Electric-Field Modulation of Interface Magnetic Anisotropy and Spin

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Electric-field modulation of interface magnetic anisotropy and spin reorientation transition in (Co/Pt)3/PMN-PT heterostructure Ying Sun, You Ba, Aitian Chen, Wei He, Wenbo Wang, Xiaoli Zheng, Lvkuan Zou, Yijun Zhang, Qu Yang, Lingjia Yan, Ce Feng, Qinghua Zhang, Jian-Wang Cai, Weida Wu, Ming Liu, Lin Gu, Zhaohua Cheng, Cewen Nan, Ziqiang Qiu, Yizheng Wu, Jia Li, and Yonggang Zhao ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b00284 • Publication Date (Web): 07 Mar 2017 Downloaded from http://pubs.acs.org on March 9, 2017

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Electric-field modulation of interface magnetic anisotropy and spin reorientation transition in (Co/Pt)3/PMN-PT heterostructure Ying Sun, †,§ You Ba, †,§ Aitian Chen, †,§ Wei He, ‡ Wenbo Wang, || Xiaoli Zheng, ‡ Lvkuan Zou, ‡ Yijun Zhang,

⊥

Qu Yang,

⊥

Lingjia Yan, †,§ Ce Feng, †,§

Qinghua Zhang, ‡,# Jianwang Cai, ‡ Weida Wu, || Ming Liu, Cheng, ‡ Ce-Wen Nan, # Ziqiang Qiu, ∇ Yizheng Wu,

△

⊥

Lin Gu, ‡ Zhaohua

Jia Li,

¶

and Yonggang

Zhao*,†,§ †

Department of Physics and State Key Laboratory of Low-Dimensional Quantum

Physics, Tsinghua University, Beijing 100084, China §

Collaborative Innovation Center of Quantum Matter, Beijing 100084, China

‡

Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of

Sciences, Beijing 100190, China ||

Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey

08854, USA ⊥

Electronic Materials Research Laboratory, Key Laboratory of the Ministry of

Education & International Center for Dielectric Research, Xi’an Jiaotong University, Xi’an 710049, China

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#

School of Materials Science and Engineering and State Key Lab of New Ceramics

and Fine Processing, Tsinghua University, Beijing 100084, China

∇

Department of Physics, University of California at Berkeley, Berkeley, California

94720, USA △

Department of Physics, State Key Laboratory of Surface Physics and Collaborative

Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China ¶

International Center for Quantum Materials, School of Physics, Peking University,

Beijing 100871, China

KEYWORDS: electric-field modulation of magnetism, (Co/Pt)3 multilayers, perpendicular magnetic anisotropy, interface magnetic anisotropy, spin reorientation transition, coexistence phase

ABSTRACT: We report electric-field control of magnetism of (Co/Pt)3 multilayers involving perpendicular magnetic anisotropy with different Co-layer thicknesses grown on Pb(Mg,Nb)O3-PbTiO3 (PMN-PT) FE substrates. For the first time, electric-field control of the interface magnetic anisotropy, which results in the spin reorientation transition, was demonstrated. The electric-field-induced changes of the bulk and interface magnetic anisotropies can be understood by considering the strain-induced change of magnetoelastic energy and weakening of Pt 5d-Co 3d hybridization, respectively. We also demonstrate the role of competition between the applied magnetic field and the electric field in determining the magnetization of the 2 ACS Paragon Plus Environment


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sample with the coexistence phase. Our results demonstrate electric-field control of magnetism by harnessing the strain-mediated coupling in multiferroic heterostructures with perpendicular magnetic anisotropy, and is helpful for electric-field modulations of Dzyaloshinskii-Moriya interaction and Rashba effect at interfaces to engineer new functionalities.

INTRODUCTION

Electric-field control of magnetism offers a promising route to achieve fast and high-density information storage with very low energy consumption.1-3 In principle, this can be realized with single-phase multiferroic materials which simultaneously display magnetism and ferroelectricity through the converse magnetoelectric effect.4 However, these materials are rare at room temperature and the effects are too small to be useful.1 In this regard, multiferroic heterostructures composed of ferromagnetic (FM) and ferroelectric (FE) materials provide an alternative and effective way to realize remarkable electric-field control of magnetism.1,

5

So far, mainly three

approaches have been demonstrated for electric-field control of magnetism in FM/FE multiferroic heterostructures, including strain-mediated coupling5-6 with the piezo-strain of the FE transferred to the FM layer, exchange bias mediated interaction5-6 and manipulation of charge carrier density.5-6 Among them, electric-field control of magnetism through the strain-mediated coupling in FM/FE multiferroic heterostructures has been widely studied because of the variety of room temperature FM and FE materials and the remarkable magnetoelectric effects. 3 ACS Paragon Plus Environment

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However, up to now, most of the work focused on the FM films with in-plane magnetic anisotropy,5-12 while there have been only a few reports on the FM films with perpendicular magnetic anisotropy (PMA)13-19 with only one report on electric-field-induced magnetization rotation from the perpendicular direction to the in-plane direction.16

Material systems with PMA are very important for increasing the information storage density and thermal stability of magnetic memory20 and they are also directly relevant to spin‐transfer‐torque random access memory, spin‐torque oscillators, and bit‐patterned media.21 Among them, Co/Pt multilayers is an important system, which exhibit relatively large PMA originated from the interface magnetic anisotropy,22-27 and its magnetic anisotropy energy can be phenomenologically separated into a bulk contribution and an interfacial one.27-28 The former involves the shape, magnetocrystalline and magnetoelastic anisotropies, and usually favors the in-plane magnetic anisotropy,25-27 while the latter (interface magnetic anisotropy) usually favors the PMA.23, 25, 27 The competition between these two contributions leads to the perpendicular-to-in-plane spin reorientation transition (SRT) with the increase of Co thickness, starting at a critical thickness,27 and the separation of the bulk and interfacial contributions to the magnetic anisotropy has been extensively adopted in the study of thickness-driven SRT in magnetic multilayers. So Co/Pt multilayers provides a good opportunity to explore the electric-field modulation of the interface magnetic anisotropy as well as the SRT. However, there has been no report



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on electric-field control of magnetism of (Co/Pt)n/FE multiferroic heterostructures so far.

Up to now, all the previous work on electric-field manipulation of PMA in FM/FE heterostructures, such as Co/Ni,18 CoxPd1-x alloy,13-14 Cu/Ni,16 and CoFeB,15, 17

deduced the total magnetic anisotropy change of the system without separating it

into the bulk and interfacial contributions. Therefore, electric-field control of the interface magnetic anisotropy, which usually favors the PMA, has not been demonstrated so far. As shown later in our work, this can only be realized with a series of samples around the SRT and a lot of measurements as well as careful and detailed considerations, while in the previous work generally only one sample was used to demonstrate electric-field manipulation of PMA for the FM multilayers.15-18 Knowing how electric field modifies the bulk and interface anisotropy is helpful for deliberately engineering the bulk or interface properties to achieve a certain modification. In particular, the ability to manipulate interface magnetic anisotropy by electric field is essential for manipulating PMA originated from the interface magnetic anisotropy. Moreover, interface possesses broken inversion symmetry which hosts new form of interaction or effect, such as the Dzyaloshinskii-Moriya interaction29-30 and Rashba effect,31 and thus the ability of using electric field to manipulate the interface would in general hold promising routes to create new phenomena and functionalities at the interface. So electric-field manipulation of interface magnetic anisotropy is highly desired regarding its significance for both fundamental issues and applications in memory devices. 5 ACS Paragon Plus Environment

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In this paper, we study electric-field control of magnetism of (Co/Pt)3 multilayers with different Co thicknesses grown on PMN-PT (011) FE substrates. Electric-field driven SRT was observed, and electric-field-induced changes of the bulk and interface magnetic anisotropies were separated. Our results show that electric-field modulation of interface magnetic anisotropy plays an essential role in driving the SRT.

EXPERIMENTAL SECTION Sample Preparation. Pt (20 nm)/Ta (10 nm)/Pt (5 nm)/(Co (t nm)/Pt (2 nm))3/Ta (5 nm) multilayers were deposited onto an one-side polished PMN-PT (011) substrate with the size of 3 × 5 × 0.5 mm3 at room temperature by DC magnetron sputtering at an Ar pressure of 0.5 Pa. The base pressure of the sputtering system was 5×10-5 Pa. The top Ta (5 nm) layer was deposited to prevent oxidation as well as serving as the top electrode. Pt (20 nm)/Ta (10 nm)/Pt (5 nm) layers were deposited as the seed layer. Au (300 nm) was deposited on the back of PMN-PT substrate as the bottom electrode. So the electric field was applied between Ta and Au. Experimental characterization. The quality of the multilayers was characterized by X-ray diffraction (XRD) on a Rigaku D/max-RB X-ray diffractometer with a Cu Kα radiation. Scanning transmission electron microscopy (STEM) measurements were operated on an ARM－200CF transmission electron microscope operated at an acceleration voltage of 200 kV (JEOL, Tokyo，Japan) and equipped with double spherical aberration (Cs) correctors. Magnetization versus magnetic field (M-H) curves of the samples were measured using Magnetic Properties Measurement System 6 ACS Paragon Plus Environment


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(MPMS) with an in situ electric field. The positive direction of electric field is defined as pointing from the top Ta to the bottom Au. Ferromagnetic resonance (FMR) measurements were carried out using the JEA-FS200 ESR spectrometer of JEOL company, equipped with an X-band microwave generator with the frequency of 9.1 GHz and a cylindrical microwave resonant cavity. The magnetic field direction is fixed while the sample is mounted to a rotating stage. The magnetic force microscopy (MFM) experiments were carried out in a homemade32-33 cryogenic atomic force microscope (AFM) using commercial piezoresistive cantilevers (spring constant k ~3 N/m, resonant frequency f0 ~42 kHz). The homemade AFM is interfaced with a Nanonis SPM Controller (SPECS) and a commercial phase-lock loop (SPECS). MFM tips were prepared by depositing nominally 100 nm Co film onto bare tips using e-beam evaporation. MFM images were taken in a constant mode with the scanning plane ~ 50 nm above the sample surface. Electrostatic interaction was minimized by nulling the tip-surface contact potential difference.

RESULTS AND DISCUSSION

(Co/Pt)3 multilayers and some other layers were grown on the (011) oriented 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 (PMN-PT) single crystal substrate (0.5 mm thick) by DC magnetron sputtering and the details about sample fabrication can be found in the Experimental section. Figure 1a shows a schematic of the sample, where the x, y and z axes correspond to the pseudo-cubic [100], [01-1] and [011] crystal axes of PMN-PT (011), respectively. Five samples of (Co/Pt)3 multilayers were prepared with 7 ACS Paragon Plus Environment

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nominal Co thicknesses (t) of 1.35, 1.4, 1.45, 1.5 and 1.6 nm, respectively. These samples were chosen in order to adopt a linear fitting to the FMR data to separate the interface effects from the bulk ones. Such methodology requires a series of samples with different thicknesses to reduce the statistical uncertainty. Moreover, we wanted to achieve a significant electric-field manipulation of PMA. The 1.35, 1.4 and 1.45 nm samples all reside across the phase boundary between the coexistence and in-plane phases, which makes them more sensitive to the external electric field since the relevant energy scales are comparable. Electric fields were applied to PMN-PT along the z direction for measurements of magnetic hysteresis loops, FMR spectra and MFM images to get samples’ magnetic anisotropies and electric-field modulation of magnetism.

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Cross-sectional low-magnification HAADF image of the 1.4 nm thick sample. Thickness of each layer is indicated by the number in the bracket with a unit of nm. (c) Magnified HAADF image of the region enclosed by the blue rectangle in (b).The spacing of (111) planes of Pt and Co are both labeled. Intensity profile inserted on the right exhibited the alternative stacking of Pt and Co layers. (d) XRD patterns of θ - 2θ scan for samples with thicknesses of 1.35, 1.4 and 1.45 nm, respectively. (e) Strain versus electric field curves of PMN-PT (011) substrate.

STEM and XRD were carried out to characterize the sample’s structure. Figure 1b shows a high-angle annular dark-field (HAADF) image for the sample with t = 1.4 nm, in which different layers can be clearly identified with sharp intensity contrast because of the different atomic numbers of these elements. Figure 1c is a magnified image of the blue rectangle region shown in Figure 1b. The heavier Pt layers exhibit relatively brighter contrast than the lighter Co layers, as revealed by the intensity profile of the Co-Pt-Co columns shown in the inset of Figure 1c. Also noticed in Figure 1c is the inclination of Co/Pt atomic lattice plane relative to the horizontal axis of Figure 1c, which is due to the face-centered cubic (fcc) (111) orientation of the (Co/Pt)3 multilayers as revealed by the XRD results (Figure 1d). It has been demonstrated that such fcc (111) orientation gives rise to the largest PMA of Co/Pt multilayer.27, 34 By using fast Fourier transform, the values of inter-planar spacing d for both Pt and Co were calculated to be dPt = 2.25 Å and dCo = 2.08 Å, respectively. It is noted that dPt for fcc (111) is smaller than that of the bulk Pt (2.265 Å), while dCo for fcc (111) is larger than that of the bulk Co (2.047 Å).35 This indicates that (Co/Pt)3 9 ACS Paragon Plus Environment

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multilayers is under strain due to the lattice mismatch between Pt and Co.23 Three well-defined peaks in the XRD patterns (Figure 1d and Figure S1a) for samples with t = 1.35, 1.4 and 1.45 nm can be assigned to the α -Ta (110), Pt (111) and Co/Pt (111) peaks,36-38 respectively. Both the α -Ta (110) and Pt (111) peaks come from the seed layers, and the Co/Pt (111) peak is intimately related to the (Co/Pt)3 multilayers with the peak position determined by the average inter-planar d spacing of (Co/Pt)3 multilayers. We also measured the strain curve of PMN-PT (011) single crystal and the result is shown in Figure 1e. An electric field applied along the [011] direction generates a tensile stress along the [01-1] direction and a compressive stress along the [100] direction in PMN-PT (011). The asymmetric strain behaviors for both the [100] and [01-1] directions have been carefully studied by Wu et al and were attributed to the following three reasons: the measurement configuration, miscut of the crystal or slight misalignment of the strain gauge on the crystal, and the complex phase components of the crystal,39 which may also account for our asymmetric strain behaviors. So the aforementioned results of STEM, XRD and strain measurements demonstrate that our samples have the desired properties with good quality.

We first characterized the magnetic anisotropy of our samples without an electric field by using the MPMS. Figure 2a shows the M-H curves measured along the z direction for samples with three representative Co thicknesses of 1.35, 1.4 and 1.45 nm (data for the 1.5 and 1.6 nm thick samples can be found in Figure S1b). As the Co thickness increases from 1.35 nm to 1.45 nm, the out-of-plane magnetization process becomes harder, indicating a reduced out-of-plane magnetic anisotropy, and the 10 ACS Paragon Plus Environment


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saturation magnetization (MS) decreases from about 1675 emu/c.c. to 1525 emu/c.c. The larger MS for the thinner sample can be attributed to the Pt polarization due to the proximity effect.23, 40 To get further information on the magnetic anisotropy of our samples, we performed angle-dependent FMR measurements. As shown in Figure 1a, θH is defined as the angle between the applied magnetic field H and the out-of-plane (z) direction, while φ as the angle between the projection of H in the xy plane and the x direction. For a certain φ, we varied θH to conduct an angle-dependent FMR measurement and the spectra are shown in Figure S1c. For each θH, a resonance field Hr (θH) can be determined from the respective FMR spectrum. To characterize sample’s out-of-plane magnetic anisotropy, the angle dependences of Hr (θH) in the zx and zy planes with ϕ = 0° and 90° , respectively, were obtained as shown in Figure 2b for the zy plane and Figure S1d for the zx plane for different samples. From Figure 2b, one can get the magnetic anisotropy by identifying the local minima of Hr. All three samples with Co thicknesses of 1.35, 1.4 and 1.45 nm present a local Hr minima in both the out-of-plane ( θ H = 0° ) and in-plane ( θ H = 90° ) directions, indicating coexistence of the out-of-plane and in-plane anisotropies. However, a clear evolution exists as a function of Co thickness. For the 1.35 nm thick sample, Hr at θ H = 0 ° is much smaller than that of at θ H = 90° indicating that the out-of-plane configuration is energetically more favorable. For the 1.4 nm thick sample, the minima at θ H = 0 ° is lifted up though it is still smaller than that at θ H = 90° . For the 1.45 nm thick sample, the minima at θ H = 0° surpasses that at θ H = 90° . So the in-plane configuration becomes more favorable with increasing thickness. Such evolution can


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be understood by considering Co thickness driven SRT in our (Co/Pt)3. In other words, the increase in the Co thickness leads to a growing population of domains with the in-plane anisotropy even though both the out-of-plane and in-plane anisotropies are present in the three samples.

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Now we explore the changes of magnetic anisotropy of (Co/Pt)3 multilayers under electric fields. Figure 3a shows the M-H curves of the 1.4 nm thick sample, measured along both the out-of-plane (z) direction and in-plane y direction with and without an electric field (data for the 1.35 and 1.45 nm thick samples are shown in Figure S2). In the out-of-plane direction, the magnetization process becomes harder and the remnant magnetization is reduced when an 8 kV/cm electric field is applied. The situation is opposite for the in-plane direction with an increment of the M-H squareness under an 8 kV/cm electric field as shown in the inset of Figure 3a. These 12 ACS Paragon Plus Environment


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results suggest that application of an electric field enhances the in-plane magnetic anisotropy of (Co/Pt)3 multilayers. The results of the angle-dependent FMR measurements for samples with different Co thicknesses (Figure 3b-d and Figure S3) more clearly reveal electric-field modulation of the magnetic anisotropy. As seen in Figure 3b-d, an electric field induces an obvious increase in the intercept of Hr (θH) in the zy plane at θ H = 0° and decrease in that at θ H = 90° , i.e., the electric field makes the in-plane y direction energetically more favorable for magnetization. For Hr (θH) in the zx plane, however, the electric-field induces the increases of Hr at both θ H = 0 ° and θ H = 90° (Figure S4), indicating that magnetization process along both the x and z directions become harder. The difference for the electric-field modulations of magnetization between the zx and zy planes can be attributed to the different strains along the x ([100]) and y ([01-1]) axes of PMN-PT (Figure 1e). From Figure 2 and Figure 3, one can conclude that a SRT can be driven either by Co thickness or an external electric field in (Co/Pt)3/PMN-PT system.

The SRT in ferromagnetic thin films has been investigated both experimentally27, 41-42

and theoretically.28, 43 The central issue of the SRT is how such transition occurs.

For systems with a uniaxial anisotropy in the z direction, the free energy density f can be expressed as f = K% 1 sin 2 θ M + K 2 sin 4 θ M , where K% 1 = K1 − 12 µ 0 M S 2 .28, 41 Here K1 , K 2 and θ M are the first-order, second-order uniaxial anisotropy constants, and the angle between magnetization and the z direction, respectively. The contribution from the shape anisotropy is now included in K% 1 as the effective uniaxial anisotropy constant. As has been shown by the previous studies,28, 42, 44-46 one can understand the 13 ACS Paragon Plus Environment

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SRT of ultrathin films in an appropriate anisotropy space phase diagram given by K% 1 and K 2 , as shown in Figure 4a, which indicates four regions describing the out-of-plane, canted, in-plane and coexistence phases, respectively, with the

K 2 = − K% 1 2 line (magenta). This diagram reveals that the SRT can happen through either a canting phase ( K 2 > 0 ) or a coexistence phase ( K 2 < 0 ). For our (Co/Pt)3 multilayers, the fact that Hr (θH) only shows minima at 0° and 90° excludes the canting scenario for which it should show a minimum at an angle between 0° and 90° .47 Instead, our data indicate a transition through the coexistence phase. To put

analysis of the SRT on a quantitative footing, we need to determine K% 1 and K 2 in our (Co/Pt)3 multilayers. Following the previous practice,47 this can be done by fitting Hr (θH) with Kittel formula for FMR and the details about Kittel formula and the fitting process can be found in S5 of Supporting Information. In the fitting process, the magnetization of each sample was used. Let us first look at the data without an electric field. The fitting curves are shown as the solid lines in Figure 2b which give ( K% 1 , K 2 ) for each sample. We plot these fitted ( K% 1 , K 2 ) in Figure 4a as the red dots for the case without an electric field. It shows that the 1.35, 1.4 and 1.45 nm thick samples are all in the region of the coexistence phase, while the 1.5 and 1.6 nm thick samples already enter the region of the in-plane phase. Thus a thickness-driven SRT occurs in our (Co/Pt)3 multilayers. More importantly, this transition proceeds through a coexistence phase. It is noted that the SRT can also occur through a canting phase in many other Co/Pt systems.44-45,

48-50

As we mentioned before, the sign of K 2

determines how SRT proceeds. Its value and especially the sign can be affected by 14 ACS Paragon Plus Environment


many factors, such as the chosen substrate, the quality of the seed layer,44 sample growth methods,44-45, 48-50 etc. For our samples studied here, K 2 shows a negative sign which favors a transition through the coexistence phase.

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Figure 3. (a) Out-of-plane magnetic hysteresis loops of the 1.4 nm thick sample with and without an electric field. Shown in the inset is the in-plane magnetic hysteresis loops of the 1.4 nm thick sample with and without an electric field. (b-d) Angle dependent FMR resonance field Hr (θH) in the zy plane with and without an electric-field, and the corresponding Kittel formula fitting for samples with thicknesses of (b) 1.35 nm, (c) 1.4nm and (d) 1.45nm.

Now let us consider the case with an electric field. As noted above, a comparison between Figure 2 and Figure 3 indicates an electric-field driven SRT in our (Co/Pt)3 multilayers. Here we adopt the same method for Figure 2 to analyze the data in Figure 15 ACS Paragon Plus Environment

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3, namely, using K% 1 and K 2 to characterize the system. So one can put all the discussion in the framework of K% 1 - K 2 phase diagram which is well-established for the SRT.28, 42 However, the application of an electric field in our system inevitably creates an in-plane strain anisotropy, which renders f = K% 1 sin 2 θ M + K 2 sin 4 θ M inadequate since an additional energy term should be added to reflect such in-plane anisotropy. To solve this problem, we effectively put the contribution from the in-plane anisotropy into K% 1 and K 2 (Supporting Information S6) as previously adopted,28 so f = K% 1 sin 2 θ M + K 2 sin 4 θ M can still be used in our discussion for Figure 3. We then resort to Kittel formula to fit the FMR data obtained with an electric field to determine K% 1 and K 2 . Such fitting was only carried out for FMR data of the zy plane for which the magnetization also lies in the same plane. While for FMR data of the zx plane, since magnetization doesn’t lie in the zx plane, no analytical expression of Kittel formula is readily available for the fitting. The fitting curves are shown as the red solid lines in Figure 3b-d. Similarly, we plot the fitted ( K% 1 , K 2 ) in the K% 1 - K 2 phase diagram as the blue dots for the case with an electric field. The cyan arrow from the red to the blue dot denotes the electric-field modulation of K% 1 and K 2 for each sample, showing vividly an electric-field driven SRT. We define the electric-field modulation of K% 1 ( K 2 ) as ∆K% 1 =K% 1 ( E ) − K% 1 ( 0 ) ( ∆K 2 = K 2 ( E ) − K 2 ( 0 ) ) and their changes with Co thickness are shown in Figure 4b. Both K% 1 and K 2 decrease with electric field with K% 1 showing larger modulation than that of K 2 . It is also noted that the 1.45 nm thick sample has the largest ∆K%1 ,



which could be attributed to its small initial anisotropy ( K%1 ( 0 ) ≈ 0 J m3 ) that makes it most sensitive to electric field.

Therefore, we demonstrate an electric-field driven SRT in our samples. It should be mentioned that although there have been many reports on the SRT in ferromagnetic thin films or multilayers driven by thickness44-45,

48-49, 51-52

or

temperature,47-48 the work on electric-field driven SRT is rather limited.16 Electric-field driven SRT provides not only a new avenue to explore this interesting phenomenon but also opportunity for applications.

(a)

(b) Out-of-plane

Canting

-0.2

1.6 nm

1.5 nm 1.4 nm

1.45 nm

-0.4

0.0

% 2 K2 = - K 1

0 kV/cm 8 kV/cm

∆ K (105 J/m3)

5

3

K2 (10 J/m )

0.0

-0.2 -0.4 % ∆K 1

1.35 nm

In-plane

∆ K2

-0.6 Coexistence

-1.0

(c)

-0.5

0.0

0.1

2

1.35 1.40 1.45 1.50 1.55 1.60

0.5

% (105 J/m3) K 1

t (nm)

(d) zy plane

0 kV/cm t*K (mJ/m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.0

z [011]

t × K 2 0 kV/cm

Pt Co

8 kV/cm -0.1

-0.2

d

% t ×K 1

y [01-1] 8 kV/cm

x [100] 1.35 1.40 1.45 1.50 1.55 1.60

t (nm)

Figure 4. (a) K% 1 - K 2 phase diagram. (b) Electric-field-induced changes of K% 1 and K 2 . (c) Plots of t × K%1 ~ t ( t × K 2 ~ t ) with and without an electric field and the


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corresponding linear fitting. (d) Schematic for strain-induced lattice changes at the Co/Pt interface.

Although electric-field driven SRT is demonstrated in our samples, so far it is not clear about the contributions from the bulk and interface magnetic anisotropies separately, which is an important issue in terms of fundamental and applications as mentioned in the introduction. For the thickness driven SRT in Co/Pt multilayers, a common practice is to phenomenologically separate the magnetic anisotropy energy K

into a volume contribution

KV

and an interface contribution

KS

as

27-28 which favor the in-plane anisotropy K = K V + 2 K S t (t is the thickness of Co),

and PMA for Co/Pt multilayers, respectively.27 Below a critical thickness ( −2 K S KV ) the interface contribution outweighs the volume contribution, resulting in a PMA in the system. As the thickness of the Co layer increases, the contribution weight of KV

( K S ) in K increases (decreases), resulting in the change of magnetic anisotropy and the resultant SRT. For the analysis of electric-field driven SRT here, we follow the same practice to separate the bulk and interfacial contributions to the total anisotropy:

K ( E ) = KV ( E ) + 2K S ( E ) t . Here KV ( E ) and K S ( E ) are explicitly written as a function of E. The mechanism of electric-field driven SRT manifest itself in KV ( E ) and K S ( E ) , which is quite different from the thickness driven SRT for which KV and K S are independent of thickness.23, 25-26 That is, in the thickness-driven case, thickness (t) variation doesn’t change K S and KV , but changes the ratio of KV and 2 K S t because of the different thicknesses, leading to the change of K . However, in the electric-field-driven case, the tensile strain along the z direction 18 ACS Paragon Plus Environment


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reduces the Pt 5d-Co 3d hybridization just at the interface due to the increase of the distance between Pt and Co, so the K S is modulated by considering the underlying mechanism as mentioned later. The electric-field driven SRT allows one to investigate the SRT using only one sample and the SRT is determined by the whole sample.

To determine the bulk and interface contributions to K% 1 and K 2 , one can use the formulas K% 1 = K% 1V + 2K% 1S t , K 2 = K 2V + 2 K 2 S t ,28, 42 here t is the thickness of Co layer in

the

(Co/Pt)3

multilayers.

These formulas can

be

rewritten as

t × K% 1 = t × K% 1V + 2 K% 1S , t × K 2 = t × K 2V + 2 K 2 S to determine the K% 1V ( K2V ) and

K% 1S ( K 2S ) by plotting t × K% 1 ~ t ( t × K% 2 ~ t ), in which K% 1V ( K2V ) is the slope and K% 1S ( K 2S ) is half of the intercept at t = 0 . Figure 4c shows such plots for the cases with and without an electric field. For t × K% 1 ~ t , the negative slope indicates a negative volume anisotropy K% 1V , favoring the in-plane anisotropy, while the positive intercept at t = 0 indicates a positive interface anisotropy K% 1S , favoring the PMA. It can be seen that electric field doesn’t change the sign of K% 1V and K% 1S , but their magnitudes.

From

Figure

4c,

we

can

get

K% 1V ( 0 ) = −0.90 MJ m3

and

K% 1S ( 0 ) = 0.65 mJ m2 , which are comparable with those reported in other Co/Pt systems.26-27, 53 Electric-field modulations of K% 1V and K% 1S can also be obtained as

∆K% 1V = K% 1V ( E ) − K% 1V ( 0) = 7960 J m3 and ∆K%1S = K%1S ( E ) − K%1S ( 0) = −0.034 mJ m2 , and the corresponding modulation ratios are 0.88% and -5.2%, respectively. Similar analysis was also applied to t × K 2 ~ t which shows a negative interface anisotropy K 2 S and a negligible volume anisotropy K2V . However, electric-field modulations

of K2V and K 2 S are too small to be resolved within our experimental uncertainty. 19 ACS Paragon Plus Environment

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Thus the main contribution to the electric-field driven SRT comes from the K% 1S modulation.

To understand how electric-field modulates K% 1V and K% 1S , we need to consider the responses of them to the strain transferred from PMN-PT to (Co/Pt)3 multilayers since strain-mediated coupling is involved for electric-field control of magnetism in our samples. The interfacial anisotropy related to K% 1S was first pointed out by Néel to reflect the modification of the spin-orbit interaction due to the lowered symmetry at an interface.26,

54

For the origin of PMA in the Co/Pt multilayers, it has been

demonstrated experimentally that Pt 5d-Co 3d hybridization, which is localized at the Co/Pt interface, causes the enhancement of the orbital magnetic moment leading to the PMA via spin-orbit coupling.55 In principle, the magnetic anisotropy of magnetic multilayers is determined by the spin-orbit interaction, which couples states below the Fermi level and ones above it.56 So, the magnetic anisotropy of magnetic multilayers strongly depends on the neighborhood of the Fermi level and may drastically change as the Fermi level moves. Kyuno et al carefully studied the role of spin-orbit interaction among Co five 3d orbitals in determining the magnetic anisotropy of Co/Pt multilayers by first-principles calculation and found that the two matrix elements d xy H SO d x 2 − y 2

(PMA), while

and

d xz H SO d yz

d x 2 − y 2 H SO d yz ,

contribute to the out-of-plane anisotropy

d xy H SO d xz

and

d 3 z 2 − r 2 H SO d yz contribute to

the in-plane anisotropy, and the combined contributions from all of them result in the magnetic anisotropy of Co/Pt multilayers. And it was also emphasized that the Pt 5d-Co 3d hybridization plays an important role in determining the relative position of 20 ACS Paragon Plus Environment


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the Fermi energy to the local density of states and the resultant magnetic anisotropy. So both experiment55 and theoretical calculation56 suggest the importance of Pt 5d-Co 3d hybridization for the PMA of Co/Pt multilayers, providing a clue for understanding the electric-field modulation of K% 1S in our work. As shown in Figure 1e, electric field generates a strong in-plane anisotropic strain in PMN-PT (011). Moreover, our previous work57-58 showed that a tensile strain is also generated along the z ([011]) direction. The schematic for the lattice change due to the electric-field-induced strains is shown in Figure 4d. It is expected that the tensile strain along the z direction will reduce the Pt 5d-Co 3d hybridization due to the increase of the distance between Pt and Co. According to the previous experimental and theoretical studies mentioned above55-56, such reduction of Pt 5d-Co 3d hybridization will weaken the PMA, which is consistent with electric-field modulation of K% 1S in our work. This is also supported by the theoretical calculation of Kyuno et al,56 which suggests that the tensile and compressive stress along the z direction lead to the reduction and enhancement of PMA for Co/Pt multilayers, respectively, due to the corresponding changes of Pt 5d-Co 3d hybridization. Then how to understand the electric-field modulation of

K% 1V ? Generally, K% 1V includes the shape, magnetocrystalline and magnetoelastic anisotropies23, 25-27 and it usually favors an in-plane anisotropy. To understand the electric-field modulation of K% 1V , we need to consider the magnetoelastic anisotropy since strain-mediated coupling is involved for electric-field control of magnetism in our samples. Here we employ a phenomenological theory of magnetoelasticity in which the magnetoelastic energy density is expressed in terms of the direction cosines 21 ACS Paragon Plus Environment

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of the M vector, αi (i = x, y, z), and the components of the strain tensor εij (i, j = x, y, z).59 For a cubic crystal, it has the following form:59

  1 1 1    Fme = B1 ε11  α12 −  + ε 22  α 22 −  + ε 33  α 32 −   + 2 B2 ( ε12α1α 2 + ε 23α 2α 3 + ε 31α 3α1 ) 3 3 3      where B1 and B2 are the magnetoelastic coupling constants. From this equation, we derived a strain-induced anisotropy change ∆K zy ,v in the zy plane following the previous practices for the (111)-oriented case60

∆K zy ,v =

 B + 2 B2 6v B1 B  ε x − ε y ) + 2 5ε x + ε y + ( ε x + ε y ) × mag  − 1 ( (ε x − ε y ) 6 6  1 − vmag  3

Here, B1 and B2 are related to the magnetostriction constant λ and the elastic stiffness

cij

as

B1 = −3λ100 ( c11 − c12 ) / 2

and

B2 = −3λ111c44 .

By

taking

ε x ( E = 8 kV cm ) = −8 ×10−4 and ε y ( E = 8 kV cm) = 3×10−4 from our experiment (Figure 1e), and other parameters from the literature with c11 = 304 GPa, c12 = 154 GPa, c44 = 75 GPa, υmag = 0.3 and λ100 = λ111 = −2.9 ×10−4 ,56,

∆K zy ,v = 5783 J m3

which

is

comparable

with

our

60

we calculated

experimental

result

( ∆K%1V = 7960 J m3 ). Therefore, electric-field modulations of K% 1V and K% 1S can be understood by considering the strain-induced change of magnetoelastic energy and weakening of Pt 5d-Co 3d hybridization, respectively, and the SRT is mainly due to the electric-field modulation of interfacial anisotropy K% 1S via strain.



(a)

(b) H = 0 Oe

1300

①

400

③

②

300 -8

(d)

-4

0 4 E (kV/cm)

(e) 4 kV/cm

(c) H = 400 Oe

States H = 0 Oe

①

1100

②

③ ②

1000 -8

8

H = 400 Oe

①

1200

(f) 6 kV/cm

-4

0 4 E (kV/cm)

(g)

③

8

(h)

0.3 Hz

8 kV/cm δ f (mHz)

0 kV/cm

M (emu/c.c.)

500 M (emu/c.c.)

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4 µm

60 40 20

-8

-4 0 4 E (kV/cm)

8

Figure 5. (a) M-E curve of the 1.4 nm thick sample without an external magnetic field. (b) The M-E curve of the 1.4 nm thick sample with a 400 Oe external magnetic field along the z direction. (c) Schematic showing the competition between the electric-field-induced in-plane anisotropy and magnetic-field-induced out-of-plane anisotropy with the corresponding energy landscapes to account for the results shown in (a) and (b). The blue arrow stands for the net magnetic moment along the z direction, and the red/green arrows denote the in-plane magnetic moments. The thicknesses of the arrows indicate the magnitude of the magnetic moment. (d-g) MFM images of the 1.4 nm thick sample under different in-situ electric fields. (d) 0 kV/cm. (e) 4 kV/cm. (f) 6 kV/cm. (g) 8 kV/cm. (h) Electric field dependence of the MFM domain contrast.

As shown in Figure 4a, the 1.4 nm thick sample is in the coexistence phase, which is interesting because of the competition between the different anisotropy fields. To get the details about electric-field control of magnetism, magnetization 23 ACS Paragon Plus Environment

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versus electric field (M-E) curves are very useful and have been widely used for electric-field control of magnetism in FM/FE multiferroic heterostructures.

5-12

However, there has been no such report on the coexistence phase of the PMA systems so far. We measured the M-E curves for the 1.4 nm thick sample without and with a magnetic field (400 Oe) along the z direction and the result is shown in Figure 5a-b. Some data obtained with other magnetic fields (100 and 250 Oe) can be found in Figure S7. In such an experiment, we first magnetized the sample with a 1 T saturation magnetic field along the z direction and then removed the magnetic field. Electric field is then swept with 0 8 -8 8 kV/cm sequence, and magnetization along the z direction was measured. As shown in Figure 5a, the magnetization drops from about 480 to 310 emu/c.c. when electric field is increased from 0 to 8 kV/cm, which can be understood as electric-field-induced enhancement of the in-plane anisotropy, which drives the system from the nonequilibrium state to the equilibrium state. However, magnetization is nearly unchanged with further changing electric field. In Figure 5b, similar initial drop occurs as that in Figure 5a. However, unlike that in Figure 5a, a symmetric butterfly-like behavior develops when electric field is further swept between ± 8 kV/cm. Similar butterfly-like electric-field control of magnetism was reported in other system,61 and is originated from the contribution of strain. However, in our (Co/Pt)3 multilayers, such a butterfly-like behavior can be attributed to the competition between the applied magnetic field along the out-of-plane direction and the electric-field enhanced in-plane anisotropy as shown by the schematic in Figure 5c. When both fields are at play (Figure 5b and the right panel 24 ACS Paragon Plus Environment


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of Figure 5c), the portions of the two states (in-plane and out-of-plane) are determined by the competition of the two fields and the corresponding energy landscapes. However, without magnetic field (Figure 5a and the left panel of Figure 5c), the system lacks an enough driving force to overcome the energy barrier to change the portions of the two states, which can account for the fact that no obvious change of magnetization occurs after its initial drop. Namely, simply reducing electric field is not enough to overcome the energy barrier to increase the magnetization. So, in this case, electric field is just a one-way effect for the magnetization modulation.

In order to microscopically study the electric-field induced magnetization change in the 1.4 nm thick sample, we used MFM with in-situ electric fields to measure its magnetic domain structures under different electric fields. The sample was vertically magnetized by a 1000 Oe magnetic field before MFM measurements. Figure 5d-g shows the MFM images on the same area with increasing electric field. The 0 kV/cm state shows significant magnetic domain contrasts, which are likely due to the magnetic domains with out-of-plane anisotropy. The MFM signals (frequency shift ( ∆f ) with the unit of Hz32-33), which are proportional to the out-of-plane magnetic field gradient, mainly originate from domains with out-of-plane magnetization. As electric field is increased from 0 kV/cm to 6 kV/cm, the fine structures of the magnetic domains undergo a complex evolution, i.e. random changes of local magnetic features. At 8 kV/cm, the fine domain structures suddenly disappear, resulting in a smooth MFM image with weak domain contrast and larger feature size (Fig. 5g). This weak MFM contrast state persists with reduction or even 25 ACS Paragon Plus Environment

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changing the sign of applied electric field. The suppression of the domain contrasts indicates a reduced out-of-plane magnetization, which is consistent with the enhanced in-plane anisotropy by electric fields. Figure 5h shows the electric field dependence of MFM domain contrasts, which are estimated by the “roughness” (rms) values of MFM images. Once induced by an 8 kV/cm electric field, the weak magnetic contrast state persists with further changing of applied electric field, indicating an irreversible change of magnetic anisotropy. It is noted that when the electric field is increased from 0 to 8 kV/cm, both the MFM domain contrast and Mr decrease to relatively lower values. However, the maximum values of MFM contrast and Mr occur at different electric fields. It can be understood as follows: the former and the latter are the microscopic and macroscopic results, respectively. In other words, the MFM image contrast is the signal of only a small area (15 × 15 µ m ) while the Mr measured by the MPMS is the total magnetization of the whole sample, which may contribute to the difference of the two behaviors. Our MFM results provide a microscopic evidence of electric-field induced magnetic anisotropy change in the (Co/Pt)3 multilayers.

CONCLUSIONS

In summary, we have studied the electric-field control of magnetism of (Co/Pt)3 multilayers with different Co thicknesses grown on PMN-PT (011) FE substrates. Electric-field driven SRT was observed, and electric-field-induced changes of the bulk and interface magnetic anisotropies were separated for the first time. The electric-field modulations of the bulk and interface magnetic anisotropies can be 26 ACS Paragon Plus Environment


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Page 28 of 37

understood by considering the strain-induced change of magnetoelastic energy and weakening of Pt 5d-Co 3d hybridization, respectively, and the SRT is mainly due to the electric-field modulation of the interfacial anisotropy. We also demonstrate the competition between the applied magnetic field and the electric-field in determining the magnetization of the sample with the coexistence phase. This work is significant for understanding the mechanism of electric-field control of magnetism through the strain-mediated coupling in FM/FE multiferroic heterostructures with FM showing the PMA. It will also stimulate research of interface magnetic anisotropy manipulations in other systems where new physics arises at the interface, such as the interfacial Dzyaloshinskii-Moriya interaction and Rashba effect.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: xx.xx/ acsami.xxxxxxx. Characterization of samples’ structures and magnetic anisotropies without an electric field, M-H curves measured under electric fields, FMR measurements in the zy plane with and without an electric field, FMR measurements in the zx plane with and without an electric field, Kittel formula for FMR data fitting, the absorption of the in-plane anisotropy into K% 1 and K2 , and M-E curves for the 1.4 nm thick sample with different magnetic fields (PDF)

AUTHOR INFORMATION 27 ACS Paragon Plus Environment

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Corresponding Author * E-mail: [email protected].

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the 973 project of the Ministry of Science and Technology of China (Grant Nos. 2015CB921402, 2014CB921002), National Science Foundation of China (Grant Nos. 51572150, 11134007, 51522212) and Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB07030200), The MFM work at Rutgers is supported by the Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, U.S. Department of Energy under Award number DE-SC0008147. Ying Sun, You Ba and Aitian Chen contributed equally to this work.

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Table of Contents

750

1.4 nm 0 kV/cm 8 kV/cm OOP

1300

0

-500

0

500

-750

M (emu/c.c.)

M(emu/c.c.)

1500

IP

H = 400 Oe

1200 1100 1000

-1500

Canting

0.0

60

270

90

2400

3200

120

240 210

5

3

300

2400

2800

0 H (Oe)

-0.2

0 kV/cm 8 kV/cm 1.6 nm

1.5 nm 1.45 nm

1.4 nm

-0.4 In-plane

-4

0 4 E (kV/cm)

0.0 -0.1

8 zy plane

0 kV/cm

t × K 2 0 kV/cm

% t×K 1

8 kV/cm

1.35 nm

Coexistence

-1.0

-8 0.1

Out-of-plane %1 2 K2 = - K

150 180

1000

2

1.4 nm

30

K2 (10 J/m )

2800

330

t*K (mJ/m )

-1000 0

3200

Hr (Oe)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 37

-0.5

0.0

% (105 J/m3) K 1

0.5

8 kV/cm

-0.2

1.35 1.40 1.45 1.50 1.55 1.60 t (nm)


Electric-Field Modulation of Interface Magnetic Anisotropy and Spin

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