Magnetic control of phonon transport in magnetic insulator thulium iron garnet | Communications Materials

Communications Materials volume 5, Article number: 243 (2024) Cite this article

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The coupling between magnons and phonons and the associated phenomena have long been a focus of research in condensed matter physics. Contrary to its recognized role in magnon relaxation, its impact on phonon transport remains largely unexplored. Here, we fill this gap by investigating the effect of magnon-phonon coupling on phonon excitation, relaxation, and transport with magneto-optical reflectometry. Through simultaneous measurements of magnon and phonon populations in magnetic insulator thulium iron garnet, we observe the excitation of excessive phonons driven by non-equilibrium magnons, demonstrating the magnetic control of phonons. Furthermore, our time-resolved experiments reveal the magnetic field-dependent phononic thermal conductivity, signaling the potential of magnetic manipulation of heat transport. Our finding indicates that phonons can be controlled by magnetic means through magnon-phonon coupling and thereby opens a new avenue to harness magneto-thermoelectric effects in magnetic insulators.

Magnons and phonons, two of the most prominent bosonic excitations governing the magnetic and thermal properties of magnetic materials, lie at the heart of condensed matter physics. The interplay between these two quantum entities, referred to as magnon-phonon coupling, plays a significant role in various intriguing phenomena, e.g., the spin Seebeck effect1,2,3,4,5,6,7,8 and quasi-equilibrium Bose-Einstein condensation of magnons9,10,11,12. Recent advancements in quantum information science have further highlighted the significance of magnon-phonon coupling, e.g., for the coherent information interconversion in quantum transducers13,14,15.

In the field of spintronics, understanding magnon-phonon coupling is crucial because of its impact on magnon relaxation, as delivering spin information over a long distance is a major challenge in spintronics. Intensive research efforts have been devoted to unraveling the effect of magnon-phonon coupling on coherent magnon lifetime, with early theoretical and experimental works establishing its pivotal role16,17. Recently, including a monumental work on the long-distance spin information transport with magnons18, there were several experimental19,20,21,22,23,24,25 and theoretical works26,27,28 emphasized the crucial role of magnon-phonon coupling for determining the magnon relaxation length.

Despite the extensive investigations into the effect of magnon-phonon coupling on magnon relaxation, its reciprocal process–the influence of magnon-phonon coupling on phonon relaxation–has largely been overlooked. There are a few reports on the magnetic control of coherent phonon transport, such as the magnetic control of a non-reciprocal surface acoustic wave transmission29,30, the coherent interconversion between propagating magnons and phonons31,32 and resonant phonon pumping driven by magnons33,34. However, the effect of magnon-phonon coupling on incoherent phonon relaxation, transport, and the resultant thermal transports remain nearly unknown.

In this work, we investigate phonon excitation and transport induced by magnon-phonon coupling in the magnetic insulator thulium iron garnet (Tm3Fe5O12, TmIG). TmIG was chosen as our material platform since its magnetic properties have strong temperature dependence. In particular, it exhibits temperature-dependent magnetic anisotropy transition from perpendicular to in-plane magnetic anisotropy at around T = 300 K, whereby magnon excitation can be easily controlled by changing temperature and magnetic field. Through optical reflectometry, we independently detect magnons and phonons by measuring Kerr rotation and reflectivity. Upon current-induced heating, we observe the excitation of magnons and phonons at the low field regime. Remarkably, the results reveal that the excited phonons are suppressed by increasing the magnetic field that suppresses the thermal magnons but does not couple to phonons directly, indicating that phonon excitation is augmented by magnons through magnon-phonon coupling. More importantly, we reveal that the relaxation time of thermally excited phonons also depends on the magnetic field, suggesting the controllability of phononic thermal conductivity by magnetic field. Theoretical analysis elucidates that the magnetic variation of the phononic thermal conductivity can be understood as the effect of nonlinear magnon-phonon scattering, wherein one magnon creates one phonon and another magnon and vice versa. Conventionally, magnons were believed to contribute to heat conduction primarily at low temperatures, and a substantial magnetic field was required to control the magnon-driven heat conduction35,36,37,38. However, our results demonstrate that magnons can influence heat conduction even at room temperature through nonlinear magnon-phonon coupling. Consequently, the thermal conductivity can be controlled using modest magnetic field, providing a new pathway for controlling thermal properties of solids.

Figure 1a illustrates our experiments schematically. We prepared a TmIG film and patterned it into a microstrip. A current injection line was fabricated on the left side of the TmIG wire to induce thermal magnons and phonons excitation. The detection of thermally excited magnons and phonons was accomplished by measuring Kerr rotation and optical reflectivity, respectively (refer to the Methods section for details). Before conducting the main experiments, we characterized the magnetic anisotropy of the TmIG. We obtained the Kerr hysteresis curve of the TmIG micro-strip by sweeping an out-of-plane magnetic field at various substrate temperatures (\({T}_{{{\rm{sub}}}}\)). As depicted in Fig. 1b, a clear square hysteresis is observed at \({T}_{{{\rm{sub}}}}\) = 280 K, indicating perpendicular magnetic anisotropy (PMA) of TmIG at this temperature. Conversely, a gradual change in the hysteresis at \({T}_{{{\rm{sub}}}}\) = 320 K indicates the presence of in-plane magnetic anisotropy (IMA) at the higher temperature. This observation demonstrates that our TmIG undergoes anisotropy change from PMA to IMA with increasing temperature. This result not only aligns with previous reports on the TmIG thin films39,40, but also confirms the controllability of PMA strength through \({T}_{{{\rm{sub}}}}\).

a Schematic illustration of the experimental setup. The electric current thermally excited both magnons and phonons in TmIG, and their thermal excitation was controlled by the magnetic field. Population of thermally excited magnons and phonons was captured by the change of Kerr rotation (\({{\Delta }}{{{\theta}}}_{{{2}}{{\omega }}}\)) and reflectivity (\({{\Delta }}{{{R}}}_{{{2}}{{\omega }}}\)), respectively. The polarization of the incident light is aligned with the \({x}\) direction. b Substrate temperature (\({T}_{\rm{sub}}\)) dependent MOKE hysteresis of the TmIG micro-strip. Magnetic hysteresis shows the transition from PMA to in-plane magnetic anisotropy (IMA) as \({T}_{\rm{sub}}\) increases.

To excite magnons and phonons, we injected an alternating current through the current injection line. As the current-induced Joule heating is a current-even effect, the thermally driven magnons and phonons were characterized by examining the second harmonic responses of the laser beam (refer to the Supplementary Note 1 and 2 for more details). Figure 2 shows the Kerr rotation (\({\theta }_{k}\)), second harmonic change of the Kerr rotation (\(\varDelta {\theta }_{2\omega }\)) and second harmonic change of the reflectivity (\(\Delta {R}_{2\omega }\)) measured at \({T}_{{{\rm{sub}}}}\) = 300 K while sweeping the out-of-plane magnetic field. A current with a density of \(2.5\times {10}^{11}\,\)A/m2 was injected into the electrode, and the reflected beam was measured at a distance 5 µm from the electrode. The Kerr rotation, \({\theta }_{k}\), exhibits a gradual change around zero magnetic fields and saturates around \({\mu }_{0}H\) = ± 5 mT [see Fig. 2(a)]. This observation suggests complete alignment of the TmIG magnetization along the out-of-plane direction above \({\mu }_{0}H\) = ± 5 mT, even under the injection of the electric current. In contrast, the variation in Kerr rotation, \(\Delta {\theta }_{2\omega }\), maintains a finite value even beyond the saturation field (~ ± 5 mT) and shows a gradual decrease with increasing magnetic field [refer to Fig. 2b]. This critical magnetic field dependence of \(\Delta {\theta }_{2\omega }\) implies the over-population of low-energy magnons whose energy is close to the magnon gap energy. This over-population of low energy magnons can be achieved either by the spin Hall effect23 or by the thermal excitations11,41. Remarkably, \(\Delta {R}_{2\omega }\), representing the population of thermally excited phonons, follows a similar trend to \(\Delta {\theta }_{2\omega }\) as we sweep the magnetic field. It gradually decreases with increasing magnetic field even after reaching the magnetization saturation field [see Fig. 2c]. Showing that the possible contributions by current-induced magnetic field are negligible to the second harmonic responses [see Supplementary Note 4], this observation suggests the possible correlation between thermal excitation of magnons and phonons, where phonons are excited not only by pure thermal fluctuations but through the interaction with magnons. We note that our discussion excludes the regime (\(\left|{\mu }_{0}H\right|\) < 5 mT) where the magnetization is not fully saturated, as the magnon number is not well-defined due to randomly distributed magnetization or random magnetic domains. Hence, we will restrict our discussion to the field-saturated regime where the magnetization is perpendicular to the film, and therefore the number of magnons can be characterized well.

a Magnetic hysteresis of the TmIG. Magnetization of TmIG perpendicularly saturated after ±5 mT. b Magnetic field response of \({{\Delta }}{{{\theta}}}_{{{2}}{{\omega }}}\). It showed critical enhancement at the low magnetic field, even after saturation of TmIG magnetization. c Magnetic field response of \({{\Delta }}{{{R}}}_{{{2}}{{\omega }}}\). It also showed critical enhancement at the low magnetic field that is akin to the enhancement of the variation of the Kerr rotation shown in (b). We fixed \({T}_{\rm{sub}}\) = 300 K, \({{{j}}}\) = 2.5 × 1011 A/m2, and the laser position 5 μm apart from the edge of heating wire. Hereafter, green, cyan solid lines and gray dotted lines are guidelines for eye, and shaded regions represent the critical enhancement of thermally excited magnons (green) and phonons (cyan). Error bars represent the standard deviation of three equivalent measurements.

To further validate the correlation between thermal excitation of magnons and phonons, we performed controlled experiments by modulating magnon excitations. The Bose-Einstein distribution function highlights the significance of both the magnon energy gap and the magnon chemical potential in determining the number of magnons. Thus, the modulation of magnon excitation can be influenced by alterations in these parameters. We first modulate the magnon energy gap by changing the \({T}_{{{\rm{sub}}}}\), which is known to influence the magnon energy gap through magnetic anisotropy modulation, as shown in Fig.1b. Figure 3a–f shows the magnetic field dependence of \(\Delta {\theta }_{2\omega }\) [Fig. 3a–c] and \(\Delta {R}_{2\omega }\) [Fig. 3d–f] with different \({T}_{{{\rm{sub}}}}\), focusing on the variation after magnetization saturation field. The results show an enhancement in \(\Delta {\theta }_{2\omega }\) (thermal magnon excitation) at higher \({T}_{{{\rm{sub}}}}\), attributed to a decrease in the PMA strength at higher \({T}_{{{\rm{sub}}}}\), thereby reducing the magnon energy gap. Notably, \(\Delta {R}_{2\omega }\) follows the same trend as \(\Delta {\theta }_{2\omega }\), indicating enhanced phonon excitation at higher \({T}_{{{\rm{sub}}}}\) and reaffirming the correlation between thermally excited magnons and phonons.

a–c Magnetic field response of \({{\Delta }}{{{\theta}}}_{{{2}}{{\omega }}}\) under different \({T}_{\rm{sub}}\). The critical enhancement of thermal magnon excitation is enlarged by the reduction of PMA strength of TmIG. d–f Magnetic field response of \({{\Delta }}{{{R}}}_{{{2}}{{\omega }}}\) under different \({T}_{\rm{sub}}\). The critical enhancement of thermal phonon excitation follows that of thermal magnon excitation. We fixed \({{{j}}}\) = 2.5 × 1011 A/m2. g–i Magnetic field response of \({{\Delta }}{{{\theta}}}_{{{2}}{{\omega }}}\) under different \({{{j}}}\). The critical enhancement of thermal magnon excitation is enlarged by the increment of magnon chemical potential. j–l Magnetic field response of \({{\Delta }}{{{R}}}_{{{2}}{{\omega }}}\) under different \({{{j}}}\). The critical enhancement of thermal phonon excitation also follows that of thermal magnon excitation. We fixed \({T}_{\rm{sub}}\) = 300 K. Error bars represent the standard deviation of three equivalent measurements.

We further controlled the magnon chemical potential by modulating the current density, \({j}\), as the magnon chemical potential is affected by the temperature gradient induced by current-induced heat. Figure 3g–l shows the magnetic field dependence of \(\Delta {\theta }_{2\omega }\) [Fig. 3g–i] and \(\Delta {R}_{2\omega }\) [Fig. 3j–l] with different \(j\), focusing on the variation of the two quantities after magnetization saturation field. The results show an enhancement in \(\Delta {\theta }_{2\omega }\) (thermal magnon excitation) at higher \(j\), attributed to a large magnon chemical potential at higher \(j\) due to large temperature gradient11,39,41. This nonzero magnon chemical potential generates additional non-equilibrium magnon excitation with a non-linear dependence on electrical heating at low magnetic fields39. Importantly, \(\Delta {R}_{2\omega }\) follows the same trend as \(\Delta {\theta }_{2\omega }\), similar to the changes in \({T}_{{{\rm{sub}}}}\). These experiments demonstrate a strong correlation between the excitation of magnons and that of phonons. It is noteworthy that the field-dependent variation in \(\Delta {R}_{2\omega }\) is only observed on TmIG and is absent on the GGG substrate, indicating that the observed \(\Delta {R}_{2\omega }\) is not caused by the thermal phonon excitation in the GGG substrate [Supplementary Note 5].

We finally explored the potential impact of the magnetic field on the phononic thermal transport. To achieve this, we conducted time-resolved measurements to assess transient thermal phonon relaxation. During these measurements, a current pulse was applied to stimulate phonons, and the reflected laser beam was measured by adjusting the delay time between the current pulse and the probe laser beam [Fig. 4a]. Given that a slightly different device with a marginally larger saturation field (\({\mu }_{0}{H}_{{{\rm{sat}}}}\) ~ 25 mT) was utilized [refer to Supplementary Note 7 for the saturation field measurement], we examined the magnetic field responses of \(\Delta {\theta }_{2\omega }\) [inset of Fig. 4b] and \(\Delta {R}_{2\omega }\) [Fig. 4b] in the new device. The results in Fig. 4b confirmed that phonons are excited at low magnetic fields and suppressed at higher magnetic fields. Subsequently, we investigated the time-dependent decay of \(\Delta {R}_{2\omega }\) after current injection, indicating the relaxation of transient thermal phonons (refer to the Supplementary Note 8 for the time-resolved decay of \(\Delta {\theta }_{2\omega }\)). We measured the decay time for two distinct magnetic fields (\({\mu }_{0}H\) = 25 mT and \({\mu }_{0}H\) = 40 mT), anticipating a significant phonon population at \({\mu }_{0}H\) = 25 mT and a smaller population at \({\mu }_{0}H\) = 40 mT. Remarkably, our results revealed that the decay time of transient thermal phonons is strongly influenced by the magnetic field, being shorter at low magnetic fields than at high magnetic fields [refer to Fig. 4c]. Given that materials with high thermal conductivity can transfer heat rapidly, our results suggest that the phononic thermal conductivity increases with reducing the magnetic field. Consequently, our findings suggest that the phononic thermal transport properties of TmIG can be modulated using a modest magnetic field, even at room temperature.

a Schematic illustration of time-resolved measurement. b Magnetic field response of \({{\Delta }}{{{R}}}_{{{2}}{{\omega }}}\) at the device for time-resolved measurement. Inset shows the magnetic field response of \({{\Delta }}{{{\theta}}}_{{{2}}{{\omega }}}\). c Time-domain decay of the transient \({{\Delta }}{{{R}}}_{{{2}}{{\omega }}}\) after turning off the heating current. Decay at the low magnetic field is faster than decay at the high magnetic field. Error bars represent the standard deviation of three equivalent measurements. d Calculated device temperature elevation as a function of \({{{k}}}_{{\rm{GGG}}}/{{{k}}}_{{\rm{TmIG}}}\) where \({{{k}}}_{{{\rm{GGG}}}}\) and \({{{k}}}_{{{\rm{TmIG}}}}\) are the thermal conductivity of GGG and TmIG, respectively. e Calculated time-domain decay of the transient device temperature after turning off the heating current. Decay at the small \({{{k}}}_{{\rm{GGG}}}/{{{k}}}_{{\rm{TmIG}}}\) is faster than decay at the large \({{{k}}}_{{\rm{GGG}}}/{{{k}}}_{{\rm{TmIG}}}\).

Thus far, our experimental investigation focused on the magnetic field responses of thermal phonon excitations, revealing a critical enhancement of phonon excitation at low magnetic fields, and a modulation of thermal transport properties by magnetic field. Here we present one possible mechanism—the modification of phononic thermal conductivity via magnon-phonon coupling—to qualitatively explain the magnetic field response of the thermally excited phonons. In this argument, we neglect the contribution from magnon thermal conductivity (See Supplementary Note 9 for details). Within the framework of the Boltzmann transport theory, phononic thermal conductivity is determined by refs. 42,43

where \({\omega }_{k}\) is the angular frequency of phonons, \({v}_{k}\) is the group velocity of phonons, \({\tau }_{k}\) is the relaxation time of phonons with a certain wave vector \(k\), and \({\partial }_{T}{n}_{{{\rm{p}}}k}\) is the temperature derivative of the phonon distribution function. Here, \(\hslash {\omega }_{k}\), \({v}_{k}\) and \({\partial }_{T}{n}_{{{\rm{p}}}k}\) are phonon-intrinsic quantities and thus determined by the energy band structure of phonons, which is independent of the magnetic field. Thus, any magnetic field dependence of the phononic thermal conductivity \({k}_{{{\rm{p}}}}\) is expected to be caused by the modification of phonon relaxation time \({\tau }_{k}\) under the influence of the magnetic field. In the presence of magnon-phonon coupling, as discussed in ref. 30 the relaxation time of phonons, \({\tau }_{k}\), can be phenomenologically characterized by

where the left-hand side is the collision integral, \({n}_{{{\rm{p}}}k,0}\) is an equilibrium phonon distribution function, \({\eta }_{{{\rm{p}}}k}\) is the relaxation rate of phonons in the absence of magnon-phonon coupling, and \({\alpha }_{{{\rm{p}}}k}\) is the phonon pumping rate arising from higher-order magnon-phonon coupling. The higher-order coupling involves two scattering processes: the splitting of one magnon into one phonon and another magnon, and the merging of one magnon and one phonon into another magnon. These two scattering processes eventually produce nonzero \({\alpha }_{{{\rm{pk}}}}\)34 as follow:

where \(\gamma\) is gyromagnetic ratio, \({b}_{2}\) is magneto-elastic constant, \(k\) is wavevector, \(M\) is saturation magnetization, \(S\) is spin, \(\rho\) is density, \({\omega }_{{{\rm{pk}}}}\) is phonon angular frequency, \({u}_{{{\rm{mk}}}},\,{v}_{{{\rm{mk}}}}\) are coefficients for Bogoliubov transformation that diagonalizes the spin Hamiltonian with dipolar interaction, \(\delta \big({\omega }_{{{\rm{mk}}}1}-{\omega }_{{{\rm{pk}}}}-{\omega }_{{{\rm{mk}}}2}\big)\) stands for the energy conservation during magnon-phonon scattering processes and \(\delta {n}_{{{\rm{mk}}}}\) is the non-equilibrium magnon number. We note that \({\alpha }_{{{\rm{pk}}}}\) increases with the non-equilibrium magnon number that is closely related with the magnetic field. In the absence of magnon-phonon coupling, i.e., \({\alpha }_{{{\rm{p}}}k}=0\), the phonon relaxation time is solely determined by the relaxation rate of phonons, \({\tau }_{k}=\) \({\eta }_{{{\rm{p}}}k}^{-1}\). However, the presence of finite magnon-phonon coupling introduces a channel through which excessive non-equilibrium magnons are transmuted to phonons, resulting in a positive \({\alpha }_{{{\rm{p}}}k}\). This increases the relaxation time of phonons as \({\tau }_{k}=\) \({\big({\eta }_{{{\rm{p}}}k}-{\alpha }_{{{\rm{p}}}k}\big)}^{-1}\), subsequently enhancing the phononic thermal conductivity. This scenario explains why the transient thermal phonons decay faster at low magnetic fields.

We further validate the above scenario by solving the heat equation, as the temperature variation effectively captures the thermal excitation of phonons. Given that our sample comprises TmIG/GGG, we calculate its temperature utilizing the thermal conductivity values of TmIG (\({k}_{{{\rm{TmIG}}}}\)) and GGG (\({k}_{{{\rm{GGG}}}}\)). We assume that \({k}_{{{\rm{TmIG}}}}\) is modulated by a magnetic field via nonlinear magnon-phonon coupling, as described in the preceding paragraph. A detailed procedure for numerical calculations is provided in Supplementary Note 10. In Fig. 4d, we depict the maximum temperature rise (\(\Delta {T}_{\max }\)) of sample as a function of \({k}_{{{\rm{GGG}}}}/{k}_{{{\rm{TmIG}}}}\). Notably, we observe an increase in \(\Delta {T}_{\max }\) with decreasing \({k}_{{{\rm{GGG}}}}/{k}_{{{\rm{TmIG}}}}\), corresponding to increased thermal phonon excitation at low magnetic fields as shown in Fig. 4b. Additionally, we analyze the transient temperature decay normalized by \(\Delta {T}_{\max }\), denoted as \(\Delta {T}_{{{\rm{norm}}}}\) [Fig. 4e]. A faster decay is evident for lower \({k}_{{{\rm{GGG}}}}/{k}_{{{\rm{TmIG}}}}\), consistent with the rapid decay of transient thermal phonons at lower magnetic fields (refer to Fig. 4c). The agreement between experimental results of thermal phonons and the temperature derived from the heat equation corroborates that the phononic thermal conductivity in our TmIG is indeed modulated by the magnetic field.

In summary, our study utilized optical reflectometry to investigate the excitation of magnons and phonons in perpendicularly magnetized TmIG under electrical heating. Our findings revealed a significant enhancement of thermal phonon excitation at low magnetic fields, which progressively diminished as the magnetic field increased. Additionally, time-resolved measurements unveiled that the transient thermal phonon decay becomes faster with decreasing magnetic field strength. We attribute these observations to the influence of nonlinear magnon-phonon coupling, wherein excessive magnon generation is converted into phonons, consequently altering the phononic thermal conductivity. Numerical simulations corroborated this, demonstrating how modulation of phononic thermal conductivity leads to enhanced thermal phonon excitation and faster decay. Our research underscores the pivotal role of magnons in magnetic insulators in contributing to phononic thermal conduction via nonlinear magnon-phonon coupling. Notably, we demonstrated magnetic control of phonons at and around room temperature using modest magnetic fields, surpassing previous findings limited to cryogenic temperatures and high magnetic fields. Given the ubiquitous nature of thermal transport in solids, we anticipate that our work will stimulate further investigations into various phonon transport properties, including the transport of spin and orbital aspects of phonons13,44,45,46,47, through the exploration of magnon-phonon coupling mechanisms.

We prepared 20 nm-thick TmIG films on the 0.5 mm-thick gadolinium gallium garnet (GGG) substrate through off-axis sputtering. Sputtering of TmIG was performed at the Ar atmosphere of pressure 3 mTorr. During the deposition of TmIG, we maintained the temperature of substrate at 400 °C. After sputtering, the deposited film was placed on a tube furnace for annealing. The TmIG film was annealed at 1000 °C for 2 h, under 100 sccm of Ar flow. The TmIG film was patterned into a 15 μm × 180 μm micro-strip using photolithography and Ar ion etching. A current injection line, composed of 2 μm × 225 μm Ti (5 nm)/Au (50 nm), was fabricated on the left side of the TmIG for current injection.

To investigate the thermal excitation of magnons and phonons in TmIG, we employed optical reflectometry. A laser with a wavelength of 405 nm was focused onto the device along the normal direction, with a laser power of 1.1 mW and a beam waist less than 1 μm. We confirmed that the local heating induced by the probing laser is negligibly small39. Reflected laser beam was split into two parts: one directed into the conventional photodiode to measure reflectivity (\(R\)), and the other passing through a half-wave retarder, Wollaston prism, and balanced photodetector to measure Kerr rotation (\({\theta }_{k}\)).

Magnons and phonons were detected by harmonic measurements with respect to the excitation current. To excite magnons and phonons, we injected an alternating current (\(I={I}_{0}\sin \omega t\), \(\omega /2\pi\) = 331 Hz) through the Ti/Au wire. As the current-induced Joule heating is a current-even effect, the thermally driven magnons and phonons were characterized by examining the second harmonic responses of the reflected laser beam. Specifically, the second harmonic response of Kerr rotation (\(\Delta {\theta }_{2\omega }\)) represents the thermally excited magnons, while the corresponding change in reflectivity (\(\Delta {R}_{2\omega }\)) indicates the presence of thermally excited phonons, as corroborated by previous studies39.

In order to investigate the variation of phonon relaxation in response to changes in magnetic field, we conducted time-resolved measurements using pulsed current and laser techniques. Through synchronization of these instruments, we were able to stroboscopically capture the transient decay of phonons (i.e., reflectivity) as a function of the delay time between the laser pulse and the current pulse. Additionally, we modulated the current pulse with a sinusoidal waveform to facilitate lock-in detection. This allowed us to measure the second harmonic change of reflectivity at the frequency of the modulation envelope, thereby obtaining transient thermal excitation of phonons with a high signal-to-noise ratio. Throughout the measurements, we maintained parameters such as \({T}_{{{\rm{sub}}}}\) = 300 K, a pulse repetition period of 0.5 ms, a laser pulse width of 5 µs, a modulation envelope frequency of 331 Hz, and an integration time of 0.3 s. The schematic illustration of the time domain waveforms for the measurement can be found in Supplementary Note 6.

The data supporting the findings of this study are included in the paper and its Supplementary Materials file. Further data sets are available from the corresponding author on reasonable request.

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This research was supported by the National Research Foundation of Korea (NRF) funded by the Korean Government (MSIP) [grant numbers: RS-2023-00275259, RS-2023-00207732, RS-2024-00351653]. This work was partly supported by the Technology Innovation Program (or Industrial Strategic Technology Development Program) (20020286) funded by the Ministry of Trade, Industry, and Energy (MOTIE, Korea), KSRC (Korea Semiconductor Research Consortium) support program for the development of the future semiconductor device; the Samsung Research Funding Center of Samsung Electronics under Project No. SRFC-MA2002-02. This work was partly supported by the Brain Pool Plus Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2020H1D3A2A03099291).

These authors contributed equally: Geun-Hee Lee, Phuoc Cao Van.

Department of Physics, KAIST, Daejeon, Republic of Korea

Geun-Hee Lee, Se Kwon Kim & Kab-Jin Kim

Department of Material Science and Engineering, Chungnam National University, Daejeon, Republic of Korea

Phuoc Cao Van & Jong-Ryul Jeong

Graduate School of Quantum Science and Technology, KAIST, Daejeon, Republic of Korea

Se Kwon Kim & Kab-Jin Kim

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S.K.K. and K.-J.K. supervised the project. G.-H.L. conceived the idea, performed the experiment, and analyzed the data. P.C.V. and J.-R.J. prepared the TmIG films. G.-H.L. and S.K.K. provided theoretical interpretation and numerical calculations. G.-H.L., S.K.K., and K.-J.K. wrote the manuscript. All authors commented and suggested proper modifications on manuscript.

Correspondence to Jong-Ryul Jeong, Se Kwon Kim or Kab-Jin Kim.

The authors declare no competing interests.

Communications materials thanks Shan Qiao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Aldo Isidori. A peer review file is available.

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Lee, GH., Cao Van, P., Jeong, JR. et al. Magnetic control of phonon transport in magnetic insulator thulium iron garnet. Commun Mater 5, 243 (2024). https://doi.org/10.1038/s43246-024-00682-2

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Received: 29 March 2024

Accepted: 22 October 2024

Published: 06 November 2024

DOI: https://doi.org/10.1038/s43246-024-00682-2

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