Nanorod Surface Plasmon Enhancement of Laser-Induced Ultrafast Demagnetization

Ultrafast laser-induced magnetization dynamics in ferromagnetic thin films were measured using a femtosecond Ti:sapphire laser in a pump-probe magneto-optic Kerr effect setup. The effect of plasmon resonance on the transient magnetization was investigated by drop-coating the ferromagnetic films with dimensionally-tuned gold nanorods supporting longitudinal surface plasmon resonance near the central wavelength of the pump laser. With ~4% nanorod areal coverage, we observe a >50% increase in demagnetization signal in nanorod-coated samples at pump fluences on the order of 0.1 mJ/cm2 due to surface plasmon-mediated localized electric-field enhancement, an effect which becomes more significant at higher laser fluences. We were able to qualitatively reproduce the experimental observations using finite-difference time-domain simulations and mean-field theory. This dramatic enhancement of ultrafast laser-induced demagnetization points to possible applications of nanorod-coated thin films in heat-assisted magnetic recording.

dimensionally-tuned to support LSPs near the peak laser frequency, the demagnetization can be increased by over 50% for ~4% AuNR coverage, without increasing the laser fluence. The AuNR coating functions in a similar capacity to NP transducers in HAMR recording heads, and the arrangement offers a possible solution to the thermal degradation problem in current HAMR prototypes by uniformly distributing or patterning the plasmon NPs across the surface of the recording medium, thus subjecting individual AuNRs to a small fraction of the overall thermal cycling.

Results
Colloidal 10 nm × 41 nm AuNR was drop-evaporated onto 20 nm ferromagnetic Ni 80 Fe 20 (permalloy) thin films to achieve an average density of 96 AuNR/μm 2 (a total AuNR cross-sectional area of 39360 nm 2 per μm 2 , or 3.94% areal coverage), with a standard deviation of 41 AuNR/μm 2 , as shown in the SEM image in Fig. 1(a). Due to capillary pressure, there is a highly non-uniform aggregation of AuNR at the edge of the evaporated spot ( Fig. 1(a), lower inset), and care was taken during subsequent experiments to avoid this edge formation. To independently verify the plasmon resonance effect of the AuNR coating, dark-field scattering spectra of the thin film samples were obtained with a white light source at 70 o incidence using a setup described elsewhere 23,24 . Molar extinction coefficient of the colloidal solution was measured using the Beer-Lambert law 25 . A stroboscopic pump-probe magneto-optic Kerr effect setup in the polar configuration, schematically shown in Fig. 1(b), was used to measure time-resolved out-of-plane magnetization, M z under the illumination of a femtosecond Ti:sapphire pulsed laser, tuned to the plasmon frequency of the AuNRs 26 . Figure 2(a) shows the dark-field scattering spectra of the AuNR-coated sample (red) normalized against the regular permalloy film (blue), as well as the molar extinction coefficient spectra of the  colloidal AuNR solution (green) and the Ti:sapphire laser (magenta). The AuNR-coated thin film shows a distinct spectral peak slightly below 800 nm, close to the central wavelength of the Ti:sapphire laser. The uncoated sample by comparison does not exhibit any discernable peaks over the entire (500-1000 nm) frequency range. The spectral peak of the AuNR-coated sample exhibits a slight blue-shift and significant broadening compared to the colloidal solution, which may be attributed to the modification of LSP due to interaction between nanorods and the close proximity of the permalloy substrate 27,28 . Simulations using a commercial finite-difference time-domain (FDTD) package (Lumerical Solutions, www.lumerical.com) reveals a qualitative agreement with experimental observations ( Fig. 2(b)).
Laser-induced ultrafast demagnetization signals in M z were recorded for a range of pump fluences, F ≈ 0.08 -0.26 mJ/cm 2 (315-1007 mW). Selected results are shown in Fig. 3 for uncoated (blue) and AuNR-coated (red) permalloy samples for different pump fluences. The characteristic sub-picosecond demagnetization, the subsequent picosecond remagnetization as well as the increase in demagnetization signal with fluence are in general agreement with existing literature [29][30][31][32][33] . A long scan range (~100 ps with 500 fs time-steps) was used in order to capture the slow remagnetization process. This temporal regime is orders of magnitude longer than the subpicosecond pulse duration and thermalization time 34 , therefore the remagnetization process can be adequately described by a single exponential expression 35 , where the characteristic remagnetization time τ is quantitatively defined as the time at which magnetization recovers by 63%.
Most interestingly, the results in Fig. 3 reveal an increase in ∆M z in the AuNR-coated sample compared to the uncoated sample at the same pump fluence. Plots of characteristic remagnetization times, τ against pump fluence are shown in Fig. 3(d). τ increases with increasing pump fluence, due to the increasing loss of magnetic correlation with increasing temperature 36 . For the AuNR-coated sample, τ is longer at all pump fluences, which complements the demagnetization data and indicates a higher 'effective temperature' in the LSP-enhanced thin films.
In order to better interpret these results, we performed first-order calculations of the localized AuNR field enhancement, and the subsequent heat generation and demagnetization in a FM thin film with 4% AuNR coverage. Using experimentally measured laser fluences F, the averaged temperature increase in the regular FM substrate after pulse absorption ∆T FM was estimated using where R py is the experimentally measured reflectance (scattering is ignored for the film sample), laser penetration depth l = 15 nm and C py and ρ py are the heat capacity and density of permalloy-80, taken from ref. 37. Given the scan range and temporal resolution (100 ps/500 fs) of the current investigation, thermalization (< 1 ps 34,35 ) was considered instantaneous. Intricacies resulting from the interplay between the various demagnetization and thermalization timescales are left for a future study. For FM film coated with AuNR, enhancement in heating originates from the enhanced electric field |E| inside the FM substrate at plasmon resonance and can be calculated as follows 38 : where Q is the heat generation, ω is the angular frequency of the laser, and ε 0 and ε are the vacuum and relative permittivity of the FM film, respectively. For a given incident electric field amplitude and polarization, E(r), and hence Q and ∆T FM , can be computed using Lumerical Solutions. To take into account random orientations of the AuNRs with respect to the linearly polarized pump pulse in our experiment, an extra factor of 0.5 was applied to the Q calculated for the case where AuNR is aligned in parallel to electric field polarization ( Fig. 4(a)), in order to better estimate an 'average' temperature increase. The capping layer around the colloidal AuNR (cetyltrimethylammonium bromide (CTAB)) was modeled as a 1 nm spacer layer with refractive index equal to that of air, which has been previously shown to be a reasonable assumption for thin CTAB layers in the near-field 39 . As a result of the field enhancement inside the AuNR, they act as sources of heat 40 and must be taken into account. COMSOL Multiphysics (version 4.3.0.233) was used to investigate conductive heat transfer from AuNRs to the FM layer using initial AuNR temperatures calculated from equation (2). The additional temperature increase in the FM layer in this case was found to be negligible over the demagnetization timescale (~ps), due to the presence of the CTAB ligand and the small area of contact between the AuNR and the FM film.
Using calculated values of ∆T FM , ∆M z at different fluences were found for both regular and AuNR-coated permalloy substrates using the temperature-dependence of magnetization, M(T) ~ (1 -T/T C ) β (Fig. 4(b)), where Curie temperature T C = 860 K for permalloy 41 and critical exponent β = 0.5 from mean-field theory 42 .
The fluence dependence of demagnetization from both experiment and modeling are presented in Fig. 5. There is a consistent enhancement in ∆M z for AuNR-coated samples over the entire experimental fluence range. At higher pump fluences, this enhancement becomes more significant, and ∆M z for the AuNR-coated sample exhibits divergent behavior due to the increased curvature M(T) at temperatures approach T C (Fig. 4(b)). At the highest experimental pump fluence (F ~ 0.26 mJ/cm 2 ), ∆M z in the AuNR-coated sample is increased by ~60% compared to the uncoated sample. By extrapolating the linear fit in Fig. 5(a), it was found that the uncoated sample would require a pump fluence F ~ 0.42 mJ/cm 2 in order to achieve the same ∆M z as the AuNR-coated sample at F ~ 0.26 mJ/cm 2 . Despite its simplicity, our model calculations were able to qualitatively reproduce the experimental results ( Fig. 5(b)). We note that the simulation does not take into account the variation in density and orientation of the drop-evaporated nanorods, or thermal diffusion to the surroundings, leading to an over-estimation in demagnetization.
In conclusion, we demonstrated the LSP-enhancement of laser-induced ultrafast demagnetization on permalloy thin films coated with drop-evaporated colloidal AuNRs supporting LSP near the peak laser frequency. Compared to the uncoated sample, an increase in demagnetization signal of > 50% was observed in the AuNR-coated samples with 4% AuNR coverage, which increases with increasing laser fluence. Despite the low areal coverage of AuNR, LSP-enhanced electric-field intensity in the permalloy substrate in the vicinity of AuNR contributes disproportionately to the overall demagnetization signal. We were able to qualitatively reproduce the experimental results with FDTD modeling and mean-field theory. , and found to be 20.348 nm, with an average roughness of 0.327 nm. 10 μL of commercial monodisperse 10 nm × 41 nm colloidal AuNR solution (Nanopartz, 7.24 × 10 11 /mL, CTABcapped) with longitudinal plasmon resonance wavelength λ = 808 nm was drop-cast onto the film surface and allowed to evaporate under closed ambient conditions to minimize density variation and band formation 43 . AuNR density and variability were measured by visually inspecting 3 × 3 μm 2 areas of the SEM images of the sample.
Experimental methods. In order to trigger ultrafast demagnetization, a 76 MHz Ti:sapphire laser (Coherent Mira 900) pump beam with 795 nm central wavelength and 135 fs pulse duration was focused on a r ≈ 40 μm spot, for a maximum pulse fluence F ≈ 0.33 mJ/cm 2 (~16 nJ/pulse). This fluence is sufficiently large to induce measurable demagnetization, but does not melt the AuNRs or cause a significant, permanent temperature increase during measurement 44 . The ratio of pump to probe intensity at sample surface was > 20:1. The probe beam was modulated at 300 Hz using a chopper and was focused on an overlapping area with r ≈ 10 μm with the help of a CCD camera. When measuring AuNR-coated samples, care was taken to position the probe beam over areas on the sample with close to average AuNR density. The delay between pump and probe was mechanically controlled via a 220 mm (1466 ps) optical delay line (Thorlabs ODL220-FS), with a delay precision of ± 0.67 fs. An external field H = 140 kA/m inclined at 30 o to the normal was applied to create a canted, out-of-plane saturation magnetization. Transient changes in M z in terms of Kerr rotation θ K , averaged over the 10 μm probe spot in the Py film, were measured using a balanced photodiode optical bridge detector, which isolates the Kerr and the reflectivity signals 45 . The detector system consists of a polarizing beam splitter (Wollaston prism) and a pair of silicon quadrant photodiodes (Thorlabs PDQ80A) with lock-in amplification referenced at the modulation frequency of the probe beam. The difference between two photodiode signals is proportional to the Kerr rotation. The experiment was carried out at room temperature.