We show by first-principles calculations that the skew-scattering anomalous Hall and spin-Hall angles of L$1_0$-ordered FePt drastically depend on different types of disorder. A different sign of the AHE is obtained when slightly deviating from the stoichiometric ratio towards the Fe-rich side as compared to the Pt-rich side. For stoichiometric samples, short-range ordering of defects has a profound effect on the Hall angles and can change them by a factor of $2$ as compared to the case of uncorrelated disorder. This might explain the vast range of anomalous Hall angles measured in experiments, which undergo different preparation procedures and thus might differ in their crystallographic quality.
We have calculated surface energies and surface magnetic order of various low-indexed surfaces of monoatomic Fe, Co, and Pt, and binary, ordered FePt, CoPt, and MnPt using density functional theory. Our results for the binary systems indicate that elemental, Pt-covered surfaces are preferred over Fe- and Co-covered and mixed surfaces of the same orientation. The lowest energy orientation for mixed surfaces is the highly coordinated (111) surface. We find Pt-covered (111) surfaces, which can be realized in the L11 structure only, to be lower in energy by about 400 meV/atom compared to the mixed…
The interface between FePt--L1$_0$ and MgO(001) alloys has been studied using density functional calculations. Because the stacking of the face-centered tetragonal L1$_0$ phase is formed by alternating Fe and Pt planes, both the Fe- and Pt-terminated contact layers were studied. Furthermore, due to the large mismatch between the in-plane lattice constants of both systems, we have chosen some common $a$ values for both alloys in order to explore in detail the adsorption energy, the electronic structure and the interface magnetism. The adsorption energy has been calculated by subtracting the ene…
We present results of the magneto-crystalline anisotropy energy (MAE) calculations for chemically ordered $L1_0$ CoPt and FePt alloys taking into account the effects of strong electronic correlations and spin-orbit coupling. The local spin density + Hubbard U approximation (LSDA+U) is shown to provide a consistent picture of the magnetic ground state properties when intra-atomic Coulomb correlations are included for both 3$d$ and 5$d$ elements. Our results demonstrate significant and complex contribution of correlation effects to large MAE of these material.
We carry out first-principles calculations which demonstrate the importance of the non-spin-conserving part of the spin-orbit interaction for the intrinsic anomalous Hall conductivity of ordered FePt alloys. The impact of this interaction is strongly reduced if Pt is replaced by the lighter isoelectronic element Pd. An analysis of the interband transitions responsible for the anomalous velocity reveals that spin-flip transitions occur not only at avoided band crossings near the Fermi level, but also between well-separated pairs of bands with similar dispersions. We also predict a strong anisot…
Achieving the compositionally ordered state in a substitutional alloy of two or more species can often be even critical for improving its functional properties. To produce a highly ordered alloy, a longtime high-temperature (up to T=1000 K) treatment of the alloy is typically necessary because of insufficient vacancy concentration (c_v) and their mobility. However, such processing affects the morphology and complicates the technology of functional alloys. We show theoretically that the ordering in the practically important FePt system (Fe_xPt_1-x with x being close to 0.5) is already achievabl…
We demonstrate by means of fully relativistic first principles calculations that, by substitution of Fe by Cr, Mn, Co, Ni or Cu in FePt-L10 bulk alloys, with fixed Pt content, it is possible to tune the magnetocrystalline anisotropy energy by adjusting the content of the non-magnetic species in the material. The changes in the geometry due to the inclusion of each element induces different values of the tetragonality and hence changes in the magnetic anisotropy and in the net magnetic moment. The site resolved magnetic moments of Fe increase with the X content whilst those of Pt and X are simu…
We perform first principles calculations of the magnetocrystalline anisotropy energy (MAE) of the L1_{0}-like Fe_{x}Pt_{1-x} samples studied experimentally by Barmak and co-workers in [J. Appl. Phys. 98 (2005) 033904]. The variation of composition and long-range chemical order in the samples was studied in terms of the coherent potential approximation. In accordance with experimental observations, we find that, in the presence of long-range chemical disorder, Fe-rich samples exhibit a larger MAE than stoichiometric FePt. By considering the site- and species-resolved contributions to the MAE, w…
Robust spin Hall effects (SHE) have recently been observed in non-magnetic heavy metal systems with strong spin-orbit interactions. These SHE are either attributed to an intrinsic band-structure effect or to extrinsic spin-dependent scattering from impurities, namely side-jump or skew scattering. Here we report on an extraordinarily strong spin Hall effect, attributable to spin fluctuations, in ferromagnetic FexPt1-x alloys near their Curie point, tunable with x. This results in a damping-like spin-orbit torque being exerted on an adjacent ferromagnetic layer that is strongly temperature depen…
The magnetic and structural properties of highly ordered (S ~ 0.82) epitaxial Fe50-xMnxPt50 thin films were investigated. We report the change in the magnetic properties of Mn doped FePt epitaxial thin films. This study differs from the earlier experimental studies on Mn doped FePt based alloys. Ordered L10 Fe50-xMnxPt50 (x=0, 6, 9, 12 and 15) thin films with a constant thickness of 45 nm were prepared by co-sputtering Fe50Pt50 and Mn50Pt50 on to MgO (100) single crystal substrate. We find a significant increase in the coercivity for Fe-Mn-Pt thin films. We have shown that this increase in mag…
We develop a first-principles procedure for the individual evaluation of the intrinsic, side-jump, and skew-scattering contributions to the anomalous Hall conductivity $σ_{xy}$. This method is based on the different microscopic conductive processes of each origin of $σ_{xy}$ in the Kubo--Bastin formula. We also present an approach for implementing this scheme in the tight-binding linear muffin-tin orbital (TB-LMTO) method with the coherent potential approximation (CPA). The validity of this calculation method is demonstrated for disordered FePt and FePd alloys. We find that the estimated value…
By performing first principles calculations we investigate the intrinsic anomalous Hall conductivity (AHC) and its anisotropy in ordered L1o FePt, CoPt and NiPt ferromagnets, and their intermediate alloys. We demonstrate that the AHC in this family of compounds depends strongly on the direction of the magnetization in the crystal. We predict that such pronounced orientational dependence in combination with the general decreasing trend of the AHC when going from FePt to NiPt leads to a sign change of the AHC upon rotating the magnetization direction in the crystal of CoPt alloy. We also suggest…
CoPt or FePt equiatomic alloys order according to the tetragonal L10 structure which favors their strong magnetic anisotropy. Conversely magnetism can influence chemical ordering. We present here {\it ab initio} calculations of the stability of the L10 and L12 structures of Co-Pt alloys in their paramagnetic and ferromagnetic states. They show that magnetism strongly reinforces the ordering tendencies in this system. A simple tight-binding analysis allows us to account for this behavior in terms of some pertinent parameters.
In the disordered local moment picture, we calculated the magnetization (M) and magnetic anisotropy energy (MAE) of FePt, CoPt, and MnAl ordered alloys and body-centered tegragonal FeCo (bct-FeCo) disordered alloy, assuming spatially fluctuated spin configurations at finite temperatures. All alloys exhibit the relation K1(T)/K1(0)=(M(T)/M(0))^n with the exponent (n) around 2. This is consistent with the two-ion anisotropy model, in contrast to the usual single-ion anisotropy model exhibiting n=3. Because these systems have different mechanisms of MAE, we suggest that this relation is a general…
The challenging problem of skew scattering for Hall effects in dilute ferromagnetic alloys, with intertwined effects of spin-orbit coupling, magnetism and impurity scattering, is studied here from first principles. Our main aim is to identify chemical trends and work out simple rules for large skew scattering in terms of the impurity and host states at the Fermi surface, with particular emphasis on the interplay of the spin and anomalous Hall effects in one and the same system. The predicted trends are benchmarked by referring to three different \emph{ab initio} methods based on different appr…
The anomalous Hall effect (AHE) in L10 FePd1-xPtx alloy films is studied both experimentally and theoretically. We find that the intrinsic contribution (?sigma^int_AH) to the AHE can be significantly increased whereas the extrinsic side-jump contribution (sigma^?sj_AH) can be continuously reduced from being slightly larger than sigma^?int_AH in L10 FePd to being much smaller than sigma^?int_AH in L10 FePt, by increasing the Pt composition x. We show that this chemical composition tuning of the intrinsic contribution is afforded by the stronger spin-orbit coupling strength on the Pd/Pt site whe…
We report on the structural, magnetic, and electron transport properties of a L1o-ordered epitaxial iron-platinum alloy layer fabricated by magnetron-sputtering on a MgO(001) substrate. The film studied displayed a long range chemical order parameter of S~0.90, and hence has a very strong perpendicular magnetic anisotropy. In the diffusive electron transport regime, for temperatures ranging from 2 K to 258 K, we found hysteresis in the magnetoresistance mainly due to electron scattering from magnetic domain walls. At 2 K, we observed an overall domain wall magnetoresistance of about 0.5 %. By …
A recent experiment in CuBi alloys obtained a large spin Hall angle (SHA) of -0.24 (Niimi et al. Phys. Rev. Lett. 109, 156602 (2012)). We find that the SHA can be dramatically enhanced by Bi impurities close to the Cu surface. The mechanisms of this enhancement are two-fold. One is that the localized impurity state on surface has a decreased hybridization and combined with Coulomb correlation effect. The other comes from the low-dimensional state of conduction electrons on surface, which results in a further enhancement of skew scattering by impurities. Furthermore, we note that a discrepancy …
We demonstrate that a giant spin Hall effect (SHE) can be induced by introducing a small amount of Bi impurities in Cu. Our analysis based on a new 3-dimensional finite element treatment of spin transport shows that the sign of the SHE induced by the Bi impurities is negative and its spin Hall (SH) angle amounts to -0.24. Such a negative large SH angle in CuBi alloys can be explained by applying the resonant scattering model proposed by Fert and Levy [Phys. Rev. Lett. 106, 157208 (2011)] to 6p impurities.
The spin anomalous Hall effect (SAHE) in ferromagnetic metals, which can generate spin-orbit torque to rotate the magnetization of another ferromagnetic layer through a non-magnetic spacer in magnetic junctions, has attracted much attention. We theoretically investigated the spin anomalous Hall conductivity (SAHC) of the L1$_0$-type alloys $X$Pt($X$=Fe,Co,Ni) on the basis of first-principles density functional theory and linear response theory. We found that the SAHC of FePt is much smaller than the anomalous Hall conductivity (AHC), leading to very small polarization for the anomalous Hall ef…
A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin current density a Kubo-Středa-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker (KKR) band structure method in combination with the Coherent Potential Approximation (CPA) allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-sc…
Exchange splitting as a descriptor for giant anomalous Hall and Nernst effects in ferromagnets
National Institute for Materials Science (NIMS)（物质材料研究机构）；Zhejiang Key Laboratory of Magnetic Materials and Applications, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences（中国科学院宁波材料技术与工程研究所磁材料与应用浙江省重点实验室）；Kyoto Institute of Technology（京都工艺纤维大学）
We have experimentally studied the effects on the spin Hall angle due to systematic addition of Pt into the light metal Cu. We perform spin torque ferromagnetic resonance measurements on Py/CuPt bilayer and find that as the Pt concentration increases, the spin Hall angle of CuPt alloy increases. Moreover, only 28% Pt in CuPt alloy can give rise to a spin Hall angle close to that of Pt. We further extract the spin Hall resistivity of CuPt alloy for different Pt concentrations and find that the contribution of skew scattering is larger for lower Pt concentrations, while the side-jump contributio…
A comprehensive magnetotransport study including resistivity ($ρ_{xx}$) at various fields, isothermal magnetoresistance and Hall resistivity ($ρ_{xy}$) has been carried out at different temperatures on the Co$_{2}$TiAl Heusler alloy. Co$_{2}$TiAl alloy shows a paramagnetic (PM) to ferromagnetic (FM) transition below the curie temperature (T$_{C}$) $\sim$ 125 K. In the FM region, resistivity and magnetoresistance reveals a spin flip electron-magnon scattering and the Hall resistivity unveils the anomalous Hall resistivity ($ρ_{xy}^{AH}$). Scaling of anomalous Hall resistivity with resistivity e…
A coherent description of the anomalous Hall effect (AHE) is presented that is applicable to pure as well as disordered alloy systems by treating all sources of the AHE on equal footing. This is achieved by an implementation of the Kubo-Středa equation using the fully relativistic Korringa-Kohn-Rostoker (KKR) Green's function method in combination with the Coherent Potential Approximation (CPA) alloy theory. Applications to the pure elemental ferromagnets bcc-Fe and fcc-Ni led to results in full accordance with previous work. For the alloy systems fcc-Fe$_x$Pd$_{1-x}$ and fcc-Ni$_x$Pd$_{1-x}$ …
We report on a systematic study of the structural, magnetic properties and the anomalous Hall effect, in the Heusler alloy Co2FeAl (CFA) epitaxial films on MgO(001), as a function of film thickness. It was found that the epitaxial CFA films show a highly ordered B2 structure with an in-plane uniaxial magnetic anisotropy. An analysis of the electrical transport properties reveals that the lattice and magnon scattering contributions to the longitudinal resistivity. Independent on the thickness of films, the anomalous Hall resistivity of CFA films is found to be dominated by skew scattering only.…
Two years after the prediction of a giant spin Hall effect for the dilute Cu(Bi) alloy [Gradhand et al., Phys. Rev. B 81, 245109 (2010)], a comparably strong effect was measured in thin films of Cu(Bi) alloys by Niimi et al. [Phys. Rev. Lett. 109, 156602 (2012)]. Both theory and experiment consider the skew-scattering mechanism to be responsible, however they obtain opposite sign for the spin Hall angle. Based on a detailed analysis of existing theoretical results, we explore differences between theory and experiment.
Using the Kubo formalism we derived expressions and implemented the method for calculating the anomalous Hall conductivity (AHC) in ferromagnets with short-range Gaussian disorder directly from first-principles electronic structure of the perfect crystal. We used this method to calculate the AHC in bcc Fe, fcc Co, L1o-FePd, L1o-FePt as well as thin bcc Fe(001) films. Within our approach we can transparently decompose the conductivity into intrinsic (IC), side jump (SJ) and intrinsic skew-scattering (ISK) contributions. The existence of ISK, which originates from asymmetric Mott scattering but …
Using the full-potential linearized augmented plane-wave method within the density functional theory, we compute all contributions to the scattering independent part of the thermoelectric conductivity tensor, namely the intrinsic contribution and the side-jump contribution. For the ferromagnetic materials bcc Fe, hcp Co, fcc Ni and L1_0 ordered alloys FePd and FePt, our investigations of the energy and temperature dependence of the intrinsic and side-jump contributions show that they are both of equal importance. Overall, our calculations are able to correctly reproduce the order of magnitude …
Recently a positive spin Hall angle (SHA) of 0.021, was observed experimentally in nonmagnetic CuIr alloys [Niimi et al., Phys. Rev. Lett. 106, 126601 (2011)] and attributed predominantly to an extrinsic skew scattering mechanism, while a negative SHA was obtained from ab initio calculations [Fedorov et al., Phys. Rev. B 88, 085116 (2013)], using consistent definitions of the SHA. We reconsider the SHA in CuIr alloys, with the effects of the local electron correlation U in 5d orbitals of Ir impurities, included by the quantum Monte Carlo method. We found that the SHA is negative if we ignore s…
We present measurements of the Spin Hall Effect (SHE) in AuW and AuTa alloys for a large range of W or Ta concentrations by combining experiments on lateral spin valves and Ferromagnetic-Resonance/spin pumping technique. The main result is the identification of a large enhancement of the Spin Hall Angle (SHA) by the side-jump mechanism on Ta impurities, with a SHA as high as + 0.5 (i.e $50\%$) for about 10\% of Ta. In contrast the SHA in AuW does not exceed + 0.15 and can be explained by intrinsic SHE of the alloy without significant extrinsic contribution from skew or side-jump scattering by …
Few layers Fe$_3$GeTe$_2$ is currently the only atomically thin ferromagnetic metal, and thus has drawn huge attention in the field of two-dimensional (2D) magnetism. In this paper, we perform a systematic first principle study on the electronic structure, magnetic anisotropy energy (MAE), and magneto-optical (MO) effects in monolayer (ML), bilayer (BL) and trilayer (TL) as well as bulk Fe$_3$GeTe$_2$. All the considered structures of Fe$_3$GeTe$_2$ are predicted to have large MAE of order $\sim$3.0 meV/f.u., being larger than reported 2D ferromagnetic semiconductors Cr$_2$Ge$_2$Te$_6$ and CrI…
A first-principles description of the spin Nernst effect, denoting the occurrence of a transverse spin current due to a temperature gradient, is presented. The approach, based on an extension to the Kubo-Streda equation for spin transport, supplies in particular the formal basis for investigations of diluted as well as concentrated alloys. Results for corresponding applications to the alloy system Au-Cu give the intrinsic and extrinsic contributions to the relevant transport coefficients. Using scaling laws allows in addition to split the extrinsic contribution into its skew scattering and sid…
A first-principles description of the spin Nernst effect, denoting the occurrence of a transverse spin current due to a temperature gradient, is presented. The approach, based on an extension to the Kubo-Streda equation for spin transport, supplies in particular the formal basis for investigations of diluted as well as concentrated alloys. Results for corresponding applications to the alloy system Au-Cu give the intrinsic and extrinsic contributions to the relevant transport coefficients. Using scaling laws allows in addition to split the extrinsic contribution into its skew scattering and sid…
Accurate prediction of chemical short-range order and its effect on thermodynamic, structural, and electronic properties of disordered alloys: exemplified in Cu$_{3}$Au
We report the evolution of crystallographic structure, magnetic ordering and electronic transport in thin films of full-Heusler alloy Co$_2$MnSi deposited on (001) MgO with annealing temperatures ($T_A$). By increasing the $T_A$ from 300$^\circ$C to 600$^\circ$C, the film goes from a disordered nanocrystalline phase to $B2$ ordered and finally to the $L2_1$ ordered alloy. The saturation magnetic moment improves with structural ordering and approaches the Slater-Pauling value of $\approx 5.0 μ_B$ per formula unit for $T_A$ = 600$^\circ$C. At this stage the films are soft magnets with coercive a…
