We report on the temperature (T), magnetic field (μ0H), and angle (Θ, Φ) dependent resonant absorption of X-band microwaves in spinel ferrite epitaxial films subjected to two distinct states of growth strain. The polar angle (Θ) dependence of the resonance field (Hres) in films with ∼0.5% ab-plane expanded unit cell establishes a distinct perpendicular magnetic anisotropy (PMA). The anisotropy field (Han) for Θ = 0° increases monotonically on lowering the temperature from 300 K to 90 K following the behavior of the saturation magnetization (Ms) keeping Han┴/Ms ≈ 1. The narrow resonance linewidth (μ0ΔHres┴ = 3.7 mT at 300 K) and its negligible (±0.3 mT) variation with temperature establish the magnetic softness of these PMA films. The dependence of Hres on Θ, Φ, and T in films subjected to compressive stress shows in-plane cubic anisotropy whose strength is nonmonotonic in temperature. The ∼2.0% compression of the unit cell basal plane also appears to accentuate noncollinearity of sublattice magnetization of such films as indicated by the T-dependence of ΔHres. The thicker films with PMA display spin wave resonances whose position allows determination of the spin wave stiffness constant together with independent determination of Han┴. The resonance characteristics of the PMA films qualify them as potential candidates for frequency agile microwave devices and magnonic circuit elements.

Thin epitaxial films of the inverse spinel ferrite NiFe2O4 and its chemically altered forms on substitution at the Ni and Fe sites have attracted renewed interest from the perspective of making spin-orbit torque (SOT) oscillators, memory and logic devices,1–5 and multiferroic heterostructures in conjunction with a ferroelectric material.6–8 The state of magnetization, magnetic anisotropy, magnetostriction, and magnetic losses in these systems are dependent on the nature of chemical substitution as well as on epitaxial growth stresses introduced by the difference in the lattice parameters of the ferrite and the substrate.9–12 Additionally, such magnetic characteristics are strongly dependent on temperature. Our recent experiments13 on the epitaxial growth of a NiZnAl-ferrite on MgAl2O4 (MAO) and MgGa2O4 (MGO) crystals revealed that a small change in the state of stress in the film from compressive to tensile rotates the easy axis of magnetization from in-plane to perpendicular to the film plane. The ferromagnetic resonance (FMR) spectra of the perpendicular magnetic anisotropy (PMA) films at ambient temperature over a broad band of GHz frequencies are characterized by very small (<5 × 10−3) Gilbert damping parameter α that indicates a soft magnetic material. These electrically insulating ferrite films with the PMA are particularly promising for fabrication of efficient SOT-oscillators and magnonic devices as the SOT-producing electrical current will not be shunted in this nonconducting ferrite unlike the case of metallic ferromagnets with PMA.14,15 The soft magnetic properties together with the insulating character may also allow nondissipative propagation of spin waves over long length scales, thus making these films suitable for wave-based computing and communication devices.16 The PMA is particularly important as it allows propagation of magnetostatic forward volume spin waves, which offer reciprocity configuration suitable for logic devices.17,18

Thus far, most of the studies of magnetization, magnetic anisotropy, magnetostriction, and microwave absorption in epitaxial spinel ferrites have focused on the ambient temperature behavior.9–12 While at temperatures above 300 K, the bulk magnetization decreases monotonically to zero at the Néel temperature, measurements at low temperatures bring forth the subtle aspects of competition between the two magnetic sublattices, noncollinearity of moments, changes in spin-lattice relaxation time, interfacial pinning of magnetization, and magnetic anisotropy.19,20 Clearly, measurements of static and dynamic magnetization in epitaxial films of ferrites displaying PMA at various temperatures are important for fundamental understanding of magnetism as well as for the operation of devices at low temperatures. A powerful instrument that allows measurements of resonant and nonresonant absorption of microwaves with high sensitivity is the cavity-based electron spin resonance spectrometer. The microwave cavity in these systems can be configured to measure the absorption as a function temperature, polar (Θ) and azimuthal (Φ) angles between the external static magnetic field and thin film sample normal, field modulation amplitude, and microwave power.20–23 

This paper describes results of cavity FMR measurements over the temperature range of ∼80–300 K on epitaxial films of NiZnAl-ferrite pseudomorphically grown on the (001) planes of two different spinel oxide crystals that provide tensile and compressive strain in the film. The FMR measurements are augmented by the measurements of static saturation magnetization as a function of temperature and the angle between the magnetizing dc field and the film normal. We note that the critical magnetic parameters such as Han, Ms and ΔHres in the films with PMA remain nearly constant, whereas Hres changes monotonically over the investigated temperature range. This should ensure the thermal stability of a frequency agile device operating at different temperatures. However, a distinct nonmonotonic enhancement of ΔHres is seen in films displaying fourfold in-plane anisotropy, which is suggestive of the Yafet–Kittel-type24 noncollinearity of moments appearing at lower temperatures. Thicker films with PMA display satellite resonances emerging from the standing spin wave (SSW) excitations, which have allowed the first-time calculation of the spin wave stiffness constant in an epitaxial spinel film with PMA. The details of these results are described as follows: Sec. II gives experimental details of the cavity FMR and static magnetization measurements together with a brief outline of film preparation and structural characterization. Further details of growth and structure of the films can be found in our earlier publications.13,25 All results along with discussion are given in Secs. III AIII D for dc magnetization, FMR of films with PMA, resonant absorption in films with in-plane anisotropy, and SSW excitations, respectively.

As described earlier,13 thin epitaxial films of the zinc and aluminum substituted NiFe2O4 were deposited by ablation of a sintered target of Ni0.65Zn0.35Al0.8Fe1.2O4 (NZAFO). The substrates used for growth were (001) cut crystals of the spinel oxides MgAl2O4 (MAO) and MgGa2O4 (MGO), whose cubic lattice parameters were 0.8083 nm and 0.828 nm, respectively. The typical deposition conditions used for film growth are a laser pulse repetition rate of 4 Hz, a laser fluence of 4 J/cm2, a target to substrate distance of 5 cm, the substrate temperature in the range of 600–700 °C, and an oxygen partial pressure of ∼250–300 mTorr. The films were cooled to room temperature at the rate of 10 °C/min after completion of deposition. The typical growth rate of the films under these conditions was ∼0.02 nm/pulse. The nature of epitaxial growth of the NZAFO films on these substrates has been characterized in detail with four-circle x-ray diffractometry and x-ray reflectivity measurements. The diffraction profiles of the films covering (004) reflection show prominent Laue oscillations from which thickness values of the films have been calculated. Further details of film growth and characterization are given in Ref. 13. In some cases, x-ray circular dichroism was used to establish the valence state of the Fe ions in the material and its purity.25 The measurements of static magnetization M as a function of temperature [M(T)] and magnetic field [M(H)] were carried out in a SQUID magnetometer for in-plane and out-of-plane orientation of the magnetic field over the temperature range of 10–350 K.

The measurements of ferromagnetic resonance were performed over the temperature range of ∼80–300 K in an electron spin resonance spectrometer (Bruker Model EMX) equipped with a TE002 mode microwave (9.6 GHz) cavity, precision goniometer for sample rotation, and a liquid nitrogen continuous flow cryostat. The goniometer allows rotation of the sample to orient the external dc field Hdc in the polar (Θ) and azimuthal (Φ) directions with respect to film normal such that the microwave magnetic field hrf is always perpendicular to Hdc. A diode detector measures the absorbed power in the cavity. A small amplitude (∼4 Oe) ac field modulates the Hdc at 100 KHz to allow phase sensitive detection of the absorbed power.

The epitaxial nature of growth of NZAFO whose lattice parameter in the bulk is 0.8242 nm on (001) MAO and (001) MGO crystals was confirmed by x-ray diffraction. Reciprocal space maps of these films of thickness <115 nm showed a fully strained pseudomorphic growth. The nature of epitaxial strain in films on MAO and MGO is compressive (∼2%) and tensile (∼0.5%). These high resolution x-ray scattering experiments do not reveal any signatures of strain relaxation in these very thin films. However, we do expect a relaxation of the lattice mismatch strain as the films become thicker.13 This reversal of the character of strain in films on MAO and MGO dramatically affects the magnetic state of these films as can be seen from the M(H) plots displayed as insets of Fig. 1 over a limited range of field for clarity. The 27 nm film on MAO is characterized by easy-plane anisotropy (inset “a”) with a very small saturation field (Hs) (<2 mT). The magnetization of this film in the out-of-plane field direction (H) saturates at a field in excess of 1 T. Contrary to this behavior, the small tensile strain in films on MGO results in a prominent perpendicular magnetic anisotropy (inset “b”). The PMA energy calculated from the difference in the area enclosed in the first quadrant of the M(H) curves for H and H configurations is ≈1.4 × 104 J/m3. The in-plane anisotropy energy for the film on MAO, on the other hand, is an order of magnitude higher. This appears to be due to the added contribution of the shape anisotropy. The origin of anisotropy in both cases is presumably the strain related magnetoelastic interaction. The behavior of saturation magnetization of the films on MAO and MGO over the temperature range of 10 K to 350 K is shown in the main panel of Fig. 1. The ambient temperature Ms of ≈150 mT and ≈180 mT for the 19 nm and 27 nm films, respectively, is in agreement with the reported value of ≈160 mT for the bulk ceramic NZAFO,6 which is significantly lower than the magnetization of the Al-free Ni0.65Zn0.35Fe2O4. This drop in the magnetization is a consequence of the nonmagnetic Al3+ ions replacing the Fe3+ ions located at the octahedral sites of the inverse spinel NiFe2O4, which suppresses the gain in magnetization as 35% of the Ni2+ ions are replaced by Zn2+.6 However, this lower value of Ms would make NZAFO more responsive to electric field modulation as a result of magnetoelastic coupling, provided the Al addition does not cause a significant drop in the magnetostriction coefficient of the Zn substituted nickel ferrite. The rapid drop of magnetization upon increasing the temperature above 10 K is also a noteworthy feature of Fig. 1. This large deviation of M(T) from the mean-field behavior may reflect a noncollinear Yafet–Kittel-type ordering24 at low temperatures, in addition to strong spin wave excitations.

FIG. 1.

Saturation magnetization (Ms) of the 19 nm and 27 nm thick NZAFO epitaxial films deposited on MgGa2O4 and MgAl2O4 crystals, respectively, plotted as a function of temperature. Inset “a” shows the magnetic field dependence of magnetization [M(H)] at 300 K for the 27 nm thick film, measured in two field configurations, H parallel to film plane (H) and H perpendicular to plane (H┴), whereas inset “b” is the M(H) data for the 19 nm film on MgGa2O4 at 300 K. The data are shown over a limited range of field for clarity.

FIG. 1.

Saturation magnetization (Ms) of the 19 nm and 27 nm thick NZAFO epitaxial films deposited on MgGa2O4 and MgAl2O4 crystals, respectively, plotted as a function of temperature. Inset “a” shows the magnetic field dependence of magnetization [M(H)] at 300 K for the 27 nm thick film, measured in two field configurations, H parallel to film plane (H) and H perpendicular to plane (H┴), whereas inset “b” is the M(H) data for the 19 nm film on MgGa2O4 at 300 K. The data are shown over a limited range of field for clarity.

Close modal

We now present the results of resonant microwave absorption in the NZAFO epitaxial films at X-band frequency in the temperature range of ∼80–300 K. The differential absorption (dP/dH) spectra of the 19 nm film on MGO that displays PMA are shown in Fig. 2(a) for the H configuration. The absorption is characterized by a single derivative peak over the entire temperature and field range, although the data are shown over a limited segment of the field for clarity. We note that the position of the resonance shifts to lower fields as the temperature drops. The dependence of the resonance frequency (f) on the applied static field and the anisotropies of the magnetic system is expressed by the Kittel equations.21,22,26 For the H case, we have

f=(g/μB/h)[HresMs+Han],
(1)

where Hres, Ms, Han, and g/ are the resonance field, saturation magnetization, out-of-plane anisotropy field, and effective g-factor, respectively. We have calculated the full width at half maximum ΔHres of the resonances by fitting the dP/dH curve to the derivative of a generalized Lorentzian function that represents absorptive and dispersive components of the frequency response.25,Figure 2(b) summarizes the temperature dependence of Hres, Ms, Han, and ΔHres assuming a free-electron-like g-factor. The room temperature values of Hres and ΔHres are in excellent agreement with our frequency-dependent measurements reported earlier13 on the same set of samples. The pronounced temperature dependence of Hres is a reflection of how the internal fields in the material change with temperature. A substantial contribution to these fields comes from the PMA. Han in this case grows on lowering the temperature as Han(T) = Han(0) – βT−n, with n ≈ 2, Han(0) ≈ 626 mT, and β = 7 × 103 (T K2). The resonance line width ΔHres remains within 3.5 mT to 4.5 mT throughout the temperature range although a distinct minimum in its value is seen near T ≈ 240 K. The resonance width derives contributions from magnetic disorder in the system as well as from the intrinsic viscous damping of magnetization precession, which is low in this nickel-based ferrite due the reduced number of Ni2+ ions and the quenched orbital angular momentum of Fe3+.

FIG. 2.

Panel (a): Ferromagnetic resonance spectra of the 19 nm thick film on MGO measured at several temperatures between 100 K and 295 K with the external magnetic field directed perpendicular to the plane of the film (Θ = 0° configuration). Panel (b) shows the temperature variation of saturation magnetization (Ms), resonance field (Hres), anisotropy field Han, and full width at half maximum of the resonance (ΔHres).

FIG. 2.

Panel (a): Ferromagnetic resonance spectra of the 19 nm thick film on MGO measured at several temperatures between 100 K and 295 K with the external magnetic field directed perpendicular to the plane of the film (Θ = 0° configuration). Panel (b) shows the temperature variation of saturation magnetization (Ms), resonance field (Hres), anisotropy field Han, and full width at half maximum of the resonance (ΔHres).

Close modal

The results of FMR measurement on the 19 nm thick film with PMA performed at several temperatures with Hdc in the plane of the sample and aligned along the (100) axis of the substrate are shown in Fig. 3(a). The resonance field for this H configuration is higher than that for the H configuration and displays opposite temperature dependence. This is indicative of PMA in these films. For the in-plane resonance, the Kittel equation21 is

f=(g/μB/h)[Hres(ϕ)+H4,ipcos4ϕ]1/2×[Hres(ϕ)+Meff+(1/4)H4,ip(3+cos4ϕ)]1/2,
(2)

where H4,ip is the cubic in-plane anisotropy field and ϕ is the angle of in-plane rotation [ϕ = 0° for H parallel to (110), the easy axis of magnetization in the plane of the film]. Our earlier results13,25 on the compressively strained films of NZAFO on MAO showed a strong in-plane cubic anisotropy at room temperature whose temperature dependence will be presented in the subsequent section. Presently, in order to check if there is any trace of this cubic anisotropy in the films deposited on MGO as well, we have measured the ϕ-dependence of the FMR field in this film at 300 K. The result of such a measurement is shown in Fig. 3(b). Interestingly, in spite of a strong out-of-plane anisotropy, we do see some vestige of the cubic in-plane anisotropy in this film as well. A two-parameter fit of Eq. (2) to these data with g/ = 2.0, as shown in Fig. 3(b), yields H4,ip= −3.1 ± 0.1 mT and Meff = −76.5 ± 0.1 mT, if we neglect this cubic in-plane anisotropy and put H4,ip= 0 in Eq. (2), it reduces to

f=(g/μB/h)(Hres(Hres+Meff))1/2.
(3)
FIG. 3.

Panel (a): FMR spectra of the 19 nm thick film on MGO measured at several temperatures between 100 K and 295 K with the external magnetic field directed parallel to the plane of the film (Θ = 90° configuration). Panel (b) shows the variation of the resonance field (Hres) and full width at half maximum (ΔHres) as the external magnetic field is rotated in the plane of the film. The distinct dips in Hres at 45° and 135° indicate in-plane anisotropy. Panel (c) shows the temperature variation of Ms, Hres, Han, and ΔHres.

FIG. 3.

Panel (a): FMR spectra of the 19 nm thick film on MGO measured at several temperatures between 100 K and 295 K with the external magnetic field directed parallel to the plane of the film (Θ = 90° configuration). Panel (b) shows the variation of the resonance field (Hres) and full width at half maximum (ΔHres) as the external magnetic field is rotated in the plane of the film. The distinct dips in Hres at 45° and 135° indicate in-plane anisotropy. Panel (c) shows the temperature variation of Ms, Hres, Han, and ΔHres.

Close modal

The effective magnetization here is Meff = Ms + Han. The in-plane anisotropy (Han) is simply the Han with sign reversed minus the contribution of the shape anisotropy. The values of Hres, Han, Ms, and ΔHres are plotted as a function of temperature in Fig. 3(c). A noteworthy feature of these data is the behavior of ΔHres. While its low ambient temperature value (≈3 mT) is consistent with the earlier frequency-dependent measurements,13 its rise on lowering the temperatures is suggestive of noncollinearity of the A and B site spins in this Zn substituted nickel ferrite.27 

We now present the results of in-plane FMR measurements on the 27 nm thick film deposited on (001) MgAl2O4, which reveals a pronounced in-plane anisotropy in static magnetization measurements (inset “a” of Fig. 1). The microwave response of this sample measured at several temperatures with Hdc directed along the (100) edge of the substrate is shown in Fig. 4(a). No resonance was seen for Hdc perpendicular to the plane of the sample as the Hres in this geometry exceeds the attainable dc field of our spectrometer. The Hres first shifts toward lower fields on increasing the temperature from 90 K and then rises to higher fields at T ≈ 220 K.

FIG. 4.

Panel (a): FMR spectra of the 27 nm thick film on MAO measured at several temperatures between 90 K and 310 K with the external magnetic field directed parallel to the plane of the film (Θ = 90° configuration). Panel (b) shows the temperature variation of Ms, Hres, Han, and ΔHres. Panel (c) shows the variation of the resonance field (Hres) and full width at half maximum (ΔHres) as the external magnetic field is rotated in the plane of the film. These data clearly establish the in-plane fourfold anisotropy.

FIG. 4.

Panel (a): FMR spectra of the 27 nm thick film on MAO measured at several temperatures between 90 K and 310 K with the external magnetic field directed parallel to the plane of the film (Θ = 90° configuration). Panel (b) shows the temperature variation of Ms, Hres, Han, and ΔHres. Panel (c) shows the variation of the resonance field (Hres) and full width at half maximum (ΔHres) as the external magnetic field is rotated in the plane of the film. These data clearly establish the in-plane fourfold anisotropy.

Close modal

Figure 4(b) summarizes the behavior of Hres and ΔHres as a function of temperature. We have also estimated the anisotropy field under the assumption of a free-electron-like g-factor and a Φ-independent anisotropy. The variation of Han with temperature is also plotted in Fig. 4(b) along with the T-dependence of the saturation magnetization. The very narrow line width (≈3 mT) seen at ambient temperature highlights the magnetic softness of these epitaxial films. Interestingly, the temperature dependence of ΔHres is similar to that seen for the film on MGO [Fig. 3(c)], which again suggests noncollinearity of the A and B site moments at lower temperatures. As shown later in Fig. 5(b), the resonance field increases steeply as the field becomes perpendicular to the plane of the film (Θ = 0°). This Θ-dependence of the resonance establishes the presence of a strong in-plane magnetic anisotropy in this compressively strained epitaxial film. However, we first establish the fourfold symmetry of in-plane anisotropy by measuring the FMR as a function of the azimuthal angle Φ. The Hres(ϕ) is displayed in Fig. 4(c). A fit of these data to Eq. (2) with g/ = 2.0 yields H4,ip = −4.91 ± 0.03 mT at room temperature. Here, the assumption of a free-electron-like g-factor is reasonable because a large fraction of the Ni2+ ions with a g of 2.3 has been replaced by Zn2+, where the 3d shell is completely full. For the Al-free Ni0.65Zn0.35Fe2O4, the g-factor is ≈2.06.20 

FIG. 5.

Panel (a) highlights the satellite resonance that appears below ∼110 K in the parallel-field (Θ = 90°) resonance spectra of the 27 nm thick film deposited on MAO. Panel (b) shows the Θ dependence of satellite and the main resonance peak. As Θ approaches 0° and 180°, the resonance could not be reached with the available external field.

FIG. 5.

Panel (a) highlights the satellite resonance that appears below ∼110 K in the parallel-field (Θ = 90°) resonance spectra of the 27 nm thick film deposited on MAO. Panel (b) shows the Θ dependence of satellite and the main resonance peak. As Θ approaches 0° and 180°, the resonance could not be reached with the available external field.

Close modal

An interesting feature of the parallel-field measurements on this NZAFO film on MAO is the emergence of a second resonance at T ≤ 120 K as shown in Fig. 5(a). This satellite FMR has a larger width compared to the width of the main resonance and its position (Hressat) shifts of lower fields on increasing the temperature from 90 K. As shown in Fig. 5(b), the polar angle (Θ) dependence of this feature is similar to that of the main resonance. The steep increase in (Hressat) as Θ approached zero, together with the fact that Hressat is <Hres, suggests that this anomalous feature may be associated with inhomogeneous in-plane magnetic ordering as the external field along the in-plane hard axis (010) approaches the saturation value.23,28,29

We have also measured the Θ and Φ dependencies of the FMR spectra in a thicker (≈114 nm) film of the NZAFO spinel deposited on (100) MGO. The PMA persists with the same robustness in this thicker film as well. It is clearly seen in Fig. 6(a) where the polar angle dependence of the resonance peak position is plotted. From the value of Hres at Θ = 0° and 90° and the measured saturation magnetization of this film, Han and Han come out to be ≈298 mT and −236 mT, respectively, with the assumption of a free-electron-like g-factor.

FIG. 6.

A representative FMR spectrum of the 114 nm thick NZAFO film on (001) MgGa2O4 measured at ∼300 K with the external field directed perpendicular to the plane of the film. The signal is amplified 100 times to reveal the satellite resonances. The numbers are mode indices. The inset shows the variation of the satellite resonance field as a function of mode number. The solid line in the figure is a fit using Eq. (4).

FIG. 6.

A representative FMR spectrum of the 114 nm thick NZAFO film on (001) MgGa2O4 measured at ∼300 K with the external field directed perpendicular to the plane of the film. The signal is amplified 100 times to reveal the satellite resonances. The numbers are mode indices. The inset shows the variation of the satellite resonance field as a function of mode number. The solid line in the figure is a fit using Eq. (4).

Close modal

The FMR scans of the thicker film (114 nm) in the perpendicular field geometry (Θ = 0) over a wide field range also show several satellite resonances that appear below the primary resonance. A typical FMR spectrum with such subresonances is shown in Fig. 6(b). The intensity of these modes drops as the angle Θ increases from 0° to 90°. The spectrum collected at Θ = 90° has no such resonances. These satellites in the spectrum can be attributed to standing perpendicular spin wave (SPSW) modes that are generated in a magnetic film subjected to a uniform rf magnetic field. The SPSW modes appear at field Hn as30,31

Hn=(ω/γ+Han)(D/γ)(n/πd)2,
(4)

where γ=g/μB/ and ω, Han, n, d, g/, and D are the angular frequency of the rf field, anisotropy field, mode number, film thickness, effective g-factor, and the spin wave stiffness constant, respectively.

The mode number n takes odd integer values when the spins at the surface of the film are pinned,32 as may be the case for an epitaxially grown thin film. The spin wave stiffness constant in Eq. (4) governs the magnon dispersion as ω = DK2, and in the mean-field approximation, it is related to exchange integral J as D=2JSa2/, where S and a are the spin and lattice constant of the spin lattice, respectively. The slope of the plot between Hn and n2 yields the stiffness constant D. In the inset of Fig. 6(b), we plot the resonances corresponding to n = 1, 3, 5, and 7. The solid line in the figure is a fit to Eq. (4), which yields D = 40.6 meV (nm)2 at 310 K assuming a free-electron-like g-factor and the anisotropy field μ0Han of 185 mT. While we have not come across any measurements of D in a spinel ferrite film with PMA, the S number we have extracted is higher by a factor of ∼3 compared to the value [≈13.2 meV (nm)2] of D reported for Zn substituted lithium ferrite in the bulk form.33 

Microwave absorption studies on spinel ferrite epitaxial films down to a temperature that is easily accessible with liquid nitrogen are important for designing low-loss magnonic circuits operating independently or in conjunction with high Tc superconductors. Here, we have carried out a detailed study of dc magnetization and resonant absorption of 9.6 GHz electromagnetic radiation in stress-tuned epitaxial films of Ni0.65Zn0.35Fe1.2Al0.8O4. These studies reveal a robust magnetic anisotropy whose direction depends on the nature of in-plane structural strain. The films under a basal-plane tensile strain display soft PMA as evidenced by the temperature and polar angle (Θ) dependence of Hres and ΔHres. The PMA field (Han) grows monotonically on lowering the temperature, but the ratio Han┴/Ms remains close to unity, thus ensuring consistency in the shape of the M(H) loop as the temperature drops to 77 K. The azimuthal angle (Φ) dependence of resonance in films on MgAl2O4 with compressive strain displays a distinct fourfold in-plane anisotropy oriented at 45° with respect to the principal axes (100) and (010), and its strength is monotonic in temperature. The resonance width reveals anomalous growth at lower temperatures suggesting a Yefet–Kittel-type noncollinearity of sublattice moments. The films with PMA also display satellite resonances at H < Hres when the external field is directed along the film normal (Θ = 0°). The satellite peaks can be assigned to excitation of standing spin wave modes in a film whose surface spins are pinned. This interesting result uniquely allows calculation of the spin wave stiffness constant of a magnetically soft spinel ferrite film displaying PMA. Our T-dependent X-band absorption studies demonstrate the potential of such ferrite films with robust PMA for applications in frequency agile microwave electronics and magnonics.

This material is based upon work supported by the Air Force Office of Scientific Research under Award No. FA9550-15RXCOR198. R.C.B. acknowledges the National Research Council, Washington DC, for the award of a senior fellowship. Partial support has also come from the Office of Naval Research under Award No. DOD-078-24086 at Morgan State University.

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