Influence of Interface Structure on Magnetic Proximity Effect in Pt

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Influence of Interface Structure on Magnetic Proximity Effect in Pt/ Y3Fe5O12 Heterostructures Xiao Liang,†,⊥,‡ Yupeng Zhu,†,⊥,‡ Bo Peng,†,⊥,‡ Longjiang Deng,†,⊥,‡ Jianliang Xie,†,⊥,‡ Haipeng Lu,†,⊥,‡ Mingzhong Wu,§ and Lei Bi*,†,⊥,‡ †

National Engineering Research Center of Electromagnetic Radiation Control Materials, University of Electronic Science and Technology of China, Chengdu 610054, People’s Republic of China ⊥ State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, China ‡ Key Laboratory of Multi-spectral Absorbing Materials and Structures, University of Electronic Science and Technology of China, Ministry of Education, Chengdu 610054, People’s Republic of China § Physics Department, Colorado State University, Fort Collins, Colorado 80523, United States ABSTRACT: The influence of interface structure on the magnetic proximity effect (MPE) in Pt/Y3Fe5O12 (YIG) bilayered heterostructures is studied by first-principles calculations based on the density functional theory (DFT). When Pt atoms are in close proximity with Y or Fe ions at the interface, Pt−Y and Pt−Fe bonds are observed. The crystalline orientations and interface termination layers of the YIG strongly modify both the strength and the length of the Pt−Fe bonding and thereby influence the magnetic properties of the Pt. Point defects including tetrahedral Fe, octahedral Fe, and Y vacancies are introduced at the Pt/YIG interface to quantitatively evaluate the influence on the MPE from individual atoms. For the Pt(100)/YIG(100) structure, the interface tetrahedral Fe vacancies can significantly reduce or even completely diminish the magnetic moments in the Pt. In a stark contrast, the octahedral Fe vacancies slightly enhance the Pt magnetism, and the nonmagnetic Y vacancies cause little influences to the Pt magnetism. These results indicate that the strength of the MPE at the Pt/YIG interface strongly depends on the interface structure. This dependence originated from the direct exchange interaction between the Fe 3d and Pt 5d electrons via electronic state hybridization as well as the electron exchange coupling between the Pt atoms. KEYWORDS: Pt/YIG heterostructures, magnetic proximity effect, interface structure, electronic structure, magnetic properties

1. INTRODUCTION Recently, the generation of pure spin currents by the use of insulating magnetic oxides has attracted great research interest due to its potential application in low energy dissipation information transport and processing. The spin current generation is usually achieved at the interface between a strong spin−orbit coupling noble metal (NM) film and a ferromagnetic oxide thin film (FM) via spin pumping or the spin Seebeck effect.1−3 Understanding the structure and magnetism of the NM/FM interface is of crucial importance for both the understanding and the improvement of spin current generation. The Pt/YIG system, in particular, has attracted great research interest. It has been widely used to study the generation of pure spin currents, as well as the manipulation of spin waves via pure spin currents. Those studies demonstrate that the Pt/YIG system is highly promising for magnetic insulator-based spintronic and magnonic applications.4 Despite the significant progress, discrepancies are observed in different experiments that aimed to interpret the interface magnetism in the Pt/YIG system. One debate is that whether © XXXX American Chemical Society

the magnetic proximity effect (MPE) exists at the Pt/YIG interface, a phenomenon occurs of ferromagnetic ordering of spins within several atomic layers of an NM film in close proximity to an FM material,5−11 which directly affects the interpretations of a number of recent important experimental observations in the Pt/YIG system. For example, a new magnetoresistance at the Pt/YIG interface has been discovered recently, which is termed by Nakayama et al. as spin Hall magnetoresistance (SMR) and is considered to be due to SHEand ISHE-induced spin scattering at the Pt/YIG interface.12,13 Huang et al., however, found that the MPE may be involved, which leads to a hybrid magnetoresistance at the Pt/YIG interface.7−11 The spin Seebeck effect (SSE) may also be contaminated by the anomalous Nerst effect (ANE) if the MPE presents at the Pt/YIG interface.14,15 What is more, it is well accepted that X-ray magnetic circular dichroism (XMCD) Received: November 19, 2015 Accepted: March 11, 2016

A

DOI: 10.1021/acsami.5b11173 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

Figure 1. Side view of the calculated crystalline structures of Pt(100)/YIG(100) (a) and Pt(111)/YIG(111) (b). A 15 Å thick vacuum layer is inserted to avoid the interaction between the two cells. Isosurfaces of spin density (at 0.02 e/Å3) in Pt(100)/YIG(100) (c) and Pt(111)/YIG(111) (d), where the blue and red isosurfaces stand for up and down spin polarizations, respectively. (e) Magnetic moment per Pt (Au) atom averaged over all of the atoms per Pt (Au) layer (solid line). The dashed lines show the average magnetic moments over all four Pt (Au) layers.

properties of the Pt/YIG heterostructures. The magnetic moments, projected density of states, and bonding status of the Pt atoms at the Pt/YIG interface are studied for different YIG crystal orientations, termination layers, and interface point defects. The magnetic proximity effect is found to be strongly related to the Fe−Pt bond formation at the interface. The crystal orientation, interface termination layer, and point defects significantly influence the interface bonding status and thereby lead to different magnetic properties of the Pt atoms. These findings may help to explain the discrepancies of recent experimental observations.

represents an effective technique for studying the MPE, but the recent XMCD measurements yielded rather controversial results on whether the MPE occurs in the Pt/YIG system.10,16 Specifically, in ref 10, a clear XMCD signal was observed at the Pt L2,3 edge, and the sign of the XMCD spectra changed with a reverse in the magnetic field direction. The measured average magnetic moment of Pt was 0.076 μB at 20 K (or 0.054 μB at 300 K) per Pt atom, matching their theoretical calculation results.8 In contrast, in ref 16, the XMCD spectra at the Pt L3 edge showed very weak signals, and the estimated average magnetic moment at room temperature was only 0.003 ± 0.001 μB per Pt atom. In addition to the debate on the MPE, the SHE, ISHE, spinmixing conductance, and magnetocaloric effect in the Pt/YIG system are found to be heavily dependent on the treatment of the interface and vary from sample to sample. The surface variation between different YIG samples drastically changes the strength of the MPE.17 Wet chemical cleaning, ion milling, or annealing can also cause significantly different ISHE and spinmixing conductance.18 Annealing the YIG film prior to Pt film deposition also changes the strength of the SSE.19 These findings highlight the importance of the interface structure to the magnetic properties of the Pt/YIG system. On the other hand, point defects such as Fe and Y vacancies are usually induced on YIG surfaces during the sample preparation process.20−22 How these point defects influence the interface magnetism in Pt/YIG remains unclear. The debates and discrepancies in the experiments therefore call for a detailed theoretical investigation on the correlation of the interface structure and magnetism properties in the Pt/YIG system. In this Article, first-principles calculations are carried out to study the effects of the interface structure on the magnetic

2. CALCULATION METHOD The method we applied in this work is the first-principles calculation method based on the density functional theory (DFT). The Perdew− Burke−Ernzerhof (PBE) exchange-correlation function23,24 for the generalized-gradient-approximation (GGA) and a plane-wave basis set within the framework of the projector augmented wave (PAW) method25,26 were employed. The cutoff energy for the plane-wave basis was 520 eV, and the convergence criterion for the electrondensity self-consistency cycles was 10−5 eV. For the sampling of the Brillouin zone, we employed the Monkhorst−Pack scheme27 and used (3 × 3 × 1) and (2 × 2 × 1) k-point grids for Pt(100)/YIG(100) and Pt(111)/YIG(111) calculations. The DFT+U formalism developed by Dudarev et al. was used to account for the strong on-site Coulomb repulsion for the localized Fe (3d) states.28 The value of “U” used for Fe (3d) states in our calculations is 4.3 eV. This value has been widely used in YIG with slight Ce doping29 and other systems containing Fe3+ cations.30,31 To model the Pt/YIG interfaces, we constructed a superlattice structure with a slab of YIG(100) (or YIG(111)) of about 6 Å thick along with four Pt(100) (or Pt(111)) atomic layers on top. A 15 Å thick vacuum layer was inserted to avoid the interaction between the two cells as shown in Figure 1a and b. During the relaxation process, the in-plane lattice constant was fixed at the experimental B


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Figure 2. Top view of the atomic structure at the interface of (a) Pt(100)/YIG(100) and (b) Pt(111)/YIG(111), and the corresponding twodimensional in-plane profile of charge density difference (CDD) distribution for (c) Pt(100)/YIG(100) and (e) Pt(111)/YIG(111), as well as the spin density distribution in Pt1 layer for (f) Pt(100)/YIG(100) and (g) Pt(111)/YIG(111). For comparison, the two-dimensional in-plane profile of CDD plot for Au(100)/YIG(100) interface is also shown in (d). The positive and negative values in charge (spin) density scaling bars mean the charge accumulation (spin up) and dissipation (spin down). value of the bulk YIG material, with the dimensions of 12.376 × 12.376 and 17.502 × 17.502 Å2 for Pt(100)/YIG(100) and Pt(111)/ YIG(111), respectively. Because of the lattice misfit, the Pt layers were under the biaxial tensile strains of 6.4% and 5.9% for Pt(100)/ YIG(100) and Pt(111)/YIG(111) structures, respectively. All atoms were fully relaxed until the calculated force on each atom is smaller than 0.02 eV/Å. The calculations considered 6-Å-thick YIG slabs because the induced moments converged at a YIG slab thickness of 6 Å when the thickness was increased from 3 to 9 Å.

in the Pt(100)/YIG(100) is much larger than that in the Pt(111)/YIG(111) structure. The ferromagnetic region also appears to penetrate deeper into the bulk Pt for the (100) crystalline orientation. The average magnetic moment per Pt atom in all 4 interface layers are shown by the dashed lines in Figure 1e. For the Pt(100)/YIG(100) structure, this value is 0.07 μB/atom, which is 2.3 times higher as compared to 0.03 μB/atom for the Pt(111)/YIG(111) structure. For comparison, we also calculated the magnetic moment of Au atoms in the Au(100)/YIG(100) structure. A negligible average moment of 0.003 μB/atom is induced in Au atoms, which is smaller by an order of magnitude than that of Pt atoms. Comparing our results to the Pt/Fe system,32,33 the MPE in Pt/Fe is found to be stronger and penetrate further than that in the Pt/YIG system. The induced average Pt moment in Pt(100)/Fe(100) is about 0.5 μB per Pt atom as determined by XMCD.32 This value is about 10 times larger than that in Pt(100)/YIG(100), which is 0.07 μB per Pt atom according to our calculations. Because of the lattice mismatching, the Pt layers are under slightly different biaxial tensile strains, which are about 6.4% and 5.9% for Pt(100)/YIG(100) and Pt(111)/YIG(111), respectively. However, the induced magnetic moments of Pt in the two cases are very different, suggesting that strains may not be the main reason for the observed MPE difference. The significant difference of the MPE in Pt/YIG structures with different crystalline orientations invites speculation and investigations on the electron density distributions at the interfaces. To reveal the reasons for the MPE difference in the calculated structures presented above, the valence charge density difference (CDD) (ρdiff) distribution was calculated. This distribution is defined as

3. RESULTS AND DISCUSSION 3.1. Crystal Orientation of YIG Surface. We first consider the influences of the crystal orientation of the YIG surface on the magnetic properties of the Pt/YIG structure. In particular, we compare the structural and magnetic properties of the Pt(111)/YIG(111) and Pt(100)/YIG(100) interfaces. The models are shown in Figure 1a and b for Pt(100)/YIG(100) and Pt(111)/YIG(111), respectively. In each YIG unit cell, the octahedral Fe (Feoct) ions arrange in 8 body-centered cubic (BCC) subunit cells. The yttrium and tetrahedral Fe (Fetet) ions are located on each surface of the 8 subunit cells. The oxygen ions surround the Y and Fe ions with dodecahedral, octahedral, and tetrahedral coordinations. We denote spin up and spin down directions to be parallel to the Fetet and Feoct ion spin polarization directions, respectively. The calculated spinisosurface at 0.02 e/Å3 is shown in Figure 1c and d for Pt(100)/YIG(100) and Pt(111)/YIG(111), respectively. For both of the structures, all 4 Pt atomic layers are strongly spin polarized, indicating the existence of the MPE, which is consistent with previous calculation results for the Pt(111)/ YIG(111) interface.8 The difference is that a small number of Pt atoms in the Pt1 layer of the Pt(111)/YIG(111) structure are down spin polarized, which was not observed at the Pt(100)/YIG(100) interface. Figure 1e shows the magnetic moment per Pt atom averaged over all of the atoms in each Pt layer for the two crystalline orientations. The magnetism of Pt

ρdiff = ρPt(Au)/YIG − ρPt(Au) − ρYIG

Here, ρPt(Au)/YIG, ρPt(Au), and ρYIG denote the valence charge density distributions of the Pt(Au)/YIG heterostructure, the C


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polarization can be observed in different Pt atoms. For Pt atom in close proximity with Feoct/Fetet, the Pt is down/up spin polarized as shown in Figure 2g. It is also interesting that, although Pt and Y atoms form a strong bond at both of the interfaces, it makes a negligible contribution to the magnetism of the Pt. This can be clearly seen if we compare the strength of spin polarization of Pt atom I and II in Figure 2a and f. This observation suggests that interface exchange coupling between the electron spins of Pt and Fe plays an important role for the MPE in the Pt. This conclusion is further supported by the investigation of the CDD at the Au(100)/YIG(100) interface as shown in Figure 2d, which shares atomic locations similar to those of the Pt(100)/YIG(100) interface shown in Figure 2a. The bond between Au and Y is as strong as that between Pt and Y, but the bond between Au and Fe is much weaker than that between Pt and Fe. As a result, negligible magnetic moments are induced in the interface Au atoms. 3.2. Effects of YIG Termination Layers. Turn now to the influences of the YIG termination layers on the interface electronic and magnetic properties. The complex crystalline structure of the YIG allows different termination layers to be in contact with the Pt for the same crystalline orientation. As shown in Figure 1a, for the Pt(100)/YIG(100) structure, in each YIG unit cell there are 3 nonequivalent crystalline planes with Fe ions on the surface, labeled as plane A, plane B, and plane C. It should be noted that the YIG crystal can also be terminated on oxygen-rich planes. However, the total energy of the Pt/YIG supercell for such an interface is very high, which does not converge according to our calculations. For planes A and C, the total number of Y, Fetet, and Feoct per unit area is identical. Therefore, we focus our discussions on the model with the YIG crystalline plane B in contact with the Pt (Pt(100)/YIG(100)-B). The top view of the corresponding atomic locations in the Pt(100)/YIG(100)-B interface is shown in Figure 3a. The difference between plane A and plane B is that in plane B, there are 2 interface Fetet ions per YIG unit cell as compared to 4 in plane A. Besides, there are no Feoct ions on the interface of plane B. The binding energy of Pt(100)/ YIG(100)-A is 0.008 eV per Pt atom lower than that of Pt(100)/YIG(100)-B and 0.023 eV per Pt atom lower than that of Pt(111)/YIG(111). Note that the binding energy is defined as Eb = EPt/YIG − EYIG − EPt, with the EPt/YIG, EYIG, and EPt denoting the total energy of the Pt/YIG bilayer system, the isolated YIG system, and the isolated Pt system, respectively. Although the Pt(100)/YIG(100)-A system is the most stable, to simulate the complex situation of the Pt/YIG interface in experiments, the different crystal orientations20,39 and surface terminations of the YIG are considered for comparison in this work. The different interface structure significantly influences the magnetic moment of the Pt. As shown in Figure 3b, the average magnetic moment per Pt atom for all 4 Pt layers is 0.016 μB/atom, which is only about 1/4 of the value of 0.07 μB/ atom of Figure 1e. The highest magnetic moment is now in the Pt2 layer with an average magnetic moment value of 0.02 μB/ atom, as compared to the maximum magnetic moment of around 0.09 μB/atom in the Pt3 layer of the Pt(100)/ YIG(100)-A case. The CDD plot is shown in Figure 3c. Clear bond formation can be observed for Pt−Y and Pt−Fetet. The Pt magnetic moment, however, is clearly weaker in Figure 3d as compared to the Pt(100)/YIG(100)-A case (see Figure 2f). Still, we can observe that the Pt atoms with the strongest up spin polarization are the ones bonding with Fetet. The Pt atoms bonding with Fetet at this interface have the highest magnetic

Pt(Au) slab, and the YIG slab, respectively. The twodimensional in-plane CDDs taken at the middle plane between the YIG surface and the Pt1 layer for Pt(100)/YIG(100), Au(100)/YIG(100), and Pt(111)/YIG(111) are shown in Figure 2c−e, respectively, where the red regions stand for the electron accumulation and the blue regions stand for the electron dissipation. Figure 2a and b shows the top views of the corresponding atomic locations at the Pt(Au)(100)/YIG(100) and Pt(111)/YIG(111) interfaces, respectively. Comparing Figure 2a, c, and d, one can see that abundant electrons are accumulated between Pt and Fe, Pt and Y, and Au and Y, but fewer electrons are accumulated between Au and Fe. The results indicate the formation of strong Pt−Fe, Pt−Y, and Au− Y bonds and weak Au−Fe bonds at the interface. These differences might be related to a tendency of strong intermetallic compound bond formation for Pt−Fe, Pt−Y, and Au−Y, but not for Au−Fe, according to their phase diagrams.34−38 Comparing Figure 2a, b, c, and e, one notices that the Pt−Feoct bonds are much weaker than the Pt−Fetet bonds at the Pt(100)/YIG(100) interface. For Pt(111)/ YIG(111), these two bonds are similar in strength. The different bonding status can be understood by investigating the bond length. The average bond lengths of Pt−Fetet and Pt− Fetet in the Pt(100)/YIG(100) and Pt(111)/YIG(111) structures are summarized in Table 1. The average bond Table 1. Summary of Pt−Fe Bond Lengths at the Pt(100)/ YIG(100) and Pt(111)/YIG(111) Interfacesa (100)

Pt−Fetet

Pt−Feoct

(111)

Pt−Fetet

Pt−Feoct

d (Å) dmax (Å) dmin (Å)

2.585 2.648 2.528

2.882 2.964 2.762

d (Å) dmax (Å) dmin (Å)

2.686 2.714 2.657

2.366 2.369 2.364

a

d is the bond length averaged over all Pt−Fe bonds at the Pt/YIG interface for each supercell. dmax and dmin are the maximum and minimum Pt−Fe bond lengths, respectively.

length of Pt−Feoct is 2.882 Å for Pt(100)/YIG(100) and 2.366 Å for Pt(111)/YIG(111). One can see that the former is notably longer than the latter. However, the Pt−Fetet bond length is comparable for the two structures, 2.585 Å for Pt(100)/YIG(100) and 2.686 Å for Pt(111)/YIG(111). Such differences result in stronger Pt−Fetet bonding and weaker Pt− Feoct bonding for Pt(100)/YIG(100) as compared to Pt(111)/ YIG(111), which leads to the difference in the CDD between Figure 2c and e. The different bonding status leads to different magnetic moments in Pt atoms at the interface as observed in Figure 1e. For Pt(100)/YIG(100), the relaxed interface allowed all Pt atoms to bond with Fetet or Y atoms, whereas for Pt(111)/ YIG(111), the Pt atom arrangement is less ordered, allowing some Pt atoms to bond with Feoct, and some not to bond with any atoms in the YIG layer. The stronger (weaker) hybridization between Pt and Fetet (Feoct) ions in the Pt(100)/ YIG(100) interface leads to higher magnetic moment of Pt atoms. To illustrate this point in detail, we plot the electron spin density distribution of the Pt1 layer at the Pt/YIG interfaces. The spin densities per area for Pt(100)/YIG(100) and Pt(111)/YIG(111) are shown in Figure 2f and g, respectively. At the Pt(100)/YIG(100) interface, all Pt atoms are up spin polarized due to strong (weak) exchange coupling between Pt and Fetet (Feoct). In contrast, at the Pt(111)/ YIG(111) interface, both up spin polarization and down spin D


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Figure 3. Top view of the atomic structure at the interface of Pt(100)/YIG(100)-B (a), the corresponding two-dimensional in-plane profile of charge density difference (CDD) distribution at the interface (c), as well as the spin density distribution in Pt1 layer for Pt(100)/YIG(100)-B (d). The positive and negative values in charge (spin) density scaling bars mean the charge accumulation (spin up) and dissipation (spin down). (b) Magnetic moment per Pt atom averaged over all of the atoms per Pt layer (solid line) and the average magnetic moments over all four Pt layers (dash line) in Pt(100)/YIG(100)-A (blue line) and Pt(100)/YIG(100)-B (red line).

moment of 0.043 μB. This value is 43% lower than that of the Pt(100)/YIG(100)-A interface (0.076 μB). This difference suggests that the magnetic moment does not localize on the Pt atoms bonding with Fetet. Instead, exchange coupling between the Pt atoms may have also played an important role in the observed magnetic moment of Pt atoms. For the Pt atoms bonding with Y, the magnetization is obviously lower, which is consistent with the case shown in Figure 2f. The projected density of states (PDOS) provides more information on the electron hybridization between Pt and Fe. Figure 4a−c shows the PDOS for the d band valence electrons of Pt, Fetet, and Feoct atoms in the heterostructure of Pt(111)/ YIG(111), Pt(100)/YIG(100)-A, and Pt(100)/YIG(100)-B, respectively. The selected Pt, Fetet, and Feoct atoms for the PDOS investigations are the nearest neighbor to each other, that is, atom I, 1, and 2 in Figure 2a, respectively. In all of the Pt/YIG structures, some of the 3d states of Fe shift above −7 eV and hybridize with the Pt 5d states due to the Pt−Fe bond formation. This is in stark contrast to previous reports on the calculated PDOS of the YIG system,40,41 where both the Fetet and the Feoct 3d valence electron states are located below −7 eV. The difference between Pt(111)/YIG(111) and Pt(100)/ YIG(100)-A is that in Pt(100)/YIG(100)-A the 3d states of Feoct are split with the t2g states remaining below −7 eV. Only the eg states hybridize with the Pt 5d states, leading to a much weaker bond than that of Pt−Fetet. In Pt(111)/YIG(111), all 3d states of Feoct are shifted above −7 eV and hybridize with Pt 5d down spin states, leading to a bond strength similar to that of Pt(5d)-Fetet(3d). If we compare Figure 3b and c for Pt(100)/ YIG(100) with different termination layers, we can see that the

PDOS of Feoct clearly shifts to below −7 eV for Pt(100)/ YIG(100)-B due to nonbonding with Pt atoms, which matches the bulk YIG PDOS.40,41 The PDOS of Fetet is similar between the two cases, which strongly hybridize with Pt. The different strength of the electron hybridization between Pt and Fe ions induces significantly different magnetic properties of Pt due to direct exchange, which leads to different MPE responses in Pt/ YIG with different interface structures. 3.3. Effects of Vacancies at Pt/YIG Interfaces. Next, we evaluate the influences of each ion at the YIG surface on the MPE in the Pt by introducing point defects in the model. In experiments, various defects can be induced at the YIG surface during the growth process. In particular, Fe and Y vacancies are observed at the YIG surface in YIG films prepared under different fabrication conditions.20−22 To investigate how these vacancies influence the MPE, one tetrahedral Fe3+ vacancy (VFetet), one octahedral Fe3+ vacancy (VFeoct), and one Y3+ vacancy (VY) are induced to the surface of YIG(100) terminated with crystalline plane A in three different models as shown in Figure 5a−c, respectively. Figure 5d−f shows the corresponding calculated 2D in-plane CDD at the interface for the VFetet, VFeoct, and VY cases, respectively. As compared to the vacancy-free case (Figure 2c), the Pt−Fetet, Pt−Feoct, or Pt−Y bonds vanished due to the presence of vacancies. The 2D in-plane spin density distribution at the Pt1 layer for the VFetet, VFeoct, and VY cases is shown in Figure 5g−i, respectively. As compared to the vacancy-free case (Figure 2f), the strength of up spin polarization of the Pt atoms connected to the VFetet is significantly reduced. Some Pt atoms are even down spin polarized, which is caused by the absence of the Pt−Fetet bond, E


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slightly. For one VFeoct at the interface, the average Pt moment increases to 0.046, 0.071, 0.095, and 0.087 μB/atom for the Pt1, Pt2, Pt3, and Pt4 layers, respectively. The VY defect shows subtle influences on the Pt magnetism. Moreover, by introducing 2 times of VFetet at the interface, that is, losing one-half of the tetrahedral ion population at the interface, the magnetic moment of Pt decreases to −0.01, 0.005, 0.023, and 0.022 μB/atom for the Pt1, Pt2, Pt3, and Pt4 layers, respectively. The average magnetic moment for each Pt atom over all 4 Pt layers decreases to 0.01 μB, which is 85.7% lower as compared to the defect-free case. Table 2 summarizes the average magnetic moment per Pt atom (M0) over all of the Pt layers, with and without various vacancies at the interface. ΔM in the table is the variation in the average magnetic moment after inducing various defects. The data show that one VFetet significantly decreases the MPE in Pt/YIG by 58.6%, which is about 8 times stronger than the influence of VFeoct. The magnetic moment variation for each Pt atom due to the defects as compared to the defect-free case can also be evaluated. For the VFetet and VFeoct cases shown in Figure 5a and b, the variation of the magnetic moment of each Pt atom (ΔM) in the Pt1 layer as a function of its distance d to the defects (considering the periodicity of the lattice) is shown in Figure 6b and c. The blue circles show the ΔM for each Pt atom of the Pt1 layer, and the red squares show the average value of the blue circles having similar d values. The negative (positive) values mean the decrease (increase) of magnetic moment in Pt atoms after the defects are induced. Clearly, d and ΔM are strongly correlated. When d is small, the ΔM of Pt atoms decreases exponentially as a function of d. With increasing d, the ΔM value tails down to lower values and settles down to constant values of −1 × 10−2 and 3 × 10−3 μB for the VFetet and VFeoct cases, respectively. This further indicates that the source of Pt magnetism is from the Pt−Fe bonds, which couples ferromagnetically to distant Pt atoms by exchange coupling between the Pt electrons. Figure 7b−d shows the PDOS of the selected Pt atoms connected to the VFetet, VY, and VFeoct, that is, atoms I and II in Figure 5a, respectively. Here, the spin polarization P is defined as the difference between the spin up and spin down states normalized by the total density of states at the Fermi level.42,43 It is found that the spin polarization of the Pt can reach 40.4% in the defect-free case. After inducing one VFetet, the value of P decreases to 16.6%. The inset shows the details of state variations near the Fermi energy. When VFetet is present, the up and down spin polarized states at the Fermi energy are obviously decreased and increased, respectively, as compared to the defect-free case, which means that the Pt converts from ferromagnetic to paramagnetic gradually because of the missing Pt−Fetet bond. The VY and VFeoct defects show little effects on the spin polarization P, and the PDOS landscape changes very slightly near the Fermi energy as compared to Figure 7a. This further demonstrates that the bonding between Pt and Fetet is stronger than that between Pt and Feoct for this particular interface structure. The Y vacancy at the interface also changes the spin polarization of the neighboring Pt because the local lattice distortion after the lattice relaxation. However, this effect is much weaker than the Pt−Fe exchange effect, as shown by the tiny variations in average magnetic moments of Pt in Figure 6a.

Figure 4. Projected density of states (PDOS) for d band valence electrons of Pt, Feoct, and Fetet in (a) Pt(111)/YIG(111), (b) Pt(100)/ YIG(100)-A, and (c) Pt(100)/YIG(100)-B structures.

and therefore the weak exchange between Pt and Feoct becomes important. The change of spin polarization of these Pt atoms induces further changes in the spin polarization of other Pt atoms via exchange coupling, leading to lower magnetization to all Pt atoms in the upper layers. An opposite trend is observed in the VFeoct case, as shown in Figure 5b, e, and h. The up spin polarization is slightly enhanced in the Pt due to the broken Pt−Feoct bond, as circled in the CDD plot of Figure 5e. The yttrium vacancy VY also causes two broken Pt−Y bonds, as circled in the CDD plot in Figure 5f. However, there is almost no change in the magnetic moment of Pt atoms because the Y3+ ions are nonmagnetic. The spin density of Pt atom II in Figure 5c, which originally bonds to the Y atoms, remains unchanged. This observation further supports the conclusion that the spin polarization in Pt atoms not bonding with Fe is due to exchange coupling, with the source of spin polarization coming from the Pt atoms bonding to Fe. Quantitative evaluation of the influences of defects on the Pt magnetism is shown in Figure 6. Figure 6a shows the calculated moment per Pt atom in each case of different interface defects, averaged over all of the Pt atoms of each layer. The VFetet significantly decreases the magnetic moment in Pt. For one VFetet at the interface, the average Pt moment decreases from 0.042, 0.070, 0.090, and 0.081 μB/atom, to 0.015, 0.019, 0.041, and 0.039 μB/atom for the Pt1, Pt2, Pt3, and Pt4 layers, respectively. However, the VFeoct increases the moment F


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Figure 5. Locations of the Fetet vacancy (a), Feoct vacancy (b), and Y vacancy (c) at the interface of Pt(100)/YIG(100)-A structure. Parts (d)−(f) show the corresponding two-dimensional in-plane profile of charge density difference distribution at the interface. Parts (g)−(i) show the corresponding two-dimensional in-plane profile of spin density distribution in the Pt1 layer. The positive and negative values in charge (spin) density scaling bars mean the charge accumulation (spin up) and dissipation (spin down).

Figure 6. (a) Magnetic moments per Pt atom in each case of different interface defects, averaged over all of the Pt atoms of each layer. The variations in magnetic moments of each Pt atom in the Pt1 layer after inducing the Fetet (b) and Feoct (c) versus its distance to the defect d. The red hollow point is the averaged value over the Pt atoms having similar d values.

4. CONCLUSIONS

Table 2. Magnetic Moment (M0) per Pt Atom Averaged over All Four Layers in the Defect-Free Case and Various Vacancy Casesa M0 (μB) ΔM (%)

without defects

VFetet

VFeoct

VY

2VFetet

0.070

0.029 −58.6

0.075 7.1

0.070 0

0.010 −85.7

In summary, we studied the magnetic proximity effect of Pt/ YIG bilayered heterostructures using first-principles calculations. The influences of the crystalline orientations, termination layers, and point defects of the Pt/YIG interface on the MPE were investigated. We observed a strong dependence of the MPE strength on the interface hybridization of the Pt(5d)− Fe(3d) electron states. Because of the different interface structures and Pt−Fe hybridization status, the magnetic

a ΔM is the variation percentage as compared to the M0 in the defectfree case.

G


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Figure 7. Projected density of states calculated for 5d orbitals of selected Pt, which is closest to the Fetet vacancy (b), Y vacancy (c), and Feoct vacancy (d). For comparison, the PDOS in the defect-free case is also shown in (a). Inset: Zoomed-in PDOS with an x coordinate range from −0.1 to 0.1 eV. The spin polarizations (P) are calculated by comparing the density of states between spin up and down states normalized by the total density of states at the Fermi level.

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moment of Pt in the Pt(100)/YIG(100)-A heterostructure is 2.3 times and 4.4 times stronger than that in the Pt(111)/ YIG(111) and Pt(100)/YIG(100)-B structures, respectively. Cation vacancies at the YIG/Pt interface can also strongly influence the MPE. Fe tetrahedral (octahedral) vacancies at the YIG/Pt interface may greatly decrease (slightly increase) the magnetic moment of Pt, while the nonmagnetic yttrium vacancies show little influence on the MPE. In addition, Au/ YIG structures show negligible MPE because of the weak hybridization of Au−Fe states. These results indicate that exchange coupling between the Pt 5d and Fe 3d electrons via interface electron state hybridization, as well as the electron exchange coupling between Pt atoms, is the dominating mechanism for the induced magnetic moments at the Pt/YIG interfaces.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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ACKNOWLEDGMENTS

We are grateful for the support of the National Natural Science Foundation of China (61475031, 51302027, 51522204), the Fundamental Research Funds for the Central Universities (ZYGX2013J028, ZYGX2014Z001), the Science Foundation for Youths of Sichuan Province (2015JQO014), the Doctoral Fund of Ministry of Education of China (20130185120009), and the Open Foundation of Key Laboratory of Multispectral Absorbing Materials and Structures, Ministry of Education (ZYGX2013K007-5). H


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Influence of Interface Structure on Magnetic Proximity Effect in Pt

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