^{1}and Eric Roddick

^{1}

### Abstract

The role of exchange interactions and thermal relaxation in advanced three-layer exchange-coupled composite perpendicular recording media with graded anisotropy was investigated through studies on magnetic viscosity,magnetic hysteresisreptation, and spin-stand adjacent track interference. For this purpose, thickness series in the NiW seed and the three magnetic layers were made and studied. For each sample, both magnetic viscosity and reptation were evaluated using a magnetometer over a series of initial magnetic states. Magnetic viscosity, which is the change in the magnetization of the sample with time, showed a distinct second-order dependence on a logarithmic time-scale. In general, viscosity appeared to be more strongly influenced by exchange-coupling interactions in the media than the thermal stability. Magnetic reptation, which is the change in the magnetization when the external field was repeatedly cycled between a nonzero field and zero field, i.e., remanence, showed two types of distinct reptation phenomena—field reptation and remanence reptation—depending on whether the magnetic state was evaluated with the external field present or removed, respectively. Both field and remanencereptation showed a second-order logarithmic dependence on the number of cycles. A comparison of viscosity and field reptation revealed a correlation, indicating that the origin of field reptation in perpendicular recording media can be associated with viscosity. Such a correlation could not be established between viscosity and remanencereptation. Spin-stand signal amplitude change of written tracks, due to adjacent track interference, also followed a second-order logarithmic dependence on the number of adjacent writes. When compared appropriately, the signal amplitude change showed an excellent correlation with remanencereptation across all media samples. This suggests that adjacent track interference in magnetic recording can be associated with remanencereptation evaluated using a magnetometer, despite their vast difference in time-scales. Moreover, this correlation was observed irrespective of the thermal stability of the media, which corroborates the hypothesis that in composite media, exchange interaction effects have a more dominant role than thermal relaxation effects in influencing switchability vis-à-vis adjacent track interference. In consequence, remanencereptation can be a useful technique to study the interplay of exchange and thermal effects in magnetic media.

The authors would like to thank L. Bitman and S. Dang for help with the viscosity and reptation measurements, and M. Marino for help with the spin-stand recording measurements. The authors would also like to thank Dr. G. Bertero for a critical reading of the manuscript and useful discussions.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. RESULTS AND DISCUSSION

A. Magnetization viscosity

B. Magnetic reptation and correlation with viscosity

C. Correlation between magnetic reptation and ATI

IV. CONCLUSIONS

### Key Topics

- Reptation
- 94.0
- Viscosity
- 52.0
- Remanence
- 47.0
- Thermal stability
- 26.0
- Exchange interactions
- 25.0

## Figures

Schematic description of the double exchange-break PMR media stack that comprises a gradation in anisotropy among the three magnetic layers. The samples consisted of a thickness series in the NiW seed, and the three magnetic layers.

Schematic description of the double exchange-break PMR media stack that comprises a gradation in anisotropy among the three magnetic layers. The samples consisted of a thickness series in the NiW seed, and the three magnetic layers.

Saturation field, *H* _{s} is plotted for the single exchange-break and double exchange-break PMR media vs. the total exchange-break layer thickness. *H* _{s} is normalized to that for media with no exchange-break layers, *H* _{s}(EBL = 0). The lines guide the eye.

Saturation field, *H* _{s} is plotted for the single exchange-break and double exchange-break PMR media vs. the total exchange-break layer thickness. *H* _{s} is normalized to that for media with no exchange-break layers, *H* _{s}(EBL = 0). The lines guide the eye.

Error rate ATI degradation slope is plotted vs. thermal stability factor *K* _{u} *V*/*k* _{B} *T* for the four series of samples. The lines guide the eye.

Error rate ATI degradation slope is plotted vs. thermal stability factor *K* _{u} *V*/*k* _{B} *T* for the four series of samples. The lines guide the eye.

(a) Plot of the hysteresis loop for one of the samples in the study. The points for which the viscosity was measured are indicated by the solid circles (b) Set of viscosity curves for different external applied field values. The lines represent best-fit second-order logarithmic curves through the points. The initial magnetization for some of the viscosity curves is indicated in both (a) and (b).

(a) Plot of the hysteresis loop for one of the samples in the study. The points for which the viscosity was measured are indicated by the solid circles (b) Set of viscosity curves for different external applied field values. The lines represent best-fit second-order logarithmic curves through the points. The initial magnetization for some of the viscosity curves is indicated in both (a) and (b).

(a) The linear coefficient of viscosity, *S* _{0} is plotted vs. the external applied field for the MAG3 series (b) *S* _{0} is plotted vs. the initial magnetization, *M* _{i} for the same series. The lines guide the eye.

(a) The linear coefficient of viscosity, *S* _{0} is plotted vs. the external applied field for the MAG3 series (b) *S* _{0} is plotted vs. the initial magnetization, *M* _{i} for the same series. The lines guide the eye.

The linear coefficient of viscosity, *S* _{0} is plotted vs. the initial magnetization, *M* _{i} for (a) NiW series (b) MAG1 series (c) MAG2 series and (d) MAG3 series. The lines guide the eye.

The linear coefficient of viscosity, *S* _{0} is plotted vs. the initial magnetization, *M* _{i} for (a) NiW series (b) MAG1 series (c) MAG2 series and (d) MAG3 series. The lines guide the eye.

The quadratic coefficient of viscosity, *S* _{1} is plotted vs. the initial magnetization, *M* _{i} for (a) NiW series (b) MAG1 series (c) MAG2 series and (d) MAG3 series. The lines guide the eye.

The quadratic coefficient of viscosity, *S* _{1} is plotted vs. the initial magnetization, *M* _{i} for (a) NiW series (b) MAG1 series (c) MAG2 series and (d) MAG3 series. The lines guide the eye.

(a) The linear coefficient of viscosity, *S* _{0} is plotted vs. the thermal stability factor *K* _{u} *V*/*k* _{B} *T* for the four series of samples (b) *S* _{0} is plotted vs. the intrinsic coercive squareness, . The lines in both (a) and (b) are guides to the eye.

(a) The linear coefficient of viscosity, *S* _{0} is plotted vs. the thermal stability factor *K* _{u} *V*/*k* _{B} *T* for the four series of samples (b) *S* _{0} is plotted vs. the intrinsic coercive squareness, . The lines in both (a) and (b) are guides to the eye.

(a) Plot of the hysteresis loop for one of the samples in the study. The set of curves in (b) and (c) illustrate the methodology for the reptation measurement (b) Set of field reptation curves, and (c) set of remanence reptation curves obtained after different external applied fields were applied and removed, respectively. The lines represent best-fit second-order logarithmic curves through the points.

(a) Plot of the hysteresis loop for one of the samples in the study. The set of curves in (b) and (c) illustrate the methodology for the reptation measurement (b) Set of field reptation curves, and (c) set of remanence reptation curves obtained after different external applied fields were applied and removed, respectively. The lines represent best-fit second-order logarithmic curves through the points.

For one of the samples, the linear and quadratic coefficients of field reptation are plotted vs. the linear and quadratic coefficients of viscosity in (a) and (b), respectively. The same for remanence reptation are plotted in (c) and (d), respectively. The dotted lines are best-fits through the points.

For one of the samples, the linear and quadratic coefficients of field reptation are plotted vs. the linear and quadratic coefficients of viscosity in (a) and (b), respectively. The same for remanence reptation are plotted in (c) and (d), respectively. The dotted lines are best-fits through the points.

The linear coefficient of remanence reptation, *R* _{0} is plotted vs. the initial remanence, for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The lines guide the eye.

The linear coefficient of remanence reptation, *R* _{0} is plotted vs. the initial remanence, for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The lines guide the eye.

The quadratic coefficient of remanence reptation, *R* _{1} is plotted vs. the initial remanence, for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The lines guide the eye.

The quadratic coefficient of remanence reptation, *R* _{1} is plotted vs. the initial remanence, for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The lines guide the eye.

The normalized recording signal amplitude due to ATI is plotted vs. the number of adjacent write iterations for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The lines represent best-fit second-order logarithmic curves through the points. The initial signal after the first adjacent write is also indicated.

The normalized recording signal amplitude due to ATI is plotted vs. the number of adjacent write iterations for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The lines represent best-fit second-order logarithmic curves through the points. The initial signal after the first adjacent write is also indicated.

The linear coefficient of remanence reptation, *R* _{0} is plotted vs. the initial remanence, for values of the latter between 0.85 and 1.0 for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The solid squares correspond to those points for which values are equal to the initial signal values obtained from the signal amplitude ATI plots in Figure 13. The lines connecting the solid squares are guides to the eye.

The linear coefficient of remanence reptation, *R* _{0} is plotted vs. the initial remanence, for values of the latter between 0.85 and 1.0 for (a) NiW series, (b) MAG1 series, (c) MAG2 series, and (d) MAG3 series. The solid squares correspond to those points for which values are equal to the initial signal values obtained from the signal amplitude ATI plots in Figure 13. The lines connecting the solid squares are guides to the eye.

(a) Plot comparing the linear coefficient of signal amplitude ATI vs. that of remanence reptation for samples from all four series. The thermal stability factor *K* _{u} *V*/*k* _{B} *T* is indicated alongside for some of the samples (b) Plot comparing the quadratic coefficients of signal amplitude ATI and remanence reptation for all samples.

(a) Plot comparing the linear coefficient of signal amplitude ATI vs. that of remanence reptation for samples from all four series. The thermal stability factor *K* _{u} *V*/*k* _{B} *T* is indicated alongside for some of the samples (b) Plot comparing the quadratic coefficients of signal amplitude ATI and remanence reptation for all samples.

(a) Plot comparing the linear coefficient of signal-to-noise ratio ATI vs. that of remanence reptation for samples from all four series. The thermal stability factor *K* _{u} *V*/*k* _{B} *T* is indicated alongside for some of the samples (b) Plot comparing the quadratic coefficients of signal amplitude ATI and remanence reptation for all samples.

(a) Plot comparing the linear coefficient of signal-to-noise ratio ATI vs. that of remanence reptation for samples from all four series. The thermal stability factor *K* _{u} *V*/*k* _{B} *T* is indicated alongside for some of the samples (b) Plot comparing the quadratic coefficients of signal amplitude ATI and remanence reptation for all samples.

(a) Plot comparing the linear coefficient of error rate ATI vs. that of remanence reptation for samples from all four series. The thermal stability factor *K* _{u} *V*/*k* _{B} *T* is indicated alongside for some of the samples (b) Plot comparing the quadratic coefficients of error rate ATI and remanence reptation for all samples.

(a) Plot comparing the linear coefficient of error rate ATI vs. that of remanence reptation for samples from all four series. The thermal stability factor *K* _{u} *V*/*k* _{B} *T* is indicated alongside for some of the samples (b) Plot comparing the quadratic coefficients of error rate ATI and remanence reptation for all samples.

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