Ultrafast Magnetization Dynamics of Chemically Synthesized Ni

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Ultrafast Magnetization Dynamics of Chemically Synthesized Ni Nanoparticles Bivas Rana, and Anjan Barman J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b04759 • Publication Date (Web): 09 Jul 2015 Downloaded from http://pubs.acs.org on July 11, 2015

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The Journal of Physical Chemistry

Ultrafast Magnetization Dynamics of Chemically Synthesized Ni Nanoparticles

Bivas Rana and Anjan Barman*

Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 098, India

Abstract We report ultrafast magnetization dynamics of chemically synthesized Ni nanoparticles by all-optical timeresolved magneto-optical Kerr effect microscope. Ni nanoparticles were assembled on Si substrate with four kinds of microstructural arrangements to study its impact on the ultrafast magnetization dynamics. Being an intrinsic material property ultrafast demagnetization time does not vary with the arrangement geometry while fast and slow relaxation times show a significant variation due to the distribution of size, shape and surface properties of nanoparticles and interface between nanoparticles and Si substrate. The precessional magnetization dynamics shows a number of non-uniform collective modes in each sample. The resonant frequencies and mode numbers show a strong dependence on bias magnetic field and arrangement geometry. The resonant frequency decreases as the microstructure changes from chain-like to random agglomerate of nanoparticles due to the formation of closure domain structures. The time-dependent three-dimensional micromagnetic simulations with finite-element method are further required for quantitative reproduction and understanding the precessional modes.

*To whom correspondence should be addressed. Email: [email protected], Tel: +91-33-23355706, Fax: +91-33-23353477. Keywords: Magnetic Nanoparticles, Ultrafast Magnetization Dynamics, Time-resolved Magneto-optical Kerr Microscopy, Spin Waves

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1. Introduction The magnetic nanoparticles have profound importance like other magnetic nanostructures due to their potential multidisciplinary applications. Magnetic data storage1 is one among those applications. One of the fundamental issues in magnetic data storage is to achieve a fast magnetization switching (reversal) of the data bits. Current data storage technology relies upon domain wall motion, which limits the operational speed in the nanosecond regime. New strategies are required to overcome the current limitations of magnetization reversal processes. Consequently, new topics like magnetization switching through precessional dynamics,2,3 ultrashort laser pulse assisted switching,4 switching by spin polarized current,5 rf magnetic field assisted ultrafast switching6 and voltage controlled magnetization switching7 are becoming subjects of intense research. Periodically arranged magnetic nanoparticles could be the ideal candidate for future spintronics devices where the spin-waves or collective precessional magnetization dynamics of nanoparticles in picosecond time scale can be used for data transformation. Therefore a thorough understanding and control of ultrafast magnetization dynamics in magnetic nanoparticles is very important for their applications in spintronics and magnetic data storage devices.8,9 Unlike lithographically patterned ordered nanomagnets and their arrays, only few studies are found on the ultrafast magnetization dynamics of magnetic nanoparticles. Those studies are mainly focused on the ultrafast switching or reversal of magnetization,6 the precessional magnetization dynamics10 and femtosecond pulsed laser induced ultrafast demagnetization. The efforts have also been made towards the investigation of the role of various physical parameters like laser fluence,11 annealing temperature,12 and size11 and surface properties of nanoparticles13 on their ultrafast magnetization dynamics in various time scales. Magnetic nanoparticles with higher magnetic anisotropy could be suitable for high density magnetic data storage devices to retain information over a longer time scale.

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However, as the magnetic anisotropy increases the dc switching magnetic field increases accordingly. The magnetization switching in magnetic nanoparticles can be triggered at a very low dc magnetic field when a rf magnetic field is applied in addition to it.6 Some studies show that the ensemble of iron nanocrystals14,15 embedded within a matrix of SiO2 can be very important candidate as they shows some interesting properties. Their in-plane and outof-plane switching dynamics are quite different and independent of the magnitude of the inplane bias magnetic field. They exhibit a very strong and fast out-of-plane magnetization response due to strong dipole interactions between the particles and very little dependence on the particular structure and arrangement of the particles. Their unique properties including high resonance frequency, strong effective damping and electrically insulating character make them very favorable for applications in sensors15. The femtosecond pulsed laser can be very useful to demagnetize the nanoparticles within few hundreds of femtosecond. The percentage of demagnetization can be controlled very systematically with the pump fluence. 11 The surface spins of the nanoparticles play a strong role on the spin-lattice relaxation mechanism.13 Therefore the size of the nanoparticles and the properties of the interface between magnetic nanoparticles and substrate determine relaxation times of magnetization after ultrafast demagnetization. For example, the rate of the fast and slow recovery component increases with the decrease of size of the nanoparticles.11,13 The ultrafast magnetization dynamics of superparamagnetic nanoparticles, embedded in a dielectric matrix shows a strongly damped precessional motion10 due to enhancement of damping at the metal dielectric interface. This proposes a possibility of controlling the spin-lattice relaxation time by modifying the surface and interface of nanomaterials. The precessional magnetization dynamics of nanoparticles strongly depend upon the quality of crystalline structure which can be controlled by annealing temperature.12 A previous report shows that the magnetization

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trajectory in nanoparticles can be controlled locally to a predefined path by applying a sequence of two perpendicular magnetic pulses.16

Magnetic nanoparticles often tends to agglomerate and form chains and clusters17,18 in order to minimize the surface energy associated with high surface to volume ratio and magnetostatic energy. These one dimensional chains of nanoparticles and the chains with different configurations are very important due to their possible applications in future spintronic devices. Therefore, understanding the ultrafast magnetization dynamics of magnetic nanoparticles in form of clusters and chains is very important for their successful implementation in future technologies. Though there are some reports on the quasistatic magnetization reversal dynamics of magnetic nanoparticles with these kinds of assembling geometry,19-21 no attempts have been made till now to study the magnetization dynamics of magnetic nanoparticles in the form of clusters and chains. Here, we investigate the ultrafast magnetization dynamics in chemically synthesized Ni nanoparticles with their different assembling geometries. We will explicitly study how the ultrafast magnetization dynamics in different time scales are influenced by the assembling geometry of the nanoparticles.

2. Experimental Methods To study the ultrafast magnetization dynamics, Ni nanoparticles with four different geometries (S1, S2, S3 and S4) were prepared by the chemical reduction of nickel chloride (NiCl2, 6H2O) by hydrazine hydrate (N2H5OH) in the presence of sodium hydroxide (NaOH).20, 22 The nanoparticles were coated with PEI (0.4 wt% for S1; 1 wt% for S2; and 4.5 wt% for S3) to help the formation of various types of assemblies. The nanoparticles were dispersed on bare Si(100) substrates by drop casting from a colloidal solution. The scanning electron micrographs (Figure 1(a)) from four different samples (S1, S2, S3 and S4) show the

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formation of chains and clusters of different configurations. S1 shows long chains with a single particle along the width of the chain with negligible branching, while S2 shows broad chains formed of a number of particles along the width. S3 shows shorter chains with plenty of ‘X’- and ‘Y’-like branching and S4 shows largely random arrangement of the particles with no preferred shape. However, the average size of the constituent particles is about 50 nm in all four samples. The observed microstructures are randomly arranged throughout the sample dispersed on the Si substrate. The EDX spectrum confirms the chemical purity of nanoparticles except for a little trace of oxygen, while the XRD pattern confirms the fcc lattice structure of Ni.20 The ultrafast magnetization dynamics was measured by using time-resolved magnetooptical Kerr effect (TRMOKE) microscope based upon a two-colour collinear pump-probe setup.23 The second harmonic (λ = 400 nm, pulse width ≈ 100 fs) of a Ti-sapphire oscillator output (Tsunami, Spectra Physics, pulse width ≈ 70 fs) was used to pump the samples, while the time delayed fundamental (λ = 800 nm) laser beam was used to probe the dynamics by measuring the polar Kerr rotation by means of a balanced photodiode detector, which completely isolates the Kerr rotation and the total reflectivity signals. The pump power used in these measurements is about 15 mJ/cm2, while the probe power is much weaker and is about 2 mJ/cm2. Since our setup is based on magneto-optical Kerr effect measurement i.e., in the backreflected geometry, we had to take some precautions for this measurement. The dispersed nanoparticles on the Si substrate offer more scattering than specular reflection for the pump and probe beams. This degrades the reflectivity and Kerr signal in different ways. First, only a small fraction of the scattered probe beam can be efficiently collected and sent to the detector, which makes the total intensity of the light on the photodiodes very small. Second, possible depolarization effect of the scattered light can reduce the effective Kerr signal.

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Third, and most damaging effect is the possibility of reaching of some scattered pump light in the detector. Since the pump beam is modulated by the chopper at 1-2 kHz frequency, which is also the reference frequency to the lock-in amplifier, even small amount of pump light reaching the detector can saturate the lock-in signal and disable the measurement of Kerr effect of the reflected probe beam. To overcome these problems, a 10 nm thick nonmagnetic capping layer of SiO2 was deposited on the Ni nanoparticles samples by rf magnetron sputtering at a base pressure of 3 × 10-8 Torr and at an Ar pressure of 10 mTorr. The SiO2 capping layer is optically transparent at the wavelengths of pump and probe beams. It also reduces the background signal significantly by smoothing out the sample surface. Furthermore, these SiO2 layers protect the samples from oxidation due to heating of the samples during the pump-probe measurement. The bias magnetic field (Hb = component of bias field along sample plane), was tilted 15° out of the plane of the sample to have a finite demagnetizing field along the direction of the pump pulse, which is eventually modified by the pump pulse to induce precessional magnetization dynamics within the nanoparticles. The pump beam was chopped at 2 kHz frequency and a phase sensitive detection of the polar Kerr effect of the plane polarized probe beam was made by using a lock-in amplifier. It is well known that for Ni Kerr rotation is smaller than the Kerr ellipticity and hence for the TRMOKE measurements of the Ni nanoparticles, we have preferred to measure the Kerr ellipticity. The complex Kerr rotation can be expressed as

2  k  k   in  n  , where the real part is the Kerr rotation and 1 

the imaginary part corresponds to the Kerr ellipticity. If we introduce a quarter wave plate in front of the optical bridge detector it will produce a π/2 phase difference between the ‘s’ and ‘p’ components so that the analyzing polarizer will see the complex Kerr rotation as



2 n  n   ik  k  i.e., the Kerr rotation and ellipticity are interchanged.24 By 1 

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measuring the (A – B) signal from the optical bridge detector as a function of the time delay between the pump and the probe beams, we then effectively measure the time-resolved Kerr ellipticity, which enhances the signal-to-noise ratio of the time-domain data as compared to the time-resolved Kerr rotation data from the same Ni nanoparticles.

3. Results and Discussions

S1

Kerr ellipticity (arb. unit)

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S2

S3

(a)

0

5

10

15

6.83 ps

S2

2.30 ps

S3

4.27 ps

S4

(b) S4

S1

20

25

(c) 0

5

10

3.71 ps 15

20

25

Time (ps)

Time (ps)

Figure 1. (a) Typical scanning electron micrographs of the Ni nanoparticles with different cluster geometry. (b) Time-resolved Kerr ellipticities showing ultrafast demagnetization and fast relaxation of the Ni nanoparticle samples. (c) Only the relaxation parts of the Kerr ellipticities are shown. The black solid lines are the fittings with a single exponential decay function (Eq. 1).

Figure 1(b) (2nd column) shows the time-resolved Kerr ellipticities revealing ultrafast demagnetization and the fast relaxation thereafter measured from samples S 1, S2, S3 and S4. For measuring the demagnetization and the fast relaxation times, we recorded Kerr ellipticity up to a time delay of 25 ps at a time step of 100 fs. The typical sample geometries are shown in Figure 1(a). Figure 1(b) shows very clear Kerr ellipticity signals for all the samples. The graphs show that the Ni nanoparticles are demagnetized within about 500-600 fs and the

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sample geometry does not affect the demagnetization time significantly. The demagnetization is believed to occur due to the thermalized population of spins above the Fermi level.25,26 The thermalization time is believed to be an intrinsic property of the material and hence independent of extrinsic parameters like sample geometry. The measured time constants corresponding to different dynamical regimes for the four samples studied here are listed in table 1. Sample

Demagnetization time

Fast relaxation time 1

Slow relaxation time

geometry

(fs)

(ps)

2 (ps)

S1

500

6.83

286

S2

600

2.30

Could not measure

S3

500

4.27

900

S4

500

3.71

140

Table 1. The measured time constants corresponding to different dynamical regimes for the four samples are listed

To find out the fast relaxation times (1), the relaxation parts are separated out from demagnetization part and are fitted with a single exponential function as shown in Figure 1(c). The single exponential decay function can be expressed as

M (t )  M (0)  Ae

 t

1

,

(1)

where M(0) is the initial magnetization, A is the relaxation coefficient and 1 is the fast relaxation time. Table 1 shows that the values of 1 vary from 2.30 to 6.83 ps for four different sample geometries. It is believed that the faster relaxation (1) of magnetization

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occurs after the ultrafast demagnetization because spins exchange energy and angular momentum with the lattice through spin-lattice or spin-orbit interaction. 1 may vary from sub-ps to several ps depending upon the strength of the spin-orbit coupling and the specific heats of the spins and phonons.27-29 The relaxation time also depends on the density of laser excitation27,28 and magnetocrystalline anisotropy. Here, all of these parameters remain unchanged except the strength of the spin-orbit interaction. In ferromagnetic solids, this spinorbit interactions are not only determined by the intrinsic atomic spin-orbit coupling, but also by the local lattice structure and symmetry.13, 30 In nanomagnets, percentage of surface spins is larger than the bulk materials. Hence, the rate of energy and momentum transfer from spin to lattice in nanomagnets is significantly influenced by the surface spins.13 The surface spins of chemically synthesized nanoparticles are attached to different ligand fields unlike the interior spins due to the structural discontinuity at the surface. In these nanoparticles, the effective spin-orbit energy (Eeff) is of the order of ξ2/ΔE, where ξ is the atomic spinorbit coupling parameter and ΔE is the ligand field splitting energy.13 The surface spins are attached to the weak ligand fields either due to formation of oxide layer or layer of chemical bi-products unlike the interior spins which are attached with stronger crystalline field. Therefore, the surface spins are expected to have much larger effective spin-orbit coupling compared to the interior spins. This signifies that the magnetization relaxation for surface spins is faster than the interior spins.11 Therefore in our samples the initial part of the first relaxation process has a major contribution from the relaxation of surface spins, whereas the later part is mainly contributed by the relaxation of interior spins. In nanoparticles, the percentage of surface spins also increases with the decrease in particles size. Hence, the fast relaxation time (1) of smaller particles should be faster than the larger particles. In our case, there is a small size and shape distribution in the nanoparticles and there is a small size distribution within the nanoparticles for each sample, which also varies from one sample to

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another. This is probably the reason for obtaining a variation in 1 for different samples. The presence of sample roughness and defects may also play an important role in the variation of

1 to some extent. In addition, different environment of the nanoparticles in different samples due to different clustering geometry also contributes to the variation in τ1. However, it is difficult to isolate the above effects systematically due to the complicated morphology of the samples. To find out the longer relaxation times, the Kerr ellipticity data for the samples were measured up to 1500 ps time delay at a time step of 5 ps. Unfortunately, we could not measure the slow relaxation from sample S2 due to the presence of very large background coming during the longer measurement time. The Kerr ellipticity data for S 1, S3 and S4 are shown in Figure 2(a). To find out the long relaxation times, the Kerr signals are fitted with a bi-exponential decay function given by

M (t )  M (0)  Ae

t

1

 Be

t

2

,

(2)

where M(0) is the initial magnetization, A, B are the relaxation coefficients and 1 and 2 are the fast and slow relaxation times, respectively. The fitted curves are shown by black solid lines in Figure 2(b). We observed a significant variation (between 140 and 900 ps) in the longer relaxation time (2) for three different samples. The second or longer relaxation process mainly occurs due to the diffusion of electron and lattice heat to the surroundings (in this case the neighboring nanoparticles and Si substrate).27,28 However, the initial part of the second relaxation process may also have a small contribution from the relaxation of interior spins via spin-orbit coupling. The diffusion rate depends upon the type of substrate and the physical contact between the excited nanoparticles with their neighboring nanoparticles and Si substrate. As the conductivity of Ni is larger than the Si, therefore the nanoparticles mostly surrounded by neighboring nanoparticles are expected to be relaxed faster than the nanoparticles directly attached to the Si substrate with less number of neighbors. Though, the 10


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bottom layer of neighboring nanoparticles may not have significant role due to the finite penetration depth of laser beam. Of course the contact area and the contact quality with the neighboring nanoparticles also play a crucial role in this case. For sample S4 the nanoparticles form cluster where the nanoparticles are surrounded by a number of nanoparticles compared to the other samples. Therefore the second relaxation time for S4 is expected to be smaller than other samples. However the nanoparticles in S1 and S3 are coated with PEI as described before. The coating layer for S3 is expected to be thicker than S1 as higher concentration of PEI was used. Therefore the heat diffusion rate for S3 should be smaller than S1. Hence, 2 for S3 is larger than that for S1.


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(a) 0

S1

286 ps

S3

900 ps

(b)

S4

500

1000

1500 0

140 ps 500

1000

1500

Time (ps)

Time (ps)

Figure 2. (a) The time-resolved Kerr ellipticity data for samples S1, S3 and S4 are shown for a longer time scale (up to 1500 ps). (b) The data are fitted with the bi-exponential decay function (black solid lines) and the extracted long relaxation times (2) are mentioned in the graphs.

The layer thickness of the samples may also have an influence on the relaxation times, especially on second relaxation time. As the nanoparticles were arranged by drop casting a diluted colloidal solution of nanoparticles on Si substrate, the average layer thicknesses of all four kinds of samples should be similar. Moreover the thickness of the samples are much larger than the penetration depth of the lasers, which is less than 15 nm, while even a single nanoparticle has diameter of about 50 nm. The second relaxation occurs primarily by

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diffusion of the energy into the neighbouring nanoparticles and the substrate. Hence, due to the much larger thickness of the samples compared to the laser penetration depth, there is practically no influence of the sample thickness on the relaxation dynamics. Next, we study the precessional magnetization dynamics of the Ni nanoparticles. First, we study how the precessional dynamics varies with the bias field magnitude (Hb). Figure 3(a) shows a scanning electron micrograph of sample S1. The geometry of the bias magnetic field and schematics of the pump and the probe beams are shown on top of the figure. The bias field (Hb) of different magnitudes was applied while keeping its direction unchanged. The hysteresis loop (M-H) of the sample is shown in Figure 3(b). Solid circular red points on

Magnetization (M/Ms)

HHbb

1 m

1.0

200

0.5

100

0.0

0

-0.5

-100

-1.0 -1500 -1000

(a)

-500

0

H (Oe) 3

1000

-200 1500

(b)

3

2

3

880 Oe

720 Oe

Frequency (GHz)

Hb = 1000 Oe

2 1

Power (arb. unit)

500

Magnetization (emu/cc)

top of the hysteresis loop denote the magnetization of the sample at different bias field


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2

6 4

Mode 1 Mode 2 Mode 3

2 0

600

800

1000

Hb (Oe)

(d)

520 Oe

2

(c) 0.0

0.5

1.0

1.5

Time (ns)

2.0

0

4

8

12

Frequency (GHz)

Figure 3. (a) Scanning electron micrograph of sample S1. The geometry of the bias field and the pump and the probe spots are shown schematically on top of the figure. (b) Hysteresis loop (M-H) of the sample is shown. Solid circular points on top of the hysteresis loop denote the static magnetization values of the sample at different bias field values, for which the precessional dynamics were measured. (c) In left column, background subtracted Kerr ellipticity signals are shown for the same

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sample as a function of Hb. The right column shows corresponding FFT power spectra. The peak numbers are assigned to the FFT power spectra. (d) The frequencies of the observed resonant modes are plotted as a function of Hb.

values, for which the precessional magnetization dynamics were measured. The hysteresis loop shows that as the magnetic field decreases from 1000 Oe to 520 Oe (i.e., the range of the bias field values used in the experiment) the magnetization (M) changes from 162 emu/cc to 144 emu/cc (i.e., from 81% to 72% of MS). In our experimental setup, the magnetic field is limited up to 2.5 kOe while the saturation magnetic field is around 3.2 kOe. Therefore, the dynamics was probed with Hb values below the saturation field. Precessional magnetization dynamics was measured by recording the time-resolved Kerr ellipticity for time delay up to 2000 ps at time steps of 5 ps. The background subtracted Kerr ellipticity data are shown in the left column of Figure 3(c). Though the Kerr signals look noisy, the general features of the dynamics can be extracted. The right column shows corresponding FFT power spectra. The peak numbers are assigned to the FFT power spectra. The FFT power spectra show a number of well resolved collective precessional modes at all values of bias fields. The frequencies of the resonant modes are plotted as a function of the bias fields (Hb) and are shown in Figure 3(d). The graph shows different branches of frequencies. The frequency of each branch decreases monotonically with the decrease in bias field. The resonant frequencies depend upon the total effective field (Heff) of the sample at the positions where the dynamics are probed. The total effective field is composed of the applied bias field (Hb), demagnetizing field (Hd) due to the sample shape and magnetization, the stray magnetic field from the neighbouring particles (Hs), magnetocrystalline anisotropy field (Ha) and the exchange field (He). In our measured samples, Ha and He are not expected to vary significantly, but Hb and Hd and Hs varies. The observed frequency branches do not fit with the analytical Kittel formula for the uniform or coherent resonant mode (not shown). In Kittel formula, the magnetization of the samples is assumed to be uniform and also constant with 13



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the change in the bias field magnitude i.e., the bias field should be above saturation. Moreover the precession of the magnetization of the nanoparticles under probe should be inphase or coherent. However, in the present measurement the magnetization varies with the bias magnetic field. In addition, very complicated domain configurations occur at varying magnetic fields for all these samples as shown in reference 20. These complicated magnetic ground states lead towards a number of nonuniform (incoherent) resonant modes depending upon the local spin configuration. The uniform coherent resonant mode may not be obtained even though the measurements are done under the bias magnetic fields above the saturation value, because the effective magnetic field varies from particle to particle mainly due to the complex structure of Hs. However the precessional frequency will increase monotonically with the increase of magnetic field above saturation value, though the variation of frequency with magnetic field may still not follow the Kittel formula for uniform coherent precessional mode. The quantitative modeling of the observed resonant modes is found to be difficult at present due to the lack of the computational resources. We have further measured the precessional dynamics of Ni nanoparticles arranged in different geometries. We could measure the precessional dynamics from samples S1, S3 and S4. However, the measurement of precessional dynamics from sample S2 was not possible due to smaller signal-to-noise ratio. Figure 4 shows the FFT power spectra of background subtracted Kerr ellipticity data for three samples (S1, S3 and S4) at a fixed value of Hb = 1 kOe applied in the plane of the samples. The FFT spectra again reveal a number of nonuniform collective modes and the mode frequencies vary significantly with the sample geometry. A general trend is observed that the frequencies of the modes decrease from S1 to S4. The reason behind that is probably the variation in magnetic ground state configurations with the change in sample geometry. As the sample is changed from S1 to S4, more closure domain

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configurations tend to occur,20 which may lead to the lower value of local magnetization and hence the corresponding mode frequencies.

S1 Power (arb. unit)

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S3

S4 0

4

8

12

Frequency (GHz)

Figure 4. The FFT spectra of background subtracted time-resolved Kerr ellipticity data are shown for three samples (S1, S3 and S4) at a fixed value of Hb = 1 kOe applied in plane of the samples.

As explained for the case of bias field dependence of precessional mode frequencies, the quantitative reproduction of the modes and their variation with the cluster and chain geometry requires detailed time-dependent three-dimensional micromagnetic simulations. However, due to the limitation of computational resources it was not possible at present and will be a subject of future research. However, we obtained a qualitative understanding about the precessional modes from the magnetic ground state configurations.

4. Conclusions We have studied the ultrafast magnetization dynamics of single domain Ni nanoparticles with distinctly different local microstructural arrangements. The magnetization dynamics were measured for four such microstructures, where the constituent nanoparticles are arranged in long chain-like, bundle-like, dendrite-like and random agglomerate arrangements. The ultrafast magnetization dynamics were measured by an all optical TRMOKE set up. The experimental results show that the ultrafast demagnetization time does

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not depend on the sample geometry as it is an intrinsic property of material. However, a variation in the fast relaxation time (1) is observed due to the finite size and shape distribution of the nanoparticles and also variation in the surface properties. A significant variation in the slow relaxation time (2) is also observed, which is mainly attributed due to the variation of nanoparticle environment and interface properties between the nanoparticles with their neighboring nanoparticles and Si substrate. We have also measured the picosecond precessional dynamics for those samples. The precessional frequency spectra for long chains with single particle along the width show a systematic decrease in the resonance frequency with the decrease in the bias field magnitude, where mainly three resonant frequency branches are observed. The decrease in the frequency of each branch is steeper than as expected from Kittel formula for uniform magnetization. This is because the bias field values were below the saturation field value and the magnetization also decreases with the decrease in bias field. The precessional frequency spectra for samples with different geometries also show a significant variation. In general, the resonant frequency decreases as we go from parallel chains (S1) to random agglomerate of nanoparticles (S4). This is qualitatively attributed to the decrease of local magnetization value due to formation of more closure domain structures as the sample is varied from S1 to S4. The observed resonant modes are basically nonuniform collective modes of the ensembles of nanoparticles. Quantitative reproduction and understanding of the precesional modes would require detailed timedependent three-dimensional micromagnetic simulations with finite-element method, which is computationally very demanding and is not possible at present. However, we obtained a qualitative understanding about the variation of the resonant modes with the bias field values as well as the geometry of the microstructural arrangements by considering their magnetic ground states. The study of precessional magnetization dynamics in one dimensional chains

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of nanoparticles and the chains with different branches are very demanding due to their possible applications in future spintronics devices.

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Ultrafast Magnetization Dynamics of Chemically Synthesized Ni

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