Ultrafast demagnetization of FePt:Cu thin films and the role of magnetic heat capacity

Johannes Kimling, Judith Kimling, R. B. Wilson, Birgit Hebler, Manfred Albrecht, and David G. Cahill

Phys. Rev. B 90, 224408 – Published 5 December 2014

Abstract

The phenomenon of different time scales of ultrafast demagnetization has attracted much attention. This so-called diversity of ultrafast demagnetization has been explained by the microscopic three temperature model (M3TM) and by the Landau-Lifshitz-Bloch model (LLBM). Here, we revisit the basic three temperature model (3TM) and provide a general criterion for explaining the different time scales observed. We focus on the role of magnetic heat capacity, which we find mainly determines the slowing down of the demagnetization time with increasing ambient temperature and laser fluence. In this context, we clarify the role of magnetic heat capacity in the M3TM and compare the 3TM with the LLBM. To illustrate the role of magnetic heat capacity, we present a simulation of ultrafast demagnetization of Ni. Furthermore, we present time-resolved magneto-optic Kerr effect measurements of ultrafast demagnetization and specific heat of ${Fe}_{46} {Cu}_{6} {Pt}_{48}$ from 300 K to close to its Curie temperature. While most of the prior experimental research used high-fluence laser pulses causing sizable temperature excursions of the sample, our experiments involve small temperature excursions, which are crucial for studying the role of magnetic heat capacity in ultrafast demagnetization. Our experimental results corroborate that the slowing down of ultrafast demagnetization is dominated by the increase of the magnetic heat capacity near the Curie temperature.

Received 10 September 2014
Revised 30 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.224408

Authors & Affiliations

Johannes Kimling^1,*, Judith Kimling¹, R. B. Wilson¹, Birgit Hebler², Manfred Albrecht², and David G. Cahill¹

¹Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
²Institute of Physics, University of Augsburg, Universitätsstrasse 1, 86159 Augsburg, Germany

^*kimling@illinois.edu

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Vol. 90, Iss. 22 — 1 December 2014

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Images

Figure 1
Simulation of the demagnetization behavior of a 15 nm thin Ni layer on a 100 nm ${SiO}_{2} / Si$ substrate using the phenomenological three temperature model. With increasing temperature (black: $T_{0} = 300$ K; red: $T_{0} = 450$ K; blue: $T_{0} = 600$ K) the time evolution of the spin temperature $Δ T_{s}$ (solid lines) changes from a fast demagnetization with subsequent fast remagnetization at 300 K to a slow demagnetization in two steps at 600 K. Also shown are the time evolution of the respective electron and phonon temperatures ( $Δ T_{e}$ : dashed lines; $Δ T_{p}$ : dash-dotted lines).
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Figure 2
Time evolution of the ratio of the in-phase and out-of-phase components of the TR-MOKE signal, $- V_{in} / V_{out}$ (symbols), measured on a 5 nm thin ${Fe}_{46} {Cu}_{6} {Pt}_{48}$ layer on a 100 nm ${SiO}_{2} / Si$ substrate. In the time range shown, the measurement data can be analyzed analogously to time-domain thermoreflectance measurements. Fit curves (solid lines) were obtained using a multilayer heat diffusion model considering the total specific heat of the ${Fe}_{46} {Cu}_{6} {Pt}_{48}$ layer as fit parameter.
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Figure 3
Temperature dependence of the specific heat $C_{tot}$ of the 5 nm thin ${Fe}_{46} {Cu}_{6} {Pt}_{48}$ layer determined from time-resolved magneto-optic Kerr effect measurements. Dominant contributions to $C_{tot}$ arise from phonons $(C_{p})$ and magnetization $(C_{s})$ . For fitting of the three temperature model to ultrafast demagnetization data we assume a constant $C_{p} = 3.46 \times 10^{6} J m^{- 3} K^{- 1}$ as indicated by the dash-dotted line. The dashed line follows a phenomenological model indicating the strong increase of $C_{s}$ when approaching the Curie temperature $T_{C} \approx 502$ K. The small electronic specific heat, set to $C_{e} = 0.03 \times 10^{6} J m^{- 3} K^{- 1}$ [16], is not indicated in the diagram.
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Figure 4
Temperature dependence of the energy transfer coefficient $g_{es}$ between electrons and magnetization determined from the three temperature model fitted to ultrafast demagnetization measurements shown in Fig. 5. Depending on the choice of the specific heat $C_{p}$ of phonons, $g_{es}$ increases (triangles) or decreases (squares) with temperature. However, above $\sim 430$ K all curves are nearly constant with temperature. In this temperature range, the specific heat $C_{s}$ of the magnetization increases significantly governing the demagnetization behavior (compare Fig. 3). Therefore, we set $C_{p} = 3.46 \times 10^{6} J m^{- 3} K^{- 1}$ , such that $g_{es}$ is approximately constant with temperature (circles). The resulting fit curves are shown in Fig. 5.
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Figure 5
Demagnetization behavior of the 5 nm thin ${Fe}_{46} {Cu}_{6} {Pt}_{48}$ layer after low-fluence laser excitation at different ambient temperatures as indicated in the diagrams. Figure (a) shows the time evolution from the onset of the laser pulse up to 4 ps, while (b) shows the time evolution plotted logarithmically from 0.1 ps up to 4 ns including cooling by thermal diffusion. Fit curves (solid lines) to the time-resolved magneto-optic Kerr effect measurements (symbols) were obtained using the phenomenological three temperature model [3TM, Eqs. (1) through (3)] considering the specific heat of the ${Fe}_{46} {Cu}_{6} {Pt}_{48}$ layer measured (see caption of Fig. 3). Energy transfer coefficient $g_{ep}$ was fixed from fitting of the 3TM to the data at ambient temperature $T_{0} = 300$ K. Fit curves to the data at $T_{0} > 300$ K were obtained using one fit parameter, $g_{es}$ , and assuming constant $g_{ep}$ in this temperature range. The parameter set is summarized in Table 2.
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