Spin stress contribution to the lattice dynamics of FePt

Abstract

<jats:p>Invar-behavior occurring in many magnetic materials has long been of interest to materials science. Here, we show not only invar behavior of a continuous film of FePt but also even negative thermal expansion of FePt nanograins upon equilibrium heating. Yet, both samples exhibit pronounced transient expansion upon laser heating in femtosecond x-ray diffraction experiments. We show that the granular microstructure is essential to support the contractive out-of-plane stresses originating from in-plane expansion via the Poisson effect that add to the uniaxial contractive stress driven by spin disorder. We prove the spin contribution by saturating the magnetic excitations with a first laser pulse and then detecting the purely expansive response to a second pulse. The contractive spin stress is reestablished on the same 100-ps time scale that we observe for the recovery of the ferromagnetic order. Finite-element modeling of the mechanical response of FePt nanosystems confirms the morphology dependence of the dynamics.</jats:p>

Heat Transport without Heating?—An Ultrafast X‐Ray Perspective into a Metal Heterostructure

“…[ 25,48 ] The calculated spatio‐temporal electron and phonon temperature maps (Figure 2) were used as input to calculate the transient strain by integrating a linear masses‐and‐springs model [ 36 ] considering the geometrical limitation of thin films on ultrafast timescales. [ 27,37 ] The modeled strain was leveled to the 330 mW UXRD data by scaling the source term accordingly. The Grüneisen coefficient of Pt and Cu had to be adjusted by approximately ±20% to match the observed expansion between 300 ps to 1 ns, where the temperatures of all metal layers are in equilibrium.…”

“…[36] It takes into account the absence of in-plane strains and the concomitant out-of-plane contraction. [37] The spatiotemporal strain η(z, t) (Figure 3) is used to calculate the X-ray diffraction pattern by dynamical X-ray diffraction theory. [26,30,38] γ S (mJ cm −3 K −2 ) 0.74 [33] 0.10 [33] 1.06 [33] 0.38 [51] -C ph (J cm −3 K −1 ) 2.85 [52] 3.44 3.94 2.33 [51] 1.80 [53] κ 0 e (W m −1 K −1 ) 66 [54] 396 [33] 81 [33,55] 52 κ ph (W m −1 K −1 ) 5 [54] 5 9.6 [55] 5 1 [53] g (PW m −3 K −1 ) 400 [56] 63 [56] 360 [56] 100 - [53] v s (nm −1 ps) 4.2 [57,58] 5.2 [56,90] 6.3 [61] 4.2 5.7 [53] Γ e 2.4 [62] (0.9) 0.9 [62] (1.1) 2.0 [62] 1.3 [62] -Γ ph 3.0 [62] (2.5) 1.7 [62] (2.1) 1.65 [62] 1.5 [62] 0.3 [53] www.afm-journal.de www.advancedsciencenews.com…”

“…[ 36 ] It takes into account the absence of in‐plane strains and the concomitant out‐of‐plane contraction. [ 37 ] The spatio‐temporal strain η( z , t ) ( Figure ) is used to calculate the X‐ray diffraction pattern by dynamical X‐ray diffraction theory. [ 26,30,38 ] The evaluation of the simulated Bragg peak shifts is plotted as continuous lines in Figures 1 and .…”

Reciprocal space slicing: A time-efficient approach to femtosecond x-ray diffraction

“…Several publications of our group were based on UXRD measurements applying the reciprocal space slicing approach. 8–10,42–48 We reviewed all of them and found that the claims and findings are still correct. In most cases, this is because the scaling factor is negligible due to large mosaicities of thin films and small diffraction angles.…”

“…It may be important to reanalyze experimental work in the field of ultrafast x-ray diffraction and strain assessment that uses some form of reduced reciprocal space analysis. 8–10,32–48 From the very early days of UXRD using plasma sources, the large convergence of the x-rays was used to speed up the measurements by area detectors. The correct scaling was often considered unimportant, maybe because experimental determination of the fluence introduces considerable uncertainties.…”