Mode-resolved detection of magnetization dynamics using x-ray di(cid:27)ractive ferromagnetic resonance

Collective spin excitations of ordered magnetic structures o(cid:27)er great potential for the development of novel spintronic devices. The present approach is to rely on micromagnetic models to explain the origins of dynamic modes observed by ferromagnetic resonance (FMR) studies, since experimental tools to directly reveal the origins of the complex dynamic behavior are lacking. Here we demonstrate a new approach which combines resonant magnetic x-ray di(cid:27)raction with FMR, thereby allowing for a recon-struction of the real-space spin dynamics of the system. This new di(cid:27)ractive FMR (DFMR) technique builds on x-ray detected FMR (XFMR) that allows for element-selective dynamic studies, giving unique access to speci(cid:28)c wave components of static and dynamic coupling in magnetic heterostructures. In combination with di(cid:27)raction, FMR is elevated to the level of a modal spectroscopy technique, potentially opening new pathways for the development of spintronic devices.

Innovative magnetic materials have played a pivotal role for the increase in data storage capacity over the past decades, and have lead to the advent of spintronic devices. Especially multilayers in, e.g., giant magnetoresistance or tunneling magnetoresistance structures, contributed signicantly as they allow for a precise design of their magnetic properties. 13 Recently, topologically ordered magnetic systems, such as skyrmions, and multiferroic materials in which ordered magnetic moments can be manipulated via the application of an electric eld, have been the focus of attention as they promise high-density and low-energyconsumption data processing solutions.
Among the various techniques to study the magnetization dynamics of these magnetic systems, such as time-resolved magneto-optical Kerr eect measurements and Brillouin-light scattering, 4 ferromagnetic resonance (FMR) is widely used. 58 The most common approaches in FMR use either a broadband coplanar waveguide (CPW) or a resonant cavity design, restricted to the study of the total magnetization only. Magnetic devices, however, consist of several dierent layers whose properties can only be inferred indirectly by comparing experimental FMR spectra with micromagnetic models. 8 Synchrotron radiation-based x-ray detected FMR (XFMR) was developed to study element-specic magnetization dynamics, thus giving layer-selective resolution of the magneto-dynamics in multilayer samples. 919 Magnetic and chemical contrast is provided by the x-ray magnetic circular dichroism (XMCD) eect, 20,21 while the phase dierence between the spin precessions can be determined using stroboscopic sampling. However, for complex spin structures such as helical or skyrmion systems, the net magnetization probed by the x-ray beam can vanish, rendering normal XFMR unsuitable. Time-resolved scanning transmission x-ray microscope (STXM), 22 on the other hand, allows for the detection of FMR modes with a spatial resolution down to a scale of ∼25 nm. 23 This XMCD-based technique has been successfully used to investigate magnetic nanoscale system such as spin waves generated by a spin torque oscillator, 22 single and coupled nanomagnets, 24 and spin wave excitation and propagation in 1D and 2D. 23 Resonant elastic x-ray scattering (REXS) in the soft x-ray regime is an ideal tool to study periodically ordered spin systems. Since the incident x-rays can be chosen as linear or circular polarized all three components of the magnetization vectors can be accessed. 25 In REXS, periodic magnetic (super)structures lead to satellites which appear around the structural peaks in reciprocal space.
Here, we introduce x-ray detected diractive ferromagnetic resonance (DFMR) as a novel synchrotron radiation-based technique, combining both REXS and FMR, to selectively probe dynamic spin modes from specic periodic features. Magnetic contrast originating from xray magnetic circular (or linear) dichroism is probed stroboscopically revealing the time dependence of the magnetization precession. With periodic magnetic structural features providing diraction peaks in a scattering geometry, the dynamics purely associated with these periodic structures can be uniquely identied. Using the rich magnetic structure of a Ytype hexaferrite as an example, we demonstrate the capabilities of DFMR. With signicant interest in chiral and rich topological spin structures for potential technological devices, techniques to probe the dynamics of these systems are of signicant importance.
DFMR essentially combines two established techniques in order to study the moderesolved magnetization dynamics. First, REXS in the soft x-ray regime reveals the static magnetic structure in reciprocal space. REXS can be carried out at a synchrotron facility using a diractometer which provides a variable sample temperature and magnetic eld environment in ultrahigh vacuum. Under the diraction condition the spatial resolution d is determined by the Bragg condition d = λ/(2 sin θ), where θ is the Bragg angle and λ the wavelength which is, e.g., 17.5 Å at the Fe L 3 absorption edge. Second, x-ray detected FMR, which is based on the XMCD eect, gives conventional FMR the ability to probe the element-specic spin dynamics. The incident x-rays are tuned to the corresponding L 2,3 absorption edge of the 3d transition metal element of interest. For XFMR, the sample is attached to a coplanar waveguide, placed inside of a variable magnetic eld, and excited with microwave radiation. The magnetization dynamics is sampled stroboscopically, i.e., the microwave frequency has to be an integer multiple of the x-ray pulse frequency of the  the sample placed onto a CPW on the cryostat inside a soft x-ray diractometer. A magnetic eld can be applied in the scattering plane along the CPW. The energy of the incident xrays is tuned to the Fe L 3 absorption edge of the hexaferrite sample. Static structural and magnetic diraction peaks are detected with a photodiode. For dynamic measurements, a specic diraction peak is selected and an amplitude-modulated RF signal (pump) is applied to the sample. The probing x-rays are pulsed at ∼500 MHz, and a comb generator provides higher harmonics of the pulse frequency to the sample. A delay line enables phase shifting of the microwave oscillation with respect to the x-ray pulses. Additionally, VNA-FMR can be measured in the diractometer (not shown here).
synchrotron of 499.68 MHz (the master oscillator clock of the Diamond storage ring). A delay line allows for a phase shifting of the microwave oscillation with respect to the x-ray pulse. This way, the XMCD can be monitored as a function of the delay between RF excitation (pump) and x-ray bunch arrival (probe), whereby x-ray absorption is often detected in transmission using the optical luminescence of the substrate. 18 DFMR combines REXS and XFMR by measuring the change in intensity of the scattered peaks resulting from the stroboscopic probing of the magnetic structure. As for XFMR, a microwave signal passing through a coplanar waveguide is used to excite the sample.
However, in contrast to XFMR, which uses a transmission geometry, the sample surface has now to face up to allow for the x-rays to scatter. Consequently, the sample has to be suitably thin such that the magnitude of the RF eld is suciently strong to drive the magnetization dynamics at the sample surface. As for XFMR, the driving RF is phase-locked to an integer multiple of the synchrotron master oscillator clock. This synchronization means that photons probe the sample at specic points in time within the RF excitation waveform, thus providing a stroboscopic measurement of the magnetic state. Using a variable length delay line allows for the measurement of the time evolution of the diracted intensity. To enhance the signal, the RF signal was amplitude-modulated at 1.9 kHz and the dynamic contributions were detected using a lock-in amplier. A schematic of the experimental setup is shown in Figure 1.
Hexaferrites are particularly interesting materials for information storage applications since they are magnetic and in some cases multiferroic at room temperature. 2628 There are three main types of hexaferrites relevant to magnetoelectric phenomena and applications.  29 which has a rich magnetic behavior. 28 Vector network analyzer (VNA) FMR measurements form an important part of the precharacterization of systems for DFMR. Broadband VNA-FMR is used for studying the magnetic resonance modes of a sample and to determine the eld needed to drive magnetic resonance at the specic frequencies, as required for DFMR. VNA-FMR measurements can also be performed in-situ in the diractometer. Figure 2a shows the RF absorption of the hexaferrite sample as a function of frequency and applied in-plane bias eld (perpendicular to the RF eld). The hysteresis loop measured in resonant x-ray diraction is shown in Figure 2b. Figure    A deeper understanding of the magnetization dynamics of the resonance modes can be achieved by carrying out DFMR on dierent scattered peaks and also by varying the polarization of the probing x-ray beam. 33 Figure 5 shows the delay scans from the magnetic  The other ferromagnetic resonance mode (mode A) shows a very dierent dynamic behavior compared to mode B. Figure 5b shows the equivalent DFMR delay scans on the three diractive peaks whilst the system was driven in the ferromagnetic resonance mode at 2 GHz in a eld of 5 mT. At this RF frequency, the periodicity of the sinusoidal delay scans is 500 ps (as seen for all three diraction peaks). For both magnetic peaks in mode A, the amplitude is again modulated with η, however, in more complex way. For q 1 a large signal is detected from 170 • to (180 • +) 90 • , consistent with a sinusoidal dependence on η, however, now oset from zero. For q 2 , a somewhat larger signal is conned to 80-140 • , now with an opposite oset. In contrast to mode B, the DFMR measured on the structural (0,0,3) peak for mode A in Figure 5b shows no variation in phase with polarization angle.
REXS measured with linear polarization of the incident beam is sensitive to the components of the magnetic moments in and out of the scattering plane. The magnetic Bragg peaks originate from pure magnetic scattering with intensity given by Eq. (17) of Ref. 25 The structural Bragg peaks arise from charge scattering as well as charge-magnetic interference scattering with intensities given by Eqs. (16) and (18)  In conclusion we demonstrate a novel experimental technique for probing magnetization dynamics arising from dierent spatial frequencies within magnetic material systems. The power of x-ray detected ferromagnetic resonance is combined with that of resonant elastic xray scattering, giving dynamic information of specic magnetically ordered periodic phases.
The data collected as a function of linear polarization of the x-rays enables us to extract the microscopic information of the magnetization dynamics. We demonstrate the ability of DFMR to study distinct magnetic phases through measurements on Y-type hexaferrite which contains a rich level of complexity. The use of this technique applied to further magnetic systems will allow complex magnetic dynamic processes to be interrogated in the future. Sample Preparation. Single crystals of Ba 2 Mg 2 Fe 12 O 22 were prepared by crystallization from high-temperature Na 2 O-Fe 2 O 3 ux melted at 1420 • C in a Pt crucible and slowly cooled to 1100 • C after a thermal recycle. The as-grown crystals were characterized by both x-ray diraction and SQUID magnetometry.  36 The beam spot size at the sample position is typically 100 × 100 µm 2 , thereby avoiding the eects of non-uniform microwave excitation. 8 The sample can be cooled to 12 K while a variable magnetic bias eld can be applied in the scattering plane. Here, this bias eld was applied in the plane of the sample, which was kept at room temperature.
A small microwave eld perpendicular to the bias eld is applied to drive the magnetization in precession at its resonance frequency. The DFMR experiments were performed using linearly polarized soft x-rays with variable polarization angle, and with the energy tuned to the Fe L 3 absorption edge at 707.7 eV. The detector slits provide an angular resolution of 3 mrad. DFMR measures the variation in intensity of the scattered peaks resulting from the stroboscopic probing of the magnetic structure with a pulsed x-ray source synchronized with magnetic dynamic processes. For this purpose, we used the 900-bunch operation mode at the Diamond Light Source, providing pulsed photon bunches (41.5 ± 0.2) ps FWHM at a repetition frequency of the synchrotron master clock (499.68 MHz). 37 For the stroboscopic measurements, the microwave frequency has to be a harmonic of the x-ray pulse frequency, hence the resonance is driven at multiples of the clock frequency, corresponding to a ∼2 ns interval between consecutive x-ray pulses. Using lters and subsequent ampliers, the CPW is excited by a narrow band, high power microwave eld of 25-30 dBm. The phase shifting of the microwave oscillation with respect to the x-ray pulses is accomplished with a programmable delay line (time step resolution 0.5 ps). The pulse width of the x-rays (∼41 ps) is limiting the maximum DFMR frequency to ∼15 GHz, 38 and it is further reduced by microwave losses to ∼11 GHz. The timing jitter of the master oscillator signal at the Diamond synchrotron measured using a spectrum analyzer at the beamline was found to be negligible. Note, however, that in the stroboscopic measurement the jitter ultimately determines the time resolution, not the x-ray pulse width. Finally, the real and imaginary parts of the DFMR signal (or the amplitude and phase) were extracted using audio frequency modulation (1.9 kHz) and lock-in detection.