Magnetic data storage is pervasive in the preservation of digital information and the rapid pace of computer development requires ever more capacity. Increasing the storage density for magnetic hard disk drives requires a reduced bit size, previously thought to be limited by the thermal stability of the constituent magnetic grains. The limiting storage density in magnetic recording is investigated treating the writing of bits as a thermodynamic process. A 'thermal writability' factor is introduced and it is shown that storage densities will be limited to 15 to 20 TBit/in^2 unless technology can move beyond the currently available write field magnitudes.
As a technology, magnetic recording has been in existence since the invention of magnetic tape recording in the 1920s and 1930s. Since the early 1980's, and the introduction of metallic thin film recording media, the industry has seen a rapid increase in storage density; up to the TByte storage available in today's PC hard drives. Because technology has kept pace with demand, magnetic information storage is now ubiquitous. Having been around for some 60 years, magnetic recording is running into difficulties imposed by physical limitations.
A previous study of the possible limits of recording density was made by Charap et al 1 . This study predicted an upper limit of 36 Gb/in 2 and, remarkably, current technology has already achieved densities over one order of magnitude beyond this value. The reason for this lies in advances in the ’non-magnetic’ aspects of recording technology, including error detection and correction and the mechanical actuator systems used to position the read and write sensors, which were not anticipated by the authors of Ref. 1. The question is; does there exist a physical upper limit to recording density which cannot be exceeded by improved technology? Here we argue that the limitation is essentially determined by the maximum tolerable Bit Error Rate and certain materials parameters which, critically, includes the saturation magnetisation of the recording medium.
Magnetic recording relies on the storage of information on media comprised of grains of a material with a high magnetocrystalline anisotropy. The grains can be considered as bistable systems capable of representing bits of information in terms of the polarity of the grains. Stability of the information is provided by an anisotropy energy barrier KV where K is the anisotropy constant and V the grain volume. It has long been realised that the phenomenon of ‘superparamagnetism’ (SPM) defines the upper limit thermal stability of magnetic materials 2 . In the case of magnetic recording information should be stable for at least 10 years, which leads to an established criterion of KV /kT > 60 for media design.
Future advances in magnetic recording density will have to circumvent the magnetic recording trilemma 3 .
The key component of the trilemma is the necessary reduction in grain size for signal to noise reasons. For thermal stability the anisotropy energy must therefore increase, to a point where conventional recording heads are unable to write the medium. Heat Assisted Magnetic Recording (HAMR) 4,5 is a potential mechanism to solve this problem, by heating the material to the vicinity of its Curie point, where the anisotropy is low, writing the data, and then cooling back to the storage temperature of the medium. In the following we show that under this scenario the fact that the applied field is greater than the coercivity of the medium is an insufficient criterion: thermal fluctuations in the material itself lead to write errors.
In fact this is a general problem for all small magnetic elements, ultimately that the recording process must be thermodynamically favourable to be reliable, and so it is the thermal writability that determines the ultimate limits of magnetic recording. We specifically address the problem of the ultimate recording medium, which is likely to consist of a combination of Bit Patterned Media and HAMR, although the underlying physics is equally applicable to normal HAMR. We proceed by calculating the Bit Error Rate (BER) induced by thermal fluctuations during the write process. Consider the ultimate recording system in which one magnetic grain is sufficient to store a binary ‘1’ or ‘0’. Our approach is to consider the equilibrium magnetization m e in the recording context. In conventional recording there are a number of grains per bit so m e has the meaning of an ensemble average magnetisation. Here, values of m e less than unity represent the probability of a non-reversed grain in a bit, which gives rise to a dc noise. Consider now the situation of recording one bit of information per grain. Since we are now dealing with individual grains, m e must be interpreted differently; in terms of the probability p sw that the magnetisation is switched into the correct state by the field during the attempt to write the information, specifically, p sw = (m e + 1)/2. Since the Bit Error Rate (BER) is essentially the proba-bility of wrongly recording the bit, we have simply that BER = 1 -p sw = (1 -m e )/2. Considering for simplicity the case of a system with perfectly aligned easy anisotropy axes, using a master equation approach it can be shown that the thermal equilibrium magnetisation is given by
where µ = M s V is the magnetic moment of the grain with M s the material saturation magnetization and V the particle volume. Eq. 1 represents the ensemble-averaged magnetisation of a collection of grains or the time-average magnetization of a single grain. The physical importance of Eq. 1 is that, if the system is
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