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Nov 10, 2016 - ABSTRACT: The magneto-optical Kerr effect is a striking phenomenon whereby the optical properties of a .... ticle spacing.1,2,5,11,12,1...
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Magneto-Optical Response of Cobalt Interacting with Plasmonic Nanoparticle Superlattices Michael B. Ross,∥ Marc R. Bourgeois,∥ Chad A. Mirkin,* and George C. Schatz* Department of Chemistry and International Institute for Nanotechnology, Northwestern University, Evanston, Illinois 60208, United States S Supporting Information *

ABSTRACT: The magneto-optical Kerr effect is a striking phenomenon whereby the optical properties of a material change under an applied magnetic field. Though promising for sensing and data storage technology, these properties are typically weak in magnitude and are inherently limited by the bulk properties of the active magnetic material. In this work, we theoretically demonstrate that plasmonic thin-film assemblies on a cobalt substrate can achieve tunable transverse magneto-optical (TMOKE) responses throughout the visible and nearinfrared (300−900 nm). In addition to exhibiting wide spectral tunability, this response can be varied in sign and magnitude by changing the plasmonic volume fraction (1−20%), the composition and arrangement of the assembly, and the shape of the nanoparticle inclusions. Of particular interest is the newly discovered sensitivity of the sign and intensity of the TMOKE spectrum to collective metallic plasmonic behavior in silver, mixed silver−gold, and anisotropic superlattices.

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Herein, using theory, we explore how a diverse selection of nanoparticle-based plasmonic architectures interact with magnetic media. If properly designed, these structures exhibit a tunable and enhanced Kerr effect throughout the visible and near-infrared regions of the spectrum. Specifically, the reflectance of thin films is varied by changing the composition (Ag or Au), the nanoparticle spacing, the nanoparticle aspect ratio, and even the manner by which metallic components are assembled. These structures are modeled using an analytic transfer-matrix approach where Co (the magnetic material) is interfaced with plasmonic layers described by Maxwell−Garnett effective medium theory, a model that has provided strong agreement with past experiments on DNA-assembled nanoparticle superlattices,5,15,36,37 although many of the conclusions from this work apply to a wide variety of bottom-up assembled plasmonic architectures coupled to magnetic media. Figure 1a presents a scheme of the thin-film architectures explored in this work. In all cases the Co and superlattice layer thicknesses are both fixed at 100 nm (the Co thickness is such that transmitted light is negligible, so light is either reflected or absorbed) and the incident angle is fixed at 30° for simplicity. The plasmonic layer is situated above the Co layer, and its optical properties are described by Maxwell−Garnett effective medium theory (EMT),5,37 which can accurately describe the optical properties of low-volume fraction plasmonic assemblies composed of spherical nanoparticles,37 of nanoparticles with multiple compositions,15 and of anisotropic nanoparticles36 (see the Materials and Methods in the Supporting Information

oble-metal nanoparticles exhibit tunable interactions with visible light, making them ideal building blocks for creating new kinds of optical materials.1−6 These strong and tunable interactions with visible light are due to localized surface plasmon resonances (LSPRs), the collective oscillation of conduction electrons.2,6,7 The rational synthesis, arrangement, and assembly of noble-metal nanoparticles has enabled synthetic approaches for creating multielemental nanoparticles,8,9 for creating optical metamaterials,10−14 for tuning extinction and color in thin films,15−18 and for coupling nearfield plasmonic interactions with far-field photonic modes.19−21 Although the LSPR is exquisitely tunable, for example, by changing the nanoparticle size, shape, or composition, plasmonic materials are often limited in the frequencies at which they are active, the width and intensity of their optical response, and the responsiveness to external stimuli.5,22−24 One promising approach to effecting tunable and responsive optical properties in plasmonic materials is to interface them with magnetic materials to create so-called magneto−plasmonic architectures.25−30 Such structures can exhibit optical properties that change in the presence of a magnetic field, which provides opportunities for creating improved sensors,31,32 magnetically responsive changes in reflectivity,25,28,33,34 and one-way optical transmission.26,35 In all of these cases, the underlying physics are based on the magneto-optical Kerr effect, whereby changes in magnetization of a film alter the amplitude and phase of light transmitted and reflected at its interfaces. To date, the majority of such studies have focused on magneto-plasmonic materials composed of either hole arrays or 2D planar gratings;29−35 few have focused on hierarchical nanoparticle-based structures where the magneto−plasmonic interaction is primarily in the far-field. © XXXX American Chemical Society

Received: October 1, 2016 Accepted: November 7, 2016

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for more information and Figures S2−S4 for the EMT properties of the different plasmonic media described herein). The transverse magneto-optical Kerr effect (TMOKE) describes changes in the reflectivity of a material when a magnetic field is applied transverse to the incident direction of light (Figure 1a). Effectively, TMOKE occurs due to changes in the amplitude and phase of reflected light at the interface of a magnetized material due to the refractive index of the magnetized material becoming anisotropic (see the Materials and Methods in the Supporting Information for more information). Investigating TMOKE provides several advantages compared with other magneto-optic interactions primarily because the incident light maintains a linear polarization after reflection, making it the most straightforward Kerr effect to measure.38 TMOKE is typically described by a figure of merit δ δ=

R(+ M) − R(− M) R(+ M) + R(− M)

(1)

where R(+M) and R(−M) are the reflectance values for opposite magnetization directions. From this, δ provides a straightforward quantity to compare different magneto-optic materials whose properties are dominated by reflectance. To understand the TMOKE response in the architectures described herein, it is useful to compare the reflectance in the absence of an applied field (Figure 1b) with the change in reflectance due to the reversal of the magnetization direction (i.e., the TMOKE δ response, Figure 1c). Figure 1b depicts the reflectivity of a bare 100 nm Co film (black), which exhibits a relatively flat and strong profile throughout the visible, typical for a thick film of a gray metal. With the addition of a plasmonic EMT layer (100 nm, 20% volume fraction) on top of the Co layer, a drastic decrease in the reflectance is observed at respective Ag (blue, 400 nm) or Au (red, 520 nm) LSPRs. This result is not surprising, as plasmon excitation increases extinction in the top layer. However, of more interest is the

Figure 1. Magneto−plasmonic optical properties in Co-superlattice materials. (a) Scheme of magneto−plasmonic nanoparticle superlattice in the transverse magneto-optical Kerr effect (TMOKE) geometry. The plasmonic superlattice is described by effective medium theory (EMT) and can be composed of Ag or Au with varying volume fractions (1−20%), mixed metal nanoparticle architectures, or anisotropic nanoparticles. Both the superlattice and magnetic (Co) layers are 100 nm thick. (b) Bulk reflectance of 100 nm Co (black), 100 nm Co with 0.20 volume fraction Ag superlattice (blue), and 100 nm Co with 0.20 volume fraction Au superlattice (red). (c) TMOKE parameters for the same structures as in panel b.

Figure 2. TMOKE dependence on nanoparticle superlattice volume fraction. (a) Reflectance for 100 nm Co films with dielectric layers characterized by (nondispersive) refractive indices of the form n + i0.01 equivalent to the Au and Ag superlattices at wavelengths red of the LSPR. (b,c) Reflectance of Au and Ag superlattices, respectively, for various volume fractions. (d) Inset from 300 to 400 nm for Ag superlattices with varying volume fractions. (e−h) Calculated TMOKE parameters for structures corresponding with panels a−d, respectively. 4733

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modest increases in background refractive index. Indeed, the changes in δ are richer than the changes observed in the bulk reflectance as a function of volume fraction (Figure 2b,c). At 1% volume fraction both the Au (Figure 2f) and Ag (Figure 2g) TMOKE traces are similar to those for the dielectric structures (Figure 2e), except the plasmonic structures exhibit an enhancement (a minima) in TMOKE at their respective LSPRs. By comparison, the TMOKE response of the Ag and Au superlattices begins to differ at higher volume fractions. Specifically, at 5, 10, and 20% volume fraction, the Au-based superlattices exhibit an increasingly negative δ response at the LSPR (520 nm), whereas the Ag-based superlattices exhibit increasingly positive TMOKE response (near 375 nm). The trend observed for Au suggests that increasingly strong extinction in the plasmonic layer (Figure 2b and Figure S2) results in more a pronounced TMOKE response. This can be understood through the TMOKE expression (eq 1); if the total reflectance is very low [R(+M)+(R(−M)], then any changes in the magnetized reflectance R(+M) and R(−M) will be magnified.31 Compared with the Au-based structures, the response of the Ag-based structures is more complex. Although Ag structures do exhibit a negative δ coincident with stronger extinction at the LSPR, there is also a positive δ response to the blue of the LSPR where Ag has a near-zero and negative effective dielectric function, an effect that is not present at equivalent Au volume fractions (Figure S2). For all volume fractions, the inflection points in the reflectance spectra (Figure 2d) are coincident with those in the TMOKE response (Figure 2h). The shortest wavelength TMOKE maximum occurs where the effective dielectric function is near-zero, as described above.41,42 When the effective dielectric function is negative the TMOKE response is near-zero because minimal light reaches the Co interface due to increased reflectance of the plasmonic layer.13 The TMOKE maximum to the red (near 375 nm) coincides with where the effective dielectric function has a positive inflection point and reaches its maximum (Figure S2), which causes pronounced dispersion in the reflectance (Figure 2d). In general, with increasing volume fraction the effective dielectric function becomes increasingly negative, which both widens the spectral area over which the TMOKE response is near zero and further separates the positive TMOKE regions correspondent with a near-zero or dispersive effective dielectric values. As stated above, similar sign changes have been observed in bulk metallic systems; however in metallic systems the dielectric functions are dictated by the elemental composition and are fixed. As such, the sign and breadth of TMOKE response cannot be tuned in the manner by which it can be in plasmonic Ag superlattices. To further demonstrate how control over superlattice structure can affect TMOKE response, different arrangements of Ag and Au nanoparticles were simulated. It was recently demonstrated that crystalline superlattices where the nanoparticle composition varies randomly (i.e., alloys, Figure 3a) exhibit vastly different extinction and reflection profiles than do superlattices with equivalent amounts of Ag and Au nanoparticles, which are assembled into homogeneous layers (i.e., bimetallics, Figure 3d).15 Fine control over superlattice structure, so-called plasmonic metallurgy, allows one to achieve diverse optical properties in structures with equivalent metallic compositions. Within the scope of magneto−plasmonic response, this allows one to relate subtle changes in reflectance

behavior of the TMOKE response, as shown in Figure 1c. Although Co exhibits a relatively flat TMOKE profile from 300 to 900 nm, similar to the reflectance, profiles for the superlattice structures display far greater complexity. The Au (red) superlattice shows negative TMOKE parameters, similar to the Co layer but with a sudden negative dip at the LSPR wavelength. The Ag (blue) superlattice exhibits more complex behavior, with negative values similar to Co for wavelengths shorter than 325 nm and longer than 375 nm, and there is a dip coincident with the LSPR just above 375 nm. In addition, the Ag superlattice also shows positive δ peaks at 325 and 375 nm and positive values in between these wavelengths. The wavelength range where δ is positive corresponds (for 20% volume fraction) to where the effective medium has a negative real effective permittivity (i.e., is metallic; see Figure S2).13 This means that the real part of the permittivity goes through zero at 325 and 375 nm, and this is correlated with the sign change in δ. Indeed, similar sign reversals have been observed in Au−Co layered systems and can be attributed to the nonreciprocity of fields propagating at the interface.31 In this metallic regime, Figure S1 shows that the skin depth of the Ag superlattice film is ∼100 nm, so the reflectivity in Figure 1 is close to that for Co. However, the TMOKE parameter is close to zero in this range, meaning that much of the light is reflected by the superlattice rather than by the Co. It is well known that the optical properties of plasmonic assemblies drastically change depending on the internanoparticle spacing.1,2,5,11,12,18 In 10−20% volume fraction silver plasmonic superlattices there are effectively three optical property regimes: (1) near-zero and negative dielectric behavior (for Ag) as mentioned above where the effective medium is metallic, (2) a region of strong extinction that is observed at the LSPR, and (3) a region with low extinction but with a refractive index elevated above the background that is observed red of the LSPR. Importantly, the relative strength of these factors can be tuned by changing the volume fraction.5 For example, Figure 2c demonstrates that 10 and 20% Ag superlattices exhibit multiple minima in the reflectance due to near-zero epsilon behavior and a maximum in reflectance coincident with where the effective dielectric function is negative (Figure S2),13,36 an effect not observed for 1 and 5% Ag superlattices.13,29 Figure 2b demonstrates the extent to which extinction can be tuned; as the Au volume fraction increases from 1 to 20%, the reflectance minimum decreases due to the increasingly strong extinction and loss in the higher volume fraction material (Figure S2). The effect of increasing refractive index is less obvious in the reflectance spectrum; it is most easily observed in the effective dielectric function (Figure S2). Thus the best structural comparison with the superlattices is a 100 nm dielectric layer with an elevated refractive index but without any extinction band, that is, without an LSPR (Figure 2a). The main effect of increasing the refractive index of the dielectric is a decrease in the reflectance toward the red. The increase in reflectance blue of 400 nm for the n = 1.35 case (analogous to 20% Ag or Au) is likely due to the emergence of optical modes in the film that will occur with elevated indices and at the shortest wavelengths.39,40 The TMOKE responses for the magneto−plasmonic materials exhibit multiple negative and positive δ maxima and minima (Figure 2f,g) that are not observed in the nonabsorbing dielectric materials (Figure 2e). This shows that near-zero and negative dielectric behavior as well as strong extinction at the LSPR are the dominant factors that affect TMOKE, not the 4734

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2). At higher Ag content, δ becomes increasingly positive near 375 nm in addition to exhibiting two minima in δ, one at 400 nm and one closer to 350 nm. The minimum at 400 nm is due to the Ag LSPR and is similar to that seen in Figure 2, whereas the minimum near 350 nm blue-shifts with decreasing Ag content. This feature is coincident with reflectance minima for all compositions (Figure 3b); it cannot be directly attributed to specific features in the effective dielectric function, although both the near-zero and minimum in the effective dielectric function blue-shift with increasing Ag content (Figure S3). Changing the ordering of Ag and Au layers, so-called bimetallic superlattices, provides a different means for tailoring superlattice structure. In this case, distinct metallic layer sequences lead to changes in overall reflectance due to thinfilm phase interference effects. For simplicity, only four architectures are considered, consisting of two 50 nm thick layers (Figure 3d); indeed all four structures exhibit different reflectance profiles, demonstrating that the properties do depend on the material ordering.15 Again, this change in reflectance manifests as differences in TMOKE response (Figure 3e); in particular, the two alternating Ag:Au structures (purple and orange traces) have vastly different spectra. When the light is incident on the Ag layer first (purple trace), a deep minimum in δ is observed near 325 nm, whereas when light is initially incident on the Au layer (orange trace), multiple positive maxima are observed in the 350−375 nm region in addition to one near 550 nm. The translation of plasmonic metallurgy to TMOKE modulation clearly demonstrates that the magneto−plasmonic response can be precisely controlled by changing the way in which Ag and Au nanoparticles are arranged in three-dimensions. It also affirms that thin-film phase retardation effects and reflectance are directly related to the TMOKE response. Anisotropic nanoparticles provide an opportunity to tune the LSPR throughout the visible-NIR.1,2,6 Within the EMT framework, an orientation averaged effective dielectric function of ellipsoidal particles (rather than spherical ones) can accurately describe superlattices composed of high aspect ratio anisotropic nanoparticles.36 In all cases considered herein the volume fraction is fixed at 5% and the ellipsoidal aspect ratio is varied from 2 to 6 for both Ag and Au (Figure S4). Increasing the aspect ratio of the ellipsoids red-shifts the longitudinal LSPR, blue-shifts the transverse LSPR (in Ag), and increases the extinction for both Ag and Au.22 In general, the reflectance for the anisotropic Ag and Au superlattices exhibits minima at both the longitudinal and transverse LSPRs (Figure 4a,b); note that all of the spectra exhibit multiple peaks and dips that can be attributed to the negative effective dielectric functions that are achieved with both Ag and Au. The TMOKE spectra exhibit a similar trend to the reflectance spectra, whereby there are multiple minima and maxima (at both the LSPR and blue of the LSPR where the dielectric function is negative) that all shift with increasing aspect ratio. Interestingly the magnitudes of the TMOKE response are similar to those for the spherical particles, although the TMOKE response near the LSPR is much narrower for the anisotropic superlattices due to the higher quality resonances.22 Additionally, there is a wide spectral region where TMOKE is near-zero that occurs when the effective dielectric function is negative for most of the anisotropic effective media (Figure S4). Similar to that observed in the higher volume fraction spherical nanoparticle Ag superlattices, these materials are strongly reflective, limiting

Figure 3. Plasmonic metallurgy in magneto−plasmonic nanoparticle superlattices. (a) Plasmonic alloys where the ratio of Ag:Au is varied in the effective medium. Reflectance (b) and TMOKE (c) for plasmonic alloys with 100% Ag (lightest orange), to 0% Ag (darkest trace), in increments of 20%. (d) Plasmonic bimetallics where the ordering of 50 nm Ag and Au effective medium layers is varied (blue EMT1 = Ag, EMT2 = Ag; purple EMT1 = Au EMT2 = Ag; orange EMT1 = Ag EMT2 = Au; red EMT1 = Au EMT2 = Au). (e) Reflectance and (f) TMOKE for plasmonic bimetallics. The alloy superlattices are described by a linear weighted average of the Ag and Au effective dielectric functions; all volume fractions are fixed at 20%.

(driven by tunable changes in extinction and phase retardation) to changes in TMOKE. The extinction in alloyed plasmonic superlattices changes linearly at the respective Ag and Au LSPRs as a function of composition (Figure 3b, Figure S3).15 Indeed, the reflectance spectra for higher Au-content alloys exhibit a deeper well at 520 nm (the Au LSPR), and higher Ag-content alloys exhibit a deeper well near 400 nm (the Ag LSPR) in addition to increased reflectance near 375 nm (where the dielectric function is negative (Figure S3)). Note that although the reflectance spectra qualitatively reproduce the linear exchange in extinction as a function of Ag:Au composition, previous data suggest that crystalline arrangements of Ag and Au bcc superlattices can dampen the Ag LSPR due to interactions with the Au interband transitions near 400 nm.13,43 Future experimental and theoretical work will be needed to verify the accuracy of the effective dielectric functions in Figure S3; within the scope of this work, EMT serves as an approximation for the plasmonic alloys. The TMOKE response for these structures exhibits similar trends in behavior as the Ag:Au alloying ratio is varied. At higher Au content, δ is negative near the Au LSPR, similar to the effect observed by changing the Au volume fraction (Figure 4735

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the effective medium. The enhancements seen at wavelengths associated with LSPR are similar to what has previously been seen in TMOKE studies where explicit particles or grating structures were considered. However, previously unobserved sign changes, peaks, and dips are observed in the TMOKE results that can be attributed to the interaction between Co and collective plasmonic response of a variety of superlattices, particularly in Ag lattices with volume fractions above 10%, mixed Ag:Au lattices, and anisotropic lattices. These complex spectra reveal sensitivity in the TMOKE measurement that significantly exceeds what can be inferred from reflectance measurements. This work thus provides a promising approach for creating multifunctional optical materials that exhibit unusual asymmetric optical properties. Though this work focused on structures where the magnetic material is planar and situated below a plasmonic assembly, it is likely that assemblies composed of both plasmonic and magnetic materials that have precisely controlled nearest-neighbor arrangements could lead to still more exotic and magnetically responsive properties.3,5,11,44−47 Such materials have promise in sensing and optical electronics applications as well as for accessing new kinds of stimuli-responsive materials.

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COMPUTATIONAL METHODS Detailed information is provided in the Supporting Information.

Figure 4. Effect of shape anisotropy in magneto−plasmonic nanoparticle superlattices. (a) Reflectance and (b) TMOKE for EMT composed of Ag ellipsoids with aspect ratios ranging from 2 to 6. (c) Reflectance and (d) TMOKE for EMT composed of Au ellipsoids with aspect ratios ranging from 2 to 6. Volume fractions of all EMT materials are fixed at 5%.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b02259. The full transfer matrix derivation is included. Also included are the dielectric functions for Ag, Au, and Co as well as the effective dielectric functions for all structures described in the main text. (PDF)

the light that reaches the Co layer and thus minimizing the changes in reflectance phase and amplitude upon magnetization. In the anisotropic systems, the similar magnitudes of the TMOKE responses to those found using spherical nanoparticles are surprising because the ellipsoidal superlattices have a much greater polarizability, meaning stronger extinction and more dispersive effective dielectric functions.36 This suggests that the main benefits derived from anisotropic nanostructures for TMOKE are spectral tunability and narrower δ response, at least for far-field interactions. It was recently demonstrated that narrow δ response can improve the refractive index sensing capability of 2D magneto−plasmonic sandwich architectures.31 Using theoretical modeling and simulations, we have discovered that the combination of Ag and Au plasmonic assemblies with Co magnetic media can be used to vary magneto-optical properties throughout the visible and nearinfrared. Specifically, the magneto-optical response of Co and nanoparticle-based assemblies can be tailored by changing the plasmonic material, the volume fraction (1−20%), the means by which the metallic components are ordered, and the shape of the plasmonic inclusions. However, it should be emphasized that the metallic components only influence the TMOKE response through their effect on the effective medium properties of the superlattice layer. As a result, a transfermatrix model for thin films combined with effective medium theory, which accurately describes the optical properties of nanoparticle superlattices, provides a comprehensive model for understanding the optical response. Our calculations demonstrate that the TMOKE spectrum is sensitive to both the local and collective plasmonic response of

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (C.A.M.). *E-mail: [email protected] (G.C.S.). ORCID

Michael B. Ross: 0000-0002-2511-0594 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Author Contributions ∥

M.B.R. and M.R.B. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based on work supported by the Air Force Office of Scientific Research Award FA9550-11-1-0275 and the National Science Foundation’s MRSEC program (DMR1121262) at the Materials Research Center at Northwestern University. M.B.R. gratefully acknowledges support through the NDSEG graduate fellowship program. 4736

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