Mesoporous materials provide a unique host for controlling interactions between nanoscale guests. Here, we use polymer-templated mesoporous silicas to control magnetic dipole-dipole coupling between soft (superparamagnetic) face-centered-cubic and hard (ferromagnetic) face-centered-tetragonal FePt nanocrystals. We find that mixed soft-hard coupled FePt chains show enhanced magnetic coercivity, compared to single-component chains, while randomly associated nanocrystals show no change. A semi-quantitative analysis of temperature dependent magnetization data indicates that the free-energy barrier to spin flipping has both significant enthalpic and entropic components. Linear channels, thus, appear to be an effective way to organize magnetic nanocrystals with constructive dipolar coupling and tunable magnetic properties.
Mesoporous materials provide a powerful way to control the properties of guest species contained within the pores. The nanoscale scale pore dimension forces molecular and colloidal species into close contact, thereby creating intimate interactions and strong coupling.1–5 While guest species ranging from conducting wires or polymers6–8 to catalysts9–11 have been explored, one of the most interesting families of guests is magnetic nanocrystals, due to the potential to modify properties by controlled magnetic interactions.12–15
Interest in magnetic nanoparticles for applications in ultrahigh-density recording and spintronics has increased dramatically over the last decade.16–20 Unfortunately, while nanocrystals represent the smallest isolated magnetic domains, most applications require nanoparticles to possess both thermal and magnetic stabilities over time. As particle sizes decrease, the magnetic-anisotropy energy of each particle becomes comparable to thermal energy, resulting in soft or superparamagnetic behavior.21,22
One way to increase spin-flip barriers is to couple different magnetic materials together. For example, exchange coupling between ferromagnetic and antiferromagnetic nanostructures can increase magnetic anisotropy.23–25 In nanocrystals, this has been used in Co/CoO core-shell nanocrystals.26 Alternatively, hard and soft magnets can be exchange coupled together,27,28 as demonstrated in nanoscale arrays of magnetically hard FePt and soft Fe3Pt.29,30 The enhancements from this exchange coupling include larger spin-flip energy barriers and higher remnant magnetization.
Exchange coupling requires contact between two phases; an alternative is dipolar coupling, which allows for through-space interactions on much longer length scales.31 For effective dipolar coupling, however, the configuration of moments is crucial, as random agglomeration of magnetic domains will lead to demagnetizing effects that decrease coercivity due to antiferromagnetic coupling between domains.32,33 One ideal configuration for dipole coupling is a linear stack of magnetic domains,34–36 and we have shown previously that such stacks can be created using mesoporous silica templates combined with cobalt nanocrystals.13
A wide range of magnetic metal nanocrystals can be created,37–40 along with some oxide ferrimagnets.41,42 In this work, however, we chose FePt nanocrystals due to their unique ferromagnetic properties at size scales less than 10 nm.43 While cubic (fcc) FePt nanocrystals show superparamagnetic behavior similar to pure metal nanocrystals, FePt nanocrystals in the face centered tetragonal (fct) structure possess an unusually high uniaxial magnetocrystalline anisotropy (Ku ∼ 5 × 107 J/cm3),43 which results in hard (ferromagnetic behavior) in nanocrystals as small as 4 nm in size.44
A variety of methods are available to create order in nanocrystal arrays,45–53,82,83 but, here, we chose to arrange nanocrystals in the pores of a mesoporous silica host, created using block-copolymer templating.54 Many phases of polymer-templated silica can be synthesized,55–58 with pore sizes ranging from 10 to 200 Å.59–61 The pore surface can also be functionalized with silanes to create varying surface functionalities.62–64 This work utilizes a p6mm hexagonal phase produced using small triblock copolymers (SBA-15) because it contains linear pores of the correct diameter to force magnetic particles to stack in straight chains. Indeed, similar materials have been used to create a variety of nanoparticle arrays,55,65 including both ferromagnetic and superparamagnetic nanoparticles.13,66–69
Here, we specifically investigate dipolar coupling between soft and hard nanomagnets. We show that by creating an optimal nanoscale architecture, dipole-coupled soft-hard nanomagnetic chains exhibit qualities similar to those found in exchange-coupled spring magnets,29,30 despite the much weaker nature of the dipolar interaction. Confinement inside the one-dimensional nanochannel of mesoporous silica modifies magnetization reversal barriers, an effect that appears to arise in part from entropic effects on the spin-flip barrier.
To create our nanocrystal arrays, SBA-15 mesoporous silica powders were synthesized using block copolymer templating methods with a Pluoronic P123 polymer template.54,55,70 Porous silica powders were produced with a pores size of 8.3 nm and a surface area of 370 m2/g, as determined by nitrogen porosimetry. After synthesis, the pores were made hydrophobic by reaction with an organic silane.54,62–64 Figure S1 shows low angle X-ray diffraction (XRD) for the porous silica powder, confirming the regular hexagonal ordering of the pores.70 Both magnetically soft (fcc) and magnetically hard (fct) FePt nanoparticles were synthesized using established recipes,44,71 and these particles were then incorporated into the silica pores by diffusion and slow solvent concentration.66–68 Figure S2 shows XRD data for both fcc and fct nanocrystals.70 Scherrer analysis of diffraction peak widths indicates nanocrystal diameters of 6.0 and 6.5 nm for the fcc and fct FePt nanocrystals, respectively. Figures 1(a)-1(c) show TEM images of empty and nanocrystal filled silica pores. Tightly packed arrays of nanocrystals can be seen in the filled pores (Figures 1(b) and 1(c)). No changes in diffraction were observed after incorporation into the mesoporous silica host, indicating the particles were not oxidized or chemically modified by the incorporation process.
In order to learn about changes in magnetic anisotropy introduced by dipolar coupling between nanocrystals in pores, SQUID magnetometry studies were carried out on pure and mixed nanocrystal stacks.70 For mixed systems, different ratios of hard- and soft-FePt nanoparticles were used in the stacks: we examined samples that were dominantly fcc FePt (low hard:high soft stacks, A-stacks) and samples that were majority fct FePt (high hard:low soft stacks, B-stacks). The amounts of hard-fct or soft-fcc FePt in the matrix were controlled by incorporation order, temperature, time, and solution concentration.
Magnetization changes with field provide information about the coercivity, which is related to the energetic barrier height for magnetization reversal (ΔE), given by ΔE = U(1−H/H0)1/n. Here, U is the energy barrier at zero applied field, H is the applied field, H0 is the field needed to overcome the barrier at zero temperature, and n reflects the switching mechanisms.72–75 The magnetization reversal energy or the activation energy for spin flipping, thus, varies monotonically with the coercivity, even though the coercivity is not linearly proportional to that activation energy.73,76 Figure 1(d) shows room temperature hysteresis curves for pure-soft and pure-hard FePt nanocrystal stacks in the channels of our silica matrix. The soft particles exhibit superparamagnetic behavior while hysteresis curve for hard nanocrystal stacks indicate a large coercive width of 3000 Oe.
Despite the superparamagnetic behavior of the fcc nanocrystals, zero-field cool/field-cool (ZFC/FC) experiments shown in Figure 1(e) indicate strong dipole coupling between stacked nanocrystals, compared to dilute, non-interacting soft FePt, not in pores.13 For the dilute case, a blocking temperature of just 15 K is observed, while the blocking temperature increases to 100 K for soft stacks in pores due to interparticle coupling (Figure 1(e)). The small magnetization increase upon field cooling further indicates strong interparticle dipole-dipole coupling–coupling suppresses fluctuations, so cooling highly coupled systems has little effect on the magnetization. Similar behavior has been observed previously for dipole-coupled chains of superparamagnetic nanoparticles.13 Because of the permanent magnetic dipoles in the fct samples, non-interaction nanocrystals cannot be produced but the lack of a blocking temperature in Figure 2(b) for the pure hard stacks reaffirms the ferromagnetic nature of those nanocrystals.
To make mixed stacks, mesoporous silica samples were first soaked in an organic solution containing one nanocrystal type, filtered, dried, and then soaked in the second solution. The first solution usually fills the majority of the pores so to make a dominantly soft mixed system (A-stacks), pores were first filled with fcc nanocrystals, and then fct nanocrystals were added. A-stacks show ZFC-FC curves (Figure 2(a)) that are qualitatively similar to pure soft-stacks in pores. Only a small increase in blocking temperature and a slight flattening of the FC curve are observed for the A-stack compared to pure soft stacks. The soft:hard nanocrystal ratio in this sample cannot be precisely determined, however, as some soft nanocrystals wash out of the pores during incorporation of hard nanocrystals. To make dominantly hard stacks (B-stacks), fct nanocrystals are first incorporated followed by fcc nanocrystals. Because strong dipole coupling between fct nanocrystals in the pores makes it almost impossible to remove fct nanocrystals once they are diffused into the mesoporous silica host, for B-stacks, we can use elemental methods to show that the FePt mass fraction increases from 25% to 38% after incorporation of the fcc nanocrystals into the fct filled sample. Figure 2(b) shows that FC-ZFC data for B-stacks are qualitatively similar to pure fct stacks.
Despite the similarities between ZFC-FC data for various mixed and pure nanocrystal stacks, the coercivities of these samples are very different. Figures 2(c) and 2(d) show 298 K hysteresis curves for mixed hard/soft nanocrystal chains compared to pure nanocrystal stacks in the pores. A-stacks (Figure 2(c)) are dominated by soft nanocrystals, but unlike the superparamagnetic fcc nanocrystal stacks this sample shows significant coercivity. This coupled system has a coercive width of 5100 Oe while the pure fct FePt shows a width of only 3000 Oe, and pure fcc has no width. We also note that when we do not know the exact fct fraction in the mixed A-sample, the pure hard stacks used for comparison have a fairly high FePt filling fraction, and so the length of the hard fct FePt chains is almost surely longer in the pure sample than in the mixed sample. Despite this fact, the coercive width is broader in the mixed A-stacks. The increase in coercivity shown in Figure 2(c), thus, provides strong evidence of coupling between hard and soft nanocrystals for FePt nanocrystals in mesoporous silica.
We note that there is a small kink in the hysteresis curves for the mixed stacks near zero applied field. This kink suggests two populations in this sample—mixed hard/soft stacks and some pure soft stacks. Short fct incorporation times were used to synthesize these samples so that the fcc nanocrystals would not wash out of the pores. It is, thus, likely that the fct nanocrystals did not have time to fully diffuse throughout the mesoporous silica network, leaving some pure fcc stacks in the interior of the porous silica grains.
Figure 2(d) shows 298 K hysteresis data for B-stacks which are dominantly hard nanocrystals. These data are somewhat easier to interpret than the data in part (a). Here, long incorporation times could be used to add soft nanocrystals to the hard samples, and so we expect all hard nanocrystals to be coupled to soft nanocrystals. In addition, we can directly compare the hard only composites and mixed systems containing the exact same fraction of hard nanocrystals. In this case, a very large enhancement in the coercivity from 3000 Oe to 7200 Oe is observed when going from pure-hard stacks to mixed stacks, which we attribute to coupling between hard and soft nanocrystals. Indeed, this coercivity change is not due to any permanent modification in the nanocrystals upon incorporation, as Figure 3(a) shows that when the soft nanocrystals are washed out of the composite, the hard stacks return to their original coercivity.
While the results presented above make a strong case for the role of dipole coupling in tuning barriers to spin reversal, they do not prove that the well-defined nanoscale architecture imposed by the mesoporous silica—i.e., one dimensional stacks of nanocrystals—is crucial to this coupling scheme. To elucidate the role of nanoscale architecture in determining magnetic properties of these materials, we made samples similar to those shown in Figures 2(c) and 2(d), but without the constraint of 1-D stacks. Figure 3(b) shows 298 K hysteresis data for random agglomerates of soft nanocrystals, hard nanocrystals, and a mixture of hard and soft nanocrystals. While the soft nanocrystal agglomerates remain superparamagnetic, comparison of the hysteresis curves shows that the random agglomeration of hard-soft particles and the pure hard particle mixture has the same coercivity.
We understand this result by the fact that magnetic interactions in disordered (and some ordered) two- and three-dimensional arrays of magnetic nanocrystals are magnetically frustrated.77,78 The system cannot produce low energy interactions for all nanocrystal pairs. For systems containing both hard and soft nanocrystals, this frustration leads to separation of hard and soft nanocrystals with the hard nanocrystals coupling mostly to each other and little hard/soft coupling.52,79 A one-dimensional stack, however, is not frustrated, and so in this geometry, strong coupling between hard and soft nanocrystals can be achieved. We note that the hysteresis curves for both hard and hard/soft mixed nanocrystals in Figure 3 are somewhat broader than the pure hard curves shown in Figures 1 and 2. This arises because slightly large nanocrystals were used for this experiment compared to the pore-filling case shown above.
It is worthwhile to consider the energetic origins of these coercivity changes for stacked nanocrystals in pores. Generally speaking, the coercivity of a magnetic sample measures the intrinsic magnetocrystalline anisotropy in a material,73,80 combined with shape anisotropy, strain anisotropy, and inter-domain coupling.72,81 These anisotropies produce a free energy barrier for spin flip (ΔG‡) that is analogous to the barrier associated with any thermally activated process. While we often think only about the enthalpic components to that free energy, for a highly coupled system like this, entropy can also be important. Here, we cannot quantitatively calculate the entropic component to the free-energy barrier, but we can use temperature-dependent hysteresis loops to show that entropy plays a role.
For almost all materials, coercivities decrease as temperature increases because there is more thermal energy available to assist in spin flips. If the kinetic barrier to spin flips contains both enthalpic (ΔH‡) and entropic (ΔS‡) components, however, the absolute free-energy barrier height (ΔG‡, not the height relative to the available thermal energy) can also increase with increasing T as per the Gibbs equation, ΔG‡ = ΔH‡ − TΔS‡. While it is unlikely that the entropic component could dominate to the point that coercivities increase with increasing temperature, entropic effects could reduce the extent to which hysteresis curves narrow at elevated temperature, and this effect is, indeed, observed in our soft-hard coupled stacks. A-type stacks show a decrease in coercivity at 298 K of 44% from the 10 K value of 9900 Oe.70 An analogous pure hard system with a matched 10 K coercivity of 9750 Oe shows a coercivity decrease of 64% upon warming to 298 K.70 This indicates that entropy must play a larger role in the barrier to spin flip for the A-type stack than for the matched pure-hard stack. Similar trends are observed for B-type stacks, although equivalently well-matched samples could not be made. The mixed-B stacks have a coercivity of 13 200 Oe at 10 K, and this value decreases by 42% upon warming to 298 K.70 In comparison, a pure hard stack with a 10 K coercivity of 15 000 Oe shows a coercivity decrease of 53% upon warming to 298 K.70 Taken together, these data indicate that when soft nanocrystals couple to hard ones in 1-D stacks, those interactions can influence the energetics of spin-flip processes by changing both the enthalpic barrier due to dipole-dipole coupling and also the entropic contributions due to collective spin flips occurring in many coupled nanoparticles.
In this work, we have, thus, shown that by stacking soft, superparamagnetic and hard, ferromagnetic FePt magnetic nanocrystals inside mesoporous silica, we can encourage anisotropic dipolar coupling between particles that leads to increase in magnetic coercivity and remanence. We further showed that part of the increased coercivity is related to entropic effects, and the magnitude of the change is sensitive to the hard:soft nanocrystal ratio in the stacks. Importantly, we showed that the nanoscale architecture induced by the porous silica host is critically important to this coupling as disordered arrays of hard and soft nanocrystals do not show increased barriers to magnetization reversal.
While this work focuses only on one-dimensional chains of nanocrystals, it illustrates an important point about nanoscale magnetic systems. Through-space dipolar coupling is often ignored in magnetic systems because it is much weaker than exchange coupling. It is very easy to flip the spins of superparamagnetic nanocrystals, however, and so dipole-dipole coupling can have a significant effect on the properties of nanocrystal arrays. There is currently an explosion in our ability to organize nanocrystals in complex patterns. In addition to the 1-D stacks in pores shown here, researchers have made both straight and zig-zag chains of nanocrystals on patterned surfaces.53,82,83 In three dimensions, a huge array of binary and tertiary colloidal crystals has been made from mixtures of nanocrystals like those used here.45,84,85 If one considers various mixtures of hard- and soft-magnetic nanocrystals in this diverse array of geometries, it becomes clear that dipole coupling between disparate populations of magnetic nanocrystals is, indeed, an interesting and powerful way to tune properties in magnetic meta-materials.
This work was supported by the National Science Foundation under Cooperative Agreement Award No. EEC-1160504 which funds TANMS, an NERC focused on Translational Aspects of Nanoscale Multiferroic Materials and by the Western Institute of Nanoelectronics which was sponsored by NERC (NRI), Intel, and the UC Discovery Program. V.H.L. was supported in part by a fellowship from Intel, Inc.