Lrm

Figure 17. Grain size dependence of the demagnetization curves of 125 polyhedral grains for hard-soft magnets (40% Nd2Fe14B [dark scale map], 30% Fe3B, 30% a-Fe [bright scale map]) and magnetization distribution for zero applied field. (Courtesy of T. Schrefl).

improve the media characteristics. The conventual longitudinal recording media (nanostructured granular CoCrPt and CoCrTa thin films) have been intensively modeled in the past [119]. The performance of the new high anisotropy media (such as SmCo, CoPt, FePt), together with the new ways of magnetic recording (such as perpendicular recording), is currently under the intensive investigation, in which the long-scale micromagnetic calculations serve as one of the tools.

Magnetic recording simulations have some peculiarities in comparison to a standard hysteresis modeling. This includes the simulation of the read and write processes, which may be done by using some well-established approximations such as the Karlquist or Lindholm [147, 148] fields for the recording head and the approximation for the magneto-resistive head used for the reading process. At the same time, more realistic modeling includes the head models explicitly, together with the micromagnetic processes, which happen simultaneously in the recording head and in the media [149]. The latter is especially necessarily for the perpendicular recording media, where the soft magnetic underlayer also should be included in the realistic model [141, 150, 151]. The aim of the simulation is normally the calculation of the signal-to-noise (SNR) ratio, which for different models, may be found summarized in Ref. [124]. The results strongly depend on the linear recording density, normally measured in kfci (kilo floppy changes per inch).

One of the major limitations of magnetic recording medium performance is the medium noise. The most important noise source is the bit transition, which is influenced by the finite size of the grains, their anisotropy values and orientations, and their size distribution. The efforts to optimize the longitudinal recording performance, both experimental and theoretical, have showed that the magnetic media suitable for high density recording require reduction of the average grain diameter and a more uniform grain-size distribution. The SNR varies inversely as the square of the transition parameter and the cross-track correlation length [119, 152]. For high-quality recording media, these parameters are approximately proportional to the grain diameter, which is achieved for smaller grains. At the same time, the exchange interactions would broaden the magnetization profile at the boundary transition. In the longitudinal recording media, the intergranular exchange is largely responsible for transition noise because of the cross-track correlations it causes [119, 153, 154]. The isolation of individual grains is achieved experimentally by the segregation of Cr at the grain boundaries. More detailed simulations show that the signal, as a function of an exchange parameter, is increased [119, 124, 153, 154] for small exchange values, the same way the noise coming from the transitions also is increased. The competition between signal and noise is very complicated and depends on the read-write parameters. It is possible that some small amount of exchange may be present in recording media without dangering the SNR [122, 153]. The SNR also is very influenced by the large dispersion of the grain sizes (normally log-normal), which leads to a zigzag character of the transition and to the coupling of the small grains to large ones that deteriorate both the signal and the noise. Simulations show that the absence of the grain-size distribution may lead to the difference in the SNR parameter up to 1 dB

for noninteracting grains and up to 4 dB at the presence of small exchange [155] for intermediate recording densities (~100 kfci). Another very important factor is the random character of the anisotropy directions. The presence of some texture may lead to a drastic enhancement of the signal. Indeed, the calculations show that, for a uniform grain size distribution and moderate exchange, the gain of approximately 2 dB could be expected [145] for a textured sample with intermediate recording density (~100 kfci). This gain is much larger for larger recording densities. For log-normally distributed grains, the effect may be even more dramatic as to reach 7 dB at 200 kfci.

One of the main limitations to further increase the magnetic recording density is the presence of thermal effects. In the efforts to decrease the transition noise, the grain size has become so small as to make the effective energy barrier (KV in the approximation of noninteracting grains where V is the grain volume), separating the two magnetization states ("up" and "down") to be comparable to the thermal energy. This is called the superparamagnetic limit and is currently the main limitation for conventional longitudinal recording. The intensive search for high-anisotropy media and new ways of magnetic recording (such as the thermally assisted one) is currently under progress.

Nanocrystalline perpendicular films with easy magnetization directions close to the normal of the film and with high magnetocrystalline anisotropy are attracting the increased interest of researchers as possible candidates for perpendicular recording. This is due to the narrow dispersion of the easy axes distribution, typically a Gaussian one with small dispersion (of the order of 5 degrees). The small grain size and perpendicular arrangement of the easy magnetization axes allow one to obtain greater recording densities, whereas the higher magnetocrystalline anisotropy increases the ferromagnetic thermal stability of the small grains.

In perpendicular recording media with a strong orientation of crystalline easy axes, intergranular exchange coupling also increases the squareness of perpendicular loops, which generally results in sharper transitions. As a result [151], media SNR may be enhanced because of the reduction of the transition parameter. With a further increase of the exchange coupling, reduction of the transition parameter becomes less significant, since the transition noise increases. In Ref. [151], the optimal exchange constant was found.

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