micromagnetic simulation geometry for an extended film. The computational area is restricted to one period of the stripe domain structure, i.e. a single a1 and a2 domain, both having a width of 3.2 μm. Periodic boundary conditions in the x- and y-direction are used to account for the continuous film geometry. The simulated magnetization pattern near the magnetic domain wall is shown as inset.

Nanomagnonics around the corner

Spintronics: Nanomagnonics around the corner

Dirk Grundler

Nature Nanotechnology 11, 407 (2016)

Reconfigurable magnonic conduits realized in domain walls: a, Spin wave of wavevector k propagating in a domain wall between two magnetic domains (top view). Spins precess at their given position (red arrows); electrons do not flow. The white arrows indicate magnetization vectors, M. b, A magnetic field, H, shifts the spin-wave nanochannel because a domain of magnetization, M, grows at the expense of the other domain. Magnetic volume charges are indicated by plus and minus signs.

Universal dependence of SW in magnonic crystals

Universal dependence of the spin wave band structure on the geometrical characteristics of two-dimensional magnonic crystals.

S. Tacchi, P. Gruszecki, M. Madami, G. Carlotti, J. W. Kłos, M. Krawczyk, A. Adeyeye, G. Gubbiotti 

Scientific Reports 5, 10367 (2015)

(a) BLS spectra taken at the Γ-point for the series S1 ADLs with different thicknesses applying a magnetic field μ₀H₀ = 0.1 T. (b) Calculated SW spatial profiles for the edge (E), the fundamental (F) and the fundamental-localized (F_loc) modes. The intensity of the color denotes the amplitude of the excitation, while the red and blue colors indicate opposite phase.

Atomistic spin dynamics: Review

Atomistic spin dynamics and surface magnons.
Corina Etz, Lars Bergqvist, Anders Bergman, Andrea Taroni and Olle Eriksson
Journal of Physics: Condensed Matter 27, 243202 

 Bridging the gap: the ASD link between ab initio methods and micromagnetics simulations.

Special on DW propagation in nanowires

Spin wave emission in field-driven domain wall motion.
X. S. Wang and X. R. Wang
Phys. Rev. B 90, 184415 (2014)

(a) Schematic diagram of a 1D head-to-head DW (top-left inset) and the snapshot of s components at t=200 for α=0,J=53.7,Dz=0.317,Dz/Dx=10, and H=0.5. Lower-left inset: The s profile of DW. Symbols are numerical results, the vertical dashed line indicates the DW center position at z=0.9, and solid lines are the Walker profile (4) with ϕ=Ht and Z=0.9. Right inset: The simulated motion evolution of the DW center (black curve), the time dependence of the DW center by the collective coordinate model (red curve), and their difference (blue curve). (b) The field dependence of average DW speed v for different Dz and Dx. Vertical dashed and solid lines correspond to critical fields Hc1 and Hc2, respectively. Inset: Simulated DW center for fields below and above Hc1 (indicated by arrows in the main figure).

Domain wall pinning in notched nanowires.
H. Y. Yuan and X. R. Wang

Phys. Rev. B 89, 054423 (2014)

Snapshots of the spin configuration around the notch as the field increases from zero up over the depinning field. (a) H=0 Oe, (b) H=100 Oe, (c) H=170 Oe, and (d) H=180 Oe. For clarity, each spin represents the average magnetization of four 4 × 4 × 4 nm cells. The nanowire dimensions are 1000 × 64 × 4 nm, and the notch dimensions are 40 × 32 × 4 nm. (e) The evolution of m¯zCD and m¯zEF with applied field.

Instability of Walker Propagating Domain Wall in Magnetic Nanowires

B. Hu and X. R. Wang

Phys. Rev. Lett. 111, 027205 (2013)

Illustration of transverse head-to-head DW of width Δ in a nanowire, with easy axis along ẑ and hard axis along x̂. In the absence of external magnetic field (upper), a static DW exists between two domains with m_z=±1. Under a field parallel to the easy axis, the Walker propagating DW moves towards the energy minimum state (m_z=-1) at a speed v while the DW profile is preserved.

Direct Imaging of Thermally Driven Domain Wall Motion in Magnetic Insulators.
Wanjun Jiang, Pramey Upadhyaya, Yabin Fan, Jing Zhao, Minsheng Wang, Li-Te Chang, Murong Lang, Kin L. Wong, Mark Lewis, Yen-Ting Lin, Jianshi Tang, Sergiy Cherepov, Xuezhi Zhou, Yaroslav Tserkovnyak, Robert N. Schwartz, and Kang L. Wang
Phys. Rev. Lett. 110, 177202 (2013)

Experimental demonstration of DW motion driven by a temperature gradient. (a) The schematic illustration of polar MOKE microscope for DW imaging. (b) and (c) M vs H hysteresis loops measured using a MOKE magnetometer for polar and longitudinal orientations, respectively. (d) Snapshots of the position of the DW as a function of time in the cold region, and hot region (e), respectively. It is noted that there is no time correlation between figures (d) and (e). The blue color corresponds to magnetization along +z direction, and white color associates with the magnetization along -z direction. Each fingerlike pattern thus contains two parallel DWs

Domain Wall Propagation through Spin Wave Emission.
X. S. Wang, P. Yan, Y. H. Shen, G. E. W. Bauer, and X. R. Wang
Phys. Rev. Lett. 109, 167209 (2012)

Schematic transverse head-to-head DW of width Δ in a magnetic nanowire. H⃗ is an external field along the wire axis defined as the z direction. DW breathing and other types of periodic DW deformations emit spin waves, denoted by the wavy lines with arrows.

Controlling AF Spin Waves

Coherent terahertz control of antiferromagnetic spin waves.
Tobias Kampfrath, Alexander Sell, Gregor Klatt, Alexej Pashkin, Sebastian Mährlein, Thomas Dekorsy, Martin Wolf, Manfred Fiebig, Alfred Leitenstorfer & Rupert Huber Nature Photonics 5, 31 (2011)

a, Crystal lattice of NiO (blue spheres, Ni²⁺; yellow spheres, O^2–) with magnetically ordered spins (blue arrows) of a selected S domain in the (111) planes (light blue) and the direction of the terahertz magnetic field B (double-ended…

SW excitation by STT

Spin-Wave Excitation in Magnetic Insulators by Spin-Transfer TorqueJiang Xiao and Gerrit E. W. Bauer
Phys. Rev. Lett. 108, 217204 (2012)

An electrically insulating magnetic film of thickness d with magnetization m (∥ẑ at equilibrium) in contact with a normal metal. A spin current J_s∥ẑ is generated in the normal metal and absorbed by the ferromagnet.

Spin waves in Heisenberg AF

Spin-wave multiple excitations in nanoscale classical Heisenberg antiferromagnets.
Zhuofei Hou and D. P. Landau, G. M. Stocks, G. Brown

Phys. Rev. B 91, 064417 (2015)

The spectra for ST(r0,q,ω) obtained from isotropic, antiferromagnetic nanofilms with the same Lxy=20 and three different thicknesses, i.e., Lz=10, 20, and 30. The results were obtained in the PBCXY [100] directions, i.e., the directions parallel to the free surfaces, with r0⇒bulkcenter at T=0.4TN with SD parameters of nt=5000,ncutoff=4000, and dt=0.2/|J|. We give the spectra for nq=0,1,2,...,5. N is the total number of initial configurations.

Imaging spin waves

Close-up on spin dynamics.

Stanislas Rohart and Guillemin Rodary

Nature Materials 13, 770 (2014) 

Imaging of spin waves in atomically designed nanomagnets.

A. Spinelli, B. Bryant, F. Delgado, J. Fernández-Rossier and A. F. Otte

Nature Materials 13, 782 (2014)

a, Schematic view of spin-wave excitation on a six-atom chain using scanning tunnelling microscopy. The highest efficiency is obtained when the tip is placed at an edge atom. b, Principle of spin-wave-assisted magnetization reversal in the chain. The switching, due to thermal and/or quantum fluctuations, is much faster when the scanning tunnelling microscope (STM) excites the chain in a spin-wave (SW) state.

Imaging Spin waves

Close-up on spin dynamics.
Stanislas Rohart and Guillemin Rodary
Nature Materials 13, 770 (2014)

Imaging of spin waves in atomically designed nanomagnets.
A. Spinelli, B. Bryant, F. Delgado, J. Fernández-Rossier and A. F. Otte
Nature Materials 13, 782 (2014)

Thermoelectric SW detection

Thermoelectric Detection of SpinWaves.
H. Schultheiss, J. E. Pearson, S. D. Bader, and A. Hoffmann
Phys. Rev. Lett. 109, 237204 (2012)

(a), (b) Schematic of the sample. The spin-wave waveguide is 2 mm long, 20 m wide, and made from 100 nm thick Permalloy on a GaAs substrate. The coplanar waveguide for rf excitation and the leads for dc voltage measurements are made from 150 nm thick Au. The CPW has a signal linewidth of 10 m and a signal-to-ground-line separation of 5 m. (c) Illustration of the z distribution of the dissipated power and resulting temperature profile.

Interactions of SWs and DWs in a nanowire

Interaction between propagating spin waves and domain walls on a ferromagnetic nanowire.
J.-S. Kim, M. Stärk, and M. Kläui, J. Yoon and C.-Y. You, L. Lopez-Diaz and E. Martinez
Phys. Rev. B 85, 174428 (2012)

(a) The SW amplitudes as a function of time (t = 5.0–5.5 ns with fH = 6.0 GHz, B0 = 200 mT, and Bext = 0.5 mT) at the TW position (x = 500 nm and x = 700 nm) (black line, the SW amplitude without a TW; red line, the SW amplitude with a TW). (b) The FFT spectra of the SW amplitude for the case of (a) at the TW position (x = 500 nm). (c) The SW amplitudes as a function of time at x = 500 nm (t = 5.0–10.0 ns with fH = 11.0 GHz, B0 = 200 mT, and Bext = 0.8 mT). (d) The FFT spectrum of the SW amplitude for the case of  (c) at the TW position. Inset shows the snapshots of the y-component magnetization for two different simulation times.

SW and DW interactions in a nanowire

Interaction between propagating spin waves and domain walls on a ferromagnetic nanowire
J.-S. Kim, M. Stärk, and M. Kläui, J. Yoon and C.-Y. You, L. Lopez-Diaz and E. Martinez
Phys. Rev. B 85, 174428 (2012)

The initial spin configuration of the trapped head-to-head TW nucleated at the position of a square notch in the center of the nanowire. The square notch size is 5 × 5 nm2. In the bottom we zoom into the central part of the wire to show the internal structure of the TW pinned at the notch. In order to generate SWs, we apply a localized sinusoidal field at a position denoted as the SW source. The SW source is located at 500 nm from the center of the nanowire. To depin the TW, we apply an external field Bext along the ±x direction.

SW diffraction

SpinWave Diffraction and Perfect Imaging of a Grating.
S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach
Phys. Rev. Lett. 108, 047204 (2012) 

Sketch of the experimental arrangement. S denotes the signal line, and G1 and G2 denote the ground lines of the coplanar wave guide. An exemplary TR-SKM phase image of the spin wave field taken at 10 mT and 4180 MHz is overlaid as a color density plot on a part of the Permalloy film.

Collective SW excitations in coupled nanodots

Collective spin-wave excitations in a two-dimensional array of coupled magnetic nanodots.
Roman Verba and Gennadiy Melkov, Vasil Tiberkevich and Andrei Slavin

Spin-wave absorption spectra (a) and mode
structure [(b) and (c)] in a magnetic dot array in a FM ground
state having one defect per 11 × 11 dots.

Phys. Rev. B 85, 014427 (2012)

Regions of stability of different ground
states of a magnetic dot array in zero applied field: above the solid blue line both the FM and the CAFM ground states are stable; below the solid blue line, but above the dashed red line only the
CAFM ground state is stable; below the dashed red line both FM and CAFM states are unstable and array switches to a state with in-plane direction of the dot static magnetization.

 

Spin wave excitations of DWs

Spin-wave excitations of domain walls in bubble-state magnetic nanoelements.
N. Vukadinovic, F. Boust
Phys. Rev. B 84, 224425 (2011)

(a) Static magnetic properties for a bidomain bubble state in a cylindrical element (quality factor Q = 1.2, thickness Lz = 24 nm, diameter D = 96 nm); (b) Equilibrium magnetization configuration and coordinate system.

Order by disorder in a triangular lattice

Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice.
A. Honecker, D. C. Cabra, H.-U. Everts, P. Pujol, and F. Stauffer
Phys. Rev. B 84, 224410 (2011)

Snapshot of a configuration during a simulation for J < 0 at T = 10−3|J | on a 12 × 12 lattice. Periodic
boundary conditions are imposed at the edges.

Simulating SWs dispersion in nanostructures

Numerical calculation of spin wave dispersions in magnetic nanostructures.
Dheeraj Kumar, Oleksandr Dmytriiev, Sabareesan Ponraj and Anjan Barman
J. Phys. D 45, 015001 (2012)

Static magnetic configurations (in-plane) of the central portion of the simulated sample with H applied (a) along the length and (b) across the width of the permalloy ample with 3 rows of 1D array of square anti-dots imprinted in it. (c and d) Corresponding simulated dispersion of symmetric modes.