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Synchronisation of spin-torque oscillators (STOs) via magnetostatic interactions is investigated. In order for arrays of STOs to be used to carry out computational tasks the STOs should remain phase-locked for as long as possible. The correlation time for two STOs is shown to depend on H3/2d, where Hd is the strength of the magnetostatic interaction between the STOs. For a one dimensional array of STOs, introducing an angle between adjacent STOs can reduce the magnetostatic energy and increase the correlation time by an order of magnitude, or more. The increase in correlation time is resilient to moderate distributions of size and position among the STOs.

To increase the storage capacity limit of magnetic recording channels, recent studies proposed multilayer magnetic recording (MLMR): the vertical stacking of magnetic media layers. MLMR readback waveforms consist of the superposition of signals from each layer recovered by a read head placed above the upper layer. This article considers the problem of equalization and detection for MLMR comprising two layers. To this end, we use MLMR waveforms generated using a grain switching probability (GSP) model that is trained on realistic micromagnetic simulations. We propose three systems for equalization and detection. The first is a convolutional neural network (CNN) equalizer followed by an MLMR Viterbi algorithm (VA) for detection. We show that this system outperforms the traditional 2-D linear minimum mean squared error (2-D-LMMSE) equalizer. The second system uses CNNs for equalization and separation of signals from each layer, which is followed by a regular VA. The third system contains CNNs trained to directly provide soft bit estimates. By interfacing the CNN detector with a channel decoder, we show that an areal density gain of 16.2% can be achieved by a two-layer MLMR system over a one-layer system.

Microwave-assisted magnetic recording (MAMR) uses the field from a spin torque oscillator (STO) to assist the switching of recording medium magnetization. In an ideal STO, the magnetization of the field generating layer (FGL) would rotate in the plane of the FGL. In practice, the FGL magnetization usually has an out-of-plane component and the FGL magnetization vector describes a cone as it rotates. The cone angle $\theta _{c}$ is the angle between the FGL magnetization and the axis normal to the plane of the FGL. This article investigates the effect of the cone angle on the recording performance and compares two types of recording media: notched and exchange-coupled composite. The results show that for FGL cone angles between 45° and 90°, the recording performance was mainly determined by the strength of the high-frequency magnetic field from the FGL. For smaller cone angles, the signal-to-noise ratio (SNR) rapidly decreased.

Heat-assisted magnetic recording on bit patterned media dots with two magnetic structures is modeled. If the magnetic structures have different Curie temperatures two bits of information can be stored in each dot by writing at high and low temperatures. The areal density capability of the dual structure media was calculated and found to be in excess of 7 Tbit/in2, even when taking account of dot position distributions and magnetostatic fields from surrounding dots.

In this article, we investigate the areal density capability (ADC) of dual-structure media for microwave-assisted magnetic recording. The recording medium consists of two, discrete exchange-coupled composite (ECC) recording structures, each with hard and soft magnetic layers. The magnetic properties of the hard and soft layers of each ECC structure were optimized using the response surface methodology. The optimization parameters included hard and soft layer uniaxial anisotropy, the strength of exchange coupling between the hard and soft layers and the frequency of the spin torque oscillator (STO). Next, the ADC was calculated for a range of STO widths. The results showed that the use of narrower STOs increased the ADC of the top recording structure, but made little difference to the ADC of the lower recording structure. To validate the ADC values a grain switching probability (GSP) model was developed which took account of the magnetization of both structures. The GSP model was used to generate longer readback waveforms for use in a software read channel model, from which the bit error rate and user areal density were derived.

Microwave-assisted magnetic recording (MAMR) is an advanced magnetic recording scheme that is expected to extend the areal density beyond that achieved by conventional perpendicular magnetic recording (PMR). This is done by introducing a high-frequency (HF) oscillating magnetic field during the writing, reducing the write field from the head needed to switch the grains. Grains with larger anisotropy, greater thermal stability, and reduced grain size can thereby be used in the media. 3-D-MAMR uses this same principle not only to assist the writing but also to select a particular layer in a multi-layer medium stack for writing, thereby realizing 3-D magnetic recording. Optimization of a 3-D-MAMR system is complicated by the large number of variables involved and interactions between the recording layers. It is generally difficult to write on a target layer without some degree of unwanted writing on a different layer in a multi-layer stack. In this paper, we perform an optimization of a 3-D-MAMR media stack using the response-surface methodology (RSM), a method used in the design of experiments (DoEs). This results in a media design in which the signal-to-noise ratio (SNR) performance in the target layer and the number of written errors in the other layer are jointly optimized.

Micromagnetic model simulations were performed to investigate spin–torque oscillators (STOs) integrated into the main pole–trailing shield (MP–TS) gap of the write head (integrated STO). First, the oscillation states of a tilted STO were investigated in a model comprising the write head, STO, and medium soft underlayer (SUL). We found that inserting the STO into a non-parallel MP–TS gap resulted in more stable oscillation. Second, we performed full micromagnetic simulations of the write head, STO, SUL, and recording layer (RL), and the oscillation of the tilted STO was investigated. We found that the RL affected the STO oscillation to some extent; however, the effect was smaller than that from the write head. We also discuss the calculation times for various structures with and without the RL, and with/without medium motion.

Microwave-assisted magnetic recording with a tilted spin-torque oscillator (STO) was examined. Tilting the STO toward the trailing shield of a write head makes it easier to achieve stable oscillation. The signal-to-noise ratio (SNR) of written tracks was examined using an analytical head field distribution based on a finite-element model of a write head. The maximum SNR was similar for a range of STO tilt angles, but the optimum position of the STO in the write head gap depended on the STO tilt angle.

Transition curvature in heat-assisted magnetic recording can limit the linear recording density and reduce the readback signal amplitude. In this paper, we describe a simple model for the prediction of the transition curvature and use the model to determine the heat source location, relative to the write head, that minimizes transition curvature.

Selective recording on multiple structures may be possible with microwave-assisted magnetic recording. The number of parameters in even a dual-structure system is such that optimization is difficult. In this paper, the response surface methodology is used to systematically optimize a dual-structure system. Optimized structures are presented for three different recording configurations, allowing random writes to either structure or writing in a predetermined order. The addition of a second structure could allow areal densities of over 3 Tbit/in2 to be achieved.

Microwave-assisted magnetic recording (MAMR) [1] is one candidate for next-generation perpendicular magnetic recording [2]. Stable oscillation is one of the most important factors for spin-torque oscillators (STOs) used in a MAMR system. We performed micromagnetic simulations and found that stable STO oscillations were hard to obtain when the STO was inserted into the main pole - trailing shield (MP-TS) gap, primarily due to the strong magnetostatic interactions between the STO and write head [3]. We also showed that the rise time of the field applied to an isolated STO greatly affected the STO oscillation [4], i.e., a shorter rise time gave better, more consistent STO oscillation. In this paper, we show that the rise time of the in-gap field acting on the STO is critical to stable STO oscillation. We also show that the combination of a tilted STO and a tilted main pole - trailing shield gap results in stable STO oscillation due to weaker magnetostatic interactions between the STO and write head. Calculation Model A micromagnetic model analysis was carried out considering a double-layered STO utilizing transmission spin torque. We used commercial micromagnetic software (Fujitsu, EXAMAG v.2.1) [5]. The thickness of the field generation layer (FGL) was 10 nm, whilst the spin injection layer (SIL) was 2 nm thick. A 2 nm thick, non-magnetic inter layer was located between the FGL and SIL. The saturation magnetization $(4 \pi M_{s})$ was 20 kG for the FGL and 6 kG for the SIL. The anisotropy fields $(H_{k})$ of both the FGL and SIL were 31.4 Oe. The exchange constants, A, were $2.5 \times 10 ^{-6}$ erg/cm3 for the FGL and $0.75 \times 10 ^{-6}$ erg/cm3 for the SIL. The Gilbert damping factor, $\alpha $, was 0.02 for both the FGL and SIL. The write head model had overall dimensions close to those of commercial write heads $(3.25 \mu \mathrm {m}\times 2.55 \mu \mathrm {m}\times 4.5 \mu \mathrm {m})$.

Multiple layer magnetic recording may be possible with the advent of microwave-assisted magnetic recording (MAMR) [1], [2]. In a MAMR system, recording on a medium with high uniaxial anisotropy is made possible by applying a high frequency (HF) magnetic field at the resonance frequency of the medium, leading to a reduction in the switching field. If two discrete recording layers, RL1 and RL2, have different resonance frequencies, selective recording on one or other of the layers may be possible by adjusting the frequency of the spin torque oscillator (STO) used to generate the HF field. The magnitude of the coercivity reduction is related to the strength of the HF field in the medium. As STOs typically have dimensions from 20 – 40 nm the HF field strength decreases rapidly with distance from the STO. For this reason, if multiple recording layers are to be used each layer must be as thin as possible and the separation between the layers cannot be large. However, if the separation between the recording layers is small, magnetostatic interactions between them are large. This can make it difficult to implement selective recording due to the magnetostatic interaction favouring parallel alignment of the magnetisation of both recording layers. It may be possible to counteract the influence of the magnetostatic field by introducing antiferromagnetic exchange coupling between the two recording layers, e.g., by using Ru or Ir spacers [3], and this is the topic of this work. The aim is to optimise the antiferromagnetic exchange coupling and to determine the effect on recording performance. The Model Dual layer recording media with a 7 nm RL1 / 2 nm Spacer / 5 nm RL2 / 3.5 nm Air / Write Head structure were modelled. Each recording layer was an exchange coupled composite (ECC) structure with $M_{s} =750$ emu/cm 3 in all layers and the hard layers below the soft layers. In the model the medium grains were discretised into 1 nm-thick layers with the exchange coupling constant between layers of the same material being 10 erg/cm 2. After optimisation of the layer thicknesses and other parameters RL1 had a 3 nm hard layer and a 4 nm soft layer. The soft layer had $K_{u}$ of 3 × 106 erg/ cm 3 and the exchange coupling between the hard and soft layers was 4 erg/ cm 2. RL2 was formed of a 2 nm hard layer and a 3 nm soft layer. The soft layer had $K_{u}$ of 5 × 106 erg/cm 3 and the exchange coupling between the hard and soft layers was 6 erg/cm 2. The hard layer $K_{u}$ of both recording layers was a variable parameter. The field distribution from a write head with a 36 nm wide main pole and a 30 nm gap between the main pole and the trailing shield was calculated using a finite element model. A STO was placed 5 nm behind the main pole to generate the HF field in the media. The STO was modelled as a 36 nm wide, 36 nm high and 14 nm thick field generating layer (FGL) with $M_{s}$ of 1591 emu/cm 3 and coherent rotation of the FGL magnetisation was assumed. Results The effect of the magnetostatic interaction on the switching of the magnetisation of RL1 is shown in Fig. 1. In the calculation a 4 ns field pulse was applied to an 8 nm $\times 8$ nm grain containing two discrete recording layers, RL1 and RL2. The hard layer $H_{k} ( = 2 K_{u}/ M_{s})$ was varied and the maximum $H_{k}$ that could be switched by the combination of the head field and STO field was calculated as a function of HF field frequency. The magnetisation of RL2 was fixed either “up” or “down” and, as Fig. 1 shows, the result was to change the maximum switchable $H_{k}$ of RL1 by about 17 kOe: this difference was due to the magnetostatic field from RL2 acting on RL1 and is measured by the quantity $\Delta H_{k}$. Next, antiferromagnetic exchange coupling with a strength $J_{IL}$ was introduced between RL1 and RL2. The inset to Fig. 1 shows the effect of $J_{IL}$ on $\Delta H_{k}$. When $J_{IL}$ was about -0.17 erg/cm 2 the influence of the magnetostatic field was eliminated and $\Delta H_{k}$ was zero. Tracks were written on media with two recording layers using HF field frequencies of 20 GHz and 50 GHz. The bit length was 30 nm (847 kfci) and the head velocity was 5 m/s. The temperature was 300 K and distributions of grain size (16.5%), $M_{s}$ (4.25%), $K_{u}$ (8.5%) and easy axes $(3^{\circ })$ were included. The signal to noise ratio (SNR) was calculated for tracks recorded on each layer using the sensitivity function of a 20 nm wide magnetoresistive (MR) read head. Fig. 2 shows the results as a function of $J_{IL}$. For RL1 the SNR increased by about 1.2 dB when $J_{IL}$ was optimised, compared with the case when $J_{IL}$ was zero. A small amount of ferromagnetic coupling between RL1 and RL2, e.g., $J_{IL} =0.1$ erg/cm 2, caused a sharp decrease in the SNR of RL1. The SNR of RL2 was higher due to the layer being nearer to the write head and consequently experiencing higher head field gradients and HF fields. The SNR of RL2 was almost unchanged by $J_{IL}$ until $J_{IL}$ reached -0.3 erg/cm 2. Reversing the order of the hard and soft layers in RL1 to put the hard layer next to the non-magnetic interlayer made RL1 more resistant to the magnetostatic fields from RL2, but reduced the SNR. This was because magnetisation reversal was initiated in the soft layer and this layer experienced a smaller HF field when it was further from the STO. The authors would like to thank the ASRC for their support of this work.

Antiferromagnetically coupled (AFC) media were modeled as a part of a microwave-assisted magnetic recording system. Recording media grains with magnetically hard and soft layers were AFC by a Ru interlayer. The magnetostatic field arising from such grains has a smaller influence on neighboring grains and recording layers during recording. Compared with single-layer recording media, the SNR of AFC media decreased much more slowly with increasing linear density, and AFC media SNR was superior at high densities. An example of an AFC medium with two recording layers is also presented.