Role of critical spin fluctuations in ultrafast demagnetization of transition-metal rare-earth alloys

V. López-Flores, N. Bergeard, V. Halté, C. Stamm, N. Pontius, M. Hehn, E. Otero, E. Beaurepaire, and C. Boeglin

Phys. Rev. B 87, 214412 – Published 11 June 2013

Abstract

Ultrafast magnetization dynamics induced by femtosecond laser pulses have been measured in ferrimagnetic Co $_{0.8}$ Gd $_{0.2}$ , Co $_{0.74}$ Tb $_{0.26}$ , and Co $_{0.86}$ Tb $_{0.14}$ alloys. Using element sensitivity of x-ray magnetic circular dichroism at the Co $L_{3}$ , Tb $M_{5}$ , and Gd $M_{5}$ edges, we see that the demagnetization dynamics is element dependent. We show that a thermalization time as fast as 280 $\pm$ 30 fs is observed for the rare earth in the alloy when the excited-state temperature is below the compensation temperature. It is limited to 500 $\pm$ 100 fs when the excited-state temperature is below the Curie temperature ( $T_{C}$ ). Therefore, for transition-metal rare-earth alloys, we propose that critical spin fluctuations in the vicinity of $T_{C}$ reduce the demagnetization rates of the 4 $f$ electrons, whereas far from $T_{C}$ the limited demagnetization rates should be avoided.

Received 9 March 2012

DOI:https://doi.org/10.1103/PhysRevB.87.214412

Authors & Affiliations

V. López-Flores¹, N. Bergeard¹, V. Halté¹, C. Stamm^2,*, N. Pontius², M. Hehn³, E. Otero⁴, E. Beaurepaire¹, and C. Boeglin¹

¹Institut de Physique et de Chimie des Matériaux de Strasbourg and NIE, UMR7504, CNRS et Université de Strasbourg, 67034 Strasbourg, France
²Institut für Methoden und Instrumentierung der Forschung mit Synchrotronstrahlung, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
³Institut Jean Lamour, Université Henri Poincaré, Nancy, France
⁴Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin, 91192 Gif-sur-Yvette, France

^*Now at Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland.

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Vol. 87, Iss. 21 — 1 June 2013

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Figure 1
Static XMCD spectra obtained at Co $L_{2, 3}$ , Gd $M_{4, 5}$ , and Tb $M_{4, 5}$ edges using a 5-kOe magnetic field. The red and black lines are the x-ray absorption spectra recorded for parallel and antiparallel orientation of the magnetic field and incoming light helicity. The blue lines are the differences defining the XMCD spectra, whereas the green lines are the integration of the XMCD spectra. For clarity the XMCD and the integrated spectra are multiplied by −1 in (a), (b), (e), and (f). In the inset we show the hysteresis obtained at the different edges: (a) Co $L_{3}$ , (b) Gd $M_{5}$ , (c) Co $L_{3}$ , and (d) Tb $M_{5}$ by cycling a 6-kOe field. The plotted graphs correspond to measurements performed at $T$ $=$ 290 K (a,b) and $T$ $=$ 400 K (c,d,e,f). The error bars obtained by repetitive XMCD measurements are the following: for RE, $S$ , and $L \pm 0.2 ℏ$ /at and for Co, $S \pm 0.1 ℏ$ /at and $L \pm 0.03$ $ℏ$ /at, corresponding to a percentage of the numerical values of $S$ and $L$ .Reuse & Permissions
Figure 2
Sketch of the element-specific magnetization (proportional to the XMCD) versus temperature for Co $_{0.74}$ Tb $_{0.26}$ , Co $_{0.86}$ Tb $_{0.14}$ , and Co $_{0.8}$ Gd $_{0.2}$ with respect to their compensation and Curie temperatures ( $T_{comp}$ and $T_{C}$ ) (Ref. 13). The compensation temperature is either above ( $T_{comp}$ $=$ 550 K for Co $_{0.74}$ Tb $_{0.26}$ ) or below ( $T_{comp}$ $=$ 10–150 K for Co $_{0.86}$ Tb $_{0.14}$ -Co $_{0.8}$ Gd $_{0.2}$ ) the sample temperature during the pump-probe experiment (the position is marked by the large filled circles). The large blue and red circles show the XMCD amplitudes obtained for the RE and resp. TM elements in the compounds at the working temperatures, taking into account the permanent heating by the IR laser. The small filled circles show the excited-state temperature after the thermalization of the electrons. This position is characterized by the minimum in the demagnetization curves observed for the TR-XMCD signal. The different pump fluences used during our experiment were adjusted to 12 mJ/cm $^{2}$ for Co $_{0.74}$ Tb $_{0.26}$ , 21 mJ/cm $^{2}$ for Co $_{0.86}$ Tb $_{0.14}$ , and 8 mJ/cm $^{2}$ for Co $_{0.8}$ Gd $_{0.2}$ , and is proportional to the increase in temperature (after the thermalization of the electrons) illustrated by the black arrows.Reuse & Permissions
Figure 3
Ultrafast dynamics of (a) Co $L_{3}$ , Tb $M_{5}$ for the Co $_{0.74}$ Tb $_{0.26}$ alloy and (b) Co $L_{3}$ , Gd $M_{5}$ edges for the Co $_{0.80}$ Gd $_{0.20}$ alloy. The respective simulations obtained by approximating the rate equations of the two-temperature model are superposed as smooth lines. For the sample Co $_{0.74}$ Tb $_{0.26}$ the best fits are obtained for τ $_{therm} = 280 \pm 30$ fs at the Tb $M_{5}$ edge and τ $_{therm} = 180 \pm 40$ fs at the Co $L_{3}$ edge. For the sample Co $_{0.80}$ Gd $_{0.20}$ the best fits are obtained for τ $_{therm} = 480 \pm 40$ fs at the Gd $M_{5}$ edge and τ $_{therm} = 200 \pm 20$ fs at the Co $L_{3}$ edge. The XMCD values at the working temperature ( $t < t_{0}$ ) are provided by using the XMCD data at the Co $L_{3}$ , Tb $M_{5}$ , and Gd $M_{5}$ edges from the static measurements as given in Fig. 1. The working temperature of the sample Co $_{0.74}$ Tb $_{0.26}$ is $T$ $=$ 400 K, whereas $T_{comp}$ $=$ 550 K. The working temperature of Co $_{0.80}$ Gd $_{0.20}$ is $T$ $=$ 290 K, whereas $T_{C}$ $=$ 450 K. During the pump-probe experiments, close values of laser fluences were used (8–12 mJ/cm $^{2}$ ), corresponding to close temperature intervals between working temperatures and the laser-excited-state temperatures where ultrafast demagnetization is observed.Reuse & Permissions
Figure 4
Ultrafast dynamics of Tb $M_{5}$ in Co $_{0.86}$ Tb $_{0.14}$ (red circles) and Co $_{0.74}$ Tb $_{0.26}$ (black squares) and the respective fit functions. The extracted thermalization time τ $_{therm}$ obtained at the Tb $M_{5}$ edge in Co $_{0.86}$ Tb $_{0.14}$ is 500 $\pm$ 100 fs, whereas in Co $_{0.74}$ Tb $_{0.26}$ τ $_{therm} = 280 \pm 30$ fs. The working temperature of the sample Co $_{0.74}$ Tb $_{0.26}$ is $T$ $=$ 400 K, whereas $T_{comp}$ $=$ 550 K. The working temperature of Co $_{0.86}$ Tb $_{0.14}$ is $T$ $=$ 400 K, whereas $T_{C}$ $=$ 700 K. During the pump-probe experiments, different values of laser fluences were used (8 and 21 mJ/cm $^{2}$ , respectively), corresponding to the difference in the temperature intervals between working temperatures and the laser-excited-state temperatures where ultrafast demagnetization is observed.Reuse & Permissions

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