Systematic Control of Strain-Induced Perpendicular Magnetic Anisotropy in Epitaxial Europium and Terbium Iron Garnets Thin Films

We show tunable strain-induced perpendicular magnetic anisotropy (PMA) over a wide range of thicknesses in epitaxial ferrimagnetic insulator Eu3Fe5O12 (EuIG) and Tb3Fe5O12 (TbIG) thin films grown by pulsed-laser deposition on Gd3Ga5O12 with (001) and (111) orientations, respectively. The PMA field is determined by measuring the induced anomalous Hall loops in Pt deposited on the garnet films. Due to positive magnetostriction constants, compressive in-plane strain induces a PMA field as large as 32.9 kOe for 4 nm thick EuIG and 66.7 kOe for 5 nm thick TbIG at 300 K, and relaxes extremely slowly as the garnet film thickness increases. In bilayers consisting of Pt and EuIG or Pt and TbIG, robust PMA is revealed by squared anomalous Hall hysteresis loops in Pt, the magnitude of which appears to be only related to the net magnetic moment of iron sublattices. Furthermore, the magnetostriction constant is found to be 2.7x10^(-5) for EuIG and 1.35x10^(-5) for TbIG, comparable with the values for bulk crystals. Our results demonstrate a general approach of tailoring magnetic anisotropy of rare earth iron garnets by utilizing modulated strain via epitaxial growth.

Ferrimagnetic insulators (FMI) have recently attracted a great deal of attention in spintronics community. On one hand, they serve as the source of pure spin currents [1] [2] [3] [4] [5], induced ferromagnetism in metals [6], graphene [7] , topological insulators [8] [9], and spin Hall magnetoresistance [10] [11] [12] [13]. On the other hand, they also serve as an excellent medium for magnon spin current transport with a long decay length [14] [15]. Among various FMIs, the rare earth iron garnets (REIGs) form an interesting family. The ferrimagnetic order in REIGs results primarily from the antiferromagnetic interaction between unequal number of Fe 3+ ions on the tetrahedral and octahedral sites in a unit cell. The RE 3+ ions can have unfilled 4f-shells and therefore a finite magnetic moment that is antiferromagnetically coupled with the tetrahedral Fe 3+ moment. REIG thin films have many attractive attributes for practical applications: high Curie temperature (Tc >500 K), relatively large band gaps (∼2.8 eV), chemical stability, and compatibility for being incorporated into various heterostructures.
REIG thin films are often grown by pulsed laser deposition (PLD). Under strain-free conditions, the magnetization of a REIG thin film lies in the film plane because the magnetocrystalline anisotropy is generally smaller than the shape anisotropy which favors the in-plane orientation. However, due to relatively large magnetostriction constant , the strain-induced magnetic anisotropy energy can be even more important in thin films. This property gives epitaxial growth of REIG films a unique advantage in controlling magnetic anisotropy. Depending on the sign of , suitable substrates can be chosen to not only manipulate the magnitude, but also the sign of the total magnetic anisotropy energy, therefore the orientation of the magnetization vector.
For example, for positive (negative) , compressive (tensile) strain is required to drive the magnetization normal to the film plane, which can be accomplished by controlling lattice mismatch in the pseudomorphic growth regime. The same mechanism was used for ferromagnetic metal thin films, but the interfacial strain quickly relaxes as the film thickness increases, consequently the so-called spin reorientation transition occurs only at some very small thickness (e.g., a few monolayers) [16] [17]. REIGs in general have larger Burger's vectors, which give rise to larger dislocation formation energies than metals (energy scales with | | 2 ); therefore, the interfacial strain at garnet interfaces can extend to a larger thickness range, which makes the film thickness an additional knob to control the magnetic anisotropy in REIG films.
In order to orient the magnetization normal to the film, the perpendicular magnetic anisotropy (PMA) field Hꓕ must be positive and larger than the demagnetizing field. For the case of strained films grown on (100) and (111)-oriented substrates, Hꓕ is given by the following equations where K1 is the first-order cubic anisotropy constant, σ|| is the in-plane stress, Ms the saturation magnetization and lmn is the magnetostriction constant for the film grown in the [lmn] direction. From these equations, it follows that Hꓕ can be controlled by tuning the in-plane stress of the film, which can be achieved by controlling growth.
In previous experiments [13] [18], it has been demonstrated that TIG (it will be referred as TmIG in this paper to avoid confusion with TbIG) can acquire strong PMA by inducing an interfacial tensile strain, since the magnetostriction constant for TmIG is negative for films grown on substituted gadolinium gallium garnet (SGGG) in [111] direction. For the cases of Eu3Fe5O12 (EuIG) and Tb3Fe5O12 (TbIG), the magnetostriction constants at room temperature are λ100 = 2110 -6 , λ111 = 1.810 -6 for EuIG; and λ100 = -3.310 -6 , λ111 = 1210 -6 for TbIG [19]; therefore, a compressive strain is required for all cases except TbIG (001). Given that a reasonable strain (<1%) can be accommodated for pseudomorphic growth of the film on the substrate, the candidates chosen for this study are gadolinium gallium garnets (GGG) in different orientations, i.e., GGG(001)/EuIG and GGG (111)/TbIG. The lattice mismatch between these REIG films and GGG gives rise to the compressive strain that is needed for a strong PMA field. Since the strain relaxes in thicker films, the average strain in films determines the magnetic anisotropy. Therefore, we accomplish the full anisotropy tuning by leveraging both the substrate structure and the REIG film thickness.
Thin films were grown by PLD from targets densified from powders synthesized using similar methods as described before [20]. High quality ultra-flat EuIG and TbIG films, with thickness ranging from 4 nm to 180 nm for EuIG, and 5 nm to 100 nm for TbIG, were deposited on (001)-and (111)-oriented GGG substrates respectively. After the standard cleaning process, the substrates were baked at ∼ 220°C for five hours with a base pressure < 10 -6 Torr before EuIG or TbIG deposition. After this annealing process, the substrates were then annealed at ∼ 600°C under a 1.5 mTorr oxygen pressure with 12% (wt. %) ozone for 30 minutes; then under these oxygen and temperature conditions, a 248 nm KrF excimer laser pulse was set to strike the target with a power of 156 mJ and at a repetition rate of 1 Hz. After deposition, the films were annealed ex situ at 800°C for 200 seconds under a steady flow of oxygen using rapid thermal annealing (RTA).
To characterize the structural properties of the deposited garnets, reflection high energy electron diffraction (RHEED) was used to track the evolution of the film growth. Right after deposition, RHEED shows the absence of any crystalline order. After the ex situ RTA process, RHEED patterns appear for both EuIG and TbIG, revealing a single crystal structure for all the samples (Fig. 1 a). Atomic force microscopy (AFM) was performed on all grown samples, indicating uniform and atomically flat films with low root-mean-square (RMS) roughness (<2 Å RMS) and with no pinholes observed (Fig. 1b). The absence of three-dimensional islands on the surface from AFM measurements confirms the uniformity of the thin films.
X-ray diffraction (XRD) was performed on all the samples to further confirm their crystalline structure,  Table I. For EuIG films with t < 14 nm and for TbIG films with t < 20 nm, the magnetic moment signal is too small to be resolved by the VSM due to the large background signal from GGG and their magnetization data are not included. The average saturation magnetization for EuIG is 4πMs = (913  7) G, which is 23.5% smaller than the reported value for bulk EuIG (4πMs = 1192.83 G) [22], which might be caused by a variation in stoichiometry as it has been observed in similar studies [21]. For the case of TbIG, the average saturation magnetization is 4πMs = (234  5) G, which is only 3.4% below the reported value for bulk TbIG (4πMs =

G).
For films with t > 10 nm, the XRD data shows that the Bragg peak corresponding to both REIGs is shifted to the left from the expected peak positions for the respective bulk crystals (Fig. 2a-b), thus indicating an elongation on the lattice parameter perpendicular to the surface, leading to a compressive in-plane strain in the lattice. Moreover, a systematic shift to higher 2 values of the diffraction peaks for both EuIG and TbIG as the thickness of the thin film increases is a direct measurement of the relaxation of the lattice parameters towards the bulk values ( Fig. 2c-d), in contrast to the results obtained by Rosenberg et al. [22]. The surprisingly slow relaxation behavior in REIG thin films contrasts sharply with ferromagnetic metal films, demonstrating a unique magnetic anisotropy control possibility by film thickness.
An important factor is the combination of the lattice-mismatch-induced in-plane compressive strain and positive magnetostriction coefficients which can drive the magnetization perpendicular to the film plane in both EuIG and TbIG. As mentioned before, in TmIG, due to negative magnetostriction constant, tensile strain is needed to obtain PMA, which was achieved by growing it on SGGG or NGG substrates. The strong PMA in those garnet films are characterized by squared magnetic hysteresis loops for out-of-plane fields but a hard-axis behavior for in-plane fields. To quantify Hꓕ in EuIG and TbIG films, magneto-transport measurements in REIG/Pt bilayers are performed at room temperature. Since these REIG films are magnetic insulators, the Hall response of Pt imprints the magnetic anisotropy of the REIG films via the magnetic proximity effect and/or the spin current effect [13]. Therefore, a 5 nm thick Pt layer was sputtered into the Hall bar geometry with a length of l = 600 µm and a width of w = 100 µm using standard photolithography. The inset of Fig. 3(a) shows the optical image of the Hall bar shape and dimensions. Measured Hall response contains two parts: the ordinary Hall effect (OHE) which is linear in field, and the anomalous Hall effect (AHE) which is proportional to the out-of-plane magnetization. Fig. 3 Fig. 3(b) shows the comparison of both measured 4πMs and ρAHE from Fig. 3(a)  Magnetic anisotropy energy of thin films in general consists of three terms and can be written as where is magnetocrystalline anisotropy which can be approximated by the first-order cubic anisotropy constant ( 1 ). In EuIG and TbIG, ( 1 ) is negative and (≈ −10 4 / 3 ); the term 2 2 corresponds to the shape anisotropy (≈ 10 4 / 3 ) which gives the in-plane demagnetizing field; is the strain-induced anisotropy which is determined by magnetostriction coefficient (λlmn) and in-plane strain (ε||). For EuIG and TbIG, is positive and large (≈ 10 5 / 3 ) as can be seen in Table I. As a result, comparing these three anisotropies, is at least one order of magnitude larger than and 2 2 . Therefore, to evaluate how the compressive strain influences the magnetic anisotropy, we first determine the anisotropy field from the hardaxis AHE loops and quantitatively study t-dependence in EuIG/Pt(5 nm) and TbIG/Pt(5 nm). The EuIG films with t up to 56 nm show out-of-plane magnetization whereas those above 56 nm show in-plane magnetization, indicating that the PMA field is overcome by the demagnetizing field above this thickness. On the other hand, TbIG shows perpendicular magnetization for all films with the thickness up to 100 nm. This is primarily due to a smaller saturation magnetization value in TbIG which causes the PMA field to be dominant over the demagnetizing field in the entire thickness range. Detailed transport measurements for the Hall resistivity for EuIG t < 56 nm and for all TbIG thicknesses. However, EuIG films need special care to determine the ⊥ for t > 56 nm. Those films have in-plane magnetic anisotropy, and the Hall voltage may contain a planar Hall component when an in-plane field is applied. In this case, ⊥ is negative, and an out-of-plane saturation field is measured instead (see Supplementary Material). Then equation (9)  for TbIG), as it has been observed in other works [27]. As described in equations (1) and (2), Hꓕ has a linear relation with the in-plane strain || , and is expected to follow the same behavior as the out-of-plane strain, εꓕ, according to equations (3) and (4). There are two regimes for the effect of lattice mismatch in thin films [28]: for film thickness t below certain critical value tc, the film will be pseudomorphic and the strain is given by = − , while for t > tc, the strain relaxes