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The characterization of mechanical vibrations is mandatory to prevent or identify damages in structures, machinery and industrial mechanisms among other fields [1]. In parallel, the development of vibrational energy harvesters has become a relevant issue due to the possibility of generating electric power from the residual vibrational energy, quite common in that kinds of systems [2]. These two aspects are simultaneously addressed in this work by the design of a single combined device formed by an electromagnetic harvester and a non-contact magnetic linear accelerometer, permitting the energy generation and simultaneous characterization of low frequency vibrating systems. The device is composed of an electromagnetic harvester with a cylindrical frame (height 62 mm, inner diameter 15 mm) and a coil (1000 turns) to collect the electromotive force. The magnetic levitation system is composed of different NdFeB magnets, with two fixed at the extremes of the frame and a magnet inertial mass levitating freely when vibration occurs. At resonance (10 Hz) maximum electrical power of 1.4 mW at 0.5 g was observed. The magnetic accelerometer is based on the GMI effect [3] , that is, huge changes in impedance as a consequence of the variations of the effective magnetic field, in this case, in an amorphous wire (Co66Fe12Si13B15Cr4, 3 cm in length, 90 µm diameter). Its response (fGMI = 300 kHz) was examined, under sinusoidal vibration (fVIB = 10-40 Hz) of a simple ferrite magnet and for a complex magnetic system, namely the electromagnetic harvester. In both cases, the magnetic system periodic motion generates an amplitude modulated (AM) signal output, being its amplitude proportional to mechanical vibration amplitude (or acceleration). Results show the possibility of the potential design of an almost self-autonomous single combined device to simultaneously generate electrical energy and characterize low frequency vibrations.References: [1] A. Fauziyah, T. R. Sulistomo, M. N. Farid, and D. Arifianto, J. Phys.: Conf. Ser., vol. 1075, p. 012011, Aug. 2018, doi: 10.1088/1742-6596/1075/1/012011. [2] R. L. Harne and K. W. Wang, Smart Mater. Struct., vol. 22, no. 2, p. 023001, Jan. 2013, doi: 10.1088/0964-1726/22/2/023001. [3] M.-H. Phan and H.-X. Peng, Progress in Materials Science, vol. 53, no. 2, pp. 323–420, Feb. 2008, doi: 10.1016/j.pmatsci.2007.05.003.

MMM 2020

Vibrational Electromagnetic Energy Harvester and GMI Accelerometer Combined Device

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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poster

Antiferromagnets (AFMs) have become the focus of intense research for potentially novel spintronic applications[1]. AFMs have been theoretically proposed to be ideal candidates to support spatially-coherent textured states, that may transport angular momentum over long distance, often called spin superfluids[2,3,4]. The stability of these states hinges upon the structure of the dispersion for excited spin waves. Here, we introduce the spin hydrodynamic equations for AFMs, modeled as two exchange-coupled spin sublattices[5], each dynamically described by a Landau-Lifshitz (LL) equation in the continuum approximation. We include an external magnetic field, the nearest-neighbor inter-lattice exchange interaction, and an easy-plane anisotropy field. Spin hydrodynamics[6] are exactly represented in terms of the spin densities, the perpendicular magnetization component, and the spin velocities, the azimuthal phase gradients, for each spin sublattice. We have identified two distinct classes of spin textures that can be identified as hydrodynamic states[6]: 1) The phase-locked state in which the spins from the two sublattices maintain a constant π phase difference; this state has previously been referred to as a spin superfluid[2]; 2) The polarization state in which the dynamics are governed by oscillating relative phases. This decomposition in terms of the total and relative phase dynamics has been effective in the study of the coupled two-component Bose-Einstein condensates[7]. For the phase-locked state, we verify that the spin dispersion is a gapped mode spectrum[2] and the state exhibits modulational instability at large enough total spin velocity[2,6]. We further study the stability properties of the polarization state by determining dispersion relations for spin wave propagation. Our results suggest that this newly identified state may be favorably excited in long-range spin transport experiments under appropriate conditions.References: [1] V. Baltz, et al., Reviews of Modern Physics, Vol. 90, No. 1, p.015005 (2018). [2] E. B. Sonin, Physical Review B, Vol. 99, No. 10, p.104423 (2019). [3] S. Takei and Y. Tserkovnyak, Physical review letters, Vol. 112, No. 22, p.227201 (2014). [4] W. Yuan, Wei, et al., Science Advances, Vol. 4, No. 4, p. eaat1098 (2018). [5] V. Puliafito, et al., Physical Review B Vol. 99, No. 2, p.024405 (2019). [6] E. Iacocca, T. J. Silva and M. A. Hoefer, Physical Review Letters, Vol. 118, No. 1, p.017203 (2017). [7] A. M. Kamchatnov, et al., Physical Review A, Vol. 89, No. 3, p.033618 (2014).

Antiferromagnetic Spin Wave Propagation on Nonuniform Magnetic Backgrounds

Synthetic antiferromagnets (SAFs) comprise coupled ultrathin ferromagnetic films with a variety of ground states that can be stabilized at room temperature by tuning the magnetic parameters such as the effective anisotropy, interlayer exchange, and Dzyaloshinskii-Moriya interactions. As a result, nonuniform spin textures such as domain walls, spin spirals, and skyrmions can be stabilized under zero applied fields [1], which can be detected using quantum spin sensing [2]. Here, we present results of micromagnetics simulations in which we examined the spin wave dispersion associated with localized modes of domain walls, spin spirals, and skyrmions in such SAF structures. For domain walls and spin spirals, the combination of dipole-dipole and Dzyaloshinskii-Moriya interaction results in spectra with frequency-wave vector nonreciprocity (Fig. 1), which results from asymmetries in the micromagnetic ground state. Skyrmion breathing modes are found to be in the low GHz range, which differs from their counterparts in confined ferromagnetic systems. We also discuss a numerical spectroscopic technique to estimate the magnetic noise at the electron spin resonance frequency for nitrogen-vacancy center measurements, which relies on estimating the magnetic susceptibility by computing the transient response to driving fields that are harmonic in time but random in space. Good agreement is found with recent experimental results [2]. This work was supported by the Agence Nationale de la Recherche under contract no. ANR-17-CE24-0025 (TOPSKY).References: [1] W. Legrand et al., Nature Materials, Vol 19, p. 34 (2020). [2] A. Finco et al., arXiv:2006.13130 (2020).

Simulating Spin Wave Noise in Synthetic Antiferromagnetic Textures

Finite difference multiscale micromagnetic – atomistic HDD reader model has been developed, allowing to simulate realistic device designs, while benefiting from atomic scale resolution in the most critical parts, such as tunnelling barrier or interface between ferromagnetic and antiferromagnetic layers. The model features LLG and LLB solvers for dynamics calculations, with consistent time steps for the atomistic and micromagnetic regions; constrained Monte-Carlo solvers for modelling of equilibrium properties, such as temperature dependence of magnetization and magnetocrystalline anisotropy. In this presentation we will demonstrate some of the model’s capabilities by considering effects of perpendicular anisotropy at the reference layer CoFeB / tunnel barrier MgO / free layer CoFe interfaces, as well as Dzyaloshinskii-Moriya interactions (DMI) arising at the same interfaces. Furthermore, effects of spin transfer torque (STT), introduced in the model via Slonczewski formalism are considered. First we compare fully atomistic, fully micromagnetic, and multiscale atomistic-micromagnetic models of a limited size trilayer, consisting of a CoFe pinned layer, antiferromagnetically coupled to a CoFeB reference layer via RKKY exchange coupling through a thin Ru layer (forming a synthetic antiferromagnet structure), and a free layer, separated from RL by an MgO tunnelling barrier. In-plane and out-of-plane field sweeps are used to characterize magnetic behaviour and to obtain the spin valve’s transfer curves, and FMR spectra are used to characterize layers’ anisotropy and magnetic noise, induced by thermal fluctuations. Then we present results of a full multiscale reader model, where the benefits of having an atomistic region around the tunnelling barrier are used to realistically simulate temperature dependent effects of interfacial anisotropy, DMI, and STT on the reader’s performance.

Multiscale micromagnetic-atomistic modelling of the effects of MgO/CoFeB interfacial anisotropy, Dzyaloshinskii-Moriya interactions, and spin transfer torque in HDD TMR reader

Bit-patterned media recording (BPMR) is a promising candidate for the next generation of magnetic storage system to achieve areal density beyond one terabit per square inch [1]. For increasing a density of BPMR, the bit islands must be close to each other. However, we have faced the problem of intersymbol interference (ISI) and intertrack interference (ITI) that severely degrade the performance of BPMR system [2]. In this paper, we propose iterative detection with multilayer perceptron (MLP) for BPMR to improve bit error rate (BER) performance. Fig. 1 shows the block diagram of proposed iterative detection scheme that consists of partial response maximum likelihood (PRML) and MLP. The PRML detector is used to reduce ISI and ITI and the MLP is utilized to improve the system performance. After data is passed through BPMR channel, the proposed detection process is as follows. (1) First, we apply the MLP comprised of three hidden layer. The MLP output are fed to equalizer and SOVA and exploited as extrinsic information. (2) The received data with scaled down MLP output are equalized by 2D minimum mean square error (MMSE) equalizer. (3) When the branch metric of Viterbi detector is calculated, the equalizer output are used to reduce the impact of ISI, and the scaled down MLP output are used to reduce the impact of ITI. Then, the Viterbi output are sent to the MLP. (4) In iterative detection process, the MLP delivers the output only to the Viterbi detector, and the Viterbi detector delivers the output only to the MLP. And, Viterbi detector outputs the estimated data. Fig. 2 illustrates the BER performance of the proposed detection scheme according to the number of iteration at 3 terabit per square inch. At the BER of 10-4, the performance of proposed scheme at 1st iteration shows best performance.References: [1] H. J. Richter et al, IEEE Trans. Magn., Vol. 42, pp. 2255-2260, (2006) [2] W. Chang and J. R. Cruz, IEEE Trans. Magn., Vol. 46, pp. 3899-3908, (2010)

Iterative Detection with Multilayer Perceptron for Bit-Patterned Media Recording

A reduction in the track width of magnetic recording systems results in a welcome increase in areal density (AD), but also in the unfortunate appearance of extreme inter-track interference (ITI) that can severely deteriorate system performance [1]. To deal with this problem, we propose to use a single-reader/two-track reading (SRTR) technique in a bit-patterned magnetic recording (BPMR) system where a single reader was used to read the desired parallel-track that was arranged as in the staggered structure [2]. Then, the received readback signal was sampled using the over-sampling technique as shown in Fig. 1. The data sequences that were obtained from the over-sampling process is then easily operated using one-dimensional (1D) equalization and detection schemes [3]. Moreover, we also present the rate-3/4 and -5/6 constrained codes for the SRTR BPMR system with the new criteria for encoding the user data bit. The error percentages of all considered data patterns i.e., 24 = 16 and 26 = 64 possible patterns for the rate-3/4 and -5/6 constrained codes, respectively, are first investigated as shown in Fig. 2. Then, the selected patterns which provide the lowest error percentage will be then given as the codeword. For instance, the first 32 patterns that give the lowest error percentage will be select as codewords for the rate-5/6 coded system as depicted in Fig. 2. Furthermore, the specified constraints at the boundaries between each codeword can be mitigated using the proposed sub-codeword which depends on its prior transmitted codeword. Besides, the decoding process can be easily operated under both the Euclidean distance and max-min based on Boolean logic functions [4] methods. The computer simulation results show that the effect of severe ITI can be mitigated through the use of our proposed coding schemes when compared with uncoded-, coded-SRTR, and conventional recording systems at the same considered user densities.References: [1] S. Nabavi, B. V. K. V. Kumar, and J.-G. Zhu, IEEE Trans. Magn., Vol. 43, p.2274–2276 (2007) [2] C. Buajong and C. Warisarn, IEEE iEECON., p.1–4, (2017) [3] J. Moon and W. Zeng, IEEE Trans. Magn., Vol. 31, p.1083–1088 (1995) [4] N. Duric and M. Despotovic, in Proc. EUROCON., p.490–493 (2005)

Constrained Codes for Single-Reader/Two-Track Reading Technique in Bit-Patterned Magnetic Recording Systems

An inter-track interference (ITI) effect can severely degrade the performance of ultra-high density magnetic recording systems such as bit-patterned media recording (BPMR) [1]. The two-dimensional (2D) modulation code can protect the severe ITI [2] which can efficiently improve the overall system performance: however, it cannot offer performance gain over the conventional system when the recording system must encounter with severe ITI from its sidetracks. Then, the flipping technique [3] was proposed to deal with that ITI sidetrack effect using the normalized soft-information values to be as bit-flipping criteria, which can efficiently improve the overall system performance. However, we found that those normalized values are difficult to confirm where is the optimal threshold value in the bit-flipping process. Therefore, this paper proposes a soft-information flipper based on long-short term memory (LSTM) networks [4] to deal with the mentioned shortcoming, which leads to improving the bit-error rate (BER) performance of three-track/three-head (3T/3H) BPMR system. Here, we directly map the soft-information, e.g., the datasets that were obtained from the 2D soft-output Viterbi algorithm (SOVA), sl,k with the hard-information that are achieved from encoding process, xl,k as shown in Fig. 1. Simulation results indicate that, at the same user density (UD), the proposed system (areal density (AD) = 3 Tb/in2) provides BER performance gain over the conventional uncoded (AD = 2.5 Tb/in2), coded [2], and normalization threshold systems (AD = 3 Tb/in2) [3] as shown in Fig. 2. Moreover, the results also reveal that the proposed system is more robust to the media noise than the other systems.References: [1] Y. Shiroishi et al., IEEE Trans. Magn., vol. 45, no. 10, pp. 3816-3822 (2009). [2] C. Warisarn, A. Arrayangkool, and P. Kovintavewat, IEICE Trans. Electron. vol. E98-C,no.6, pp. 528-533 (2015). [3] C. Warisarn, W. Busyatras, and L. M. M. Myint, AIP Advances., vol. 8, pp. 056509 (2018). [4] S. Hochreiter and J. Schmidhuber, Neural Computation, vol. 9, no. 8, pp. 1735–1780 (1997).

Soft-Information Flipper based on Long-Short Term Memory Networks for Ultra-High Density Magnetic Recording

L10-phase Iron Platinum (L10-FePt) has been widely studied [1] for application in Heat-Assisted Magnetic Recording (HAMR). An important aspect for successful HAMR media is controlling the Curie temperature dispersion, which for L10-FePt a strong dependence on finite-size effects is reported [2] [3]. This poses a serious problem as the inevitable grain size distribution causes a Curie temperature (Tc) distribution which potentially limits recording density. We employed an atomistic model based on the VAMPIRE code [4] to study finite-size effects in L10-FePt grains using nearest-neighbour Heisenberg Hamiltonian exchange. Our grains had variable surface geometries (cylindrical, parallelepiped, and randomly-generated shape) and sizes (1 to 10nm). Importantly, our model gives access to the magnetisation properties of each atomic layer of the grains which provides insights into the magnetisation profile along a specific dimension. We hypothesised a correlation between the Tc distribution of L10-FePt and the percentage of atomistic bond loss on the grain surface as a function of grain size. Our result establishes a size threshold at 2.5nm below which the impact of finite-size effects starts to permeate into the centre of the grain and contributes to the overall drop of the grain Tc [Fig.1]. The magnetisation profile [Fig.2] further illustrates this. In larger grains surface disorder (lower magnetisation) is seen to penetrate only a few layers, whilst in smaller grains surface effects begin to dominate. Consequently, the grain Tc profile was also found to follow a similar trend. Our findings are consistent with semi-analytical mean-field calculations and have been extended to incorporate different crystal structures, which strongly suggests that if using a suitable correlation factor the Tc distribution of a generic material can be correlated to the percentage of atomistic bond loss on the surface as a universal parameter.References: [1]: D. Weller et al., Journal of Vacuum Science & Technology B, 34, 060801 (2016) [2]: O. Hovorka et al., Applied Physics Letters, 101, 052406 (2012) [3]: A. Lyberatos et al., Journal of Applied Physics 114, 233904 (2013) [4]: R. F. L. Evans et al., Journal of Physics: Condensed Matter, 26, 103202 (2014). More information about VAMPIRE can be found at: http://vampire.york.ac.uk/features/

The Influence of Finite-Size Effects on the Curie Temperature of L10-FePt

Heat assisted magnetic recording (HAMR) has become a very promising candidate for next-generation information storage technology. As recording bit lengths decrease down near ten nanometers in order to further increase the storage density, the recording performance (mainly the signal to noise ratio) cannot satisfy demands. In this study, a new method to characterize the recording pattern quality has been proposed in order to better understand the observed change in performance and help provide improved HAMR designs. In this method, for a given bit length (21nm, 15nm, and 10.5nm), more than 100 recording bit patterns are written micromagnetically, summed and averaged, generating a pattern contour with a crescent shape (Figure 1). This shape is due to the circular shape of the moving heating spot. A single tone binary sequence is used. Thermal Exchange-Coupled Composite media is used, where a moderate anisotropy material serves as the writing layer and an FePt layer serves as the storage layer [1]. By fitting the convex arm of the contour to a parabolic function, the curvature of the contour can be quantified (Figure 2): 10.5nm: 0.0184 (DC) and 0.0178(AC); 15nm: 0.0198 (DC) and 0.0189(AC); 21nm: 0.0222 (DC) and 0.0204(AC) (nm-1). The results show that smaller bit length gives a contour with lower curvature, which means that the recording patterns are less affected by the heat spot shape, less overlapping with each other and better separated. AC-erased media show even smaller curvatures than their DC-erased counterparts, suggesting that AC-erased media could provide better performance.References: [1] Z. Liu and R. Victora, IEEE Transactions on Magnetics, Vol. 52, No. 7, p. 1-4(2016)

Curvature Change of Heat Assisted Magnetic Recording Patterns with Different Bit Lengths

We used the nanoscratch method to study the response of perpendicular recording media (Co-Cr-Pt magnetic layer) to thermal-mechanical contact. Nanoscratched and non-scratched areas are characterized for magnetic and physical (morphological) properties at elevated temperatures by atomic force microscopy (AFM) and magnetic force microscopy (MFM). The figure below shows a 2T patterned MFM image and phase angle, i.e., the magnetic signal of recording media. The magnetic signal is not distorted. In the non-contact surface area far from the nanoscratch, the magnetic signal (strength) was gradually weakened with increasing annealing temperature to 300 oC due to the thermal agitation of magnetic spins. Still, the area close to the scratch center recovers the magnetic signal at elevated temperatures, indicating a partial recovery of ferromagnetism of an unscratched area. On the other hand, for the nanoscratched area, the magnetic signal at high local stressed zone was completely lost and did not recover after heating the film at 100 oC. Regarding the nanoscratch morphology, the as-scratch depth is about 8 nm at 25 oC. Surprisingly, the scratch is recovered to a depth of 1 - 2 nm at a temperature between 100 and 300 oC. This is attributed to the oxidation of the fresh surface (scratch) of the magnetic film. However, the scratch deepens at 400 - 600 oC so that the scratch depth is 8 nm, which is the same as the as-scratched depth. The deepening process at 400 - 600 oC is attributed to the evaporation of PtO2. We have proposed the mechanism of scratch recovering and deepening and also stress distribution caused by nanoscratch. The results of this study may help design future HAMR media to secure long term reliability of HDD.

Effects of Thermo-Mechanical Contact on Ferromagnetic Thin Film of PMR (perpendicular magnetic recording) Media

A FeCoB nanomagnet with perpendicular magnetic anisotropy (PMA) is important as a storage element for Magnetic Random Access memory (MRAM), because of their single-domain magnetic state and a high-thermal stability. In order to achieve a required high- performance of MRAM, both the enhancement of the PMA and a high-controllability of PMA are required. A parameter, which characterizes the PMA strength in a nanomagnet, is the anisotropy field Hanis. The Hanis is the magnetic field, which is applied in-plane and therefore perpendicularly to the easy axis of a nanomagnet and at which initially-perpendicular magnetization turns completely to the in-plane direction. A half of product of Hanis and nanomagnet magnetization is a common estimate of the PMA energy [1]. We measure the Hanis as a function of a perpendicularly- applied external magnetic field Hz using a Hall setup. In-plane magnetic field Hx and Hz were applied simultaneously. Under a fixed Hz, the Hx was scanned. Measured in-plane component of magnetization Mx changes linearly with respect to Hx (at least in region -0.7 Hanis < Hx <0.7 Hanis). From the slope of the measured linear dependence, the Hanis is evaluated. Figure 1 shows the measured Hanis vs Hz for a magnetically-softer FeB nanomagnet (Hc=70 Oe) and magnetically-harder FeCoB nanomagnet (Hc=560 Oe). In both nanomagnets, the dependence becomes linear at Hz >3 kG as it is predicted theoretically. From the slop of the linear dependence the strength of the Spin-Orbit interaction at nanomagnet interface is estimated. The dependence at smaller Hz gives an estimate of the intrinsic magnetic field, which always exists along nanomagnet magnetization, and the demagnetization field.References: [1] M.T. Johnson, P.J.H. Bloemen, F.J.A. Den Broeder, and J.J. De Vries, Reports Prog. Phys. Vol. 59, p.1409 (1996).

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