Perpendicular exchange coupled composite structures were prepared, utilizing *L*1_{0}-FePt as hard layer and [Co/Ni]_{N} multilayer as soft layer. Magnetic characteristics revealed the gradually change of the magnetization reversal mechanism from incoherent rotational mode to dominant wall motion as the thickness of soft layer increases. Furthermore, FORC analysis were employed to characterize the interactions of our ECC magnetic system, the result indicates that the exchange coupling interaction were enhanced with the increasing thickness of soft layer.

## I. INTRODUCTION

ECC (exchange coupled composite) structure has been more and more popular in recent years. As we know, the criterion for a thermally stable grain is given by *K*_{μ}*V*≥60 *k*_{B}*T*, where *K*_{μ} is the anisotropy constant, V the grain volume, *k*_{B} the Boltzmann constant, and T the temperature. With the increasing of the recording density, we must scale down the volume of the magnetic grains inside recording bits to maintain a proper signal-to-noise ratio. The shrinkage of the grain volume is compensated by the application of the high *K*_{μ} materials. However, high *K*_{μ} makes it hard to write with a conventional recording head. To solve the contradiction between thermal stability and writability, ECC media were proposed and demonstrated by Wang and Victora, in which the hard layer and the soft layer are coupled to reduce the switching field while maintaining thermal stability.^{1–3} Among those high *K*_{μ} materials, *L*1_{0}-FePt is proved to be a promising candidate for ultra-high density magnetic recording thus is a common choice as the base layer in ECC films.

First-order reversal curve (FORC) diagrams have been widely used in both geology and physics. It is an effective experiment tool to identify the weight of the switching volume of input for a system satisfying the Classical Preisach model of hysteresis.^{4} A FORC diagram provides a detailed characterization of the hysteresis responses of a magnetic system.^{5–7} With a proper transformation, one can get the distribution of the switching field, the interaction field and some other detailed information which cannot be extracted from the hysteresis loop.

A FORC diagram is generated from a collection of first-order reversal curves, A FORC curve is measured as follows: a large positive magnetic field is applied to saturate the sample, then this field is ramped down to a reversal field *H*_{r}, a FORC curve is the magnetization curve from the reversal field *H*_{r} to the saturation field *H*_{S}. The magnetization at an applied filed H on the FORC curve is denoted by M(*H*_{r},*H*). The FORC distribution is defined as the mixed second derivative:

where this is well defined for H > *H*_{r}. According to the Classical Preisach Model, the FORC only characterizes the irreversal part of the system because the second derivative of the reversal part will be 0. However, the reversal part can be calculated by mathematically extending M(*H*_{r},*H*a) to the entire {*H*_{r},*H*} plane by defining:

This is called the “Extended FORC”, which is developed by Pike.^{7} When the FORC distribution is plotted, it is convenient to change coordinates from {*H*_{r},*H*} to {*H*_{C}=(H-*H*_{r})/2, *H*_{u}=(*H*+*H*_{r})/2}. A FORC diagram is a contour plot with *H*_{C} and *H*_{u} in which *H*_{C} represents the switching field and *H*_{u} the local interaction field. FORC is a useful tool to study the magnetic interaction between grains.^{8}

In this paper, we report the angular variation magnetic study of the ECC *L*1_{0}-FePt/[Co/Ni]_{N} multilayers to investigate the magnetic reversal mechanism. Then we employ FORC analysis and give a comprehensive description of the interactions existing in our films by calculating series of FORC parameters.

## II. EXPERIMENTS

Our sampels were prepared by the magnetron sputtering with a base pressure better than 2*10^{−8} Torr. 3nm-thick and 5nm-thick *L*1_{0}-FePt films with (001) orientation was deposited on the single crystal Mg0(100) substrates at 450 °C. The chemical ordering parameter of FePt is calculated by comparing the experimental ratio of (001) peak to (002) peak with the theoretical ratio which is 2. After the samples were cooled down to room temperature, [Co(0.2 nm)/Ni(0.6 nm)]_{N} multilayers with various periodic number N were deposited on the top of FePt. Finally all samples were coverd with a 3-nm-thick Pt layer for preventing oxidation. The crystalline structure of the samples was characterized by x-ray diffraction (XRD) and the out-of-plane hysteresis loop (OP) and FORC curves were measured by a vibrating sample magnetometer(VSM: MicroSense EV9) with a maximum field of 22 kOe. After the measurements, FORC analysis was carried out using our python FORC package.

## III. RESULTS AND DISCUSSION

Fig. 1 shows the XRD θ-2θ scans of the 5-nm-thick FePt and FePt(5nm)/[Co/Ni]_{5} ECC films, respectively. *L*1_{0}-FePt (001) and (002) peaks can be clearly observed for both samples, which indicates that the *L*1_{0} phase with (001) orientation is steadily formed. By calculating the intensity ratio of (001) to (002) peak, we obtain the chemical ordering of FePt is 0.83. No peak from Co and Ni is detected.

Fig. 2 shows the normalized OP magnetic hysteresis loops of *L*1_{0}-FePt (5nm)/[Co/Ni]_{N} (N=3, 5, 10). As the thickness of soft layer grows, the coercivity of ECC composite is reduced from 5.62 kOe (N=0) to 2.45 kOe (N=10). No distinct two-step reversal process is observed in the OP loops. This is ascribed to the strong coupling between the hard layer and the soft layer, which brings about a rapid magnetic reversal in hard layer once the soft layer is switched at a lower field. Fig. 3 illustrates the variation of the squareness of the OP loops ($MR/MS$), which is defined as the ratio of the remanent magnetization to the saturation magnetization. It can be seen that as the thickness of soft layer increases, the squareness drops from 0.94 to 0.73. The reverse of the soft layer at zero magnetic field leads the decrease of the remanent magnetization, since there is a demagnetized field. Fig. 4(a) shows the derivative (dM/dH) of OP loops and Fig. 4b summarizes the influence of the thickness of the soft layer on the maximum switching field H_{SW} and its distribution ΔH_{SW}. When the soft [Co/Ni]_{N} (N=3, 5) is thin, the maximum switching field is similar to the coercivity. However, when N=10, the peak of the switching field occurs before the field of coercivity. In general, the soft layer will reverse first, and then driving the magnetization reversal of the hard layer. For thin soft layer incoherent magnetization reversal is expected, but for thick soft layer, domain wall will form at the interface between the soft and the hard, and then further increase of the applied field driving the domain wall propagating into the hard layer.^{9} The difference between the peak and the coercivity is due to the rapid magnetization reversal of the far end of the soft layer from the interface. The distribution of switching field increases with the increase of layer of the soft layer. For the *L*1_{0}-FePt/[Co/Ni]_{N} composite with thin soft layer, the incoherent magnetization reversal narrows the switching field distribution.^{10} But for the composite with thick soft layer, the successive magnetization reversal of the soft layer and the hard layer widen the distribution of the switching field. Thus, both Figs. 3 and 4 imply that the reversible magnetization switching arises in thick soft layer.

Fig. 5 shows the angular dependence of remnant coercivity of three *L*1_{0}-FePt/[Co/Ni]_{N} (N=3, 5, 10) ECC samples with different soft layer thickness. At small angles, *H*_{C} and *H*_{CR} are almost the same and the ratio of *H*_{C} and *H*_{CR} are close to 1 for all films. The angular dependence remain flat up to about 30°, and then increase at higher angle, consistent with the simulation result from Victora, which indicates that the magnetization reversal mechanism is more likely to be in the incoherent rotation mode. As the thickness of the soft layer grows, the angle dependent remnant coercivity is close to the domain wall motion model.

To gain more insights of the magnetization reversal process of the composites, extended FORC diagrams of FePt/[Co/Ni]_{N} (N = 3, 5, 10) ECC composite have been measured (Figure 6). There are two series of contour lines. The contour lines whose center is the origin of the coordinate plane represents the reversible rotation of the soft layer, and the dense contour lines whose center is close to the horizontal H_{C} axis represent the irreversible magnetization reversal of the ECC composite. It can be seen clearly that as N grows, the center of irreversible contour gets closer to *H*_{C} = 0, which coincides with the decreasing of coercivity. Besides, the reversible region at *H*_{C} = 0, which demonstrates the soft layer, becomes more and more bright. This is reasonable because the soft layer is “reversal” and as N grows, the “reversal” part will account for a larger proportion. The most significant change of FORC diagrams is the emergence of 2 “ridges”, as N goes up to 10. One major “ridge” goes up-right and another goes down-right. The emergence of 2 “ridges” actually indicates there exists 2 kinds of interactions in our sample, the major “ridge” reflects the influence of exchange coupling interaction while the other one reflects magneto-static interaction.^{6,8} In order to get more detailed information of FORC diagrams, we calculate series of parameters according to the FORC data. Table I is our computation results of ECC films along with 5nm-thick and 11nm-thick FePt films, and FePt/[Co/Ni]_{N} (N = 3, 5, 10) ECC composite. The 11nm-thick FePt film has the similar thickness with the FePt/[Co/Ni]_{10} film. Here, d*H*_{m}*/dH*_{C} is the slope of *H*_{m}(*H*_{C}) at the distribution peak of the major “ridge”. FORC plot is a contour plot where H_{C} represents the switching field, H_{u} represents the local interaction field and the color indicates the density Δm of particles with H_{C} and H_{u}. If for every Hc we get Hm by argmax (Δm(H_{u})) with respect to H_{u}, we will get series of H_{C} and H_{u}, we can use a line to fit these points thus get the slope of this line which can be seen as a ‘‘ridge’’ of the contour plot in a 3D vision. *b*_{C} and *b*_{u} is the full width at half maximum of the distribution in a cross section through *H*_{C} = peak(*H*_{C}) and *H*_{u} = peak(*H*_{u}). Δ*H*_{u} is calculated with equation (1), which can characterize the mean value of the distribution of interaction.

Range (*H*_{u}) is the vertical range of FORC diagrams. As we can see, in the family of 5nm FePt samples, both *b*_{u} and range (*H*_{u}) increase significantly as N grows, which means the variance of the distribution of interaction becomes larger. Besides, Δ*H*_{u} also grows from 0.33 to 0.59, which demonstrates that the mean value of the distribution of interaction increases. Combining these results, it can be concluded that the interaction between magnetic grains is enhanced as soft layer gets thicker. In addition, all of the values of d*H*_{m}*/dH*_{C} are positive values and becomes strikingly larger as N grows. A positive value of d*H*_{m}*/dH*_{C} means exchange coupling interaction. The computation results of d*H*_{m}*/dH*_{C} shows an enhancement of exchange coupling interaction in our ECC films.

. | dH_{m}/ dH_{c}
. | b_{c}(Oe)
. | b_{u}(Oe)
. | $\Delta Hu$ . | range(H_{u}) (Oe)
. |
---|---|---|---|---|---|

FePt(5nm) | 0.076 | 1640.6 | 1193.2 | 0.33 | 1846.6 |

FePt(5nm)/[Co/Ni]_{3} | 0.812 | 1759.2 | 1627.4 | 0.52 | 2378.5 |

FePt(5nm)/[Co/Ni]_{5} | 1.33 | 1783.0 | 2118.1 | 0.55 | 2834.0 |

FePt(5nm)/[Co/Ni]_{10} | 1.53 | 1678.5 | 3079.2 | 0.59 | 3947.4 |

FePt(11nm) | 1.08 | 2222.9 | 2062.4 | 0.41 | 2959.6 |

. | dH_{m}/ dH_{c}
. | b_{c}(Oe)
. | b_{u}(Oe)
. | $\Delta Hu$ . | range(H_{u}) (Oe)
. |
---|---|---|---|---|---|

FePt(5nm) | 0.076 | 1640.6 | 1193.2 | 0.33 | 1846.6 |

FePt(5nm)/[Co/Ni]_{3} | 0.812 | 1759.2 | 1627.4 | 0.52 | 2378.5 |

FePt(5nm)/[Co/Ni]_{5} | 1.33 | 1783.0 | 2118.1 | 0.55 | 2834.0 |

FePt(5nm)/[Co/Ni]_{10} | 1.53 | 1678.5 | 3079.2 | 0.59 | 3947.4 |

FePt(11nm) | 1.08 | 2222.9 | 2062.4 | 0.41 | 2959.6 |

^{a}

*dH*_{m}/*dH*_{c}: The slope of *H*_{m}(*H*_{c}) at the distribution peak of the major “ridge”, *b*_{c}: full width at half maximum of the distribution in a cross section through *H*_{c} = peak(*H*_{c}), *b*_{u}: full width at half maximum of the distribution in a cross section through *H*_{u} = peak(*H*_{u}), $\Delta Hu$: calculated with equation (1), *range*(*H*_{u}): the vertical range of FORC diagrams which is calculated by max(*H*_{u}) – min(*H*_{u}).

Comparing all the results of FePt(11nm) and FePt(5nm)/[Co/Ni]_{10}, it is apparent that the ECC film has a significant larger exchange coupling interaction due to the coupling of the soft layer and hard layer. FePt(11 nm) and FePt(5 nm)/[Co/Ni]_{10} have the similar thickness, and nearly the same magnetization. Then the two films should have the similar magnetic interaction. However, the magnetic interactions are different according to the FORC. This difference is due to the different magnetic configuration. The exchange coupling between the soft and the hard contributes to the enhanced coupling interaction.

## IV. CONCLUSION

Perpendicular exchange coupled composite FePt(5nm)/[Co/Ni]_{N} were prepared. Highly ordered *L*1_{0}-FePt acts as the hard layer and [Co/Ni]_{N} as the soft layer. ECC characteristics have been revealed by the squareness of the hysteresis loop, switching field distribution, and the angular dependent remnant coercivity. The angular dependent remnant coercivity generally follow the two-spin model, but gradually changing from the incoherent magnetization reversal to the domain wall assisted magnetization reversal with the increase of the soft layer thickness. Magnetic characteristics revealed the change of the magnetization reversal mechanism from incoherent rotational mode to dominant wall motion as the thickness of soft layer increases. In order to gain more insights of the magnetization reversal process of the composites, FORC analysis were employed to characterize the interactions of our ECC magnetic system, the result indicates that the exchange coupling interaction were enhanced with the increasing thickness of soft layer.

## REFERENCES

_{0}-FePt based exchange coupled composite films with soft [Co/Ni]

_{N}multilayers