Broadband ferromagnetic resonance is used to investigate magnetization dynamics, damping, interfacial spin transport, and perpendicular magnetic anisotropy (PMA) of (111)-oriented epitaxial thin films of the ferrimagnetic insulator Tm3Fe5O12 (TmIG) on substrates of (111)-oriented Gd3Ga5O12. A PMA field of ∼162 mT is found at 350 K, in the temperature range where spin–orbit torque switching was previously reported [Avci et al., Nat. Mater. 16, 309–314 (2017)]. A Landé g-factor of 1.56 strongly supports large intrinsic spin–orbit coupling due to the presence of the heavy rare earth Tm. Gilbert damping coefficients α are compared for three samples: a 28 nm thin TmIG film (α ∼ 0.014), a TmIG (28 nm)/Pt (6 nm) bilayer (α ∼ 0.022), and a TmIG (28 nm)/Cu (3 nm)/Pt (6 nm) trilayer (α ∼ 0.024). Applying the spin pumping formalism, we find that the real part of the effective interfacial spin mixing conductance Geff↑↓ = 5.7 × 1014 Ω−1 m−2 is comparable to that of well-studied garnet/Pt interfaces. Our work strengthens the candidacy of TmIG for spintronics applications requiring PMA in insulating thin films.

Spintronic multilayer devices are an attractive solution for data storage, and computational and sensor devices.1,2 Insulating thin film ferrimagnetic garnets display a variety of relevant and interesting properties, such as low magnon damping in Y3Fe5O12 (YIG)3–5 and Lu3Fe5O12 (LuIG),6 perpendicular magnetic anisotropy (PMA) in Sm3Fe5O12,7 Tb3Fe5O12,8 Eu3Fe5O12,9,10 Dy3Fe5O12,11 and Tm3Fe5O12 (TmIG),12–16 and both of the above combined in BixY3−xFe5O12.17 In an important advance toward applications,18 spin–orbit-torque switching has been observed in TmIG/Pt bilayers15,19,20 and TmIG/W bilayers,16 thus demonstrating an all-electrical control of magnetization. TmIG/Pt (and TmIG/W) remains the material system of choice21–23 for studying spin–orbit-torque switching in a magnetic insulator with PMA, with its relatively low coercivity of ∼15 mT thought to be an enabling factor. However, the spin-dependent properties of the interface with Pt have not hitherto been probed with the sensitive technique of broadband ferromagnetic resonance (FMR), even though TmIG/Gd3Ga5O12 (GGG) retains a spontaneous magnetization of ∼100 kA m−1 at TmIG thicknesses as small as 1.9–5.4 nm.14,21,24 Furthermore, TmIG thin films have a magnetically dead layer of the order of 1.4 nm (1 unit cell), due to the gradual change in composition at the interface with paramagnetic GGG.

Spin pumping is the flow of pure spin current from the aggregation of spin angular momentum in FMR.25–27 It has been suggested (along with spin Hall and spin Seebeck effects) for devices exploiting pure spin flow between metals and ferro- or antiferromagnetic insulators, through flow-compensated charge or magnonic transport.28 Furthermore, the theory of spin pumping provides a convenient means to relate measurements of FMR damping with interfacial spin transport properties as parameterized by an effective spin mixing conductance.26 FMR also provides a sensitive probe of magnetic anisotropy and has been previously exploited for the study of TmIG thin films.29 Here, we exploit broadband FMR to investigate magnetization dynamics, damping, interfacial spin transport, and PMA in TmIG/Pt and TmIG/Cu/Pt heterostructures.

TmIG epitaxial films of thickness t =28 nm were grown by pulsed laser deposition on 5 × 5 × 0.5 mm (111)-oriented Gd3Ga5O12 substrates. Full details of thin film growth and static magnetic properties are provided in Refs. 14 and 15. For the present work, the upper layers of platinum and copper/platinum were deposited on top of the TmIG films in vacuum (∼10−7 Torr) by electron-beam evaporation. Although TmIG films were exposed to air following pulsed laser deposition, in situ heating to ∼200 Centigrade was performed in ∼100 mTorr of O2 to reduce aqueous surface contamination prior to the deposition of the metals.

Static magnetic properties were confirmed by vibrating sample magnetometry. The room-temperature saturation magnetization of ∼111 kA m−1 was slightly reduced to ∼86 kA m−1 at a temperature of 350 K. The coercive fields at room temperature and 350 K were ∼11 mT and ∼6 mT, respectively (Fig. 1).

FIG. 1.

Magnetization hysteresis M(H) as a function of applied field H, for the 28 nm-thick TmIG film at room temperature and 350 K.

FIG. 1.

Magnetization hysteresis M(H) as a function of applied field H, for the 28 nm-thick TmIG film at room temperature and 350 K.

Close modal

Broadband FMR measurements were performed using a coplanar waveguide in a cryostat with external magnetic field H which was sinusoidally modulated with amplitude ∼0.1 mT and frequency 3.3 kHz. The coplanar waveguide (0.5 mm wide) was excited by a signal of frequency f (9–15 GHz) and a power of ∼16 dBm. The central conductor of the waveguide was terminated in a coplanar short and coated in an insulating polyimide (10 μm thick). TmIG films were placed film-side-down onto the coplanar short, a magnetic antinode of the excitation. Ferromagnetic resonant power absorption IFMR was detected by monitoring energy losses in the coplanar waveguide with a −10 dB directional coupler, remotely situated. A lock-in amplification with reference to the 3.3 kHz field modulation yielded a signal proportional to dIFMR/dH which was monitored on sweeping μ0H at 0.5 mT s−1. The center position H0 and half-width-half-maximum linewidth ΔH of the resonance spectra were determined by fitting a double asymmetric Lorentzian function [Fig. 2(a)]. At a temperature of 350 K, we obtained H0 and ΔH for 9 GHz < f <15 GHz [Fig. 2(b)], and for magnetic fields applied in and out of the plane of the film [Fig. 2(c)]. At temperatures between 200 K and 300 K, we obtained H0 and ΔH for fixed f =10 GHz and H applied out of the plane in the film [Fig. 2(d)].

FIG. 2.

Example of ferromagnetic resonance (FMR) spectra of a 28 nm-thick TmIG film at a temperature of 350 K. (a) Acquired spectra and fit in the out-of-plane configuration, for frequency f =8 GHz. The fit yields a resonance field μ0H0 = 309.8 mT and resonance linewidth μ0ΔH = 6.9 mT. (b) Evolution of FMR spectra on varying f between 9 and 15 GHz at 0.5 GHz intervals. (c) Resonance field vs frequency. The linear fits (red lines) yield an anisotropy field of μ0HA = 153 mT. (d) For f =10 GHz and H out-of-plane, H0 and ΔH are, respectively, observed to be the decreasing and increasing functions of temperature T.

FIG. 2.

Example of ferromagnetic resonance (FMR) spectra of a 28 nm-thick TmIG film at a temperature of 350 K. (a) Acquired spectra and fit in the out-of-plane configuration, for frequency f =8 GHz. The fit yields a resonance field μ0H0 = 309.8 mT and resonance linewidth μ0ΔH = 6.9 mT. (b) Evolution of FMR spectra on varying f between 9 and 15 GHz at 0.5 GHz intervals. (c) Resonance field vs frequency. The linear fits (red lines) yield an anisotropy field of μ0HA = 153 mT. (d) For f =10 GHz and H out-of-plane, H0 and ΔH are, respectively, observed to be the decreasing and increasing functions of temperature T.

Close modal

The FMR resonance field H0(f) for TmIG films at 350 K was smaller in the out-of-plane configuration than in the in-plane configuration [Fig. 2(c)]. We extracted an effective saturation magnetization μ0Meff = −52.6 mT (Meff = −41.9 kA m−1) from the H-axis intercept of the linear fit to the out-of-plane data [Fig. 2(c)]. This quantity represents the sum of the static saturation magnetization μ0MS and the perpendicular anisotropy field μ0Ha, and its negative sign is due to a negative Ha, indicating PMA. Given the saturation magnetization μ0MS ∼ 108 mT (MS ∼ 86 kA m−1) of this sample (Fig. 1), we evaluated the out-of-plane magnetic anisotropy field at 350 K as μ0Ha = μ0(MSMeff) ∼ 161 mT. The perpendicular anisotropy constant was then Ka = μ0MSHA/2 = 8.2 kJ m−3. The PMA in TmIG films is due to a dominant magnetoelastic energy from epitaxial strain12–14 which overcomes the shape anisotropy that favors an in-plane easy axis in ferromagnetic thin films.

The out-of-plane resonance field H0(f = 10 GHz) was a decreasing function of temperature in the range of 200–350 K [Fig. 2(d)], implying that |Ha| and thus the strength of PMA were increasing on lowering the temperature. Rotating the sample with respect to the waveguide at 350 K in the in-plane configuration at f =8 GHz did not result in systematic changes of H0, thus establishing that any anisotropy between different in-plane directions must lie below the ∼0.1 mT resolution of the experiment. Given that H0(f) was highly linear, we interpreted its slope with the standard Larmor result df/dH0 = μ0γ/2π with gyromagnetic ratio γ = 2πB/h, μB the Bohr Magneton, and h the Planck constant. A Landé g-factor of g =1.56 was evaluated from the slope of the out-of-plane H0(f) curve [Fig. 2(c)].

The out-of-plane FMR linewidth at 8 GHz was μ0ΔH ∼ 20 mT at 200 K, decreasing gradually to ∼10 mT at 350 K [Fig. 2(d)]. One possible candidate for this evolution is impurity relaxation mechanisms, which leads to the negative temperature coefficient of linewidth in most thin films of YIG.30 Linewidths for the in-plane geometry were more variable (generally larger) than for the out-of-plane geometry, which we may attribute to the influences of a 2-magnon scattering which causes linewidth to increase only in the in-plane geometry and differences in extrinsic broadening. We fit the frequency-dependent out-of-plane linewidth ΔH(f) with a straight line of intercept ΔH0 (the extrinsic magnetic inhomogeneity term) and slope proportional to intrinsic Gilbert damping α,

ΔH=ΔH0+[hgμ0μB]af,
(1)

where H is in units of A m−1, and g =1.56 as determined. We find α = 0.014 for TmIG. The addition of Pt or Cu/Pt upper layers resulted in α = 0.022 and α = 0.024, respectively (Fig. 3), at 350 K.

FIG. 3.

FMR resonance linewidth ΔH as a function of frequency f for the bare TmIG film and a bilayer and trilayer with Pt and Cu/Pt. The slope of the linear fits yields dimensionless Gilbert damping α.

FIG. 3.

FMR resonance linewidth ΔH as a function of frequency f for the bare TmIG film and a bilayer and trilayer with Pt and Cu/Pt. The slope of the linear fits yields dimensionless Gilbert damping α.

Close modal

Our magnetic anisotropy determinations at 350 K (μ0Ha = 162 mT, Ka = 8.2 kJ m−3) are consistent with room-temperature values of μ0Ha ≥ 199 mT and Ka = 11.88 kJ m−3 from previous magnetometry,14 given that both the previous and the present work find these values to be decreasing functions of temperature. Furthermore, our magnetic anisotropy fields lie in the range reported by Ref. 29, where films of a range of stoichiometries grown by off-axis sputtering were studied by FMR. Given that the magnetocrystalline anisotropy of this material is negligible,14Ka may be modeled as the sum of the magnetoelastic term KME and the shape anisotropy—μ0MS2/2 [Eq. (1) in Ref. 14]. For our values of MS and KA, this calculation yields KME = 12.8 kJ m−3. This value is smaller than the 17.5 kJ m−3 evaluated by Ref. 14 from magnetostriction coefficients measured for bulk TmIG.

Our Landé g-factor of 1.56 falls markedly short of the free-electron value of ∼2. This departure is attributed to the admixing of orbital magnetism due to the presence of heavy (high spin–orbit) elemental Tm. Our g-factor is close to the tabulated value for the bulk TmIG of 1.63.31 

Gilbert damping α = 0.014 is very similar to the value reported by Ref. 29 for thin film TmIG. It is of similar order to α ∼ 0.01 of typical metallic films such as Py32 and greatly exceeds α ∼ 0.0002 of thin film yttrium iron garnet (YIG).4 This is likely to be due to a large intrinsic spin–orbit coupling revealed by a depressed g =1.56 and because TmIG lacks the distinctive cation chemistry of YIG and LuIG (orbital angular momentum L =0).33,34 These factors likely also determine the relatively large damping of ∼0.024 found in Eu3Fe5O12,9 which is similar to TmIG in incorporating a heavy rare earth ion with large spin–orbit coupling.

Spin pumping in TmIG/Pt or TmIG/Cu/Pt is expected to enhance Gilbert damping in proportion to the size of the pure spin flow, providing a convenient route to evaluate the real part of the effective interfacial spin mixing conductance,26 

Geff=2e2h2πMtgμB(Δα),
(2)

where (2e2/h) is the conductance quantum,35,M = 86 kA m−1 is the TmIG magnetization,15,t =28 nm is the TmIG thickness, and Δα is the Gilbert damping change associated with the presence of Pt or Cu/Pt. Here, we have assumed that the Pt thickness (6 nm) is large in comparison to its characteristic spin diffusion length such that the impedance it presents to spin flow tends to a limiting constant whose effect is subsumed by Geff↑↓. Thus, spin pumping Geff↑↓ represents a lower bound on interfacial mixing conductance G↑↓, but here, the difference between these two quantities is expected to be small.36 

We find Geff↑↓ = 5.7 × 1014 Ω−1 m−2 for the TmIG/Pt bilayer. This value is not greatly changed in the TmIG/Cu/Pt trilayer (Geff↑↓ = 7.8 × 1014 Ω−1 m−2) which argues against the exchange-coupled magnetism in Pt as the dominant mechanism for the damping enhancement.37,38 The trilayer control also mitigates the interfacial atomic diffusion as a mechanism for damping enhancement.

Reference 36 reported Geff↑↓ = 7.5 × 1014 Ω−1 m−2 for bilayers of YIG and Pt measured via spin pumping, which is similar to Geff↑↓ = 5.7 × 1014 Ω−1 m−2 we find above for TmIG and Pt. There is, however, a significant spread in the values reported for YIG/Pt; for example, the spin Hall magnetoresistance (SMR) study of Ref. 39 determines a considerably smaller value of G↑↓ = 1.2 × 1014 Ω−1 m−2 for YIG/Pt.

For TmIG/Pt, SMR experiments have provided an insight into G↑↓ hitherto. Our spin pumping result is similar to G↑↓ = 6.5 × 1014 Ω−1 m−2 (Ref. 19) from the SMR of TmIG/Pt and exceeds G↑↓ = 1.3 × 1014 Ω−1 m−2 (Ref. 14) obtained via the SMR of TmIG/Pt Hall bars. Thus, similar to the YIG/Pt case, there is a significant spread in reported values from SMR and spin pumping. The determination of G↑↓ via SMR requires both the spin Hall angle and the spin diffusion length scale for thin Pt to be measured or assumed, but reported values of these two parameters vary significantly depending on measurement regimes and methods. This practical issue has been explored for TmIG/Pt in Ref. 40, wherein it is noted that G↑↓ > 1015 Ω−1 m−2 may be readily argued from SMR data. Furthermore, SMR data suggest a high sensitivity to interface annealing,40 implying that the differences in the Pt deposition process (DC magnetron sputtering in the previous work vs electron beam evaporation used here) in addition to interfacial contamination or roughness could affect the spin mixing conductance. We also highlight significant differences in the sample thickness and geometry—the TmIG films in previous SMR experiments14,39 were thinner (8 nm-thick) than those used in the present work (28 nm-thick) and below 10 μm in lateral size, such that the pinning and other size effects affect a direct comparison with the sample of the present work which experienced a microwave excitation across millimeter-scale lateral dimensions.

In summary, we have used FMR to determine the perpendicular magnetic anisotropy and Gilbert damping α of insulating epitaxial ferrimagnetic TmIG films and heterostructures grown by pulsed laser deposition. A 28 nm-thick TmIG film on GGG(111) exhibits Landé g = 1.56 and α = 0.014 at 350 K. The addition of Pt or Cu/Pt overlayers resulted in α = 0.022 and α = 0.024, respectively, consistent with a damping contribution from spin pumping from the TmIG into the metal overlayer. The FMR data reveal a spin transparency of Geff↑↓ = 5.7 × 1014 Ω−1 m−2 for the TmIG-metal interface, similar to the values obtained from spin Hall magnetoresistance in TmIG/Pt (Ref. 19) and to the values obtained from YIG/Pt. The moderate damping in TmIG, comparable to that of low-damping metals, and the high spin mixing conductance, low electrical conductivity, low coercivity, and PMA argue for TmIG as a key material for spintronic devices.

The authors thank Satoru Emori for helpful discussions. The work at Stanford and SLAC was supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DE-AC02-76SF00515 (Y.H. and H.Y.H.), and the Laboratory Directed Research and Development program at the SLAC National Accelerator Laboratory (S.C. and A.G.S.). The work at MIT was supported by CSPIN, a STARnet Center, and by SMART, an nCORE Center of the Semiconductor Research Corporation sponsored by the National Institute of Standards and Technology. A.Q. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) and from the Max-Planck-Institute of Microstructure Physics.

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