Spectroscopy of phononic switching of magnetization in the terahertz gap

All-optical schemes for switching magnetization offer a pathway towards the creation of more advanced data-storage technologies, both in terms of recording speed and energy-efficiency. It has previously been shown that picosecond-long optical pulses with central frequencies ranging between 12 and 30 THz are capable of driving magnetic switching in yttrium-iron-garnet films, provided that the excitation frequency matches the characteristic frequency of longitudinal optical phonons. Here, we explore how the phononic mechanism of magnetic switching in three distinct ferrimagnetic iron-garnet films evolves at optical frequencies below 10 THz, within the so-called terahertz gap. We find that at long wavelengths the magnetic switching rather correlates with phonon modes associated with the substrate. Our results show that the process of phononic switching of magnetization, previously discovered in the mid- to far-infrared spectral range, becomes much more complex at frequencies within the terahertz gap.

Magnetization reversal forms the basis of many data storage technologies including hard disk drives, magnetic tapes and magnetic random access memory.Magnetization can be reversed through various mechanisms, such as through the direct application of magnetic field [1], either by itself or in combination with heat [2], or through spinpolarized current pulses [3].A particularly appealing alternative lies in the use of optical pulses.Several light-based strategies that give rise to magnetic switching have been Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. recently elucidated.One approach, for example, relies on the process of ultrafast thermally-induced demagnetization in multi-sublattice ferrimagnetic alloys, leading to magnetic switching via the exchange of angular momentum between the antiferromagnetically-coupled constituents [4][5][6].Highlyefficient all-optical switching can also be engineered through ultrafast modification of the magnetocrystalline anisotropy [7] or through the resonant excitation of optical phonon modes [8].The latter schemes are especially interesting since they do not rely on the significant deposition of energy to drive the magnetic switching, but rather harness the laser pulse's optical properties [9].
Phononic switching of magnetization-the process through which magnetization is solely reversed by the excitation of optical phonons at resonance-poses an intriguing and somewhat counter-intuitive mechanism for magnetic reversal [8,10].The thriving research field of non-linear phononics has revealed that infrared-active transverse optical (TO) phonon modes, when driven at resonance to high amplitude [11,12], can give rise to a wealth of transient effects and functionalities such as promoting superconductivity to room temperature or transforming insulators into metals [13,14].In contrast, the phononic switching of magnetization appears to correlate with the frequency of infrared-inactive longitudinal optical (LO) phonon modes found within the ferrimagnetic iron-garnet [8], at least within the frequency range 10 to 30 THz (wavelength 10 to 30 µm).The displacement of domain walls in antiferromagnetic NiO also appears to become largest when pumping at frequencies characteristic of LO phonon modes [15].While the exact microscopic origin of this phononic mechanism of magnetic switching is not yet fully resolved, the peculiar non-uniform spatial distribution of the switched magnetization unambiguously reveals the role of macroscopic strains.
The unit cell of YIG contains a total of 80 atoms, and so the lattice dynamics of iron-garnet crystals is very complex with a large number of phonon modes [16].At frequencies above 10 THz (wavelengths shorter than 30 µm), the phonons mostly correspond to asymmetric oxygen-metal vibrations, which are intrinsically polar.This leads to a considerable splitting in the frequency of LO and TO phonon modes, which seems to be essential for phonon-induced magnetization switching [8,15].In contrast, at lower frequencies, optical phonons become more collective in character, comprising more complex motions of a larger number of atoms.Therefore, it can be assumed there would be less polar behaviour of such phonon modes, and the LO-TO splitting becomes small to absent.While the phononic switching of magnetization discovered in reference [8] clearly correlated in frequency with the spectrum of LO phonon modes, it is an open question as to whether this correlation persists at lower frequencies (longer wavelengths).
In this letter, we experimentally investigate how phononic switching of magnetization manifests when using narrowband optical pulses with central frequencies in the terahertz gap (3.3 THz to 10 THz).We show that phononic switching of magnetization can be achieved in three different YIG samples across a wide spectral range, with wavelengths between 30 and 90 µm.The studied samples differ by their orientation [either (001) or (111)], their magnetocrystalline anisotropy (cubic or uniaxial) as well as by their composition.As a result, each of the three studied films has a different domain structure, namely small stripe-like, uniform, and large stripe-like.Despite all these material differences, we observe light-induced switching that occurs in similar spectral ranges.However, at lower frequencies (longer wavelengths), we find that the magnetic switching no longer correlates with LO phonon modes.
In this work, we studied three widely-different samples of magnetic garnets, all of which are single crystals grown via liquid phase epitaxy, which has been the prevalent growth mechanism for garnet films in the last decades [17].The crystallographic unit cell consists of 4 formula units of Y 3 Fe 3+ 2 Fe 3+ 3 O 2− 12 .The Fe 3+ ions occupy inequivalent positions within the unit cell, namely either in an octahedral or tetrahedral oxygen ion cage.Exchange coupling between iron ions in these positions creates the net ferrimagnetism of YIG.
The aforementioned iron ions in the tetrahedral and octahedral sites can be occupied by a wide range of cations, allowing for excellent control of the saturation magnetization of YIG films.Likewise, the yttrium ion can be substituted by several rare-earth cations, which can lead to the formation of an additional magnetic sublattice [18].These substitutions can also shift the many phonon modes of YIG.
The first sample is a 7.5 µm-thick lutetium and bismuth doped YIG film with composition (Lu 1.69 Y 0.65 Bi 0.66 )(Fe 3.85 Ga 1.15 )O 12 , grown on (001) oriented gadolinium gallium garnet (GGG, Gd 3 Ga 5 O 12 ), hereafter referred to as Lu:YIG.This film has an extremely weak, fourfold, in-plane magnetic anisotropy of strength 4 kAm −1 , which creates four in-plane orthogonal equilibrium orientations of the magnetization [19].In its relaxed state, it displays a magnetization state with large domains that are easily affected by, for example, the Earth's magnetic field.
The second sample is a 7.3 µm-thick calcium, cobalt, and germanium doped film with composition (YCa) 3 (FeCoGe) 5 O 12 , grown on (001) oriented GGG with a miscut of 4 degrees, hereafter referred to as Co:YIG [8].The replacement of a small part of Fe-ions with Co results in a relatively strong cubic magnetic anisotropy with K 1 < 0 [20], causing the easy axes to coincide with the cube diagonals.This leads to a rather complicated domain pattern [21] with the magnetization having a total of eight equilibrium orientations.A modest magnetic field is sufficient to prepare a non-volatile single-domain state.The miscut allows better visibility of domains, without affecting magnetic properties of the sample [7].
The third sample is a 5µm-thick pure YIG film, grown on a (111)-oriented GGG substrate, hereafter referred to as pure YIG.It displays a regular stripe pattern magnetic domain structure (figure 3(a)) within its interior, which arises from competition between the uniaxial magnetocrystalline and shape anisotropies [22].The application of a magnetic field easily aligns the stripes with the direction of the field, with the alignment persisting after removal of the magnetic field.
We perform our experiments at the free-electron laser (FEL) facility FELIX in the Netherlands [23].This light source delivers transform-limited optical pulses at a rate of 25 MHz with a central wavelength λ tunable between 3 and 1500µm.For the experiments presented here, we used the spectral range λ = 30 to 90 µm (frequencies 3.3 to 10 THz).These so-called micropulses are enclosed within a 8 µs-long burst ('macropulse') coming at a rate of 10 Hz.A single macropulse, with a typical spectral full-width at half-maximum of not more than 1% (see supplementary materials), was focused onto the sample surface to a spot with a wavelength-dependent diameter varying between ≈300 and ≈500 µm.While the exact energy of the macropulses (0.5-2 mJ) depends on the specific settings of the FEL, the optical resonator within the FEL gives rise to minimal fluctuations of pulse-energy across the entire duration of a single experiment (≈8 h).Moreover, the reproducible spectral dependence of the pulse energy is frequently measured during the experiment to allow for comparison of results obtained during different experiments.Every measurement was repeated several times, and at different levels of pump pulse energy.The data shown in figures 1-3 are averaged over all the measured points.
To resolve the macropulse-induced switching of magnetization, the magnetic domains of the thin films were visualized using magneto-optical microscopy.The sample is illuminated with linearly-polarized light (white or green [520 nm]) and the transmitted light is collected by an objective lens and passed through an analyzer onto a CCD.The latter is synchronized with the arrival of the macropulse, and has an exposure time of 1 ms.The Co:YIG and pure YIG samples were oriented such that they were normal to both the impinging macropulse and the illuminating light, whereas the Lu:YIG sample was tilted by 30 degrees to allow the in-plane magnetization to be resolved.
In order to quantify the magnetization switching as a function of pulse parameters, two algorithms were used.For the Lu:YIG and Co:YIG thin films, which display rather large domains, a thresholding algorithm is used.After subtraction of the non-magnetic background, the magneto-optical images typically show a lighter and darker area corresponding to different magnetization orientations (figures 1(a) and 2(a)).Each pixel is then classified as being white or black with the threshold defined by the mean pixel intensity, after which the ratio of switched pixels to the total number of pixels is calculated.This is then normalized to the image displaying the strongest switching, i.e. the largest domains of switched magnetization.This threshold-based algorithm cleanly separates the switched and unswitched areas of magnetization, providing a clear and unambiguous measure of the switched area.
For the pure YIG sample that displays a small stripe-like domain structure rather than large domains, the aforementioned threshold-based algorithm cannot be straightforwardly used to quantify the magnetic switching, since the initial magnetic state is highly non-uniform.Instead, the structural similarity index measure is calculated for each pair of images taken before and after optical exposure, which compares the images based on (i) luminance, (ii) contrast, and (iii) structure [24].As a result, a value between 0 (no similarity) and 1 (perfect similarity) is obtained.To facilitate straightforward comparison, we invert this measure so that '1' corresponds to complete switching and '0' corresponds to a complete absence of switching, after which the values are normalized to the highest value.
Magnetic hysteresis loops were measured using light of wavelength λ = 520 nm, which is focused on the surface of the sample.High sensitivity is obtained by our use of a photoelastic modulator in combination with a lock-in amplifier.An electromagnet is used to apply a magnetic field either parallel or perpendicular to the plane of the film.
Upon exposing the Lu:YIG film to a macropulse with certain wavelength, we observe that the phononic switching manifests in the creation of two distinct 'wings' of switched magnetization (figure 1), away from the centre of the image where the infrared macropulse impinges on the sample.Note that only two magnetic domains are observed, even though the sample exhibits a four-fold in-plane anisotropy.We find that this pattern is rather typical when the thin film is exposed to a macropulse, whereas a single micropulse generally gives rise to four magnetic domains [10].We speculate that this drastically different pattern stems from the slower processes of domain formation that occur across the time scale of microseconds.Furthermore, note that the switched area extends beyond the image, which unfortunately results in a certain saturation effect when quantifying the spectral dependence.
The magnetic switching identified in Lu:YIG spans two distinct spectral ranges within λ = 30-58 µm and λ = 80-90 µm.At shorter wavelengths, full exposure to the unattenuated macropulse appears to broadly saturate the spatial extent of the magnetic switching.With attenuation of the pump pulse, however, a more defined spectral dependence is observed, with the switching becoming substantially diminished in the range λ = 32 to 36 µm and absent at λ = 33µm This behavior is uncorrelated with the wavelength-dependent energy of the pump, as shown in the bottom panel of figure 1(c).At wavelengths above 60 µm, the switching is absent, possibly correlating with the reduction in the energy of the pump pulse, except for the spectral region 75 to 90 µm where switching is again observed.
The phononic switching of magnetic states in Co:YIG film was studied before in the wavelength range of 10-30 µm [8].The result of exposing the same Co:YIG film to pump pulses with longer wavelength is presented in figure 2(c).For the entire spectral range, an observable effect could only be found when exposing the sample to an unattenuated macropulse.We clearly observe that the switching can be achieved again in two spectral ranges, from λ = 35 to 65 µm and 85 to 92 µm.Note that the pump power spectrum is flatter for this measurement compared to that of the other two samples, having a much reduced intensity in the range below 60 µm.
The phononic switching in the pure YIG sample (figures 3(a)-(b)) takes the form of magnetization reorienting from a state where domain walls run parallel to each other to a more disordered state where the domain walls become oriented in seemingly random directions.This reorientation appears at all wavelengths in the range 30 to 55 µm when the pump pulse is attenuated by 3 dB (0.5 to 1 mJ, wavelength dependent) and 5 dB (0.3 to 0.6 mJ).At these wavelengths the unattenuated pump pulse (1 to 2 mJ) damages the sample.In the range λ = 55 to 65 µm, reorientation is absent, which coincides with a drop in pump pulse intensity.However, when the drop in intensity was compensated by removing any attenuation from the pump beam (0.5 to 1 mJ), reorientation still did not occur.In the ranges 65 to 75 µm at 3 dB attenuation (0.3 mJ) and the range 85 to 90 µm with no attenuation (0.5 mJ) reorientation was observed.0 dB attenuation measurements were only performed in the region from 60 to 90 µm, to prevent damage to the film.
Wavelength-dependent switching of magnetization was observed in all three studied samples (figures 1(c), 2(c) and 3(e)), showing the mechanism of magnetic switching is rather general and appears to be independent of the irongarnet's doping, orientations and magnetic anisotropies.We note that the three samples produce different switched magnetization patterns due to their difference in magnetic anisotropies, but that the switching occurs in similar wavelength ranges due to the similarity in phonon modes of the samples.Moreover, our measurements are consistent in showing that the switching probability does not correlate with any particular changes in the macropulse energy.Indeed, the size of the switching correlates to some extent to the macropulse energy (seen most clearly in figure 1(c) below 60 µm), but the pulse energy by itself cannot explain the wavelength dependence of the observed switching (e.g. the part of figure 1(c) above 60 µm).For Lu:YIG, the dip at 33 µm does indeed correlate with the disappearance of switching.However, this effect, indeed likely due to the reduction in pump energy, can be compensated by decreasing pump attenuation as is shown in figure 1(c).This is in contrast to the region above 60 µm, where the pump energy is more or less constant and switching is absent between 60 and 75 µm but not between 75 and 90 µm.The specific wavelengths at which switching occur differ slightly between samples, presumably owing to the differences in phonon modes resulting from differing dopings.
In the previously-studied wavelength regime (up to 30 µm), the magnetization switching was clearly achieved with pumping frequencies resonant with the LO phonon modes [8].However, at longer wavelengths, this behaviour appears to change, as we do not observe such correlation in Co:YIG (compare figure 2(c), middle and bottom panels).Turning our attention to the GGG substrate, there appears to be resonant behaviour with the GGG phonons of the substrate as measured by infrared ellipsometry [8], depicted in the top panels of figures 1(c), 2(c) and 3(e).Specifically, all three samples show switching around λ =85 µm, where multiple GGG phonon modes can be found.Furthermore, magnetization switching in the pure YIG sample also occurs around λ =68 µm, where another GGG phonon mode exists, and is otherwise absent in spectral regions without GGG phonon modes.Lastly, we point out that for Co:YIG (figure 2) switching is observed at around λ =90 µm, a spectral range where GGG phonon modes exist, but YIG phonon modes are absent.We speculate that slight differences of sample thickness (which are all on the order of several micrometers) may also play a role in the spectral dependence of the switching, since the impinging radiation has a wavelength much longer than the sample thickness.
In conclusion, our results reveal that the mechanism of phononic switching of magnetization persists at light frequencies below 10 THz (wavelengths above 30 µm) albeit with more complexity.In particular, at wavelengths above 50 µm, we observe that magnetic switching correlates neither with longitudinal nor TO phonon modes characteristic of the YIG sample.Instead, the switching appears to correlate with the frequencies of infrared-active phonon modes associated with the substrate.As an outlook, further works must explore how the substrate microscopically influences the switching process, as well as quantifying the speed and efficiency of the general mechanism comprising phononic switching of magnetization.

Figure 1 .
Figure 1.(a) Typical background-subtracted image of the in-plane magnetization of Lu:YIG, taken after exposure to a 37 µm infrared macropulse.The magnetization orientation is indicated by the pink arrows.(b) The magnetic hysteresis of Lu:YIG.(c) Top panel: Imaginary parts of the dielectric function ϵ(ω) (purple) and the loss function −1/ϵ(ω) (green) for GGG [8].Middle panel: Reflectivity spectrum of Lu:YIG.Bottom panel: Spectral dependence of the area of magnetization switched by a single macropulse.The three curves correspond to measurements performed with different levels of attenuation as shown.The black line corresponds to the spectral variation of the macropulse energy (with 0 dB attenuation).

Figure 2 .
Figure 2. (a) Background-corrected image of the magnetization state of Co:YIG after excitation with a 55 µm infrared pulse.The pink arrows indicate the in-plane projection of the magnetization.(b) The hysteresis curve of Co:YIG.(c) Top panel: Imaginary parts of the dielectric function ϵ(ω) (purple) and the loss function −1/ϵ(ω) (green) for GGG [8].Middle panel: Reflectivity spectrum of Co:YIG, as well as the dielectric loss function of Co:YIG (orange) and the the absorption (blue).Bottom panel: the area of magnetization switched in Co:YIG by a single macropulse (green) and the spectral dependence of the macropulse energy (black line).

Figure 3 .
Figure 3. Cropped image of the magnetic domains taken (a) before, and (b) after exposure to a 40 µm pump pulse, for the full images see supplementary material.(c) Sketch of the magnetization directions inside the pure YIG thin film, with the vectors on the faces portraying the projections of the net magnetization.Adapted from reference [22].(d) The hysteresis curves of pure YIG obtained with an out-of-plane (blue) and in-plane (orange) magnetic field.(e) Top panel: Imaginary parts of the dielectric function ϵ(ω) (purple) and the loss function −1/ϵ(ω) (green) for GGG [8].Middle panel: Reflectivity spectrum of pure YIG.Bottom panel: The area of magnetization reorientation by a single macropulse with varying wavelength and attenuation as indicated as well as the energy of the infrared macropulse.