Session L19: Magnetic Nanoparticles: Scattering and Fluctuations

Fluctuation and dynamics of magnetic skyrmions

Recently discovered skyrmions is an example of a topological phase that manifest in magnetic systems as a hexagonal lattice of spin vortices. Understanding driven dynamics and spontaneous fluctuations of the skyrmions is fundamentally important to determine the robustness of the topological particles which is an important factor to consider for their use in magnetic logic and storage applications. We have shown that resonant x-ray scattering is a powerful tool to study skyrmion [1,2]. We will report on ultrafast x-ray scattering studies on skyrmion material Cu2OSeO3 using laser pump-x-ray probe. The excitation of the skyrmion phase shows a nonlinear dependence on the excitation density, in contrast to the excitation of the conical phase which is linearly dependent on the excitation density [3]. We will also discuss a new experimental technique that uses a time-delayed femtosecond x-ray pulse pair to perform correlation spectroscopy at nanosecond time scales to study fluctuations on Fe-Gd thin film samples that exhibit stripe and skyrmion phase [4]. When the applied field was tuned for skyrmions in the sample, the fluctuations were found to de-correlate within a period of about 4 nanoseconds. At the stripe-skyrmion phase boundary, the fluctuation period decreased to only a fraction of a nanosecond indicative of enhanced fluctuation at the stripe-skyrmion phase boundary.

[1]. M. C. Langner, S. Roy et al., Phys. Rev. Lett. 112, 167202 (2014).
[2]. J. C. T Lee et al, Appl. Phys. Lett. 109, 022402 (2016).
[3]. M. C. Langner, S. Roy et al, Phys. Rev. Lett. 119, 107204 (2017)
[4]. M. H. Seaberg et. al., Phys. Rev. Lett, 119, 067403 (2017).   

Coherent X-ray diffraction analysis of nanopatterned magnet with icosahedral symmetry

We have carried out coherent resonant X-ray diffraction experiments on arrays of nanopatterned magnets with icosahedral symmetry. Coherent speckle patterns were collected on the reflection-mode geometry allowing the direct access to the nanopatterned magnetic moments on thick Si substrates without requiring any extra sample treatment for the experiemnts. Subtracting the two coherent speckle patterns from right and left circular polarizarization reflect on the domain structure. Obtained domain structure was compared with micro-magnetic simulation to compare the groud-state structure of the patterned nano-magnet with quasicrystal symmetry.   

Revealing Long-Range Magnetic Order in High-Density Nanowire Arrays

High density arrays of ferromagnetic nanowires are critical to realizing next-generation 3D spintronic technologies, such as spin transfer torque-based racetrack memory. Segmented nanowires have emerged as exciting routes towards magnetic memory. To attain anticipated densities, the nanowires must be extremely close to each other. However, the effect of long range ordering interactions remains largely untested, and intersegment/interwire coupling may result in the formation of long-range magnetic correlations.
We used polarization analyzed small angle neutron scattering to probe Fe_xGa_1-x/Cu nanowire arrays, extracting a three-dimensional picture of magnetic ordering. In these wires, competing interactions induce complex, long-range magnetic order including antiferromagnetic interwire stripe patterns, in-plane interwire ferromagnetism, and intrawire fan structures. The magnetic ordering was tunable through either the external field or the segment aspect ratio. We develop a theoretical framework for more accurately treating interwire magnetic interactions in nanowire arrays. This work suggests that arrays of segmented nanowires possess a complex and highly-tunable, long-range magnetic domain structure which must be carefully considered in the design of nanowire-based devices.   

Spin Fluctuations in Small Magnetic Tunnel Junctions

Inelastic scattering of electrons by both phonons and magnons has been known to alter electronic transport through magnetic tunnel junctions (MTJs) [1]. More recently, spin-transfer torque driven thermal and even quantum fluctuations of the magnetic moments of the leads of small MTJs have been demonstrated to alter the magnetoresistance of the junction, leading to interesting nonlinear I-V behavior [2]. In this talk, I show how a simple model for spin-fluctuations of an MTJ gives rise to both inelastic charge transport and spin-transfer torque, taking both effects on equal footing. We qualitatively reproduce the electrical response of small MTJs, and show that inelastic charge transport dominates at low temperatures and biases, while spin-transfer torque is the dominant mechanism behind the nonlinear response at high temperatures and/or biases.

[1] S. Zhang, P. M. Levy, A. C. Marley, and S. S. P. Parkin, Physical review letters 79, 3744 (1997)
[2] J. Z. Sun and D. C. Ralph, Journal of Magnetism and Magnetic Materials 320, 1227 (2008); A. Zholud et al. arXiv:1703.09335 (2017)   

Thermal field noise from magnetic nanostructures

We show that thermally excited modes in magnetic nanostructures produce GHz-frequency stray field fluctuations, and that these fluctuations are large enough to be detected by diamond NV center magnetometry. In recent work, van der Sar et al. measured fluctuating stray fields 50 nm from a 30 nm-thick Permalloy film using nitrogen vacancy (NV) centers in diamond, demonstrating magnetometry of the thermally excited spin waves.[1] Here, we use micromagnetic modeling to calculate field noise for a series of Permalloy-like disks, 3 nm thick, with diameters ranging from 25 nm to 5000 nm. We calculate the pulsed-field response of the disks and use the fluctuation-dissipation theorem to obtain the stray field noise. Different vector components of the field fluctuations highlight spectral density peaks corresponding to modes with different symmetries. Typical field fluctuation amplitudes are on the order of 1 nT/Hz^1/2 at a spot 100 nm above the disk centers. Field noise at this level is measurable through T₁ relaxometry of NV centers. The NV spin state has a base line T₁ on the order of milliseconds, but field noise accelerates relaxation; at the field noise levels we calculate, T₁ is on the order of 1 μs, well above background.

[1] T. van der Sar, et. al., Nat. Comm, 6, 7886, (2015).   

Theory of Higher Order Spin Noise Spectrum and Its Measurement

Optical spin noise spectroscopy is a perturbation-free technique that enables one to characterize spin dynamics by detecting thermodynamic spin fluctuations via the Faraday or Kerr effect. However, most of the research has concentrated on the second-order spin noise correlator, i.e., the power spectrum, whereas higher-order correlators can also be measured and analyzed. Here, we theoretically show that the measurement of higher-order spin noise correlators can tell us more information about the physical system, such as the correlation effect, time-reversal symmetry breaking processes, and higher-order fluctuation dissipation theorems. These would be difficult to detect with other experimental techniques. We illustrate these ideas with experimental data on magnetization fluctuations in a ferromagnetic Pt/Co/Pt trilayer.   

Broadband optical spectroscopy of stochastic ferromagnetic fluctuations across a spin-reorientation transition

We use the magneto-optical Kerr effect to measure frequency spectra of stochastic magnetic fluctuations between 1 kHz and 1 MHz in a Pt/Co/Pt trilayer with anisotropy that has been laterally graded through a spin-reorientation transition. On regions of the film with strong perpendicular anisotropy, the fluctuation power obeys a power law over three orders of magnitude in frequency. Fluctuation spectra measured in regions with weaker anisotropy show a cutoff frequency below which the spectra are approximately frequency independent. We identify this cutoff as characterizing the maximum lifetime of ferromagnetic states, and find that it is sensitive to magnetic anisotropy, temperature, and applied magnetic field. Finally, the fluctuations show higher-order correlations which reveal temporal symmetry breaking, appearing upon application of magnetic field. These measurements establish magnetization fluctuation spectroscopy as a sensitive tool for characterizing ferromagnetic behavior and phase transitions.   

Magnetization Dynamics of Spin to Charge conversion in Nickel Nanoparticles

In this talk, we discuss the study of tunneling magnetoresistance and magnetic relaxation in single nickel nanoparticles using electron tunneling at 30mK. Our key observation is a strong magnetic field dependence of the effective charge noise. This effect is explained in terms of spin to charge conversion. From the rms of the charge noise we find the rms of the magnetization, and its magnetic field dependence. The magnetization relaxation time peaks at magnetic field of approximately 1T, with the relaxation time of T1=ms at that field. We will discuss the latest results on implementation of nickel nanoparticles with long spin relaxation time in these in spin-transfer torque switching.   

Depth-Profiling Magnetic Interfaces Formed Intrinsically in FePt3 by Ion-Beams

Using ion-beams to locally modify material properties is rapidly gaining momentum as a technique of choice for the fabrication of magnetic nano-elements because the method provides the capability to nano-engineer in 3D, which is important for many future spintronic technologies. The precise definition of the resulting element shape is crucial for device functionality. In this work, the intrinsic sharpness of a magnetic interface formed by nano-machining FePt₃ films using He⁺ irradiation is investigated. Through careful selection of the irradiating ion’s energy and fluence, ferromagnetism is locally induced into a fractional volume of a paramagnetic (PM) FePt₃ film by modifying the chemical order parameter. Using a combination of magnetometry, transmission electron microscopy and polarised neutron reflectometry it is demonstrated that the interface over which the PM to ferromagnetic modulation occurs is confined to a few atomic monolayers only. Using density functional theory, the mechanism for the ion-beam induced magnetic transition is elucidated and shown to be caused by an intermixing of Fe and Pt atoms in anti-site defects above a threshold density.   

Strain Induced Depth Dependent Magnetization Variation in Co thin films on PMN-PT Studied Using Polarized Neutron Reflectometry (PNR)

Strain induced clocking of nanomagnetic computing devices, often termed as “Straintronic devices” are inherently non-volatile and can be switched with ultra-low energy consumption [1-3]. These are nanoscale heterostructures of piezoelectric/ magnetostrictive materials. Electric field applied in the piezoelectric layer generates a strain which is transferred to the magnetostrictive layer inducing magnetization rotation. Variation in the transferred strain from the piezoelectric layer along the thickness of the magnetostrictive layer may lead to variation in magnetization rotation. This work studied this depth dependent magnetization variation in magnetostrictive Co films of 60 nm thickness on PMN-PT (001) substrates (1cm x 1cm x 0.5 mm) using PNR. PNR Measurements under different applied magnetic fields (saturation, remanence and near coercive field) and electric fields (0-400V) confirmed depth dependent magnetization rotation. Maximum rotation occurred near the PMN-PT/ Co interface and decreased towards the Co surface, which is reflective of the strain transfer simulated in COMSOL.
1. Nano Lett. 16, 1069 (2016). 2. Phys. Rev. Lett. 111, 027204 (2013). 3. Nano Lett. 10, 1219 (2010). 4. http://www.ncnr.nist.gov/reflpak.   

Real-space imaging of non-collinear antiferromagnetic order with a single spin magnetometer

Recently, Antiferromagnets have attracted considerable attention for next generation spintronic devices owing to their unique properties such as ultrafast magnetization dynamics and insensitivity to external magnetic field. To harness these functionalities, nanoscale control and imaging capabilities that are now routine for ferromagnets must be developed for antiferromagnetic (AF) systems. Here, using a non-invasive scanning nanomagnetometer based on a single nitrogen-vacancy (NV) defect in diamond, we demonstrate real-space visualization of non-collinear AF order in a magnetic thin film, at room temperature [1]. We image a 70 nm long spin cycloid in multiferroic BiFeO₃ thin film and also show electric field manipulation of the cycloid propagation direction. Besides highlighting the unique potential of NV magnetometry for imaging complex AF orders at the nanoscale, these results demonstrate how BiFeO₃ can be used as a versatile platform for the design of reconfigurable nanoscale spin textures. [1] I. Gross et al., Nature, 549, 252 (2017).   

Indirect K-edge Bimagnon Resonant Inelastic X-ray Scattering Spectrum of α-FeTe

We calculate the K-edge indirect bimagnon resonant inelastic X-ray scattering (RIXS) intensity spectra of the bicollinear antiferromagnetic order known to occur in the α-FeTe chalcogenide system. Utilizing linear spin wave theory for this large-S spin system we find that the bimagnon spectrum contains four scattering channels (two intraband and two interband). We find from our calculations that for suitable energy-momentum combination the RIXS spectra can exhibit a one, two- or three- peak structure. The number of peaks provides a clue on the various bimagnon excitation processes that can be supported both in and within the acoustic and optical magnon branches of the bicollinear antiferromagnet. Unlike the RIXS response of the antiferromagnetic or the collinear antiferromagnetic spin ordering, the RIXS intensity spectrum of the bicollinear antiferromagnet does not vanish at the magnetic ordering wave vector (π/2, −π/2). It is also sensitive to next-next nearest neighbor and biquadratic coupling interactions. Our predicted RIXS spectrum can be utilized to understand the role of multi-channel bimagnon spin excitations present in the α-FeTe chalcogenide.
  

Enhancing spin coherence in a pair of coupled spin 1/2 atoms assembled via STM

Detecting and controling individual spin centers and their interactions have been common interests for quantum and nanospintronic technologies. However, in solid-state nanostructures, the electron spin states are extremely fragile due to interaction with the electric and magnetic fluctuations arising from nearby electrodes or neighboring spins. In this work, we demonstrate that a singlet–triplet transition in a pair of antiferromagnetically coupled spin–1/2 atoms yields enhanced spin coherence compared to other transitions. We used scanning tunneling microscope to assemble two hydrogenated titanuim atoms on MgO(001). By selecting a spacing between two atoms that gives a large interaction energy, we obtain spin states having a high degree of protection from disrupting fields, and also provides thermal initialization into the singlet state. The spin coherence for the singlet–triplet transition is found to be ~3 times longer than other transitions, and the coherence time is further enhanced by reducing the interactions with tunneling electrons. Our work provides fundamental understandings of the spin dynamics in artificially built nanostructures. Additionally, these spin–1/2 Heisenberg antiferromagnets may serve as a promising architecture for quantum computation and simulation.