Compositional dependence of spintronic properties in Pt/GdCo films 

GdCo ﬁlms have been widely used in spintronic applications, owing largely to their tunable degree of ferrimagnetic compensation. However, all key properties likewise depend on the alloy composition, and a systematic study of the interdependent spintronic properties with composition has not been reported. Here, we report the compositional dependence of key spintronic properties, including anisotropy, symmetric

Rare-earth (RE) transition-metal (TM) amorphous alloys are a promising class of ferrimagnetic materials for spintronics.RE-TM alloys consist of a RE sublattice antiferromagnetically coupled to the TM sublattice.Altering the proportion of RE and TM atoms allows one to control the magnetic properties of RE-TM films, including the saturation magnetization, M s , net spin density, coercivity, and magnetic anisotropy.This tunability has been used to engineer RE-TM films with low M s or low net angular momentum, in order to exhibit spintronic phenomena such ultra-small room temperature stable skyrmions, 1,2 high-speed current-driven domain wall motion, [2][3][4][5] and voltage-controlled skyrmion generation. 6owever, despite the large volume of work performed on RE-TM films, a comprehensive study of the spintronic properties of RE-TM alloys, particularly in technologically relevant thin films, has yet to be conducted.
In this Letter, we analyze the magnetic properties of 3 nm GdCo across a wide range of compositions with the ultimate aim of quantifying the strength of the Dzyaloshinskii-Moriya interaction (DMI) as a function of composition using 1D domain wall (DW) motion experiments in patterned magnetic racetracks.DMI is an antisymmetric exchange interaction that stabilizes chiral spin textures, a necessity for skyrmion stability and current-driven DW motion.However, extracting this parameter from DW dynamics measurements requires knowledge of other parameters, such as DW width, which depend on material parameters that vary significantly with composition.Here, we undertake a systematic study to quantify all key parameters, providing a roadmap for compositional engineering of skyrmion host materials including magnetic anisotropy and exchange stiffness.
Films of Ta(4)/Pt(4)/Gd x Co 1-x (3)/Ta(4)/Pt(2) were grown by D.C. magnetron sputter deposition (numbers in parenthesis indicate nominal thickness in nanometers) under a background pressure <2 Â 10 À7 Torr on thermally oxidized Si wafers with 0 x 0:7.The GdCo layer was grown by co-sputtering from Gd and Co targets with deposition rates of $3.5 and $1 nm/min, respectively, and with target power densities ranging from 0 to 8.8 and 4.9 W/cm 2 , respectively.The lower Pt layer was selected to induce interfacial DMI and inject spin in the adjacent GdCo layer, enabling current-driven DW motion.A thin GdCo layer was chosen to maximize the interfacial DMI while minimizing potential bulk DMI contributions, as have been previously reported in thick RE-TM films. 7The Ta/Pt cap was used to prevent sample oxidation while preserving an asymmetric heterostructure for DMI maximization.
The 3 nm GdCo composition series saturation magnetizations, M s , are shown in Fig. 1(a).Magnetic compensation occurs at x % 0:52, in contrast to the commonly reported bulk compensation composition of x % 0:22. 8,9We have previously explained this discrepancy in terms of a combined environment and dead layer model, in which a RE dead layer results in a reduced average magnetic moment per RE atom (RE atomic magnetic moment) in RE-TM films <10 nm relative to thick films, and the average atomic magnetic moments of both the RE and TM decrease with increasing RE concentration at room temperature. 10In this model, the thickness of the RE dead layer is independent of RE-TM film thickness and increases with RE concentration, leading to expected Gd dead layer thicknesses of 0.5-2 nm for x ¼ 0:1 !0:7 [see Fig.This results in Gd and Co atomic magnetic moments that depend on the number of Co nearest neighbors, which decreases with increasing x.Thus, at room temperature, the Gd and Co atomic magnetic moments decrease monotonically with increasing x, approaching zero for pure Gd.The combined environment and dead layer model allows for the accurate estimation of individual sublattice contributions, M Gd and M Co (where M s ¼ M Gd À M Co j j ), in the grown series, shown as red and blue dashed lines in Fig. 1(a).
Figure 1(b) shows the effective magnetic anisotropy, K u;eff , of the GdCo series, measured using hard-axis hysteresis loops via vibrating sample (VSM) and magneto-optical Kerr effect (MOKE) magnetometry.The films exhibit perpendicular magnetic anisotropy (PMA) for compositions 0:27 Շ x Շ 0:60.Subtracting the magnetostatic component gives the uniaxial anisotropy constant K u ¼ K u;eff þ 1 2 l 0 M 2 s .K u decreases significantly with increasing Gd concentration at low x and then increases and plateaus from x ¼ 0:25 !0:45 before finally tending toward zero for x > 0:5.The variation of K u with x suggests two primary contributions.2][13][14] In GdCo, this interaction appears to drop rapidly with increasing Gd content.6][17][18][19] This bulk PMA term increases with the number of RE-TM pairs, with pair models indicating a maximum in the pair-ordering induced anisotropy from 0:3 < x < 0:5, consistent with the observed K u trend in Fig. 1(b).
Before examining the DW dynamics, we consider the dependence of the exchange stiffness A with composition, which is necessary to predict the DW width D ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi A=K u;eff p that plays a key role in the dynamical equations of motion.Symmetric exchange in GdCo arises from inter-and intra-sublattice contributions: two ferromagnetic interactions (Gd-Gd and Co-Co) and an antiferromagnetic Gd-Co interaction, The exchange stiffness of each interaction is given by 20,21 2][23] The atomic volumes were taken to be v Gd ¼ 3:305 Â 10 À29 m 3 and v Co ¼ 1:100 Â 10 À29 m 3 , derived from their bulk densities.Thick film GdCo J ij values from Hansen et al. 9 and Gangulee and Kobliska 20 were used for calculations [Fig.2(a)].Both J GdÀGd and J GdÀCo are independent of composition; however, J CoÀCo decreases linearly with increasing Gd concentration.Additionally, in GdCo thin films, the Gd dead layer results in an alloyed composition that is Gd poor compared to its nominal composition.The true alloyed composition x can be estimated from the nominal composition x using the relations 10 with t ¼ 3 nm the nominal film thickness and t Gd;max ¼ 2:22 nm the maximum Gd dead layer thickness determined previously. 10ssuming J CoÀCo is dependent on x, Eq. ( 3) is used to determine J CoÀCo at nominal composition x.To determine the S i , we utilize the combined environment and dead layer model referenced previously, which predicts the average atomic spin for each species in 3 nm GdCo [Fig.2(b)].The Gd spin value is reduced from its standard bulk value of 3:5 h=at due to dilution with a non-magnetic Gd dead layer at room temperature and monotonically decreases with increasing x due to decreased Co nearest neighbors.Combining J ij and S i yields the exchange stiffness of each interaction in GdCo, shown in Fig. 2(c).As expected, due to the low Curie temperature of Gd (T c;Gd % 290 K), A GdÀGd is insignificant compared to the other two interactions at room temperature.Additionally, the Co-Co interaction dominates except at relatively high x > 0:4.The value of A tot is reduced by an order of magnitude from x ¼ 0 !0:5 as the Co-Co exchange is reduced due to fewer Co-Co pairs.We have estimated D ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi A tot =K u;eff p using the sum of the inter-and intrasublattice exchange stiffness, as shown in Fig. 2(d).Despite the large decrease in exchange stiffness over this range, the corresponding reduction in anisotropy results in a relatively weak variation of D, ranging from $3 to 9 nm in the studied range.
GdCo PMA samples with x ¼ 0:27 !0:49 were patterned into 40 Â 100 lm 2 magnetic racetracks for DW motion experiments [Fig.3(a)].Kerr microscopy was used to observe DW displacement.Two types of experiments were conducted: depinning and velocity measurements.In the depinning experiment, a low DC density, j $10 9 A=m 2 À Á , was applied along the length of the track and an assisting out-of-plane (OOP) magnetic field was slowly ramped from zero until a critical field, H dp , was reached and the propagated freely along a length of the track of at least $30 lm.With no applied longitudinal field, H x , both up-down and down-up DWs exhibit the same linear relationship between j and H dp , consistent with previous observations [Fig.3(b)]. 2,24The slope of Fig. 3(b) gives the spin-orbit torque (SOT) effective field per unit current density, v, the proportionality constant between current density j and spin Hall effective field, H SH ¼ vj. Figure 3(c) shows v as a function of composition.6][27] To separate the compositional dependence of v from its M s dependence, the effective spin-Hall angle was calculated using 28 where e is elementary charge.h eff SH is found to increase with increasing x [Fig.3(d)].A similar increase in h eff SH in TbCo with increasing Tb content was reported in Ref. 29, and theoretical work has shown significant SOT generated by RE atoms, particularly when alloyed. 30The determination of h eff SH here relies on DW depinning measurements that observe net SOT phenomena.As a result, the extracted h eff SH does not distinguish between individual sublattices (that is, Pt/Co vs Pt/Gd interaction); only the combined effect is measured.The increase in h eff SH with RE content suggests that the RE sublattice enhances spin transmission in RE-TM alloys.
We next examine DW velocity v as a function of j and H x .DW displacement was measured by Kerr microscopy.Current pulses of 5 ns were used to drive DW motion.In magnetic racetracks, the DMI stabilizes homochiral N eel DWs via an effective field, H D , perpendicular to the wall.The homochiral N eel walls enable translational current-induced DW motion.The DW velocity, v, in ferrimagnetic materials is well-described by the 1D model: 31 where c eff is the effective gyromagnetic ratio and a eff is the effective Gilbert damping, ferrimagnetic analogues of the ferromagnetic magnetic properties. 2,32v was first measured under H x ¼ 0 and varying j [Figs.4(a)-4(c)].v initially increases linearly with j before saturating at an asymptotic velocity, In the saturation regime, v varies linearly with H x , and extrapolation to zero yields H D .However, the saturation current density, j sat , which we define here as the current density required to reach 90% of v max with H x ¼ 0, is composition dependent.This is evidenced by comparison of Figs.4(a show divergent behavior near x % 0:42, suggesting that the angular momentum compensation composition of 3 nm GdCo is near that point.We observe >10Â higher a eff on the Gd-dominated side of angular momentum compensation compared the Co-dominated side.We attribute this significant increase in a eff to the presence of the Gd dead layer potentially increasing surface roughness, which has been shown to enhance damping. 33 eff and c eff are combined to determine the DW mobility l, shown in Fig. 5(e).l decreases exponentially with increasing Gd content, primarily due to the reduction in the DW width, D, over this range.The $30x reduction in l from x ¼ 0:27 !0:49 is almost equivalent to the increase in v [Fig.3(c)] observed over the same range, resulting in near-constant slopes in the v vs j data at all x at small j [Figs.4(a)-4(c)].The saturation velocity, v max , at H x ¼ 0 is shown in Fig. 5(b).With no applied longitudinal field, v max ¼ p D 2 S , with S ¼ h Ms l B g eff the net spin density.The v max data exhibit constant v max % 300 m/s except near the angular momentum compensation point (S ¼ 0), where v max % 400 m/s.][4] The v max data suggest that except at S % 0, the ratio D=S remains approximately constant.
Finally, the effective DMI field, H D , was extracted from the v vs H x data and is presented in Fig. 5(c).The measured H D ranges from  250 to $1700 Oe with a minimum at x ¼ 0:4.There is no clear H D trend evident as a function of composition.However, H D depends on M s and D, which both also depend on composition.To isolate the strength of the DMI as a function of Gd composition, H D was converted to D using 31,34 The results are plotted in Fig. 5(f), where a clear trend emerges.We observe a monotonic decrease with increasing Gd content across the entire PMA composition range, suggesting that the Pt/Co interaction is primarily responsible for the occurrence of DMI in GdCo films and that the addition of Gd only dilutes the strength of the DMI.The value of D at x ¼ 0:44 is smaller than the reported DMI in a 6 nm film at the same composition. 2At x ¼ 0:27, we find a similar value of D compared to a previous report on a 5 nm film. 35In heavy metal/ferromagnetic systems, D / 1 t when induced at an interface, 36 making the reduced D values observed in 3 nm GdCo surprising.Composition gradients in RE-TM alloys have been shown to induce a bulk DMI with D / t. 7 This could add a second contribution to the DMI in films >3 nm that results in larger D values that is insignificant in our thinner films.We note that the measured v values [Fig.3(c)] are also lower than the reported SOT in 6 nm GdCo, 2 which, combined with a reduced D, results in lower DW velocities than previously observed.Because DMI is sensitive to interfacial quality, [37][38][39][40] we ascribe both of these effects to increased surface roughness in thin GdCo films, potentially due to the significant dead fraction of Gd present in 3 nm films, particularly at high Gd concentrations.
In summary, we have analyzed the spintronic properties of 3 nm GdCo.A number of GdCo magnetic properties critical to spintronic devices and stabilization of chiral spin textures are found to strongly depend on RE concentration.The total effective anisotropy is found to strongly decrease with increased Gd concentration, consistent with a Pt/Co interfacial origin.We also observe a subdominant increase in uniaxial anisotropy that is maximized at x % 0:4, consistent with a pair-ordering bulk anisotropy origin that is often used to explain bulk PMA in RE-TM alloys.The combination of DW velocity and depinning measurements under longitudinal and polar applied fields allows for determination of a variety of dynamic magnetic properties in Pt/GdCo heterostructures, including DMI effective field, damping, spin density, spin transfer efficiency, and effective spin-Hall angle.These fundamental measurements are combined with knowledge of the ferromagnetic and antiferromagnetic exchange interactions in GdCo to determine the magnitude of antisymmetric exchange constant D. D is found to monotonically decrease with increasing Gd content, suggesting that the Pt/Co interface is the primary source of DMI in Pt/GdCo films.This thorough characterization of GdCo's spintronic properties should allow for improved design of materials for next-generation DW and skyrmionics devices.12 W. Y. Kim, H. K. Gweon, K. J. Lee, and C. Y. You, "Correlation between interfacial Dzyaloshinskii-Moriya interaction and interfacial magnetic anisotropy of Pt/Co/MgO structures," Appl.Phys.Express 12(5), 053007 (2019).13 P. F. Carcia, "Perpendicular magnetic anisotropy in Pd/Co and Pt/Co thin-film layered structures," J. Appl.Phys.63 (10), 5066-5073 (1988).
4(d) of Suzuki et al. 10 ].Additionally, at room temperature, the two dominant exchange interactions in RE-TM films are the RE-TM and TM-TM interactions.

FIG. 1 .
FIG. 1. Magnetic properties of 3 nmGd x Co 1Àx films.(a) Saturation magnetization, M s , as a function of composition.The solid black line is the combined environment and dead layer model fit.10The red and blue dashed lines are expected Gd and Co sublattice contributions predicted by the model (M Gd and M Co ), respectively.(b) Effective anisotropy energy density (black squares), K u;eff , and uniaxial energy density (red circles), K u , as a function of composition.The shaded region in (a) and (b) indicates perpendicular magnetic anisotropy.

FIG. 2 .
FIG. 2. Symmetric exchange in GdCo films.(a) Previously reported exchange energy values in thick GdCo films as a function of alloyed Gd composition, x (see the text).Red and blue data points are from Hansen. 9The black dotted line is from Gangulee. 20(b) Expected average atomic spin of Gd and Co in 3 nm GdCo as a function of nominal composition, x.(c) Calculated 3 nm GdCo exchange stiffness, separated by each interaction.(d) Calculated domain wall width, D, of 3 nm GdCo samples exhibiting PMA. v ) and 4(b), in which v approaches saturation at j sat % 16 Â 10 11 A/m 2 and j sat > 20 Â 10 11 A/m 2 , respectively.Figures 4(d)-4(f) show measurements of v vs H x at three representative compositions.The DMIstabilized homochiral DWs result in H D with opposite signs for up-down and down-up DWs.As a consequence, up-down and down-up DWs have inverse responses to H x , i.e., larger H x decreases v upÀdown but increases v downÀup [Figs.4(d)-4(f)].The consistent sign of H D for each type of DW across x ¼ 0:27 !0:49 indicates no chirality change (or equivalently sign flip in D) across this composition range.As j decreases below j sat , the v vs H x data become increasingly nonlinear [Fig.4(e)].A linear fit assuming saturation behavior would result in a large overestimation of H D .To properly account for the curvature of v vs H x at v < v max , the data in Figs.4(a)-4(c) and Figs.4(d)-4(f) were fitted to the full 1D model [Eq.(6)].The v of each sample determined from the previous depinning experiments [Fig.3(c)] was used to convert the applied current density to a spin-Hall effective field.The fits of the 1D model are shown as solid lines in Fig. 4. The combined results of the DW motion experiments are shown in Fig. 5.Both a eff and g eff [Figs.5(a) and 5(d)]

FIG. 3 .
FIG. 3. Domain wall depinning experiments.(a) Image of magnetic racetrack device used for de-pinning and DW velocity experiments showing a down-up DW.Inset, series of images showing DW displacement in Gd 0.47 Co 0.53 with j drive ¼ þ11:5 Â 10 11 A/m 2 and a train of 5 ns current pulses totaling 100 ns between images.(b) Exemplary plot of depinning field, H dp , vs applied DC drive current, j, in Gd 0.49 Co 0.51 .(c) SOT effective field per unit current density of 3 nm GdCo films as a function of composition.(d) Effective spin-Hall angle as a function of composition.

FIG. 4 .
FIG. 4. Current-induced domain wall velocity measurements in Pt/GdCo heterostructures at three representative compositions.(a)-(c) Domain wall velocity, v, vs applied current density, j, with no applied longitudinal field.Dotted line indicates j used for corresponding v vs H x measurement below.(d)-(f) Domain wall velocity vs applied longitudinal magnetic field, H x .Solid lines are fits to the 1D model (see the text).The error bars are the standard error of 5-20 measurements.
This work was supported in part by the DARPA TEE Program and the Samsung Global Research Outreach (GRO) Program.