The projected end of Moore's law has spurred a tremendous effort into the discovery of new magnetic materials and heterostructures to advance logic and logic-in-memory devices. [1][2][3] Such magnetic technologies require reliable switching and low switching energy to replace high-power consumption transistors in modern electronic devices. New material systems, for instance, multiferroic and magnetoelectric heterostructures or spin-orbit torques from heavy metal/topological insulators, have been studied intensively, and yet still display major drawbacks such as low endurance, low detection signal, or high current shunting. [4][5][6][7][8] Recently, ferrimagnetic insulators (FIs) 9 have generated interest due to the realization of high quality thin films with perpendicular magnetization using a variety of fabrication techniques. [10][11][12][13] This development has led to the demonstration of efficient current-induced control of magnetization, [14][15][16] current-driven domain wall motion, 17 and high temperature quantum anomalous Hall effect in FI/topological insulator heterostructures. 18 Unlike conducting ferromagnets through which both charge and spin current can propagate, only spin current can pump through the surface of FIs to generate spin torque for modulating the magnetization, 16 which significantly reduces heat dissipation as well as writing current. Furthermore, overcoming the demagnetizing field in FIs that exhibit perpendicular magnetic anisotropy drives the switching current threshold lower when compared to a magnet with in-plane anisotropy. [19][20][21] For a magnetic with perpendicular magnetic anisotropy in a spinorbit torque heterostructure, the critical current expression 19 emphasizes the need to reduce the anisotropy field H K for switching efficiency. When approaching nanoscale dimensions and the mono-domain limit for device miniaturization, however, thermal fluctuation can cause instability, which can only be overcome by increasing the anisotropy field. Thus, there is a need to understand and quantify the evolution of H K in FIs with perpendicular magnetic anisotropy so that optimized conditions can be engineered for future devices at scale. Previous studies have demonstrated the change in thin film anisotropy from
in-plane to out-of-plane using strain 10,22 or tuning of perpendicular anisotropy field by changing film composition and therefore changing tensile strain. 12 The use of strain independently for anisotropy field tuning between thin films that possess perpendicular magnetization has not been reported nor thin film magnetoelastic coefficients been quantified.
Bulk ferrimagnetic TmIG crystallizes in a cubic crystal structure with a lattice constant of approximately 12.32 Å. Prior work [10][11][12][13][14][15] has shown that TmIG can be grown epitaxially on (111)-oriented GGG substrates and have a strain-induced perpendicular magnetic anisotropy described by Eq. (1) (see the supplementary material),
or
where K 1 is the cubic anisotropy constant, B 2 is the magnetoelastic coefficient, M s is saturation magnetization, and β is the shear distortion angle from cubic symmetry (Fig. 1). Here, B 2 ¼ À3λ 111 c 44 where λ 111 is the magnetostriction coefficient and c 44 is the shear stiffness constant. In bulk, K 1 = -0.58 kJ m -3 , λ 111 = -5.2 × 10 -6 , c 44 = 76.6 GPa, and M s = 110 emu cm -3 . 9,15 K 1 and λ 111 being negative reveals that the distortion angle in a film must be larger than π 2 (e.g., from an isotropic in-plane tensile strain) to overcome shape anisotropy and achieve an out-of-plane easy axis.
In this work, we report the systematic tuning of magnetic anisotropy of (111)-oriented TmIG thin films using epitaxial strain imposed from a suite of commercially available rare earth garnet substrates that includes Gd (GSGG). The strain tuning of the magnetic anisotropy field by a factor of 14 in the considered strain range is shown. The magnetoelastic anisotropy constant, B 2 , is found to be approximately 2500 kJ m -3 , more than 2× larger than the reported bulk value, for moderate cubic distortions and found to decrease sharply at cubic distortions of 90.74°and larger. The results demonstrate strain tuning as a pathway to design magnetic anisotropy in insulating ferrimagnets for device scaling purposes and future integrated heterostructures.
(111)-oriented single crystal TmIG films were fabricated using pulsed laser deposition by ablating a stoichiometric Tm 3 Fe 5 O 12 target from PVD products with a 248 nm KrF excimer laser with a pulse duration of ∼25 ns. Commercially available (111)-oriented single crystal 0.5 mm thick GGG, YSGG, SGGG, NGG, and GSGG from MTI Corporation were used to systematically tune the epitaxial strain. The substrates provide an ideal in-plane tensile strain spanning 0.485%-1.83% with distortion angle nominal values ranging from 90.22°to 90.93°, which were determined based on the database from the manufacturer and Poisson's ratio of TmIG υ = 0.3. 8 (Table S1 in the supplementary material). Film growth was carried out at a temperature of 850 °C, a fluence of 1.2 J cm -2 , a laser repetition frequency of 6 Hz, and an O 2 background pressure of 180 mTorr. These conditions were found to maintain relatively uniform crystallinity and out-of-plane magnetic anisotropy among all films. All substrates (∼2.5 × 2.5 mm 2 in size) were deposited on simultaneously to keep process conditions constant between samples. Thereby the nominal difference between films is the imposed strain from each individual substrate. Structural characterization of TmIG thin films in the form of 2θ À ω x-ray diffraction, x-ray reflectivity, and reciprocal space mapping was performed using a Rigaku Smartlab diffractometer with CuK α radiation. The film thicknesses were determined from x-ray reflectivity and were nominally 17 nm (Table S2 and Fig. S1 in the supplementary material). Magnetic characterization was performed at room temperature using a Lakeshore vibrating sample magnetometer in order to assess the evolution of magnetization and magnetic anisotropy. The paramagnetic signal from the underlying substrate was removed from the reported loops by subtraction of the high field slope in moment vs magnetic field scans. Hysteresis loops were fit to the Stoner-Wohlfarth macrospin model using the native curve_fit function in Python3. Anisotropy energy values extracted from the fits themselves agree with the empirically measured anisotropy fields within the covariance of the fits.
A. Structural characterization X-ray diffraction was used to assess the epitaxy, crystallinity, and strain state of the TmIG films. X-ray symmetric scans around the 444 diffraction peaks of the 17 nm TmIG films are shown in Fig. 2(a). Intensity oscillations around film peaks indicate excellent crystallinity and smooth interfaces. The evolution of the film peak position with respect to the substrate peak position reveals an increasing out-of-plane compressive strain in agreement with the expected increasing in-plane tensile strain from the substrate. To confirm the epitaxial growth of TmIG on each substrate, reciprocal space maps (RSMs) around the 624 peaks were performed [Fig. 2
show that the films are fully strained with the same in-plane lattice constants as their associated substrates. TmIG grown on GSGG experiences a small relaxation through a slight shift of the film peak with respect to the substrate (ΔQ
). The evolution of out-of-plane lattice parameters of TmIG films observed in RSM scans also relatively agree with that observed in symmetric x-ray scans (Table I).
In order to determine anisotropy energy [Eq. ( 1)], the distortion angle, β, is then evaluated. The distortion angle can be calculated from RSM scans using the assumption that in-plane strain will result in a change in the d 111 spacing and distorting cubic edges (BA, BC, and BD in Fig. 1).
The distortion angle β is then determined by
where
, a is the cubic lattice constant of substrate and d 111 is out-of-plane spacing (diagonal of the cube), which are both obtained from RSM data [a sub (Q x ) and a film (Q z )]. Table I shows lattice constants of substrates and films calculated from x-ray diffraction measurements. The distortion angles are found to be greater than 90°revealing the in-plane (out-of-plane) tensile (compressive) strain that generally increases with increasing in-plane strain and demonstrates the control of the biaxial strain state in TmIG thin films. With the distortion angle calculated, magnetic measurements allow us to then quantify the evolution of the magnetic anisotropy.
Room temperature magnetic hysteresis measurements were run on all samples with the magnetic field in-the-plane and out-of-theplane of the film surface to determine the saturation magnetization, magnetic anisotropy direction, and anisotropy field. All films possess an out-of-plane easy axis with comparable saturation magnetization excepting the film grown on GSGG. Figure 3(b) shows out-of-plane hysteresis loops for all TmIG films. The saturation magnetization vs distortion angle is shown in Fig. 3(c). The saturation magnetization is approximately constant (∼90 emu cm -3 ) for distortion angles at and below 90.74°with a sudden drop in magnetization for the film on GSGG (β = 91.17°). While unclear, this drop in magnetization may be correlated with the slight relaxation observed from RSM results as well as topographic features that are unique to this film (Fig. S2 in the supplementary material).
For a sample with perpendicular magnetic anisotropy, the anisotropy field is the field needed for the magnetization to
overcome the energy barrier between in-plane and out-of-plane states. 23,24 In this work, anisotropy fields are determined by measuring in-plane magnetic field strength that saturates the magnetization and quantitatively extracted from the second derivative of the in-plane loops 25 (Fig. 4). Figure 5(a) shows the magnetic anisotropy field vs distortion angle, β. This tuning window is defined by strain independently at our specific deposition condition and does not consider tuning from different growth parameters such as oxygen background pressure. The anisotropy tends to increase with increasing distortion angle with the exception of GSGG and SGGG. To further access this trend in the anisotropy field, magnetoelastic contributions are calculated next. Since the values of shear stiffness for thin films are unknown (and thusly for magnetostriction), we report here the value of magnetoelastic constants B 2 ¼ À3λ 111 c 44 for our TmIG thin films in each substrate reflecting the relationship between lattice deformation and its magnetization. 26 We see that B 2 stays relatively constant for the thin film at low strains (but is ∼2 times larger than bulk) until β reaches ∼90.74°[Fig. 5(c)]. The small B 2 values in these thin films justify their small anisotropy fields despite the contribution from large lattice distortion. The thin film magnetoelastic coefficient may differ from bulk for several reasons: unlike bulk, the film is clamped to a substrate so it is not free to deform in-plane but free to deform out-of-plane, surface magnetostriction, and other surface effects (structural and chemical defects) may become significant at these film thicknesses, and compositional variance. The enhanced B 2 in films may be a result of one or more of the above factors. To shed some light on the evolution of the magnetic properties, x-ray photoelectron spectroscopy was performed on the TmIG target and films on various substrates. The XPS data show that the composition of the films and the target are the same within the error of the analysis, yet there is a uniform Fe deficiency among all (Fig. 6). Thus, the evolution of anisotropy field, anisotropy energy, and magnetoelastic constant between films is a result of the strain from substrates.
In summary, we have investigated the modulation of magnetic anisotropy of rare earth garnet TmIG (111)-oriented single crystal thin films subjected to different isotropic in-plane tensile strains. Overall, the magnitude of the magnetoelastic anisotropy energy increases with increasing strain, with the exception of the thin film grown on GSGG where a significant decrease in saturation magnetization, anisotropy field, and magnetoelastic anisotropy constant is observed. The magnitude of the anisotropy field can be increased up to a factor of 14, with a maximal anisotropy field of ∼3900 Oe, within our studied strain range and deposition condition. Such tunability provides a knob to engineer the performance and scalability of magnetic devices that employ TmIG. Finally, we find that the magnetoelastic anisotropy constant B 2 is approximately more than 2× larger than in bulk at low strains.
See supplementary material for the derivation of the magnetoelastic anisotropy, x-ray reflectometry, and atomic force microscopy.
J. Appl. Phys. 127, 153905 (2020); doi: 10.1063/1.5142856
Published under license by AIP Publishing.