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Ultrafast ferromagnetic fluctuations preceding magnetoelastic first-order transitions

First-order magnetic transitions are of both fundamental and technological interest given that a number of emergent phases and functionalities are thereby created. Of particular interest are giant magnetocaloric effects, which are attributed to first-order magnetic transitions and have attracted broad attention for solid-state refrigeration applications. While the conventional wisdom is that atomic lattices play an important role in first-order magnetic transitions, a coherent microscopic description of the lattice and spin degrees of freedom is still lacking. Here, we study the magnetic phase transition dynamics on the intermetallic LaFe13-xSix, which is one of the most classical giant magnetocaloric systems, in both frequency and time domains utilizing neutron scattering and ultrafast X-ray diffraction. We have observed a strong magnetic diffuse scattering in the paramagnetic state preceding the first-order magnetic transition, corresponding to picosecond ferromagnetic fluctuations. Upon photon-excitation, the ferromagnetic state is completely suppressed in 0.9 ps and recovered in 20 ps. The ultrafast dynamics suggest that the magnetic degree of freedom dominates this magnetoelastic transition and ferromagnetic fluctuations might be universally relevant for this kind of compounds.

3 crystallographic symmetries and are interpreted based on soft-mode phonons and their coupling with magnetic moments 10 . By contrast, there is a discontinuity of crystal unit cell volumes found in the latter with the crystallographic symmetry unchanged. The frequently adopted mechanism for this case is the itinerant electron metamagnetism (IEM) 11 . An IEM transition, i.e., a FOMT from Pauli paramagnetic (PM) to ferromagnetic (FM) states in an itinerant magnetic system induced by external magnetic fields, is formulated based on the Landau-Ginzburg free energy expansion taking into account the renormalization effect associated with spin fluctuations. A sharp peak in electronic density of states below the Fermi level tends to render a negative fourth-order coefficient of the free energy expansion and an IEM is expected as demonstrated in many rare-earth and transition-metal compounds 11 .
Among these compounds, LaFe13-xSix has attracted broad attention for its superior magnetocaloric performances 6,12 . With x in a very narrow doping range around 1.5, the system undergoes a sharp FM-PM FOMT at Curie temperature (TC) of about 190 K, where there is a strong magnetoelastic coupling as reflected in a dramatic negative thermal expansion (ΔV/V ~ 1.5%, where V is the unit cell volume). Above TC, a moderate magnetic field can induce a FOMT, giving rise to giant magnetic entropy changes of about -25 J kg -1 K -1 . TC of this system can be elevated up to 350 K by substituting Fe with Co atoms or by adding interstitial hydrogen atoms, which hardly reduces the magnetic-entropy changes 13,14 . For instance, La(Fe0.94Co0.06)11.9Si1.1 has maximum magnetic-entropy changes of -20 J kg -1 K -1 at TC ~ 280 K 14 . Moreover, the thermal and magnetic hysteresis at the FOMT is small compared with other giant magnetocaloric materials 6 . In terms of real applications, LaFe13-xSix is also costeffective given that it consists of earth-abundant elements. 4 Despite the outstanding magnetocaloric performances mentioned above that make this system promising for solid-state refrigeration applications, the exact mechanism of its FOMT remains unclear. A fundamental understanding of FOMT may foster the future designing of advanced magnetocaloric materials. IEM has been frequently used to account for the transition, but spin fluctuations themselves as the core of this mechanism have merely been investigated yet [15][16][17] . In recent neutron diffraction measurements, spin fluctuations arising from PM correlations were discovered above TC 18 . In addition, nuclear resonant inelastic X-ray scattering shows partial phonon density of state (PDOS) of Fe sublattices is renormalized across TC in LaFe11.5Si1.5 (ref. 8). Thus spin-phonon coupling is believed to play a critical role in this system 8 . To thoroughly clarify the FOMT, it is necessary to conduct research considering lattice and magnetic degrees of freedom in both static and dynamic respects. Here, we present an investigation comparing LaFe11.6Si1.4 and LaFe11.2Si1.8, which exhibit a FOMT and a second-order magnetic transition (SOMT), respectively. Combining quasi-elastic neutron scattering (QENS) and ultrafast X-ray powder diffraction (XPD) based on Xray free electron laser (XFEL), we are able to establish the differences between the two materials, and pinpoint the ultrafast FM fluctuations as the decisive factor in the FOMT and hence in the giant magnetocaloric effect.
LaFe13-xSix intermetallics crystalize in the cubic NaZn13-typed structure with space group 3 6 . As shown in Fig. 1a the phonon softening at the transitions, we track the peak at 24 meV as a function of temperature. As plotted in Fig. 1d, both compositions display remarkable softening.
The decreases of energy at heating from 100 to 300 K are similar for both, but the change of LaFe11.6Si1.4 is slightly sharper, consistent with its nature of FOMT.
Obviously, the magnetic softening of phonons across TC are not unique to FOMT, but also for SOMT. In this sense, phonon softening is impossible to solely account for differences between these two compositions. As such, in addition to phonons, we also examine the magnons. The FM states of both compositions show almost identical spin excitations below TC. At 100 K, for example, strong spin excitations develop from the first Bragg peak, (200), and persist up to about 2 meV (Supplementary Fig. 2).
Hereafter, we turn our attention to the PM states where spin fluctuations are expected.
In Fig. 2a, we plot the dynamic structure factor S(Q,E) as a function of momentum transfer (Q) and energy transfer (E) at selected temperatures near TC. In LaFe11.6Si1.4, at 210 K just above TC, intense diffuse scattering is observed in the low-Q region. The intensity goes weaker as temperature rises from 210 to 300 K, but pronounced diffuse scattering is still detected at 300 K. In LaFe11.2Si1.8, similar diffuse scattering is found 6 (see Supplementary Fig. 3). In search for possible differences between them, we exclude the elastic intensity by integrating the spectra in the intervals of - As the extra magnetic scattering intensity is peaked at 0.5 Å -1 , detailed constant-Q spectra are investigated at different temperatures for LaFe11.6Si1.4 (Fig. 2c) as well as for LaFe11.2Si1.8 (Fig. 2d). Below TC, the spectra exhibit strong elastic peaks. Just above TC, QENS components are superimposed underneath the elastic peaks. As the temperature continues to rise, the QENS components become broader and weaker. Even so, it is still visible at 1.6TC. However, it is apparent that LaFe11.6Si1.4 exhibits much stronger QENS intensity at the same reduced temperature. Also, the QENS components in LaFe11.6Si1.4 are more temperature-dependent as the intensity is significantly suppressed when the temperature is changed from 210 to 250 K.
Henceforward, spectral fitting is used to extract accurate information on spin dynamics from the QENS intensity. At 210 K for LaFe11.6Si1.4, the spectrum at 0.5 Å -1 is well reproduced by a combination of a delta function and two Lorentzian functions, which are all convoluted to the instrument resolution function (see Fig. 3a). The delta function represents the elastic scattering while the Lorentzian function accounts for the dynamic diffuse scattering containing information on dynamic spin correlations with finite timescales. The wider spectrum is, the faster spin fluctuations exist. This fitting yields 7 a full-width-at-half-maximum (Γ) of 5.237 and 1.152 meV, which are compared to 5.613 and 1.538 meV at 250 K, respectively. As shown in Fig. 3b, a similar fitting is applied to the spectrum of LaFe11.2Si1.8 at 250 K, which gives rise to Γ of 6.309 and 1.099 meV, respectively. Note that these line widths correspond to a typical picosecond timescale. Except for the three spectra mentioned above, others can be well reproduced by a combination of a delta function and one single Lorentzian function. As shown in Supplementary Fig. 4, the narrower one disappears with the wider one remained. The temperature-and Q-dependent fitting results are summarized in Supplementary Fig.

5.
Based on the precise separation of scattering intensity presented above, we sum up the At a given reduced temperature, it is evident that LaFe11.6Si1.4 has a slightly smaller ξPM than LaFe11.2Si1.8.
Unlike the PM scattering diverging towards lower Q, the intensity of the narrower Lorentzian function shows a well-defined peak at Q ~ 0.5 Å -1 , as shown in Fig. 3e and f. This position is close to the crystallographically forbidden Bragg peak (100) and the Q ~ 0.5 Å -1 peak represents ultrafast FM fluctuations 21 . This peak is fitted to a Gaussian Our ultrafast XPD study was carried out at the SPring-8 Angstrom Compact freeelectron LAser (SACLA). As the ultrafast XPD setup is constrained to room temperature, we select the Co-doped sample LaFe10.6Co1.0Si1.4, which undergoes a FM-

9
PM FOMT at about 304 K accompanied by a dramatic negative thermal expansion (ΔV/V ~ 1.5%, where V is the unit cell volume) with the cubic symmetry remained 13 .
An 800 nm laser is used to pump the material across the phase transition. The measurements were completed using the Diverse Application Platform for Hard X-ray diffraction in SACLA (DAPHINS) system 23 , where the powder sample was extruded from a nozzle at a fixed rate and the XPD images were acquired in a transmission Debye-Scherrer geometry. The schematic diagram of the experimental setup is shown in Fig. 4a and more details are given in Methods.
We used an incident laser fluence from 1.26 to 8.74 J cm -2 to excite the FOMT. Shown  Supplementary Fig. 7.
Immediately after the laser excitation, the (224) Bragg peak is found to shift to higher angles. The peak-shift maximizes at the time delay of 0.9 ps, with the peak subsequently shifting back to lower angles. At 20 ps, the peak position is almost identical to the Bragg peak (224) position before the optical excitation. Based on the aforementioned six Bragg peaks whose shifts are summarized in Supplementary Fig. 8, we derive lattice constants of 11.517 and 11.444 Å before and at 0.9 ps after the laser excitation as shown in Fig. 4c. These lattice constants are in agreement with the lattice constants of the FM and PM phases under thermal equilibrium 13 . Thus at 8.74 J cm -2 , the pump laser induces a full transient phase transition from FM to PM states.
In Fig. 4b, the peak position moves continuously between the equilibrium positions that define the FM phase (Q = 2.6720 Å -1 ) and PM phase (Q = 2.6908 Å -1 ) labeled with the vertical dashed lines, both during the transient phase transition and the recovery that followed. Considering the first-order nature of the phase transition under thermal equilibrium, the lattice constants shown in Fig. 4b and c reflect the averaged information of a phase-coexistence state. In fact, there is a pronounced broadening of all six Bragg peaks at the earlier stages, indicative of phase-coexistence ( Supplementary Fig. 9). As such, a more sophisticated fitting has to be employed.
To quantitatively describe the phase fraction, the (224) Bragg peaks are fitted to a sum of two Voigt functions centered at Q = 2.6720 Å -1 for the FM phase and Q = 2.6908 Å -1 for the PM phase. The fitted peak widths are summarized in Supplementary Fig. 10.
The FM phase fraction is evaluated by the ratio of the fitted area of the FM peak to the total area of the (224) peak. ultrafast XPD experiments carried out in iron and gold elemental metals 26,27 , but well consistent with that of other magnetic systems 28,29 . The ultrafast suppression thus suggests that the phase transition is dominated by factors other than the lattice.
Specifically, the typical size (l) of the particles used in our experiment is on the order of ~1 µm (Supplementary Fig. 11), which is significantly longer than the optical penetration depth of the 800 nm pump laser. As we are directly observing the evolution of crystalline Bragg peaks from the entire micron-sized particle, for complete

Data availability
The data of the present study are available from the corresponding author upon reasonable request.

Samples and magnetizations
LaFe11.6Si1.4, LaFe11.2Si1.8, and LaFe10.6Co1.0Si1.4 were prepared using an arc-melting method followed by a long time annealing to reduce the impurity phase of α-Fe, as previously described 6 . The obtained materials for the present study were of single-phase without Fe impurity identified in lab X-ray diffraction measurements. Scanning  40 .

Ultrafast XPD with XFEL
The XFEL experiments were carried out at BL03, SACLA in Japan 41