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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 4 — Feb. 18, 2008
  • pp: 2322–2335
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Wideband detection of transient solid-state dynamics using ultrafast fiber lasers and asynchronous optical sampling

Vladimir A. Stoica, Yu-Miin Sheu, David A. Reis, and Roy Clarke  »View Author Affiliations


Optics Express, Vol. 16, Issue 4, pp. 2322-2335 (2008)
http://dx.doi.org/10.1364/OE.16.002322


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Abstract

We demonstrate optical time-domain spectroscopy from femtoseconds to nanoseconds using an ultrafast dual-fiber-laser system with kilohertz continuous scanning rates. Utilizing different wavelengths for the pump and probe beams, we exploit this system’s broad range of timescales for quantitative studies of thermal transport and the detection of coherent spin and lattice excitations in epitaxial magnetic thin films. The extraordinary temporal dynamic range provides a way to connect the fast and slow timescales in the observation of dissipation and decoherence processes.

© 2008 Optical Society of America

1. Introduction

Time-resolved pump-probe optical spectroscopy based on ultrafast lasers is often used to study laser-induced transient-dynamics in solid-state materials. An intense laser-pump pulse induces a fast perturbation of the material properties, the evolution of which can be studied through concomitant changes in the optical properties, as measured by a time-delayed probe pulse. Typically the probe pulse is derived from the pump, and delayed by mechanical means [1

1. B. Perrin, “Investigation of short-time heat transfer effects by an optical pump-probe method,” in Microscale and Nanoscale Heat Transfer, topics in Applied Physics, S. Voltz, ed., (Springer, Berlin, 2007), Vol. 107, pp. 333–359. [CrossRef]

]. In this paper, we demonstrate a new approach for performing dynamic measurements over a very large temporal range using a newly developed instrument based on ultrafast fiber lasers and asynchronous optical sampling (ASOPS) [2

2. P. A. Elzinga, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump probe spectroscopy by asynchronous optical-sampling,” Appl. Spectrosc. 41, 2–4 (1987). [CrossRef]

]. The potential of the technique is illustrated by measurements on the thermal, mechanical, and magnetic properties of epitaxial iron thin films and their supporting substrates. Particular emphasis is placed on coherent magnetization oscillations and their relaxation. A key aspect of this is how to separate the spin-wave effects from the non-magnetic contributions to the transient optical response.

Optical pump-probe spectroscopy applications are already well developed for characterizing the transient dynamics of materials. Examples include acoustic wave propagation, thin film thickness and adhesion to the substrate, the evaluation of thermal properties such as thin film thermal conductivity and thermal boundary resistance [3

3. G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006). [CrossRef]

], and the generation and detection of coherent optical phonons [4

4. R. Merlin, “Generating coherent THz phonons with light pulses,” Solid-State Commun. 102, 207–220 (1997). [CrossRef]

]. These measurements are traditionally performed using slow mechanical scanning of an optical retro-reflector to achieve the pump-probe time delay. This limits the speed and efficiency of data acquisition, especially when extended time delays are required. In the present study, based on the ASOPS technique with kilohertz scanning rates, we present a much improved experimental approach covering time delays from femtoseconds to several nanoseconds. We emphasize that the scanning over several nanosecond time delays takes full advantage of the ASOPS technique by eliminating the need for mechanical translation over large distances, which usually requires systematic error compensation [5

5. W. S. Capinski and H. J. Maris, “Improved apparatus for Picosecond Pump-and-Probe Optical Measurements,” Rev. Sci. Instrum. 67, 2720–2726 (1996). [CrossRef]

].

2. Experimental details

The experiments reported here are motivated by a need to connect long and short time scales associated with the relevant excitation processes in epitaxial magnetic thin films. These include optically stimulated thermal transport, lattice excitations and spin dynamics. The ultrafast pump-probe system presented here is an ideal instrument to access the disparate time-scales of these coupled processes.

Multicolor (non-degenerate) pump-probe measurements were carried out using a specially designed dual-fiber-laser system from Menlo Systems GmbH [9]. A schematic of the experimental arrangement is shown in Fig. 1, including the dual-laser system, the electronic detection scheme and the key optical components. The dual-laser system uses two separate passively mode-locked lasers based on Er-doped fiber, with each laser providing output pulses of 1.5 nJ energy and 80 fs duration at the fundamental wavelength of 1560 nm. The two lasers have slightly different repetition rates, with one laser (the slave) locked to the other (the master) with a fixed offset frequency. The slave laser is frequency doubled by second harmonic generation (SHG) to 780 nm wavelength, with a pulse duration of 150 fs and 0.4 nJ energy. A residual beam at 520 nm corresponding to third harmonic generation (THG) is also available at a reduced level of <0.01 nJ. The SHG beam from the slave laser, was used mostly as the probe, while, in some cases, the THG can still be used for optical probing at a secondary wavelength.

Fig. 1. Schematic of the experimental setup with collinear pump-probe geometry: RRE - repetition-rate synchronization electronics; BS - beam splitter; DM - dichroic mirror; PM - parabolic mirror; CF - color filter; D, D1, D2 - detectors; SFG – sum-frequency generation.

Continuous scanning in the time-domain was achieved by stabilizing the repetition rate asynchronism (frequency difference) between the two mode-locked lasers. The individual laser repetition rates are close to 100 MHz while being stabilized [9] to a small and constant difference repetition frequency (DRF), selectable between 0.2-7 kHz. The fixed rate difference between the pump and probe lasers ensures that a continuous variable time delay is realized [2

2. P. A. Elzinga, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump probe spectroscopy by asynchronous optical-sampling,” Appl. Spectrosc. 41, 2–4 (1987). [CrossRef]

, 6

6. E. Lill, S. Schneider, and F. Dorr, “Rapid optical sampling of relaxation-phenomena employing two time-correlated picosecond pulse trains,” Appl. Phys. 14, 399–401 (1977). [CrossRef]

–10] between the two laser pulses. The maximum temporal scanning interval (τ s) is the time-interval between pump pulses, which is given by the inverse frequency of the master laser (τ s=1/f1). The temporal resolution is determined by the most significant of: the limited detector bandwidth, the laser pulse duration and the pulse-to-pulse jitter. The detector bandwidth contribution is taken into account through τ b=Δf/f1B [8

8. A. F. Bartels, F. Hudert, C. Janke, T. Dekorsy, and K. Kohler, “Femtosecond time-resolved optical pump-probe spectroscopy at kilohertz-scan-rates over nanosecond-time-delays without mechanical delay line,” Appl. Phys. Lett. 88, 041117 (2006). [CrossRef]

], where B is the effective bandwidth of the detection and corresponds to 50 MHz in the present studies. A computer-based digital-oscilloscope (Compuscope 14200, GaGe Applied Technologies) with 100 MHz analog bandwidth is used for data acquisition, which records the detector response with a refresh rate given by DRF. The sampling rate of the digital oscilloscope corresponds to a 10 ns interval, which coincides with 1/f1 to provide direct conversion to τ s in the experiment. Hence, with our experimental apparatus, the corresponding bandwidth limit to the time resolution (τ b) varies from 40 fs to 1.4 ps based on the accessible Δf values provided by the dual-laser system. Depending on the particular measurement resolution requirements, a suitable value for Δf was chosen during the experiment for time delay scanning, and the accumulation and averaging of 104 - 107 temporal traces was used for noise suppression.

To optimize our temporal resolution and accomplish real time triggering during the data acquisition process, we have constructed an optical cross-correlator using a beam splitter derived portion from the master laser together with a residual beam at the fundamental wavelength (1560 nm) from the SHG unit of the slave laser. The two laser beams are focused by a 90° off-axis parabolic mirror on a beta barium borate (BBO) crystal to obtain a sum frequency generated (SFG) cross-correlation beam at 780 nm, monitored by an amplified photodiode with 150 MHz analog bandwidth. The mirror-based focusing helped to increase the efficiency of SFG generation compared with lens-based focusing by eliminating chromatic aberrations to provide a better beam overlap inside the BBO crystal. The measured temporal width of the cross correlation signal is 160 fs.

Fig. 2. Coherent optical phonon reflectivity oscillations detected in an Sb thin film grown on (111) Si substrate. Pump (1560 nm) and probe (789 nm) beams are both s-polarized and collinear. FFT in the inset corresponds to the oscillatory part of the signal after subtraction of slowly varying background.

Even with optical triggering, additional time-resolution constraints are imposed by the timing-jitter contribution of the dual-fiber-laser system that accumulates during the course of an experiment. To estimate the timing jitter, we have measured a second cross-correlation after a time delay of 10 ns between successive pump pulses. Comparing the first (160 fs) and the second (300 fs) cross-correlation widths, we determine that the timing jitter accumulates at a rate of ~15 fs for every nanosecond of time delay, following the trigger signal. To minimize the effects of timing jitter at short time delays, we carefully matched the travel distances of the optical beam paths of the pump and probe beams with the corresponding ones inside the cross-correlator. In this way, a maximum bandwidth of 6 THz could be reached, which was important for achieving the detection of coherent optical phonons in Sb and Bi. An example of coherent optical phonon detection in an Sb thin film, using a pump laser fluence of 25 µJ/cm2, is shown in Fig. 2. Both A1g and Eg modes are detected and their frequencies (4.51 THz and 3.39 THz, respectively) are in excellent agreement with the first-order Raman scattering results [11

11. J. S. Lannin, J. M. Calleja, and M. Cardona, “Second-order Raman scattering in the group-Vb semimetals: Bi, Sb, and As,” Phys. Rev. B 12, 585–593 (1975). [CrossRef]

] and prior time-domain data reports [12

12. G. A. Garrett, T. F. Albrecht, J. F. Whitaker, and R. Merlin, “Coherent THz phonons driven by light pulses and the Sb problem: What is the mechanism?,” Phys. Rev. Lett. 77, 3661 (1996). [CrossRef] [PubMed]

]. Thus, optical phonon frequencies, measured at small pump power excitation levels, provided a successful test for the experimental setup calibration. Further details will be given in a forthcoming publication.

The laser output beams were individually expanded to reduce beam divergence, while a dichroic mirror is used to direct, collinearly, two-color beams toward a parabolic mirror which focused them on the sample at an oblique angle of incidence of 30°. A 90° off-axis parabolic mirror was employed for eliminating the chromatic aberrations and to facilitate precise dual-color focusing overlap; this was necessary for achieving phase matching during the coherent excitation and probing. The pump and probe individual wavelengths could be interchanged by replacing the beam expander lenses for focusing to a spot size of about 10 µm or smaller, while maintaining a pump-probe spot size ratio of 2. A half-waveplate followed by a polarizer (not shown in Fig. 1) was placed into the probe optical beam path to adjust the pump-probe intensity ratio to a factor of 10–100. Changes in the time-dependent sample reflectivity were measured with an amplified differential photodetector (Thorlabs, PDB 120A). The difference between the reflected probe light and a reference derived from the incident probe light in two matched diodes, is amplified and the output is low-pass filtered to a 50 MHz bandwidth to suppress the detection of the laser repetition rate signal at 100 MHz. The use of the fast detector combined with the optical trigger eliminates the need for modulator referencing in conjunction with lock-in amplifier, as is the case in single laser pump-probe techniques [1

1. B. Perrin, “Investigation of short-time heat transfer effects by an optical pump-probe method,” in Microscale and Nanoscale Heat Transfer, topics in Applied Physics, S. Voltz, ed., (Springer, Berlin, 2007), Vol. 107, pp. 333–359. [CrossRef]

,3–5

3. G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006). [CrossRef]

,13

13. R. J. Stevens, A. N. Smith, and P. M. Norris, “Signal analysis and characterization of experimental setup for the transient thermoreflectance technique,” Rev. Sci. Instrum. 77, 084901 (2006). [CrossRef]

].

The dual-laser ASOPS system, providing a large temporal dynamic range, is extremely advantageous for studies of samples in which several excitations are active over a wide range of time scales. Such is the case for epitaxial thin films of Fe deposited on MgO and Ge substrates. We illustrate the power of this approach through a series of transient reflectivity measurements to detect the thermoreflectance signal and coherent strain wave propagation, while coherent magnetization oscillations were probed with polarization analysis under an external magnetic field. Separation of the magneto-optical Kerr effect (MOKE) from non-magnetic contributions, using the probe beam polarization, is discussed in the following.

Magnetization dynamics can be observed by monitoring the precession frequency which is strongly dependent on the field strength. The external magnetic field was applied along the sample surface using a small permanent magnet with its pole axis placed parallel with the sample and perpendicular to the horizontal optical scattering plane. The permanent magnet enabled us to obtain measurements quickly and conveniently; however it should be pointed out that the magnetic field it produces is not spatially uniform and includes both in-plane and out-of-plane components, although it did not vary significantly across the measurement spot size of at most 10 µm. The permanent magnet provided a magnetic field of up to 2500 Oe and its strength could be tuned by varying the magnet-to-sample separation distance.

Fig. 3. Scheme used for component-resolved MOKE separation described in the text. Vertical (s-polarized) and horizontal (p-polarized) lines represent the incident probe polarization on the sample. Sample-induced MOKE polarization rotation, for longitudinal and polar magnetization components, is sketched using displacement of arrows. Dashed lines at 45° represent the orientation axis of the analyzer placed in the probe beam after reflection on the sample.

Additional experimental details will be presented as we describe the results in the following sections. We emphasize here the efficiency of the ASOPS scanning as compared to mechanical scanning. The former is typically done at kilohertz rates, while fast mechanical delay lines are moving with speeds on the order of 0.5 m/s. Thus, the ASOPS scanning speed is at least 4 orders of magnitude larger than mechanical scanning for time delays approaching 10 ns.

3. Transient thermoreflectance

The first example we present refers to transient thermoreflectance measurements performed on metallic layers grown on a single crystal substrate. This is where the unprecedented ability of our approach to connect long and short time regimes really comes into its own, enabling us to follow the thermal transport from the initial excitation to much later times corresponding to heat propagation deep in the substrate. Two epitaxial 70 nm thick Fe films were grown by molecular beam epitaxy (MBE) on (110) Ge and MgO substrates, and covered with a 4 nm overlayer of Au to protect the surface from oxidation under ambient exposure. The presence of the thin Au overlayer is assumed to be negligible in the following analysis. The metallic film thickness of Fe was chosen to be much larger than the laser probing depth at 780 nm, thus suppressing any contribution to the measured transient reflectance due to the direct optical excitation of the substrate. Typically, a laser fluence of 0.5-2 mJ/cm2 is used in the experiment which gives a temperature rise of 5–20°C in the film. A linear fluence dependency of the thermoreflectance signal was observed over the whole fluence interval.

First, at short time delays (ps), the transient reflectance is dominated by the non-equilibrium excitation of a hot electron plasma near the thin film surface, which is rapidly thermalized through electron-phonon relaxation [17

17. M. I. Kaganov, I. M. Lifshitz, and L. V. Tanatarov, “Relaxation between electrons and the crystalline lattice,” Sov. Phys. JETP 4, 173–180 (1957).

]. Figure 4 compares the thermal cooling curves following the pump pulse excitation at 1560 nm, plotted over the entire range of maximum time delay of 10 ns corresponding to the pump laser repetition rate. The analysis was focused on describing the later stages of cooling from the picosecond to nanosecond time scale, using a simple heat diffusion model proposed by Stevens et al. [18

18. R. J. Stevens, A. N. Smith, and P. M. Norris, “Measurement of thermal boundary conductance of a series of metal-dielectric interfaces by the transient thermoreflectance technique,” J. Heat Transfer 127, 315–322 (2005). [CrossRef]

,19

19. The heat diffusion model (equations 2–7 from [15]) can be applied if the time constant of heat diffusion in film (τf) and interface time constant (τi) follows τfi=d σk/kf<1 (equation 10), where d is the film thickness. If σk~108 to 109 W/m2K and kf is from few tens to few hundreds W/Km then d should be <100 nm, which verifies that d for our samples (70 nm) satisfies this criterion.

]. A least squares minimization procedure was implemented to adjust the numerical solution of the heat diffusion equation, with appropriate boundary conditions, to the experimental data. In addition to letting the film-substrate boundary conductance (σ k) and heat penetration depth (δ) vary as free parameters, we also allow the film thermal conductivity (kf) to be adjustable, while keeping specific heats and substrate thermal conductivity (ks) at known values corresponding to the bulk material. In addition, we have compensated for heat accumulation effects during repetitive pulse excitation [5

5. W. S. Capinski and H. J. Maris, “Improved apparatus for Picosecond Pump-and-Probe Optical Measurements,” Rev. Sci. Instrum. 67, 2720–2726 (1996). [CrossRef]

,13

13. R. J. Stevens, A. N. Smith, and P. M. Norris, “Signal analysis and characterization of experimental setup for the transient thermoreflectance technique,” Rev. Sci. Instrum. 77, 084901 (2006). [CrossRef]

,20

20. E. G. Gamaly, A. V. Rode, and B. Luther-Davies, “Ultrafast ablation with high-pulse-rate lasers. Part I: Theoretical considerations,” J. Appl. Phys. 85, 4213 (1999). [CrossRef]

] by adding a constant background offset (Rb) to the experimental data before comparing with the solution of the diffusion equation.

Fig. 4. Thermoreflectance experimental data (fit curves) are plotted as dots (lines). The curves are rescaled and displaced for clarity.

4. Coherent strain wave propagation

Ultrashort laser pulses can also excite coherent uniaxial strain waves propagating perpendicular to the sample surface toward the bulk [25

25. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light-pulses,” Phys. Rev. B 34, 4129–4138 (1986). [CrossRef]

]. Such strain waves can be detected via oscillatory contributions of the transient reflectivity with frequency equal to 2nvcos(θ)/λ, where v is the speed of sound, n is the index of refraction at the wavelength λ, and θ is the angle of incidence inside the probed material. To probe the bulk strain wave propagation after surface excitation, we have used either bare Ge substrates or 10–15 nm Fe epitaxial films deposited on (100) and (110) Ge substrates and covered with Au overlayers. Semitransparent film thicknesses for the excitation and detection wavelengths were chosen to facilitate direct probing of strain propagation in the substrate. Systematic investigations were performed by switching the individual pump and probe wavelengths. In Fig. 5 we compare an experimental curve obtained on a 10 nm Fe film grown on a (100) Ge substrate that is probed at 780 nm wavelength, with a measurement on a bare (100) Ge wafer when probing at the complementary wavelength of 1560 nm.

A long oscillation on the nanosecond time scale can be observed with the 1560 nm wavelength on the bare (100) Ge. We attribute the detection enhancement of the photoacoustic contribution to a resonant condition for probing at the direct bandgap absorption edge, as was seen previously for the case of GaSb-GaAs heterostructures [26

26. J. K. Miller, J. Qi, Y. Xu, Y.-J. Cho, X. Liu, J. K. Furdyna, I. Perakis, T. V. Shahbazyan, and N. Tolk, “Near-bandgap wavelength dependence of long-lived traveling coherent longitudinal acoustic phonons in GaSb-GaAs heterostructures,” Phys. Rev. B 74, 113313 (2006). [CrossRef]

]. In the case of non-resonant probing at 780 nm, the presence of a thin absorptive Fe film at the 1560 nm pump wavelength permitted partial optical transmission of the probe in Ge, thus allowing the observation of the bulk strain propagation. In the short lived oscillation curves in Fig. 5 corresponding to such thin Fe films deposited on Ge substrates, we observe that changing the probing wavelength to 780 nm rapidly reduces the amplitude of the signal when the strain wave propagates deep into the substrate. Such behavior could be explained based on the shorter optical penetration depth in Ge at 780 nm compared with the one at 1560 nm. The reflectivity oscillations are still clearly visible up to 200 ps, enabling an accurate sound velocity determination.

An even more drastic increase of the oscillation amplitude decay occurs when probing at a wavelength of 520 nm, consistent with a corresponding large increase of wavelength dependent absorption [27

27. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983). [CrossRef]

]. The inset in Fig. 5 compares two fast-Fourier-transform (FFT) spectra of the oscillatory part of the time resolved spectra, measured with a 780 nm probe on 10 to 15 nm thick iron films grown on (100) and (110) Ge substrates. Using the peak frequencies and 4.74 for the index of refraction [27

27. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983). [CrossRef]

], we obtain 4.96 and 5.43 km/s for the longitudinal sound velocity along the [100] and [110] crystallographic directions, respectively, in excellent agreement with the earlier published data for crystalline Ge [28

28. H. J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves - data for silicon and germanium single crystals, and for fused silica,” J. Appl. Phys. 24, 988–997 (1953). [CrossRef]

].

Fig. 5. Experimental transient reflectivity in the upper curve (two lower curves) is measured using 780 nm (1560 nm) pump beam wavelength. The curves are rescaled and displaced for clarity. FFT in the inset corresponds to the oscillatory part of the signal of experimental curves for Au/Fe/Ge (100) and Au/Fe/Ge (110).

In additional measurements at the complementary probe wavelength (520 nm), it is observed that the reflectivity oscillation frequency increases by about 52% when replacing 780 nm with 520 nm wavelength for the optical probe pulses (not shown in Fig. 5). This result confirms that the corresponding increase of 2nvcos(θ)/λ is in agreement with the above determination of v and the prior index of refraction measurement at 520 nm [27

27. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983). [CrossRef]

]. We note here that the wavelength dependent detection studies could be used to obtain both v and the index of refraction.

5. Coherent magnetization oscillations

A simple estimate for the oscillation amplitude decay time can be made using τ=1/2πfα, where τ is the exponential decay time, α is the intrinsic Gilbert damping rate, and f is the resonant frequency. Such an expression is valid when applying large magnetic fields perpendicular to the sample surface. When arbitrarily choosing a resonant frequency of 20 GHz, and considering the value for α reported for high quality Fe and FeCo alloys [32

32. F. Schreiber, J. Pflaum, Z. Frait, Th. Muhge, and J. Pelzl, “Gilbert damping and g-factor in FexCo1-x alloy films,” Solid-State Commun. 93, 965–968 (1995). [CrossRef]

], one would expect a relaxation time of around 4 ns. Thus, extending the time delay for accurate measurements of intrinsic Gilbert damping is highly desirable.

Fig. 6. Coherent magnetization oscillation measurement for (110) Fe/Ge sample. Oscillatory trace detected at 780 nm probe wavelength, and H≈1000 Oe, is shown in (a), the lower dotted (red line) curve is the experiment (fit) after background subtraction; (b) equivalent magnetic field linewidth values are plotted as dots (see text) and the line is a fit; (c) shows a comparison of the experimental results obtained at 780 nm and 520 nm probe wavelengths, and H≈100 Oe, in the upper and lower curves, respectively. ΔI/I is the fractional transmission through analyzer in a) and c).

To compare our data with prior experiments using ferromagnetic-resonance (FMR), the following frequency expression is considered, obtained from the Landau-Lifshitz equation [33

33. M. Farle, “Ferromagnetic resonance of ultrathin metallic layers,” Rep. Prog. Phys. 61, 755–826 (1998). [CrossRef]

]:

(2πfγ)2=[Hcos(θMθH)+Hk1][Hcos(θMθH)+Hk2+4πMeff]
(1)

A connection between the frequency-swept linewidth and the field-swept linewidth is provided in [34

34. S. S. Kalarickal, P. Krivosik, M. Z. Wu, C. E. Patton, M. L. Schneider, P. Kabos, T. J. Silva, and J. P. Nibarger, “Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods,” J. Appl. Phys. 99, 093909 (2006). [CrossRef]

] and can be deduced by differentiation of Eq. (1) with respect to the external field value:

Δf=γ2πΔH1+(γMf)2
(2)

where ΔH takes the following form when a Lorentzian lineshape is assumed in the frequency domain:

ΔH=ΔHi+232πfγα
(3)

ΔHi includes the contribution from inhomogenous broadening. The connection between the decay time τ and Δf is given by the equation:

Δf=1πτ.
(4)

We can now convert the measured decay times into equivalent magnetic field linewidth values that are often used in FMR for determination of intrinsic damping and inhomogeneous broadening. The result for a few measured frequencies is plotted in Fig. 6(b) for the primary mode precession around the effective magnetic field direction. From the linear dependence of the converted ΔH values versus frequency and equation (3), we obtain ΔHi=16 Oe and a linear slope of 2.85 Oe/GHz. We find reasonable agreement (16 % smaller linear slope and 2x larger ΔHi) between our results and prior data [35

35. J. J. Krebs, F. J. Rachford, P. Lubitz, and G. A. Prinz, “Ferromagnetic resonance studies of very thin epitaxial single-crystals of iron,” J. Appl. Phys. 53, 8058–8060 (1982). [CrossRef]

] obtained using FMR and a Fe/GaAs (110) sample with 20 nm thickness.

The detection techniques presently described can be extended to the measurement of standing spin-wave modes detectable in thicker films [30

30. M. van Kampen, C. Jozsa, J. T. Kohlhepp, P. LeClair, L. Lagae, W. J. M. de Jonge, and B. Koopmans, “All-optical probe of coherent spin waves,” Phys. Rev. Lett. 88, 227201 (2002). [CrossRef] [PubMed]

], or to new studies of nanostructured magnetic samples [41

41. A. Barman, S. Wang, J. Maas, A. R. Hawkins, S. Kwon, J. Bokor, A. Liddle, and H. Schmidt, “Size dependent damping in picosecond dynamics of single nanomagnets,” Appl. Phys. Lett. 90, 202504 (2007). [CrossRef]

] as well as the interlayer exchange coupling present [42

42. P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, “Layered magnetic structures: Evidence for antiferromagnetic coupling of Fe layers across Cr interlayers,” Phys. Rev. Lett. 57, 2442–2445 (1986). [CrossRef] [PubMed]

] in multilayered magnetic thin films.

6. Conclusions

Non-degenerate optical pump-probe spectroscopy in collinear geometry, based on the ASOPS technique and a dual-fiber-laser system, provides an effective tool for measuring the transient solid-state dynamics, spanning over almost five orders in magnitude of temporal dynamic range. The need of connecting extended timescales for monitoring different types of excitation is thus realized in practice. We demonstrate several such applications for slow relaxation measurements such as the thermal transport across interfaces and the study of long-lived coherent oscillations corresponding to coherent acoustic and magnetic excitations. Further studies are enabled and could include: the coherent control of spin and phonon dynamics; the separation of intrinsic damping and inhomogeneous broadening in magnetic materials; more accurate measurements of heat and charge transport; and measurements of acoustic phonon propagation at extended depths into the material.

Acknowledgments

We are grateful to P. Kubina and M. Mei for helpful discussions and customized design of the dual-fiber-laser system; and to K. Shahid and I. M. Oraiqat for various software contributions. This work was supported by the NSF Frontiers in Physics FOCUS Center under grant PHY-0114336.

References and links

1.

B. Perrin, “Investigation of short-time heat transfer effects by an optical pump-probe method,” in Microscale and Nanoscale Heat Transfer, topics in Applied Physics, S. Voltz, ed., (Springer, Berlin, 2007), Vol. 107, pp. 333–359. [CrossRef]

2.

P. A. Elzinga, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump probe spectroscopy by asynchronous optical-sampling,” Appl. Spectrosc. 41, 2–4 (1987). [CrossRef]

3.

G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006). [CrossRef]

4.

R. Merlin, “Generating coherent THz phonons with light pulses,” Solid-State Commun. 102, 207–220 (1997). [CrossRef]

5.

W. S. Capinski and H. J. Maris, “Improved apparatus for Picosecond Pump-and-Probe Optical Measurements,” Rev. Sci. Instrum. 67, 2720–2726 (1996). [CrossRef]

6.

E. Lill, S. Schneider, and F. Dorr, “Rapid optical sampling of relaxation-phenomena employing two time-correlated picosecond pulse trains,” Appl. Phys. 14, 399–401 (1977). [CrossRef]

7.

W. T. Barnes, Jr., “Modulated gain spectroscopy,” Ph.D. Dissertation , Purdue University, West Lafayette, Indiana (1980).

8.

A. F. Bartels, F. Hudert, C. Janke, T. Dekorsy, and K. Kohler, “Femtosecond time-resolved optical pump-probe spectroscopy at kilohertz-scan-rates over nanosecond-time-delays without mechanical delay line,” Appl. Phys. Lett. 88, 041117 (2006). [CrossRef]

9.

http://www.menlosystems.com

10.

S. Adachi, S. Takeyama, and Y. Takagi, “Dual wavelength optical sampling technique for ultrafast transient bleaching spectroscopy,” Opt. Commun. 117, 71–77 (1995). [CrossRef]

11.

J. S. Lannin, J. M. Calleja, and M. Cardona, “Second-order Raman scattering in the group-Vb semimetals: Bi, Sb, and As,” Phys. Rev. B 12, 585–593 (1975). [CrossRef]

12.

G. A. Garrett, T. F. Albrecht, J. F. Whitaker, and R. Merlin, “Coherent THz phonons driven by light pulses and the Sb problem: What is the mechanism?,” Phys. Rev. Lett. 77, 3661 (1996). [CrossRef] [PubMed]

13.

R. J. Stevens, A. N. Smith, and P. M. Norris, “Signal analysis and characterization of experimental setup for the transient thermoreflectance technique,” Rev. Sci. Instrum. 77, 084901 (2006). [CrossRef]

14.

K. Postava, H. Jaffres, A. Schuhl, F. Nguyen Van Dau, M. Goiran, and A. R. Fert, “Linear and quadratic magneto-optical measurements of the spin reorientation in epitaxial Fe films on MgO,” J. Magn. Magn. Mater. 172, 199–208 (1997). [CrossRef]

15.

J. Zak, E. R. Moog, C. Liu, and S. D. Bader, “Magneto-optics of multilayers with arbitrary magnetization directions,” Phys. Rev. B 43, 6423 (1991). [CrossRef]

16.

G. C. Cho, W. Kütt, and H. Kurz, “Subpicosecond time-resolved coherent-phonon oscillations in GaAs,” Phys. Rev. Lett. 65, 764–766 (1990). [CrossRef] [PubMed]

17.

M. I. Kaganov, I. M. Lifshitz, and L. V. Tanatarov, “Relaxation between electrons and the crystalline lattice,” Sov. Phys. JETP 4, 173–180 (1957).

18.

R. J. Stevens, A. N. Smith, and P. M. Norris, “Measurement of thermal boundary conductance of a series of metal-dielectric interfaces by the transient thermoreflectance technique,” J. Heat Transfer 127, 315–322 (2005). [CrossRef]

19.

The heat diffusion model (equations 2–7 from [15]) can be applied if the time constant of heat diffusion in film (τf) and interface time constant (τi) follows τfi=d σk/kf<1 (equation 10), where d is the film thickness. If σk~108 to 109 W/m2K and kf is from few tens to few hundreds W/Km then d should be <100 nm, which verifies that d for our samples (70 nm) satisfies this criterion.

20.

E. G. Gamaly, A. V. Rode, and B. Luther-Davies, “Ultrafast ablation with high-pulse-rate lasers. Part I: Theoretical considerations,” J. Appl. Phys. 85, 4213 (1999). [CrossRef]

21.

C. A. Paddock and G. L. Eesley, “Transient thermoreflectance from thin metal-films,” J. Appl. Phys. 60, 285–290 (1986). [CrossRef]

22.

P. B. Johnson and R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B 9, 5056–5070 (1974). [CrossRef]

23.

M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24 , 4493–4499 (1985). [CrossRef]

24.

R. J. Stoner and H. J. Maris, “Kapitza conductance and heat-flow beween solids at temperatures from 50 to 300 K,” Phys. Rev. B 48, 16373–16387 (1993). [CrossRef]

25.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light-pulses,” Phys. Rev. B 34, 4129–4138 (1986). [CrossRef]

26.

J. K. Miller, J. Qi, Y. Xu, Y.-J. Cho, X. Liu, J. K. Furdyna, I. Perakis, T. V. Shahbazyan, and N. Tolk, “Near-bandgap wavelength dependence of long-lived traveling coherent longitudinal acoustic phonons in GaSb-GaAs heterostructures,” Phys. Rev. B 74, 113313 (2006). [CrossRef]

27.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983). [CrossRef]

28.

H. J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves - data for silicon and germanium single crystals, and for fused silica,” J. Appl. Phys. 24, 988–997 (1953). [CrossRef]

29.

G. Ju, A. V. Nurmikko, R. F. C. Farrow, R. F. Marks, M. J. Carey, and B. A. Gurney, “Ultrafast time resolved photoinduced magnetization rotation in a ferromagnetic/antiferromagnetic exchange coupled system,” Phys. Rev. Lett. 82, 3705–3708 (1999). [CrossRef]

30.

M. van Kampen, C. Jozsa, J. T. Kohlhepp, P. LeClair, L. Lagae, W. J. M. de Jonge, and B. Koopmans, “All-optical probe of coherent spin waves,” Phys. Rev. Lett. 88, 227201 (2002). [CrossRef] [PubMed]

31.

V. A. Stoica, R. Merlin, R. A. Lukaszew, and R. Clarke, “Time-resolved spin dynamics studies of ferromagnetic thin films grown by molecular beam epitaxy,” presented at APS March meeting, Los Angeles, CA, USA, 21–25 March 2005.

32.

F. Schreiber, J. Pflaum, Z. Frait, Th. Muhge, and J. Pelzl, “Gilbert damping and g-factor in FexCo1-x alloy films,” Solid-State Commun. 93, 965–968 (1995). [CrossRef]

33.

M. Farle, “Ferromagnetic resonance of ultrathin metallic layers,” Rep. Prog. Phys. 61, 755–826 (1998). [CrossRef]

34.

S. S. Kalarickal, P. Krivosik, M. Z. Wu, C. E. Patton, M. L. Schneider, P. Kabos, T. J. Silva, and J. P. Nibarger, “Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods,” J. Appl. Phys. 99, 093909 (2006). [CrossRef]

35.

J. J. Krebs, F. J. Rachford, P. Lubitz, and G. A. Prinz, “Ferromagnetic resonance studies of very thin epitaxial single-crystals of iron,” J. Appl. Phys. 53, 8058–8060 (1982). [CrossRef]

36.

J. R. Sandercock and W. Wettling, “Light scattering from thermal magnons in iron and nickel,” IEEE Trans. Magn. 14, 442–444 (1978). [CrossRef]

37.

R. W. Damon and J. R. Eshbach, “Magnetostatic modes of a ferromagnetic slab,” J. Phys. Chem. Solids 19, 308–320 (1961). [CrossRef]

38.

M. Madami, S. Tacchi, G. Carlotti, G. Gubbiotti, and R. L. Stamps, “In situ Brillouin scattering study of the thickness dependence of magnetic anisotropy in uncovered and Cu-covered Fe/GaAs(100) ultrathin films,” Phys. Rev. B 69, 144408 (2004). [CrossRef]

39.

H. Puszkarski, “Theory of surface states in spin wave resonance,” Prog. Surf. Sci. 9, 191–247 (1979). [CrossRef]

40.

G. S. Krinchik and V. A. Artem’ev, “Magneto-optical properties of Ni, Co and Fe in ultraviolet visible and infrared parts of spectrum,” Sov. Phys. JETP 26, 1080–1085 (1968).

41.

A. Barman, S. Wang, J. Maas, A. R. Hawkins, S. Kwon, J. Bokor, A. Liddle, and H. Schmidt, “Size dependent damping in picosecond dynamics of single nanomagnets,” Appl. Phys. Lett. 90, 202504 (2007). [CrossRef]

42.

P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, “Layered magnetic structures: Evidence for antiferromagnetic coupling of Fe layers across Cr interlayers,” Phys. Rev. Lett. 57, 2442–2445 (1986). [CrossRef] [PubMed]

OCIS Codes
(120.6810) Instrumentation, measurement, and metrology : Thermal effects
(300.6500) Spectroscopy : Spectroscopy, time-resolved
(310.6870) Thin films : Thin films, other properties
(320.5390) Ultrafast optics : Picosecond phenomena
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Spectroscopy

History
Original Manuscript: November 27, 2007
Revised Manuscript: January 29, 2008
Manuscript Accepted: January 31, 2008
Published: February 4, 2008

Citation
Vladimir A. Stoica, Yu-Miin Sheu, David A. Reis, and Roy Clarke, "Wideband detection of transient solid-state dynamics using ultrafast fiber lasers and asynchronous optical sampling," Opt. Express 16, 2322-2335 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-4-2322


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References

  1. B. Perrin, "Investigation of short-time heat transfer effects by an optical pump-probe method," in Microscale and Nanoscale Heat Transfer, topics in Applied Physics, S. Voltz, ed., (Springer, Berlin, 2007), Vol. 107, pp. 333-359. [CrossRef]
  2. P. A. Elzinga, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, "Pump probe spectroscopy by asynchronous optical-sampling," Appl. Spectrosc. 41, 2-4 (1987). [CrossRef]
  3. G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, "Characterization of mechanical and thermal properties using ultrafast optical metrology," MRS Bull. 31, 607-613 (2006). [CrossRef]
  4. R. Merlin, "Generating coherent THz phonons with light pulses," Solid-State Commun. 102, 207-220 (1997). [CrossRef]
  5. W. S. Capinski and H. J. Maris, "Improved apparatus for Picosecond Pump-and-Probe Optical Measurements," Rev. Sci. Instrum. 67, 2720-2726 (1996). [CrossRef]
  6. E. Lill, S. Schneider, and F. Dorr, "Rapid optical sampling of relaxation-phenomena employing two time-correlated picosecond pulse trains,?Appl. Phys. 14, 399-401 (1977). [CrossRef]
  7. W. T. Barnes, Jr., ?Modulated gain spectroscopy, ? Ph.D. Dissertation, Purdue University, West Lafayette, Indiana (1980).
  8. A. F. Bartels, F. Hudert, C. Janke, T. Dekorsy, and K. Kohler, "Femtosecond time-resolved optical pump-probe spectroscopy at kilohertz-scan-rates over nanosecond-time-delays without mechanical delay line," Appl. Phys. Lett. 88, 041117 (2006). [CrossRef]
  9. http://www.menlosystems.com
  10. S. Adachi, S. Takeyama, and Y. Takagi, "Dual wavelength optical sampling technique for ultrafast transient bleaching spectroscopy," Opt. Commun. 117, 71-77 (1995). [CrossRef]
  11. J. S. Lannin, J. M. Calleja, and M. Cardona, "Second-order Raman scattering in the group-Vb semimetals: Bi, Sb, and As," Phys. Rev. B 12, 585-593 (1975). [CrossRef]
  12. G. A. Garrett, T. F. Albrecht, J. F. Whitaker, and R. Merlin, "Coherent THz phonons driven by light pulses and the Sb problem: What is the mechanism?," Phys. Rev. Lett. 77, 3661 (1996). [CrossRef] [PubMed]
  13. R. J. Stevens, A. N. Smith, and P. M. Norris, "Signal analysis and characterization of experimental setup for the transient thermoreflectance technique," Rev. Sci. Instrum. 77, 084901 (2006). [CrossRef]
  14. K. Postava, H. Jaffres, A. Schuhl, F. Nguyen Van Dau, M. Goiran, and A. R. Fert, "Linear and quadratic magneto-optical measurements of the spin reorientation in epitaxial Fe films on MgO," J. Magn. Magn. Mater. 172, 199-208 (1997). [CrossRef]
  15. J. Zak, E. R. Moog, C. Liu, and S. D. Bader, "Magneto-optics of multilayers with arbitrary magnetization directions," Phys. Rev. B 43, 6423 (1991). [CrossRef]
  16. G. C. Cho, W. Kütt, and H. Kurz, "Subpicosecond time-resolved coherent-phonon oscillations in GaAs," Phys. Rev. Lett. 65, 764-766 (1990). [CrossRef] [PubMed]
  17. M. I. Kaganov, I. M. Lifshitz, and L. V. Tanatarov, "Relaxation between electrons and the crystalline lattice," Sov. Phys. JETP 4, 173-180 (1957).
  18. R. J. Stevens, A. N. Smith, and P. M. Norris, "Measurement of thermal boundary conductance of a series of metal-dielectric interfaces by the transient thermoreflectance technique," J. Heat Transfer 127, 315-322 (2005). [CrossRef]
  19. The heat diffusion model (equations 2-7 from [15]) can be applied if the time constant of heat diffusion in film (?f) and interface time constant (?i) follows ?f/?i = d ?k / kf <1 (equation 10), where d is the film thickness. If ?k ~ 108 to 109 W/m2K and kf is from few tens to few hundreds W/Km then d should be < 100 nm, which verifies that d for our samples (70 nm) satisfies this criterion.
  20. E. G. Gamaly, A. V. Rode, and B. Luther-Davies, "Ultrafast ablation with high-pulse-rate lasers. Part I: Theoretical considerations," J. Appl. Phys. 85, 4213 (1999). [CrossRef]
  21. C. A. Paddock and G. L. Eesley, "Transient thermoreflectance from thin metal-films," J. Appl. Phys. 60, 285-290 (1986). [CrossRef]
  22. P. B. Johnson and R. W. Christy, "Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd," Phys. Rev. B 9, 5056-5070 (1974). [CrossRef]
  23. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, "Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W," Appl. Opt. 24, 4493-4499 (1985). [CrossRef]
  24. R. J. Stoner and H. J. Maris, "Kapitza conductance and heat-flow beween solids at temperatures from 50 to 300 K," Phys. Rev. B 48, 16373-16387 (1993). [CrossRef]
  25. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, "Surface generation and detection of phonons by picosecond light-pulses," Phys. Rev. B 34, 4129-4138 (1986). [CrossRef]
  26. J. K. Miller, J. Qi, Y. Xu, Y.-J. Cho, X. Liu, J. K. Furdyna, I. Perakis, T. V. Shahbazyan, and N. Tolk, "Near-bandgap wavelength dependence of long-lived traveling coherent longitudinal acoustic phonons in GaSb-GaAs heterostructures," Phys. Rev. B 74, 113313 (2006). [CrossRef]
  27. D. E. Aspnes and A. A. Studna, "Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV," Phys. Rev. B 27, 985-1009 (1983). [CrossRef]
  28. H. J. McSkimin, "Measurement of elastic constants at low temperatures by means of ultrasonic waves - data for silicon and germanium single crystals, and for fused silica," J. Appl. Phys. 24, 988-997 (1953). [CrossRef]
  29. G. Ju, A. V. Nurmikko, R. F. C. Farrow, R. F. Marks, M. J. Carey, and B. A. Gurney, "Ultrafast time resolved photoinduced magnetization rotation in a ferromagnetic/antiferromagnetic exchange coupled system," Phys. Rev. Lett. 82, 3705-3708 (1999). [CrossRef]
  30. M. van Kampen, C. Jozsa, J. T. Kohlhepp, P. LeClair, L. Lagae, W. J. M.de Jonge, and B. Koopmans, "All-optical probe of coherent spin waves," Phys. Rev. Lett. 88, 227201 (2002). [CrossRef] [PubMed]
  31. V. A. Stoica, R. Merlin, R. A. Lukaszew, and R. Clarke, "Time-resolved spin dynamics studies of ferromagnetic thin films grown by molecular beam epitaxy," presented at APS March meeting, Los Angeles, CA, USA, 21-25 March 2005.
  32. F. Schreiber, J. Pflaum, Z. Frait, Th. Muhge, and J. Pelzl, "Gilbert damping and g-factor in FexCo1-x alloy films," Solid-State Commun. 93, 965-968 (1995). [CrossRef]
  33. M. Farle, "Ferromagnetic resonance of ultrathin metallic layers," Rep. Prog. Phys. 61, 755-826 (1998). [CrossRef]
  34. S. S. Kalarickal, P. Krivosik, M. Z. Wu, C. E. Patton, M. L. Schneider, P. Kabos, T. J. Silva, J. P. Nibarger, "Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods," J. Appl. Phys. 99, 093909 (2006). [CrossRef]
  35. J. J. Krebs, F. J. Rachford, P. Lubitz, and G. A. Prinz, "Ferromagnetic resonance studies of very thin epitaxial single-crystals of iron," J. Appl. Phys. 53, 8058-8060 (1982). [CrossRef]
  36. J. R. Sandercock and W. Wettling, "Light scattering from thermal magnons in iron and nickel," IEEE Trans. Magn. 14, 442-444 (1978). [CrossRef]
  37. R. W. Damon and J. R. Eshbach, "Magnetostatic modes of a ferromagnetic slab," J. Phys. Chem. Solids 19, 308-320 (1961). [CrossRef]
  38. M. Madami, S. Tacchi, G. Carlotti, G. Gubbiotti, and R. L. Stamps, "In situ Brillouin scattering study of the thickness dependence of magnetic anisotropy in uncovered and Cu-covered Fe/GaAs(100) ultrathin films," Phys. Rev. B 69, 144408 (2004). [CrossRef]
  39. H. Puszkarski, "Theory of surface states in spin wave resonance," Prog. Surf. Sci. 9, 191-247 (1979). [CrossRef]
  40. G. S. Krinchik and V. A. Artem’ev, "Magneto-optical properties of Ni, Co and Fe in ultraviolet visible and infrared parts of spectrum," Sov. Phys. JETP 26, 1080-1085 (1968).
  41. A. Barman, S. Wang, J. Maas, A. R. Hawkins, S. Kwon, J. Bokor, A. Liddle, H. Schmidt, "Size dependent damping in picosecond dynamics of single nanomagnets," Appl. Phys. Lett. 90, 202504 (2007). [CrossRef]
  42. P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, "Layered magnetic structures: Evidence for antiferromagnetic coupling of Fe layers across Cr interlayers," Phys. Rev. Lett. 57, 2442-2445 (1986). [CrossRef] [PubMed]

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