Dependence of Nucleation Field on the Size of Soft Phase in Magnetic Hard–Soft Exchange Coupling Nanocomposites

Abstract

Hard–soft exchange coupling nanocomposites have critical applications in various important materials. The magnetic properties of nanocomposite permanent magnetic films improve with a higher nucleation field (H_ns) of the soft magnetic phase. H_ns is sensitive to the thickness (d_s) of the soft magnetic layer. Understanding the dependence of H_ns and irreversible field (H_irr) on d_s, especially at the nanometric scale, is crucial for comprehending the magnetic mechanism and facilitating the design and preparation of high-performance nanocomposite permanent magnets. However, during the high-temperature deposition process, diffusion between hard and soft magnetic phases occurs, leading to the generation of other phases. This makes it challenging to accurately reflect the relationship between H_ns and d_s. To address this issue, we successfully fabricated high-quality SmCo₅/Fe nanocomposite bilayer films with different soft magnetic thicknesses and high textures by controlling the preparation process. We conducted a quantitative analysis of the relationship between H_ns and d_s within the range of 2–40 nm. Based on the experimental results, we propose a new theoretical simulation formula that enhances the understanding of the characteristics at the interface between the soft magnetic and hard magnetic phases. The theoretical simulation results show that a thin softened hard layer of about 4–6 nm thickness exists at the interfacial region, which concurrently reverses with the soft magnetic phase during the demagnetization process. Our results offer the generality and critical basis for the further study of hard–soft nanocomposite magnetic materials.

1. Introduction

Hard and soft magnetic materials are two distinct yet crucial types of magnetic materials. Hard magnetic materials exhibit significant magnetic anisotropy, in contrast to soft magnetic materials, which possess lower anisotropy. When these two materials are combined to form nanocomposite magnetic materials, novel phenomena and properties emerge due to the magnetic exchange coupling effects between the phases [1,2,3,4,5,6,7]. Hard–soft systems have been extensively studied because of their important applications in permanent magnetic materials, high-density magnetic recording media, giant magnetostrictive materials, etc. [8,9,10,11,12,13,14,15,16,17]. For example, the anisotropic nanocomposite permanent magnetic material which contains the coupled and aligned hard and soft phases has the theoretically predicted giant maximum energy product (BH)_max. It is expected to be a good candidate for the next generation of permanent magnetic materials. Isotropic nanocomposite magnets, containing randomly oriented hard magnetic grains, have been widely employed in magnetic devices due to their enhanced remanence. The hard–soft exchange coupled system has also been utilized in state-of-the-art high-density magnetic recording media to tune their coercive force H_c or irreversible field H_irr [10,11].

One key and basic feature in the hard–soft exchange coupling nanocomposite system is the significantly modified nucleation field (reversal field) of soft-phase H_ns relative to that of the bulk single soft phase. H_ns can be greatly enhanced by reducing ds, particularly in the nanometric scale. The value of H_ns is influenced by both the size of the soft phase and the strength of the exchange coupling between the hard and soft phases [1,2]. quantitatively characterizing the dependence of H_ns on ds forms a crucial basis for understanding the magnetic properties and reversal mechanisms in hard–soft magnetic materials. For instance, when designing a hard–soft nanocomposite permanent magnetic material with a specific coercive force or a single-phase hysteresis loop, the relationship between H_ns and ds can essentially guide us in determining the appropriate size of the soft phase to ensure the desired properties.

H_ns, as a function of ds, has been studied theoretically in hard–soft exchange coupled systems [2,18,19,20,21]. However, there is currently no unified theoretical formula that applies to a wide range of sizes of soft magnetic phases and different theoretical formulas are only applicable to specific size ranges.

The dependence of H_ns on d_s has been also experimentally studied. S.S. Yan et al. successfully fabricated well-textured SmFe/NiFe bilayer films and obtained the accurate value of H_ns when d_s varied from 34 to 170 nm [8]. To quantitatively describe the relationship between H_ns and d_s, a fitting formula, ${\mathrm{H}}_{\mathrm{n}\mathrm{s}}=\frac{{\mathrm{H}}_{\mathrm{n}0}}{{\mathrm{d}}_{\mathrm{s}}^{\mathrm{N}}}$, was used to match the experimental data, yielding a satisfactory result [8]. S. Sawatzki et al. fabricated SmCo₅/Fe/SmCo₅ tri-layer films and determined the value of H_ns for smaller d_s but in a narrow range: d_s = 6.3~12 nm [9]. Their tri-layer films, however, were fabricated at a high temperature. Diffusion between the Sm-Co and Fe layers was inevitable and an Fe-Co intermixed phase was introduced. So, the dependence of H_ns on d_s could not be determined strictly. Obtaining the precise value of H_ns for small d_s is typically difficult, as it requires achieving both a large coercive force and excellent texture for the hard phase. The quantitative relationship between H_ns and d_s in the sub-tens nanometer range remains significantly under-explored in experimental investigations.

A high-quality sample is a necessary prerequisite to determine accurately the quantitative dependence of H_ns on d_s. An ideal sample should have the following characteristics: (i) no diffusion between the hard and soft magnetic phases; (ii) the hard magnetic phase has a high coercive force considering that the value of H_ns increases as the size of the soft phase decreases; (iii) the hard phase should be well textured.

To address these issues, high-quality nanostructured SmCo₅/Fe double layers with different soft-phase sizes with large coercive forces and strong textures were successfully fabricated through strict control of the preparation process in the present work. We conducted a quantitative analysis of the relationship between H_ns and d_s within the range of 2–40 nm. Based on the experimental results, we propose a new theoretical simulation formula that enhances the understanding of the characteristics at the interface between the soft magnetic and hard magnetic phases. These results not only contribute to the understanding of the magnetic mechanism of nano-composite magnets but also provide important guidance for the design of high-performance nano-composite magnets.

2. Experimental Details

2.1. Materials

By adjusting the ratio of Sm and Co, a Sm-Co composite target was prepared. To compensate for the different yields of Sm and Co during the sputtering process of the Sm-Co composite target, we added an additional 38% of Sm in the composite target. The composition of the target, as measured by ICP, was 1:3.6. And the atomic ratio of Sm:Co of Sm-Co/Fe bilayer was 1:4.3, determined by EDX. Both Cr and Fe targets utilized commercially available pure metal targets with a purity higher than 99.999%.

2.2. Experimental Process

SmCo₅(50 nm)/Fe (x nm) bi-layer film was fabricated on substrate MgO (110) by an ultra-high vacuum magnetron sputtering machine. Both Sm-Co and Fe targets mounted in the high vacuum chamber faced the substrate. The base pressure was better than 8 × 10⁻⁷ Pa. The size of soft layer Fe x was tuned from 0 to 40 nm. A thickness about 50 nm of Cr was used as a buffer layer. In an attempt to achieve a desirable texture and high coercive force in the Sm-Co hard-layer films, we experimented with various parameters. The optimal experimental conditions are as follows: the sputtering power for the Sm-Co composite target should be at least 150 W, and the sputtering temperature should be 600 °C. For more details please see the Supplementary Materials. To avoid the diffusion between the hard Sm-Co and soft Fe magnetic phases, the Sm-Co layer was first deposited at 600 °C to achieve a good texture and high coercive force and then cooled to room temperature to deposit the Fe soft layer. A thickness of about 50 nm of Cr was used as a capping layer to protect the film from oxidation.

2.3. Characterization Techniques

The surface morphologies of Sm-Co/Fe bilayer were characterized using atomic force microscopy and scanning electron microscopy. And the atomic ratio of Sm:Co was determined by EDX. The phase structure of the films was characterized by X-ray diffraction (XRD) patterns recorded at room temperature measured on a D8 Advance (Brüker, Billerica, MA, USA) diffractometer with a Cu Kα radiation with a wavelength about 1.5418 Å. The angle range spanned from 40 to 85, with a step of 0.02 and a scanning rate of 0.02° per second. The magnetic measurements were performed on SQUID-VSM designed by the Quantum Design (San Diego, CA, USA). The measurement temperature was room temperature, with a magnetic field range of 0–7 T, and both the ramp-up and ramp-down field rates were set at 200 Oe per second.

3. Results and Discussion

We tried many experimental parameters in an effort to achieve a good texture and high coercive force of the Sm-Co hard-layer films. We found that the high sputtering power and deposition temperature play important roles in developing the strong texture on the MgO (110)/Cr substrate, possibly due to the induced high kinetic energy of sputtered atoms conductive to make SmCo grow along the (110) as much as possible. Finally, the Sm-Co layer film with an excellent texture and high coercive force was achieved. Figure 1 shows the XRD patterns of the Cr (50 nm)/SmCo (50 nm)/Fe (x nm)/Cr (50 nm) films with x as 20 and 30 nm. Only (200) diffraction peak of SmCo₅ was detected at 41.6030 and 41.6001 degrees and the full width at half maximum (FWHM) of the (200) diffraction peaks was 0.7049 and 0.7006 degrees for films with x as 20 and 30 nm, respectively. The grain size of SmCo was estimated to be around 2.6 nanometers based on the following Scherrer formula using the above data:

$$D=\frac{K\lambda }{\beta \cos \theta }$$

(1)

where K is the Scherrer factor, which is chosen as 0.89 here, λ is the wavelength of the incident light; β is the full width at half maximum (FWHM) of the diffraction peaks and θ is the diffraction angle. Specially, no (111) peaks exist, further demonstrating the excellent texture, which is much better than the Sm-Co film deposited on the SiO₂/Cr substrate [14]. This indicates that the hard Sm-Co monolayer successfully achieves an excellent texture on the MgO (110) substrate via optimizing the sputtering fabrication parameters.

The magnetic hysteresis loops of the Sm-Co monolayer measured at 300 and 25 K shown in Figure 2 exhibit a very good rectangular shape along the easy axis (MgO [0 0 1]) and extremely low remanence along the hard axis (MgO [1 −1 0]), further confirming the strongly textured Sm-Co phase. The coercive forces derived from the hysteresis loops measured at 300 and 25 K are 24.0 and 43.4 kOe, respectively. The increase in coercive force from 300 to 25 K should arise from the enhancement of Sm-Co magnetocrystalline anisotropy.

Figure 3a,b present the magnetic hysteresis loops of SmCo/Fe bi-layer films with different thicknesses of soft phase d_s from 2 to 40 nm measured at 25 and 300 K, respectively. For nanocomposite permanent magnetic materials, the exchange coupling between the hard and soft phase is dominated by the direct exchange coupling, a kind of short-range interaction effective within one atomic distance. During the demagnetization process, atom spins of the hard phase can have an influence on the rotation of those of the soft phase with a maximum distance of domain wall width through a cascade of interactions between neighbor atom spins. For the very large size of soft phase, e.g., 40 nm, the spins far from the hard phase very easily rotate, meaning that the H_ns of the soft phase is very low. During the demagnetization process, that part of soft phase first rotates, while the direction of the hard-phase spins still persists until the applied magnetic field reaches the H_irr, where the hard phase starts to reverse. Therefore, a two-step demagnetization curve is observed. We can see that the H_irr of the hard phase in the hard–soft bi-layer film is much lower than the H_c (or H_irr) of the single hard-layer film, which should be attributed to the formation of a domain wall upon the rotation of the soft phase, prompting the rotation of the hard phase [22]. With the decrease in d_s, the total soft-phase spins become closer to the hard phase and their rotations turn out to be harder; therefore, H_ns increases. As d_s further decreases, H_ns becomes very large. At a critical size of soft phase d_sc, H_ns is identical to H_irr, i.e., the rotation of the soft phase immediately leads to the reverse of the hard phase, signifying that the hard and soft phases start to reverse together and a single-phase behavior in the demagnetization curve is observed.

The critical size of soft phase d_sc at which the demagnetization curve changes from the single-phase behavior to two-step behavior is about 6 nm at 25 K and 8 nm at 300 K (Figure 3). In the hard–soft nanocomposite system, d_sc is usually calculated in terms of the theoretical model invoked by Kneller and Hawig: d_sc = $\mathsf{\pi }\sqrt{{\mathrm{A}}_{\mathrm{s}}/2{\mathrm{K}}_{\mathrm{k}}}$, where A_s is the exchange energy of the soft phase and K_k is the magnetocrystalline anisotropy constant of the hard phase [1]. d_sc was calculated for the Sm-Co/Fe hard–soft system (A_s = 2.53 × 10⁻¹¹ J/m and K_k = 1.71 × 10⁷ J/m³) [23] using the above formula and the value of d_sc was 2.7 nm, which is inconsistent with our experimental results. This inconsistency suggests that d_sc is not determined only by A_s and K_k. H_irr or H_c of the initial single hard phase (Figure 3) may also have an influence on d_sc. A higher H_irr or H_c will lead to a smaller d_sc [23].

We can determine the reversal field (nucleation field) of the soft phase H_ns, the irreversible field of the hard phase H_irr and the coercive force H_c for different d_s based on the experimentally measured demagnetization curves (Figure 3), which are shown in Figure 4. It can be seen that H_ns gradually increases with the decrease in d_s for d_s ≥ 20 nm. The increase in H_ns becomes more rapid when d_s ≤ 20 nm. It rises up sharply for d_s ≤ 10 nm. The value of H_irr was fixed at 17.6 ± 0.1 kOe at 25 K and 9.0 ± 0.1 kOe at 300 K for a relatively large size d_s (15 nm ≤ d_s ≤ 40 nm). In this d_s range, the Bloch domain wall could be formed in the demagnetization process due to the 180° rotation of the soft-phase spins far from the hard phase, which will exert equal force on the hard phase, giving rise to the identical H_irr. It is interesting to observe that H_irr starts to increase with the decrease in d_s for d_s ≥ 15 nm, which is highly likely attributed to the incomplete Bloch domain wall formed at the same magnetic field exerting the reduced force on the reverse of the hard phase. Anyhow, we strictly and accurately obtained the dependence of H_ns and H_irr on d_s in experiments (Figure 4). The results can serve as an important basis for research on understanding the mechanism and practical design of a hard–soft system for different applications. For example, the nanocomposite magnet usually needs high H_c and H_irr. In this case, the preferred size of soft phase d_s should be lower than 10 nm. The hard–soft exchange coupling system utilized in high-density magnetic recording media, however, requires a lower H_irr. In this case, a designed d_s larger than 10 nm is favored. In addition, for the nanocomposite magnet with high (BH)_max, a hysteresis loop with characteristics of single-phase behavior is necessary, the determined relationship between H_ns and d_s can tell us how much size of soft phase can be adopted in order to obtain the desired coercive force.

There have been some important theories and simulations on the relationship between H_ns and d_s. E. Goto et al. hypothesized an extremely hard magnetic layer and its magnetization during the demagnetization process was immobile before reaching its irreversible field in the hard and soft magnetic bi-layer film system [18]. Based on this model, an analytic solution was resolved as the following formula:

$${\mathrm{H}}_{\mathrm{n}\mathrm{s}}=\frac{{\mathsf{\pi }}^2\mathrm{A}}{2{\mathrm{M}}_{\mathrm{s}}{\mathrm{d}}_{\mathrm{s}}^{\mathrm{N}}}$$

(2)

where A and M_s are the exchange coupling constant and saturation magnetization, respectively, and N is a constant and derived to be 2. T. Leineweber and H. Kronmüller analyzed the relationship between H_ns and d_s using the micromagnetic method [19]. They found that H_ns was related to the width of the Bloch wall of the hard magnetic layer, and H_ns~d_s were divided into three regions:

$$\begin{gathered} {\mathrm{H}}_{\mathrm{n}\mathrm{s}}={\mathrm{H}}_{\mathrm{n}}^0\left(\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{m}\mathrm{a}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c} \mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}\right) \mathrm{f}\mathrm{o}\mathrm{r} 2{\mathrm{d}}_{\mathrm{s}}\le \mathsf{\pi }{\mathsf{\delta }}^{\mathrm{h}} \\ {\mathrm{H}}_{\mathrm{n}\mathrm{s}}=‘\mathrm{r}\mathrm{a}\mathrm{p}\mathrm{i}\mathrm{d} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{e}’ \mathrm{f}\mathrm{o}\mathrm{r} \mathsf{\pi }{\mathsf{\delta }}^{\mathrm{h}}\le 2{\mathrm{d}}_{\mathrm{s}}\le 8\mathsf{\pi }{\mathsf{\delta }}^{\mathrm{h}} \\ {\mathrm{H}}_{\mathrm{n}\mathrm{s}}\propto {\left({2\mathrm{d}}_{\mathrm{s}}\right)}^{-\mathrm{N}},\mathrm{N}\approx 1.75,\mathrm{f}\mathrm{o}\mathrm{r} 2{\mathrm{d}}_{\mathrm{s}}\ge 8\mathsf{\pi }{\mathsf{\delta }}^{\mathrm{h}} \end{gathered}$$

(3)

where πδ^h is the width of the Bloch wall and h denotes the hard magnetic layer. It can be seen from Formula (3) that H_ns keeps constant when 2d_s is less than πδ^h and goes through a rapid descent process until 2d_s reaches 8πδ^h. With further increasing d_s, the relationship between H_ns and d_s is similar to Formula (1), with N chosen as 1.75.

When d_s is large, H_ns is small and relatively easy to determine experimentally. S.S Yan et al. experimentally measured H_ns of SmFe/NiFe bi-layer films when d_s was in a range of 34~170 nm [8]. Since d_s is large, they used the formula ${\mathrm{H}}_{\mathrm{n}\mathrm{s}}\propto {\left({2\mathrm{d}}_{\mathrm{s}}\right)}^{-\mathrm{N}}$ in Formula (3) to fit the dependence of H_ns on d_s, and a good fitting was achieved for N = 1.73, which is close to the N value of Formula (3). Usually, it is difficult to obtain the accurate value of H_ns for small d_s in experiments because it needs a high-quality sample with good texture and high H_irr of the hard phase. We successfully determined the experimental value of H_ns for very small d_s = 2–40 nm. We used Formula (2) to fit the dependence of H_ns on d_s. However, no ideal result was achieved, as indicated in Figure 5a,b. Although the values of N obtained are 2.05 and 2.14 at 300 and 25 K, respectively, close to the values obtained by E. Goto et al. using Formula (1) [18], the fitting curves do not conform to the experimental data very well.

In hard–soft nanocomposite magnetic systems, due to the strong exchange coupling between the hard and soft magnetic layers, the magnetic moment of the soft magnetic layer will not reverse during the demagnetization process until the external magnetic field increases to the nucleation field H_ns of the soft phase. When the external magnetic field continues to increase and lies between the soft magnetic nucleation field H_ns and the hard magnetic irreversible field H_irr, the magnetic moment of the soft magnetic layer reverses, while that of the hard magnetic layer is theoretically supposed to persist completely [18]. When the external magnetic field is larger than H_irr, the magnetic moment of the hard magnetic layer starts to rotate. The theoretical expectation that the hard magnetic layer is totally immobile during the reverse of the soft layer is just the ideal case. In real hard–soft systems, the magnetic anisotropy of the hard phase is not infinite. Moreover, an interfacial region between the hard and soft phases should exist, which would give rise to the softening of partial thickness of the hard layer close to the soft layer. This thin softened hard layer should also concurrently reverse during the soft magnetic layer reversal process, which means that a certain thin hard layer will become the soft layer, causing an increase in d_s. Actually, a thin hard layer in the interfacial region rotating much easier concurrently with the reversal of the soft layer has been experimentally demonstrated [24,25,26]. Based on the analysis above, a modified formula is obtained:

$${\mathrm{H}}_{\mathrm{n}\mathrm{s}}=\frac{{\mathsf{\pi }}^2\mathrm{A}}{2{\mathrm{M}}_{\mathrm{s}}{\left({\mathrm{d}}_{\mathrm{s}}+\mathrm{a}\right)}^{\mathrm{N}}}$$

(4)

where a is a parameter representing the extra soft magnetic layer from the softened thin hard layer in the interfacial region. The dependence of H_ns on d_s determined by our experimental SmCo/Fe nanocomposite bi-layer films is fitted by Formula (4). A perfect fitting is achieved, as indicated in Figure 5c,d. The values of N and parameter a produced from the fittings are shown in

Table 1. The values of N and parameter a produced from the fittings by formula ${\mathrm{H}}_{\mathrm{n}\mathrm{s}}=\frac{{\mathsf{\pi }}^2\mathrm{A}}{2{\mathrm{M}}_{\mathrm{s}}{\left({\mathrm{d}}_{\mathrm{s}}+\mathrm{a}\right)}^{\mathrm{N}}}$.

Measured Temperature	N	a/nm
25 K	2.046	4.8
300 K	2.044	6.6

. The obtained N is very close to what has been achieved by E. Goto et al. using Formula (2) [16]. The values imply that 4.8 nm at 25 K and 6.6 nm at 300 K of the hard magnetic layer easily reverse, accompanying the reversal of the soft layer during the demagnetization process. The derived value of a at 25 K is smaller than that at 300 K, which is reasonable because the much-enhanced magnetocrystalline anisotropy of the hard layer at low temperatures makes its softening part become hard. Our results have important practical significance in designing a high-performance nanocomposite magnet at room temperature. In order to effectively pin the magnetic moment of the soft phase, the size of the hard phase should be larger than a certain thickness, e.g., about 6.6 nm in a Sm-Co/Fe bi-layer system, otherwise the total hard phase will reverse together with the soft phase, which will result in a very low coercive force of the whole nanocomposite magnet.

4. Conclusions

In order to study the quantitative relationship between the nucleation field and soft magnetic size of hard–soft exchange coupling nanocomposites, high-quality SmCo-Fe bilayer films with high texture and coercivity were successfully obtained by strictly controlling the preparation conditions using magnetron sputtering. The coercive force derived from the hysteresis loops measured at 300 K can reach up to 24.0 kOe. The soft magnetic size of α-Fe varies between 0 and 40 nanometers. The results show that H_ns gradually increases with the decrease in ds for ds ≥ 20 nm. The increase in H_ns becomes more rapid when d_s ≤ 20 nm. It rises sharply for d_s ≤ 10 nm. Based on the existing general theoretical formula, we propose a new fitting formula that can fit the relationship between H_ns and d_s very well and provide a reasonable theoretical explanation for the new formula. The fitting results also essentially reveal that there is indeed a thin layer with a thickness of about 4–6 nm of softened hard magnetic phase at the interfacial region, which reverses simultaneously with the soft magnetic phase when the external magnetic field increases to the nucleation field of soft phase H_ns. Our results clarify the fundamental mechanism underlying the reversal process of the hard–soft exchange coupling system and offer a basis for further critical study and design of hard–soft nanocomposite materials with desired properties.