Introduction

Magnon spintronics, which concerns about utilizing magnon currents to carry, transmit and process information, is a fascinating and dynamic field because magnons have the potential to realize low-power dissipation and high-performance novel logic devices for future information technologies1. Recent studies on spin pumping (SP), spin Seebeck effect (SSE) and terahertz (THz) emission in antiferromagnets (AFMs) have shown more extensive potential for AFMs to develop ultrafast and high-density spintronic devices compared to ferromagnets (FMs)2,3,4,5,6,7,8,9,10,11,12,13,14. As the quanta of spin waves, magnons are deeply influenced by the spin configuration in the magnetically ordered materials. However, due to the vanishing net magnetization in AFMs, detecting and manipulating the configuration of the AFM magnetic sublattice and associated magnons require more demanding experimental conditions, such as strong magnetic field over dozens of Tesla and resonance sources with frequency over THz3,5,10,11,12,13. In contrast, ferrimagnets, which simultaneously possess finite net magnetization, AFM-like magnetic structures and spin dynamics15,16,17, are considered to be promising material platforms to circumvent these obstacles and exhibit unique properties in magnon spintronics.

The compensated ferrimagnets have attracted much attentions recently due to novel spin transport phenomena in the vicinity of the compensation temperature (Tcomp)16,17,18,19,20,21,22,23,24,25,26, where the antiparallelly aligned moments from multiple magnetic sublattices cancel each other out, and the net magnetization vanishes. Moreover, the magnetic structures of different sublattices in compensated ferrimagnets not only have high temperature sensitivity, but also undergo complex spin–flip transitions around Tcomp. Additionally, abundant noncollinear magnetic structures may exist near Tcomp. Significant progress has been made in understanding the intriguing spin transport properties around Tcomp of ferrimagnets, such as the high switching efficiency induced by spin–orbit torques (SOTs)20,21,22,23, the field-dependent anomalous Hall effect (AHE), and the magnetoresistance18,25,26. It is expected that the changes and evolution of the spin texture near Tcomp will also substantially tune magnon transport. Furthermore, the presence of noncollinear spins can result in the splitting and hybridization of magnon bands, leading to a rich variety of excitation modes and unconventional magnon transport properties27,28,29,30.

As one important type of compensated ferrimagnets, rare-earth iron garnets (ReIGs, Re3Fe5O12, where Re = Gd, Tb, etc.) have garnered significant interest in magnon transport due to their ultralow magnetic damping, complex spin texture and rich spin wave properties31,32,33,34,35. Among them, terbium iron garnet (TbIG) exhibits a natural noncollinear double-umbrella spin texture far below the Tcomp36,37,38. Our recent work demonstrated that the SSE is remarkably amplified around the transition of the noncollinear double-umbrella state of TbIG associated with the reorientation of magnetic moments of sublattices35. It also suggests that the SSE is a sensitive probe for complex magnetic structures and related magnon39. In this work, we construct a high-quality epitaxial TbIG/Pt heterostructure and systematically investigate the characteristic temperature- and field-dependent SSE due to the noncollinear configuration around the compensation temperature, where the double-umbrella feature is irrelevant40. We find a wealth of anomalous behaviors in SSE, manifested as a transition of the spin Seebeck coefficient (SSC) amplitude from saturation to decline, accompanied by a sign change at high field above Tcomp, while there are dips at near-zero magnetic field below Tcomp. Theoretical calculations well support the abnormal characteristics of SSE above Tcomp by the evolution of noncollinear magnetic structure and attribute the dips below Tcomp to the magnon-polaron (MP) anomaly.

Results and discussions

160-nm-thick TbIG film was grown on (111)-oriented Gd3Sc2Ga3O12 (GSGG) substrate using pulsed laser deposition (see the “Methods” section for details). The crystal quality of the film was initially examined by X-ray diffraction (XRD). The XRD 2θ−ω patterns for the (444) reflections of the GSGG (111)/TbIG sample are depicted in Fig. 1a, clearly showing two main Bragg peaks assignable to GSGG and TbIG (444) diffractions. The out-of-plane lattice constant of the TbIG film was determined to be 12.44 Å, which is very close to the bulk value41. Figure 1b presents the XRD φ-scan patterns around the (008) peaks of the TbIG film and the GSGG. The consistent, clear threefold symmetry peaks observed for both TbIG and GSGG indicate the epitaxial growth and single crystal structure of the TbIG film on the substrate. The crystal quality was further characterized using a scanning transmission electron microscope (STEM) in high-angle annular dark-field (HAADF) mode. Figure 1c shows a cross-sectional STEM image viewed along the \([1{\bar{1}}0]\) direction, where the yellow dashed line indicates the atomically sharp interface between GSGG and TbIG. The image shows a perfect continuation of the garnet lattice without any detectable dislocations throughout the thickness of the TbIG film. Figure 1d displays a (111) plane-view STEM image exhibiting a remarkable snowflake pattern. The high-magnification images in upper-right corners of yellow dotted frames in Figs. 1c, d reveal fine details of the atomic arrangement, where a [111] projection of the garnet lattice of concentric hexagons is overlaid on the STEM image to show a perfect match. A set of the selected area of the electron diffraction patterns via fast Fourier transform (FFT) corresponding to Figs. 1c, d are shown in Fig. S1 at Supplementary Information (SI).

Fig. 1: Structural and magnetic properties of TbIG film.
figure 1

a XRD 2θ-ω scans of TbIG (160 nm) grown on (111)-oriented GSGG. b φ-scan (008) patterns of the 160 nm TbIG film deposited on the GSGG (111) substrate. High-resolution STEM images of the GSGG/TbIG in a cross-sectional view along the c \([1{\bar{1}}0]\) direction and d (111) plane-view. The upper-right insets in yellow dotted frames in c and d present a magnified region for improved visibility with an atomic model overlaid onto real atoms. e The schematic of the crystal structure of TbIG. The red, blue, and orange balls represent the Tb, Fe, and O atoms, respectively. f The net magnetization (left axis) and coercive field (right axis) as functions of temperature.

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Typically, the crystal structure of TbIG displays cubic symmetry, as depicted in Fig. 1e. As seen, TbIG consists of three magnetic sublattices: a dodecahedral Tb sublattice (c sites), an octahedral Fe sublattice (a sites), and a tetrahedral Fe sublattice (d sites). Actually, the two Fe sublattices, locked by robust antiferromagnetic superexchange interaction, can be treated as a single net Fe magnetic sublattice (MFe), which is aligned antiparallel to the Tb magnetic sublattice (MTb) at zero magnetic field. Since the SSE was investigated above 160 K, where the cone angle of Tb ions is very close to zero, distinctly different from the reported low-temperature double umbrella structure35,38,40. The static magnetic properties of TbIG were characterized using a vibrating sample magnetometer (VSM). The net magnetization M and coercive field HC, extracted from the hysteresis loops (see Fig. S2 in SI), are plotted in Fig. 1f as functions of temperature. The Tcomp is clearly identified within the yellow region (180–200 K), characterized by an almost vanishing M and a divergence of HC. The effective Fe (Tb) sublattice dominates the net magnetization above (below) Tcomp.

We adopted the longitudinal SSE measurement geometry to clarify the evolution of the magnetic configuration, as shown in Fig. 2a. To validate the reliability of the experimental setup, we first examined the low-field voltage (V) as a function of the heater power at T = 300 K and μ0H = 0.5 T, where the magnetic field just exceeds the in-plane coercivity of TbIG. The observed linear dependence on the heating power, passing through the origin of coordinate (Fig. 2b), strongly suggests that the measured voltage V predominantly stems from the SSE. For quantitative characterization at various temperatures, the SSC is derived from \(S={E}_{{\rm{y}}}/{{\nabla }}T\), with \({E}_{{\rm{y}}}={V}_{{\rm{SSE}}}/{L}_{{\rm{y}}}\). More details about the device fabrication and temperature gradient (∇T) calibration are provided in the “Methods” section and Fig. S3 in SI.

Fig. 2: Experimental set-up of SSE in TbIG/Pt heterostructure and the temperature and magnetic field dependence of SSC.
figure 2

a Device schematic for LSSE measurements in the GSGG (111)/TbIG (160 nm)/Pt (5 nm) sample. b VSSE as a function of the heater power at 300 K under an applied magnetic field of 0.5 T. c Temperature dependence of the SSC at μ0H = 0.5 T. d SSC as a function of magnetic field at typical temperatures.

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We further investigated the temperature dependence of SSC at μ0H = 0.5 T, as depicted in Fig. 2c. In the high-temperature region (300–200 K), the SSC displays a negative value, which slightly decreases as the temperature decreases. However, when the temperature approaches the magnetic compensation region (200–180 K), the SSC undergoes a sharp and cliff-like change from negative to positive at approximately 194 K, corresponding to the Tcomp of TbIG. This phenomenon has been observed in other compensated ReIGs as well and is attributed to the flip of all sublattice magnetization31,32,33,34,35. The inevitable defects (the energy-dispersive X-ray spectroscopy data shown as Fig. S4 in SI) and strain effect from the substrate in our TbIG film result in a lower Tcomp compared to the bulk value (~250 K)42,43. The decline of the SSC below 180 K is due to the strong suppression of thermal magnon excitation44,45,46.

We have subsequently examined the magnetic field dependence of the SSC at typical temperatures. Remarkably, the magnetic field dependence of the SSC strongly relies on the temperature, as shown in Fig. 2d. At 309.26 K, the SSC exhibits a characteristic sign change at a very low coercive field and quickly saturates to a constant value. At 203.07 K, closer to Tcomp, the SSC displays a rapid saturation in the low-field range as anticipated. Interestingly, an anomalous behavior is observed, where the SSC undergoes a transition at a critical field (±HT) and then decreases rapidly to almost zero with further increasing the magnetic field. When the temperature crosses the Tcomp to 191.14 K, apart from the sign change of the SSC at a low coercive field, dip anomalies appear at ±Hd. With further decreasing temperature to 108.76 K, these two types of abnormal SSC no longer exist.

The intriguing anomalous behaviors observed in the vicinity of the Tcomp inspired us to investigate the SSE more meticulously. The magnetic field-dependent SSC is first measured above Tcomp, as shown in Fig. 3a. Here, we define the temperature difference of the investigated temperature with respect to Tcomp, ΔT = T–Tcomp. As ΔT decreases from 21.95 to 2.03 K, the ±HT gradually shifts to a lower value, and the amplitude of SSC decreases rapidly when the magnetic field exceeds ±HT. Furthermore, the rate of decline accelerates, even changing the SSC sign as the temperature approaches Tcomp. Such an unconventional evolution process suggests that the arrangement and dynamics of spins are hypersensitive near Tcomp and may play crucial roles behind these unusual phenomena.

Fig. 3: Experimental and theoretical results of SSC and magnetization for T > Tcomp, respectively.
figure 3

a Experimental results of SSC and b Theoretical calculations of \(-{M}_{{\rm{F}}{\rm{e}}}^{x} \) (the negative value of net Fe magnetic moment projection in the magnetic field direction) as functions of magnetic field at typical temperatures above the Tcomp. The μ0H-ΔT phase diagrams of c SSC and d θFe for more refined temperatures mapping at positive field region, corresponding to a and b, respectively. The orientations of magnetization vectors MFe and MTb in different phases are shown schematically by green and yellow arrows in d, respectively. The θFe is the angle between MFe and H.

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Theoretical calculations were conducted to investigate the evolution of distinct sublattices in TbIG with varying magnetic fields and temperatures through a mean-field approach. The compensation temperature deduced from the theoretical model is 182.5 K, slightly lower than the experimental value. This can be attributed to the material parameters used in the calculation47, especially for the exchange parameters between Tb and Fe magnetic moments which are difficult to evaluate precisely in the present strained thin film43. We find that the negative value of the projection of the net Fe magnetic moment in the magnetic field direction (\(-{M}_{{\rm{F}}{\rm{e}}}^{x}\)) in the region of T > Tcomp, as shown in Fig. 3b, possesses very similar curve shapes as the SSC in Fig. 3a. Our findings suggest that the reorientation of the equilibrium net Fe magnetic moment is the key to the observed SSC feature in Fig. 3a, providing more detailed insight consistent with the strong correlation between the Fe orientation and the SSE signal revealed in ref. 35.

To facilitate a more intuitive analysis, we construct μ0H-ΔT phase diagrams in Figs. 3c, d to visualize the relation between the phase space of SSC and θFe. The latter denotes the angle between the net magnetic moment of the Fe sublattice and the magnetic field. We identify three distinct regions, clearly demarcated by two dividing dashed curves. The pure blue part is the region (I), where the value of S always stays at its negative maximum, signifying that MFe is along the magnetic field direction and antiparallel with MTb, with θFe equaling 0°. When the magnetic field surpasses HT (the cyan dashed curve), the system enters the transition region (II), manifested by the blue gradient part, where the MFe and MTb exhibit a noncollinear canting configuration. The θFe deviates from 0° but remains less than 90°, resulting in the rapid decrease of S to 0 μV/K. The purple dashed curve indicates S = 0 μV/K and θFe = 90° for the SSC experiment and theoretical evolution of the Fe moment, respectively. Below this curve, the SSC and θFe transition into the region (III), identified by the red gradient area, where MFe and MTb continue to exhibit a noncollinear canting magnetic structure but with an angle range of 90° < θFe < 180°, leading to the sign of SSC changing to positive. Our findings reveal that the magnetic field can highly tune the flipping process of the different sublattices in TbIG near Tcomp, allowing for continuous tunability of SSC in the TbIG/Pt heterostructure. Moreover, the anomalous behavior of the SSE makes it a promising probe for interpreting magnon transport with complex spin structures. More importantly, this tunable effect can be achieved near zero magnetic fields, which holds promise for the development of ReIGs-based low-power magnon spintronic devices.

Following comprehensive SSE measurements conducted for T < Tcomp, a dip-shape was observed in the positive low-field range, alongside with peak-shape in the negative field, as indicated by the two green arrows in Fig. 4a. Taking the positive field region of ΔT = −0.98 K as an example, we define the position and intensity of the dip anomaly in the SSC curve as μ0Hd and ΔSd, respectively. The dip anomalies in the positive field regions shift towards lower magnetic fields, and the magnitude increases with temperature rising to the Tcomp. The temperature-dependent evolution is summarized in Fig. 4b. When ΔT decreases from −0.98 to −7.91 K, μ0Hd (left axis) exhibits a nearly linear increase, while the relative intensity (ΔSd/S, right axis) of the dip-anomaly shows a monotonic reduction. Additionally, the dip or peak anomalies occurring in the variation of the magnetic field have similar characteristics with the abnormal SSE induced by magnon polarons observed in YIG and GdIG33,44,48,49,50,51,52, which might be assumed to have an analogous origin. The decrease of the critical magnetic resonant field μ0H(TA)LA with the increase of temperature was also observed previously in the MP-induced anomalies in YIG and GdIG33,48,49,50, which was attributed to the softening of the crystal lattice and the reduction of elastic modulus50,53. However, the temperature dependence of μ0H(TA)LA in YIG and GdIG is much weaker than the results in TbIG reported here. Moreover, as the crystal lattice does not experience a phase transition when approaching Tcomp, the reduction of Hd and the ~28% enhancement of SSC are not likely induced by the change of phonon dispersions. Therefore, the abnormal trend of the dip anomalies is probably related to the unique evolution of magnetic sublattices and the corresponding transition of magnon spectra.

Fig. 4: The temperature dependence of dip-anomaly for T < Tcomp.
figure 4

a SSC as a function of the magnetic field immediately below the Tcomp. The temperature evolution of dip anomalies is indicated by the green arrows. The position and intensity of dip-anomaly are denoted by μ0Hd and ΔSd, respectively. b The temperature dependence of μ0Hd (left axis) and relative intensity of anomaly ΔSd/S (right axis).

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We then investigated the magnon dispersions obscured in our SSE results. In the range of T < Tcomp, the anomaly induced by the variation of the spin texture is ruled out because calculation results indicate that the magnetic moments of Fe and Tb sublattices remain nearly antiparallel in the direction of the magnetic field. To inspect the role of magnon-phonon hybridization, the SSC enhancement Δζtot due to magnon polarons was calculated (details of the calculation in SI), compared to SSC values without magnon–phonon hybridization, as presented in Fig. 5a at some typical temperatures. Obviously, the MP-anomaly feature similar to that observed in the experiment emerges. After extracting the maximum intensity of magnon polarons induced SSC (|Δζtot|max) and the corresponding position (μ0Hd), depicted in Fig. 5b, we observe the same temperature evolution as the experimental anomaly. To explicitly understand the MP-anomaly signal, we analyze the magnon spectra for the three typical magnetic fields (H1, H2, H3) at ΔT = −9.5 K as denoted in Fig. 5a. The corresponding results in the low-frequency region are plotted in Figs. 5c–e, where the red (blue) curve is the β- (α-) magnon branch dominated by the Fe (Tb) sublattice in TbIG. The α and β branches have opposite spin polarizations, contributing negative and positive SSC signals in the T < Tcomp range, respectively. The orange curves represent the linear dispersion curves of the LA and TA phonons with sound speeds cl = 7.2 km/s and ct = 3.3 km/s, respectively54. With increasing the magnetic field, the α branch magnon is lifted. When H = H2, the dispersion curve of the α branch becomes nearly parallel to the LA phonon dispersion in the relatively low-frequency range, which indicates abundant magnon-polarons states contributing to the MP-anomaly of the SSE signal. Otherwise, the α branch only has a single intersecting point with LA phonon, as shown in Figs. 5c, e, leading to negligible enhancement from the magnon polarons. It is valuable to point out that although the dispersions in Figs. 5c–e look very similar to GdIG49, the suitable group velocity induces the parallel relation between the α branch and LA phonon rather than the TA phonon. Since the magnon polaron anomaly is related to the modification of magnon lifetime due to magnon–phonon hybridization, such effect can in principle taken into account in the magnon diffusion model55 by introducing magnetic field dependences in the transport coefficients.

Fig. 5: The temperature dependence of MP-anomaly for T < Tcomp and the magnetic field evolution of the magnon spectra of TbIG.
figure 5

a The calculated SSC enhancement due to magnon polarons as a function of the magnetic field below the Tcomp. b The ΔT dependence of the position of magnon polaron μ0Hd (left axis) and the corresponding maximum intensity of SSC |Δζtot|max (right axis). c–e Magnon spectra of bulk TbIG in the low-frequency regime ( < 0.5 THz) for ΔT = −9.5 K and three typical magnetic fields μ0H1 = 0.2 T, μ0H2 = 0.5 T, and μ0H3 = 0.8 T denoted in (a). The orange curves represent the dispersion relations of the longitudinal (LA) and transverse (TA) acoustic phonon.

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In summary, we have observed rich abnormal SSE behaviors dependent on the magnetic field in TbIG/Pt in the vicinity of the compensation temperature. These behaviors can be classified into two types. When T > Tcomp, the SSC primarily manifests as a decrease in amplitude and potential sign reversal, arising from the sensitive spin-flipping of the Fe sublattice induced by temperature and magnetic field. When T < Tcomp, the SSC exhibits dip anomalies in the low magnetic field region, primarily attributed to the large parallel and contact region between the Tb-dominated α-magnon and LA phonon dispersions. Compared to previous works on SSE anomalies due to magnon polarons, the anomaly magnetic field is usually insensitive to temperature because of the weak temperature dependence of the magnon spectrum in materials like YIG44, Fe3O456, and Cr2O33. For GdIG, the strong temperature dependence of Gd3+ rare-earth magnetic moment results in a strong thermal effect on the magnon-polaron anomaly far below the compensation temperature33,49. The possibility of the MP-anomaly around compensation temperature is however not clear before, which is positively answered here. On the other hand, specified to the sign change in SSE around the compensation temperature, beyond the previous observation due to the flipping of collinear aligning sublattice magnetic moments, we here discover more interesting features due to the variation of the non-collinear magnetic configuration. Our work not only fills the gap in understanding complex spin wave dynamics induced by noncollinear magnetic structures and magnon–phonon hybridization near Tcomp of ReIGs but also provides new opportunities for exploring magnon-based low-power spin caloritronics devices and sensors.

Methods

Sample preparation and device fabrication

TbIG films were grown on (111)-oriented Gd3Sc2Ga3O12 (GSGG) substrates via pulsed laser deposition with a laser power of ~1.5 mJ and repetition frequency 4 Hz. The substrate was kept at 750 °C and chamber atmosphere of 3.0-Pa oxygen during deposition. The sample was then crystalized by in situ annealing at 750 °C for another 2 h in a pure oxygen atmosphere of 6 × 104 Pa. After cooling down to room temperature, we fabricated a 5-nm-thick Pt layer on the TbIG film by AJA magnetron sputtering system. The Pt layer was deposited on the TbIG film at room temperature by DC magnetron sputtering, where the base pressure of the sputtering system was lower than 2 × 10−6 Pa and the Ar pressure was 0.4 Pa during deposition. The deposition rate of Pt was 0.68 Å/s. The LSSE pattern was fabricated via a 3D Lithography machine (TuoTuo Technology) as follows. A Hall bar geometry was patterned by optical photolithography and argon plasma etching. A 100-nm-thick Al2O3 insulating layer was then followed by atomic layer deposition (ALD). Finally, a vertically aligned 50-nm-thick chromium (Cr) heater was deposited to form a local on-chip SSE device.

VSM, STEM, and SSE measurements

Magnetic property measurements were carried out using a vibrating sample magnetometer option of the Physical Property Measurement System (PPMS-VSM, Quantum Design). The structures were characterized via Cs-TEM (JEM-ARM300F) after the sample was prepared by a focused ion beam (Helios G4 UX). The SSE experiments were conducted utilizing a PPMS. AC current was set in an on-chip heater to generate a vertical temperature gradient ∇T (along the z direction in Fig. 2a) by Lake Shore 155 source meter. The open-circuit voltage was recorded as the SSE signal (VSSE, along the y direction in Fig. 2a) by Stanford Research SR830 lock-in amplifiers when an in-plane magnetic field H is swept by PPMS (along the x direction in Fig. 2a).

Theoretical calculation

The magnetic configurations were calculated using the mean-field approach with an effective Hamiltonian. The magnon spectra and spin Seebeck coefficient calculation are based on the realistic atomistic Hamiltonian model. More details about the theoretical calculations are available in SI.