Magnetic insulators are essential for computing and communication devices that rely on spin transport without net charge transport.
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https://doi.org/10.1103/PhysRevB.102.054402Most studies to date have effectively treated ferrimagnetic oxides as ferromagnets: the cation magnetic moments are presumed to remain collinear and coherent while they are excited, such that they behave as one “net” magnetization (i.e., the vector sum of the cation moments). However, it is reasonable to question how much these cation moments can deviate from the ferromagnetic-like dynamics. Such deviations may be plausible, considering that the coupling among the cations may not be perfectly rigid or that different magnetic cations in the sublattices may exhibit different rates of spin relaxation (effective damping).
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https://doi.org/10.1109/TMAG.2010.2078493 Indeed, a recent experimental study on biaxial yttrium iron garnet demonstrates peculiar spin-torque switching results,
1414.
Y. Zhou,
C. Guo,
C. Wan,
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https://doi.org/10.1103/PhysRevApplied.13.064051 suggesting that ferrimagnetic oxides—even with a large net magnetization—could deviate from the expected ferromagnetic-like dynamics. Given the application potential and fundamental interest, it is timely to explore the dynamics of specific sublattices and cations in ferrimagnetic oxides.In this Letter, we present unprecedented experimental insight into resonant spin dynamics in a multi-cation ferrimagnetic oxide. Specifically, we investigate sublattice- and cation-specific dynamics in NiZnAl-ferrite (Ni0.65Zn0.35Al0.8Fe1.2O4), a spinel ferrimagnetic oxide with two magnetic sublattices (
Fig. 1): (i) the tetrahedrally coordinated sublattice, Td, predominantly consisting of FeTd3+ cations and (ii) the octahedrally coordinated sublattice, Oh, predominantly consisting of FeOh3+, FeOh2+, and NiOh2+ cations. We utilize x-ray ferromagnetic resonance (XFMR),
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24, 013030 (2022).
https://doi.org/10.1088/1367-2630/ac465f which leverages x-ray magnetic circular dichroism (XMCD) that is sensitive to chemical elements, site coordination, and valence states. With this XFMR technique, we detect the precessional phase and amplitude for each magnetic cation species.Our cation-specific XFMR measurements are further augmented by the following attributes of NiZnAl-ferrite. First, the NiZnAl-ferrite film exhibits about two orders of magnitude lower magnetic damping than the ferrite in an earlier XFMR study,
2020.
P. Warnicke,
E. Stavitski,
J.-S. Lee,
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W. E. Bailey,
V. G. Harris, and
D. A. Arena, Phys. Rev. B
92, 104402 (2015).
https://doi.org/10.1103/PhysRevB.92.104402 yielding a far greater signal-to-noise ratio in XFMR measurements. This permits comprehensive measurements at multiple applied magnetic fields, which allow precise quantification of the precessional phase lags among the cation species. Second, NiZnAl-ferrite is an intriguing testbed for exploring whether the excited magnetic cations retain collinear coupling. The nonmagnetic Zn2+ and Al3+ cations dilute the magnetic exchange interactions in NiZnAl-ferrite,
2828.
W. D. Wilber,
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2929.
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H.-M. Jeon,
J. Peoples,
M. Schmitt,
K. Mahalingam,
M. Hill,
M. Mcconney,
M. Gray,
U. Alaan,
A. Bornstein,
P. Shafer,
A. N'Diaye,
E. Arenholz,
G. Haugstad,
K.-Y. Meng,
F. Yang,
D. Li,
S. Mahat,
D. Cahill,
P. Dhagat,
A. Jander,
N. Sun,
Y. Suzuki, and
B. Howe, Adv. Mater.
29, 1701130 (2017).
https://doi.org/10.1002/adma.201701130 Due to the diluted exchange interactions, the magnetic Fe2+/3+ and Ni2+ cations may not remain rigidly aligned. Finally, with diverse magnetic cations in NiZnAl-ferrite, we address whether cations with different spin–orbit coupling can exhibit distinct spin relaxation
1212.
G. F. Dionne, IEEE Trans. Magn.
47, 272 (2011).
https://doi.org/10.1109/TMAG.2010.2078493 by quantifying the FMR linewidths and precessional cone angles for the different cations. Taken together, we are able to probe—with high precision—the possible deviation from the oft-assumed ferromagnetic-like dynamics in the ferrimagnetic oxide.Our study focuses on a 23-nm thick epitaxial NiZnAl-ferrite film grown on (001) oriented, isostructural MgAl2O4 substrates by pulsed laser deposition.
2929.
S. Emori,
B. Gray,
H.-M. Jeon,
J. Peoples,
M. Schmitt,
K. Mahalingam,
M. Hill,
M. Mcconney,
M. Gray,
U. Alaan,
A. Bornstein,
P. Shafer,
A. N'Diaye,
E. Arenholz,
G. Haugstad,
K.-Y. Meng,
F. Yang,
D. Li,
S. Mahat,
D. Cahill,
P. Dhagat,
A. Jander,
N. Sun,
Y. Suzuki, and
B. Howe, Adv. Mater.
29, 1701130 (2017).
https://doi.org/10.1002/adma.201701130 The NiZnAl-ferrite film, magnetized along the [100] direction, was probed at room temperature with a circularly polarized x-ray beam at Beamline 4.0.2 at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory. The XFMR measurements follow a pump-probe method: the continuous-wave RF excitation (4-GHz pump) is synchronized to a higher harmonic of the x-ray pulse frequency (500-MHz probe), and the transverse component of the precessing magnetization is probed stroboscopically. A variable delay between the RF pump signal and the timing of the x-ray pulses enables mapping of the complete magnetization precession cycle. A photodiode mounted behind the sample collects the luminescence yield from the subjacent MgAl2O4 substrate. The luminescence yield detection enables the investigation of high-quality epitaxial films on single-crystal substrates.
21,23,24,2721.
A. A. Baker,
A. I. Figueroa,
C. J. Love,
S. A. Cavill,
T. Hesjedal, and
G. van der Laan, Phys. Rev. Lett.
116, 047201 (2016).
https://doi.org/10.1103/PhysRevLett.116.04720123.
Q. Li,
M. Yang,
C. Klewe,
P. Shafer,
A. T. N'Diaye,
D. Hou,
T. Y. Wang,
N. Gao,
E. Saitoh,
C. Hwang,
R. J. Hicken,
J. Li,
E. Arenholz, and
Z. Q. Qiu, Nat. Commun.
10, 5265 (2019).
https://doi.org/10.1038/s41467-019-13280-524.
M. Da̧browski,
T. Nakano,
D. M. Burn,
A. Frisk,
D. G. Newman,
C. Klewe,
Q. Li,
M. Yang,
P. Shafer,
E. Arenholz,
T. Hesjedal,
G. van der Laan,
Z. Q. Qiu, and
R. J. Hicken, Phys. Rev. Lett.
124, 217201 (2020).
https://doi.org/10.1103/PhysRevLett.124.21720127.
C. Klewe,
S. Emori,
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H. M. Jeon,
B. M. Howe,
Y. Suzuki,
Z. Q. Qiu,
P. Shafer, and
E. Arenholz, New J. Phys.
24, 013030 (2022).
https://doi.org/10.1088/1367-2630/ac465f This is in contrast to transmission detection that is limited to polycrystalline films on thin membrane substrates.
18,2018.
Y. Guan,
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V. G. Harris, and
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92, 104402 (2015).
https://doi.org/10.1103/PhysRevB.92.104402 A more detailed description of the XFMR setup is provided in Refs.
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C. Klewe,
Q. Li,
M. Yang,
A. T. N'Diaye,
D. M. Burn,
T. Hesjedal,
A. I. Figueroa,
C. Hwang,
J. Li,
R. J. Hicken,
P. Shafer,
E. Arenholz,
G. van der Laan, and
Z. Qiu, Synchrotron Radiat. News
33, 12 (2020).
https://doi.org/10.1080/08940886.2020.1725796 and
2727.
C. Klewe,
S. Emori,
Q. Li,
M. Yang,
B. A. Gray,
H. M. Jeon,
B. M. Howe,
Y. Suzuki,
Z. Q. Qiu,
P. Shafer, and
E. Arenholz, New J. Phys.
24, 013030 (2022).
https://doi.org/10.1088/1367-2630/ac465f. We note that Ref.
2727.
C. Klewe,
S. Emori,
Q. Li,
M. Yang,
B. A. Gray,
H. M. Jeon,
B. M. Howe,
Y. Suzuki,
Z. Q. Qiu,
P. Shafer, and
E. Arenholz, New J. Phys.
24, 013030 (2022).
https://doi.org/10.1088/1367-2630/ac465f examines NiZnAl-ferrite on the same beamline with x-ray magnetic linear dichroism (XMLD); our present study is distinct in precisely quantifying cation-specific spin dynamics, leveraging the order-of-magnitude greater XMCD signal compared to XMLD.By tuning the photon energy to the element- and coordination-specific features in the static XMCD spectra, we are able to probe the magnetism of different elements, valence states, and sublattice sites individually. Static XMCD spectra at the L3 edge of Fe and Ni are shown in
Fig. 2. The applied field of 200 mT in the static XMCD measurements was far greater than the coercive field of ≈0.2 mT of the magnetically soft NiZnAl-ferrite film.
2929.
S. Emori,
B. Gray,
H.-M. Jeon,
J. Peoples,
M. Schmitt,
K. Mahalingam,
M. Hill,
M. Mcconney,
M. Gray,
U. Alaan,
A. Bornstein,
P. Shafer,
A. N'Diaye,
E. Arenholz,
G. Haugstad,
K.-Y. Meng,
F. Yang,
D. Li,
S. Mahat,
D. Cahill,
P. Dhagat,
A. Jander,
N. Sun,
Y. Suzuki, and
B. Howe, Adv. Mater.
29, 1701130 (2017).
https://doi.org/10.1002/adma.201701130 The XMCD spectra show pronounced peaks from different cations on the Oh and Td sublattices. While an XMCD spectrum is generally a complicated superposition of different coordinations and valence states [as illustrated in the modeled curves in
Fig. 2(a)], the three distinct peaks in the Fe L3 spectrum at 708.0, 709.2, and 710.0 eV are attributed to FeOh2+, FeTd3+, and FeOh3+, respectively, to a good approximation.
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C. Kons,
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K. L. Krycka, Phys. Rev. Mater.
4, 034408 (2020).
https://doi.org/10.1103/PhysRevMaterials.4.034408 The opposite polarities of the FeTd3+ and FeOh2+/3+ peaks reflect the antiferromagnetic coupling between the Td and Oh sublattices at static equilibrium. Ni2+ cations predominantly occupy the Oh sublattice,
29,3029.
S. Emori,
B. Gray,
H.-M. Jeon,
J. Peoples,
M. Schmitt,
K. Mahalingam,
M. Hill,
M. Mcconney,
M. Gray,
U. Alaan,
A. Bornstein,
P. Shafer,
A. N'Diaye,
E. Arenholz,
G. Haugstad,
K.-Y. Meng,
F. Yang,
D. Li,
S. Mahat,
D. Cahill,
P. Dhagat,
A. Jander,
N. Sun,
Y. Suzuki, and
B. Howe, Adv. Mater.
29, 1701130 (2017).
https://doi.org/10.1002/adma.20170113030.
R. A. D. Pattrick,
G. van der Laan,
C. M. B. Henderson,
P. Kupier,
E. Dudzik, and
D. J. Vaughan, Eur. J. Miner.
14, 1095 (2002).
https://doi.org/10.1127/0935-1221/2002/0014-1095 such that the XMCD peak at 853.5 eV is assigned to NiOh2+.XFMR measurements were carried out at the photon energies specific to the cations found above. For each cation, we performed phase delay scans to map out the precession at different field values across the resonance field μ0Hres.
Figure 3(a) displays a set of phase delay scans taken at a photon energy of 710.0 eV, corresponding to FeOh3+. Each scan was taken at a fixed bias field between 17.0 and 21.6 mT. The phase delay scans exhibit pronounced oscillations with a periodicity of 250 ps in accordance with the 4-GHz excitation. Since the excitation here is continuous-wave, the oscillations are undamped and fit with simple sinusoids.
Figure 3(b) depicts delay scans for FeTd3+ (709.2 eV) and FeOh3+ (710.0 eV) taken at μ0H = 19.3 mT (the center of the resonance curve). The opposite sign of the two oscillations indicates a phase shift of about 180° between the two sublattices. The result in
Fig. 3(b), thus, suggests that the moments of FeTd3+ (709.2 eV) and FeOh3+ in NiZnAl-ferrite maintain an antiferromagnetic alignment during resonant precession.In the remainder of this Letter, we quantify the precessional phase and relaxation of each cation by analyzing our field-dependent XFMR results, summarized in
Fig. 4.
Figure 4(a) shows that all cations in NiZnAl-ferrite exhibit a characteristic 180° phase reversal across the resonance of a damped harmonic oscillator. Quick visual inspection reveals that all Oh cations are approximately in phase. Furthermore, the Oh and Td cations are approximately 180° out of phase, as expected for the precession of antiferromagnetically coupled moments.To quantify the phase lag among the cations precisely, the field dependence of the precessional phase ϕ for each cation is modeled with
ϕ=ϕ0+arctan(ΔHhwhmH−Hres),(1)where ϕ0 is the baseline of the precessional phase (set to 0 for FeOh3+) and ΔHhwhm is the half-width-at-half-maximum FMR linewidth. Equation
(1) is equivalent to the expressions in Refs.
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J. X. Deng,
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G. van der Laan,
R. J. Hicken, and
Z. Q. Qiu, Phys. Rev. Lett.
117, 076602 (2016).
https://doi.org/10.1103/PhysRevLett.117.076602 and valid when the effective magnetization (including the out-of-plane magnetic anisotropy) μ0Meff≈1 T
2929.
S. Emori,
B. Gray,
H.-M. Jeon,
J. Peoples,
M. Schmitt,
K. Mahalingam,
M. Hill,
M. Mcconney,
M. Gray,
U. Alaan,
A. Bornstein,
P. Shafer,
A. N'Diaye,
E. Arenholz,
G. Haugstad,
K.-Y. Meng,
F. Yang,
D. Li,
S. Mahat,
D. Cahill,
P. Dhagat,
A. Jander,
N. Sun,
Y. Suzuki, and
B. Howe, Adv. Mater.
29, 1701130 (2017).
https://doi.org/10.1002/adma.201701130 is much larger than the applied bias field μ0H≈20 mT. We quantify Hres and ΔHhwhm by simultaneously fitting the field dependence of the precessional phase ϕ [Eq.
(1)] and of the precessional amplitude A,
A∝ΔHhwhm2ΔHhwhm2+(H−Hres)2.(2)To account for reduced sensitivity far from the resonance, the fits in
Figs. 4(a) and
4(c) are weighted using the error bars from the sinusoidal fits of the phase delay scans [e.g.,
Fig. 3(b)]. The results of the fitting are shown in
Figs. 4(a) and
4(c) and
Table I.
TABLE I. Resonance field Hres, linewidth ΔHhwhm, relative precessional phase lag ϕ0, and precessional cone angle θcone for each magnetic cation species, as derived from fitting the field dependence of the precessional phase [Eq.
(1)] and amplitude [Eq.
(2)].
Cationμ0Hres (mT)μ0ΔHhwhm (mT)ϕ0 (deg)θcone (deg)FeOh3+19.21 ± 0.030.43 ± 0.0301.0 ± 0.1FeOh2+19.22 ± 0.030.44 ± 0.031.7 ± 1.21.0±0.1NiOh2+19.23 ± 0.020.43 ± 0.021.5 ± 1.21.1±0.1FeTd3+19.22 ± 0.030.43 ± 0.03−178.5±1.41.1 ± 0.1If the magnetic moments of the four cations were perfectly collinear, the phase lag should be ϕ0=0 for the Oh cation species whereas ϕ0=180° for the Td cation species. Taking FeOh3+ as the reference, the results in
Table I show that ϕ0 deviates by ≈1.5° from the perfect collinear scenario. However, we caution that the uncertainty of ϕ0 in
Table I is likely underestimated. Indeed, by examining the residuals of the fits displayed in
Fig. 4(b), we observe a scatter in the measured precessional phase of at least ≈2°. It is sensible to conclude that the Oh cations maintain a relative precessional phase lag of (0±2)°, whereas the Oh and Td cations maintain a phase lag of (180±2)°. Even with the diluted exchange coupling from nonmagnetic Zn2+ and Al3+ cations, the magnetic Fe2+/3+ and Ni2+ cations retain a coherent, collinear alignment.Reducing the experimental uncertainty to well below 2° would be extremely challenging. For each cation, a small drift in the beamline photon energy with respect to its XMCD peak (
Fig. 2) might shift its apparent precession phase due to an overlap in the cation specific XMCD features. For instance, considering that the difference between the FeTd3+ and FeOh3+ peaks is only ≈0.8 eV, an energy drift of ≈0.01 eV could cause a phase shift of ≈2°. The nominal resolution of the electromagnet at ≈0.1 mT may also contribute to the scatter in the field dependence of the XFMR phase. Moreover, the timing jitter of the master oscillator of up to ≈3 ps limits the time resolution of the phase delay scans. Taking all the above factors into account, the resolution of ≈2° in our present study is in fact at the practical limit.We now provide insight into the spin relaxation of each magnetic cation species by quantifying the cation-specific FMR linewidth ΔHhwhm. In particular, we examine whether different spin relaxation, captured by ΔHhwhm, emerges for magnetic cations with different strengths of spin–orbit coupling. For instance, Fe2+ with nonzero orbital angular momentum, hence possibly greater spin relaxation to the lattice, might be expected to yield greater ΔHhwhm, compared to Fe3+ with nominally zero orbital angular momentum.
1212.
G. F. Dionne, IEEE Trans. Magn.
47, 272 (2011).
https://doi.org/10.1109/TMAG.2010.2078493 However,
Fig. 4(c) and
Table I show that all magnetic cations in NiZnAl-ferrite exhibit essentially the same linewidth, μ0ΔHhwhm=(0.43±0.03) mT. This value is quantitatively consistent with ΔHhwhm from conventional FMR on a NiZnAl-ferrite film, in which linewidth broadening from magnetic inhomogeneity is negligible.
2929.
S. Emori,
B. Gray,
H.-M. Jeon,
J. Peoples,
M. Schmitt,
K. Mahalingam,
M. Hill,
M. Mcconney,
M. Gray,
U. Alaan,
A. Bornstein,
P. Shafer,
A. N'Diaye,
E. Arenholz,
G. Haugstad,
K.-Y. Meng,
F. Yang,
D. Li,
S. Mahat,
D. Cahill,
P. Dhagat,
A. Jander,
N. Sun,
Y. Suzuki, and
B. Howe, Adv. Mater.
29, 1701130 (2017).
https://doi.org/10.1002/adma.201701130 The identical FMR linewidth—to within an uncertainty of ≲10%—indicates that the exchange interactions in NiZnAl-ferrite lead to uniform spin relaxation across all magnetic cations.To further characterize cation-specific spin relaxation, we quantify the precessional cone angle of each magnetic cation species. A magnetic cation with greater spin relaxation (e.g., losing more dynamically excited spin angular momentum to the lattice) would precess with a smaller cone angle. The cone angle θcone is obtained from the amplitudes of the XFMR signal IXFMR and XMCD peak IXMCD via
θcone=2 arcsin(IXFMRIXMCD).(3)We find that all cation moments precess with a cone angle of θcone≈1.0−1.1°. From the invariance of the linewidth and precessional cone angle to within ≲10%, we confirm that the exchange interactions in NiZnAl-ferrite are strong enough to lock all magnetic cations at the same relaxation rate.Our finding is distinct from recent work on a ferrimagnetic DyCo alloy, showing different damping parameters for two magnetic sublattices after femtosecond-laser-induced demagnetization.
3434.
R. Abrudan,
M. Hennecke,
F. Radu,
T. Kachel,
K. Holldack,
R. Mitzner,
A. Donges,
S. Khmelevskyi,
A. Deák,
L. Szunyogh,
U. Nowak,
S. Eisebitt, and
I. Radu, Phys. Status Solidi A Rapid Res. Lett.
15, 2100047 (2021).
https://doi.org/10.1002/pssr.202100047 In Ref.
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