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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 &amp; 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/

MMM 2020

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

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MMM 2022

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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/

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We investigate the correlations of magnons inside a nanomagnet and identify an unconventional phase so-called magnon antibunching, i.e., where there is a large probability for occupation of the single-magnon state. This antibunched state is very different from magnons at thermal equilibrium and microwave-driven coherent magnons. We further obtain the steady state analytically and describe the magnon dynamics numerically, and ascertain the stability of such antibunched magnons over a large window of magnetic anisotropy, damping and temperature. This means that the antibunched magnon state is feasible in a wide class of low-damping magnetic nanoparticles. To detect this quantum effect, we propose to transfer the quantum information of magnons to photons by magnon-photon coupling and then measure the correlations of photons to retrieve the magnon correlations. Our findings may provide a promising platform to study quantum-classical transitions and for designing a single magnon source.References: 1. H. Y. Yuan and Rembert A. Duine, arXiv:2005.13637v1. 2. H. Y. Yuan, Peng Yan, Shasha Zheng et al., Phys. Rev. Lett. Vol. 124, p.053602 (2020). 3. H. Y. Yuan, Shasha Zheng, Z. Ficek et al., Phys. Rev. B Vol. 101, p.014419 (2020).

Magnon antibhunching in a nanomagnet

Spin wave (SW) based computing i.e. magnonics relies on propagating SW as information carriers. Being quasiparticles, magnons (the SW quanta) have a fine lifetime characterizing the exponential decay of the magnons population. Consequently, up to now, all magnonic devices operate within a short time-window. Finding a SW amplification paradigm is hence a prerequisite for the development of magnonics as a credible CMOS alternative. Two schemes are envisioned for SW amplification: Parametric pumping1 and spin-orbit-torque (SOT)2. Here we will discuss SOT amplification in BiYIG/Pt bilayer3. By passing current in the Pt layer, the spin accumulation resulting from the spin-Hall effect induces a positive torque that compensate the Gilbert damping of BiYIG. At subcritical values, the current has a linear effect that decreases the losses of the system and leads to a lower effective damping. Once the current in the Pt layer reaches a threshold values, the vanishing effective damping allows for the onset of the auto-oscillation regime4. Coherent propagating spin waves are strongly scattered by auto-oscillations5 leading to a strong decrease of their attenuation length6. Here we propose an amplification mechanism that circumvent this detrimental effect. We show using micro Brillouin light scattering spectroscopy (µ-BLS) on a 500 nm Pt/BiYIG waveguide that the precise timing of the dc current in the Pt layer with respect to the radiofrequency pulse in the strip antenna enables experimental observation of a lossless propagation of spin-waves. We take advantage of the strong BLS signal of BiYIG (nearly two orders of magnitude the one of YIG3) to extensively characterize the auto-oscillations non-linear dynamic regime in the presence of SOT. Work supported by ANR grant CE24-0021(MAESTRO).References: 1 T. Brächer, P. Pirro, and B. Hillebrands, Phys. Rep. 699, 1 (2017) 2 V.E. Demidov, A. Anane, S.O. Demokritov, J. Appl. Phys. 127, 170901 (2020) 3L. Soumah, A. Anane, Nat. Commun. 9, 3355 (2018) 4 M. Collet, G. de Loubens, and O. Klein, Nat. Commun. 7, 10377 (2016) 5 B. Divinskiy. O. Demokritov, and V.E. Demidov, Nat. Commun. 10, 5211 (2019) 6 M. Evelt, V.E. Demidov, M. Collet, Appl. Phys. Lett. 108, 172406 (2016)

Insight on the Time-Resolved Spin Wave Amplification in Nano-Magnonic Devices using Spin-Orbit-Torque

We report the evolution of spin conductivity at the YIG/Pt interface when the Pt is subject to an electrical current annealing. By injecting a large current density (12 ×1011A/m2) into Pt nanostrips and reaching a local temperature of 550 K, we observe a clear increase of the spin density emitted and probed at the YIG interface in three different measurements: spin Hall magnetoresistance, spin pumping and non-local magnon transport. As shown in Fig.1, the amplitude of FMR spectra by spin pumping enhances gradually in applying local Joule heating, leading to double the efficiency of spin transmmision by one-hour annealing. On the other hand the FWHM of the spectra remains the same over the whole annealing process (inset of Fig.1), indicating no farther extra damping at the YIG/Pt interface[1] appearing and relaxation processes occuring mainly in extended YIG films beside the strip. Fig.2 shows the non-local magnon transport signals mostly excited by spin orbit torque (SOT) (corresponding to the 1st hamonic signal in ref. [2] and Σ signal in ref. [3]). The non-local voltage enhances by 3 times by one strip annealing (either the injector or detector) and by 9 times by both strips annealing. Finally we estimated that the spin mixing conductance of evaporated Pt on YIG is increased from 0.8 to 1.9×1018 m−2. To sum up, the local annealing allows achieving spin mixing conductance of evaporated Pt on YIG similar quality to sputtered one and is of particular interest for very thin YIG films where chemical etching of the interface has to be avoided.References: [1]: O. Mosendz, V. Vlaminck, J. Pearson, et. al., Physical Review B 82, 214403 (2010). [2]: L. Cornelissen, J. Liu, R. Duine,et. al., Nature Physics 11, 1022 (2015). [3]: N. Thiery, A. Draveny, V. Naletov, et. al., Physical Review B 97, 060409 (2018)

Enhancement of the spin mixing conductance at YIG/Pt interfaces by electrical annealing

Spin waves represent a promising avenue for implementing unconventional wave-based computing platforms. However, combining controlled generation, manipulation and long-distance propagation of submicrometric wavelength spin waves is an outstanding challenge. Recently, nanoscale spin textures such as structured domains, domain walls and vortices, have raised interest as versatile active components in magnonic devices. In this framework, we demonstrated that nanopatterning spin textures via thermally assisted magnetic scanning probe lithography (tam-SPL) [1] allows the stabilization, in exchange bias systems, of 2D domains with arbitrary shape and spin configuration, 1D domain walls and 0D magnetic solitons such as vortices with tailored topology and position [2]. Here, first we show the channeling and steering of spin-waves in arbitrarily shaped nanomagnonic waveguides based on straight and curved domain walls, and a prototypic nanomagnonic circuit comprising two converging waveguides, allowing for the tunable spatial superposition and interference of confined spin-wave modes [3]. Then, we present an optically inspired platform for controlling the generation, propagation, and interference of short-wavelength spin waves, using nanopatterned spin textures in synthetic antiferromagnets, at remanence [4]. We demonstrate the spatial engineering of spin-wave wavefronts, the directional emission and focusing of spin-wave beams, and the generation of robust interference patterns which span multiple times the wavelength. Furthermore, we show that SAF allows to combine concepts borrowed from optics, with phenomena naturally arising from the nonreciprocal spin wave dispersion, such as resilience to spurious back reflections. The ability to control magnons via nanopatterned spin-textures at remanence opens up a range of new possibilities for developing energy-efficient unconventional computing concepts.References: [1] E. Albisetti, D. Petti, M. Pancaldi et al., Nat. Nanotechnol. Vol. 11, p. 545 (2016). [2] E. Albisetti, A. Calò, M. Spieser et al., Appl. Phys. Lett. Vol. 113, p. 162401 (2018). [3] E. Albisetti, D. Petti, G. Sala et al., Commun. Phys. Vol. 1, p. 56 (2018). [4] E. Albisetti, S. Tacchi, R. Silvani et al., Adv. Mater. Vol. 32, p. 1906439 (2020).

Optically Inspired Nanomagnonics with Patterned Spin Textures in Synthetic Antiferromagnets

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).

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