Spin Hall Magnetoresistance in Pt/BiFeO$_{3}$ Bilayer

Anpeng He(贺安鹏)$^{1}$, Yu Lu(卢羽)$^{2}$, Jun Du(杜军)$^{2\hyperlink{s}{*}}$, Yufei Li(李宇飞)$^{3}$,\\ Zhong Shi(时钟)$^{3}$, Di Wu(吴镝)$^{2}$, and Qingyu Xu(徐庆宇)$^{1,2\hyperlink{s}{*}}$

doi:10.1088/0256-307X/40/11/117402

⇦Chinese Physics Letters, 2023, Vol. 40, No. 11, Article code 117402⇨ Spin Hall Magnetoresistance in Pt/BiFeO$_{3}$ Bilayer Anpeng He (贺安鹏)1, Yu Lu (卢羽)2, Jun Du (杜军)2*, Yufei Li (李宇飞)3, Zhong Shi (时钟)3, Di Wu (吴镝)2, and Qingyu Xu (徐庆宇)1,2* Affiliations 1School of Physics, Southeast University, Nanjing 211189, China 2National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China 3School of Physics Science and Engineering, Tongji University, Shanghai 200092, China Received 28 July 2023; accepted manuscript online 8 October 2023; published online 14 November 2023 ^*Corresponding authors. Email: jdu@nju.edu.cn; xuqingyu@seu.edu.cn Citation Text: He A P, Lu Y, Du J et al. 2023 Chin. Phys. Lett. 40 117402 Abstract Multiferroic materials are general antiferromagnets with negligibly small net magnetization, which strongly limits their magnetoelectric applications in spintronics. Spin Hall magnetoresistance (SMR) is sensitive to the orientation of the Néel vector, which can be applied for the detection of antiferromagnetic states. Here, we apply SMR on the unique room-temperature antiferromagnetic multiferroic material BiFeO$_{3}$ (BFO). The angular dependence of SMR in a bilayer of epitaxial BFO (001) and heavy metal Pt is studied. By rotating the sample under a magnetic field of 80 kOe in the film plane, the resistance shows the maximum when the field is perpendicular to the current while it shows the minimum when the field is along the current. This can be well explained by the SMR in the bilayer of heavy metal/antiferromagnet with the relative orientation between the Néel vector and current direction. In contrast, the angular dependence of the resistance of Pt directly deposited on a SrTiO$_{3}$ (001) substrate shows a 90$^{\circ}$ shift with the magnetic field rotating in the film plane, which originates from the Hanle magnetoresistance of Pt. The obtained spin mixing conductance at the Pt/BFO interface clearly confirms the efficient spin transmission. Our results provide a possible solution for applications of antiferromagnetic multiferroic materials in spintronics.

DOI:10.1088/0256-307X/40/11/117402 © 2023 Chinese Physics Society Article Text Ferromagnetism and ferroelectricity are two important physical properties widely used in information storage technologies. The coexistence of these two properties in single-phase multiferroic materials may provide mutual manipulation by the magnetic and electric fields, which can fulfill the urgent demand for the rapid development of modern information technologies of high compactness, low power consumption, and multifunction, etc. However, the empirical contradicting rules for magnetism and ferroelectricity make single-phase multiferroic materials very rare.[1] The reported single-phase multiferroic materials generally have an antiferromagnetic structure.[2] Among them, BiFeO$_{3}$ (BFO) might be the only single-phase multiferroic materials with both above room-temperature antiferromagnetism ($T_{\rm N}\sim 643$ K) and ferroelectricity ($T_{\rm C}\sim 1103$ K).[2] The well-shaped polarization–electric field ($P$–$E$) loops with saturated polarization of about 60 µC$\cdot$cm$^{-2}$ make BFO among the best ferroelectric materials.[3] However, BFO has a G-type antiferromagnetic structure. Though there is a spin canting between the neighboring antiferromagnetic aligned spins, the cycloidal modulation makes the macro-magnetization very small, which strongly limits its applications.[4,5] Though the antiferromagnetic state in BFO can be utilized by integration with thin ferromagnetic film through the exchange bias, the coupling is quite weak with a blocking temperature much lower than room temperature or an easily oxidized interface.[6,7] Thus, it is very plausible to explore other methods to detect the antiferromagnetic structure in BFO, which is converted to an electrical signal directly. Spin Hall magnetoresistance (SMR) was first observed in Pt/Y$_{3}$Fe$_{5}$O$_{12}$ (YIG) bilayers, with simultaneous interconversion between a charge current and a spin current, via the spin Hall effect (SHE) and inverse spin Hall effect (ISHE).[8-10] A charge current ${\boldsymbol J}_{\rm{e}}$ is applied in the film plane of Pt, which generates a spin current ${\boldsymbol J}_{\rm{s}}$ perpendicular to the film plane with spin polarization ${\boldsymbol \sigma}$ parallel to the surface and orthogonal to ${\boldsymbol J}_{\rm{e}}$ due to the SHE. The spin current is reflected back to Pt at the Pt/YIG interface and its strength depends on the relative orientation of ${\boldsymbol \sigma}$ and the magnetization of YIG. The ISHE in Pt induces an additional electrical current from the reflected spin current, which is always parallel to the original one, leading to the observed SMR. The angular dependence of reflectivity of spin current on the orientation of magnetization is an even function. Thus, the contribution from the magnetization of sublattices in antiferromagnet is additive, instead of cancelling. SMR has been observed in the structure with conventional antiferromagnetic layers, such as NiO, SrMnO$_{3}$, and Cr$_{2}$O$_{3}$.[11-14] However, until now, the study of SMR on multiferroic antiferromagnets is still lacking. Recently, Miao et al. reported the SMR in 5% La doped BFO, which exhibits SMR behavior similar to that of the ferromagnet, due to the weak ferromagnetism.[15] In this work, we prepare the bilayer structure of Pt on the epitaxial BFO (001) without a ferromagnetic signal, in which SMR is observed with the typical angular dependence of antiferromagnets. The BFO layer is deposited on single-crystal SrTiO$_{3}$ (STO) (001) substrates by pulsed laser deposition (PLD). During the deposition, the substrate temperature is fixed at 850 ℃ with an oxygen pressure of 2 Pa. The thickness of the BFO layer is controlled by the laser pulse number to be about 60 nm. The BFO sample is taken out from the PLD chamber, and the Hall bar structures of 5-nm-thick Pt are deposited by magnetron sputtering at room temperature, with a base pressure of less than $1 \times 10^{-5}$ Pa and Ar pressure of 0.3 Pa during the film deposition. Though the vacuum condition is broken during the sample transfer from the PLD chamber to the magnetron sputtering chamber, the quality of the interface is ensured by the observation of exchange bias in the BFO/NiFe bilayer prepared under the same procedure.[16] For the study of comparative magnetoresistance (MR), the STO (001) substrates are etched by NH$_{4}$F buffered-HF solutions and then annealed at 950–1050 ℃ for 1–2 h in flowing O$_{2}$ to produce the single-termination step-terrace surfaces.[17] The crystalline structure of BFO film is studied by x-ray diffraction (XRD; Rigaku Smartlab 3) with Cu $K_{\alpha}$ radiation ($\lambda=1.5406$ Å). The $P$–$E$ hysteresis loops are measured by a commercial ferroelectric tester (Precision Multiferroic, Radiant Technologies) with the bottom electrode as the ground. The local ferroelectric properties are measured by an Asylum Research Cypher scanning probe microscope. Olympus AC240TM Pt/Ti-coated silicon cantilevers are used in the piezoresponse force microscopy (PFM) measurements. The magnetic properties are measured by a superconducting quantum interference device-vibrating sample magnetometer (SQUID-VSM; Quantum Design). The angular dependence of longitudinal resistance is measured by a standard four-point probe method at 300 K in a cryostat under a magnetic field of 80 kOe. Figure 1(a) shows the XRD pattern of the BFO layer on the STO (001) substrate. As can be seen, all the peaks are indexed to the pseudo-cubic structure due to the closely matched lattice constants between STO (3.905 Å) and BFO (3.965 Å in the pseudo-cubic structure).[18,19] Due to the smaller lattice constant of STO, compression happens in the film plane of BFO, leading to the elongation of a $c$ lattice constant along the out-of-plane direction. The calculated $c$ lattice constant of the BFO film is 4.07 Å.[3] The ferroelectric property of the BFO film is studied by measuring the $P$–$E$ loops. However, the leakage current of the 60-nm-thick BFO film is too large, which strongly blockades the observation of well-shaped $P$–$E$ loops. To confirm the ferroelectric nature of the BFO film, we increase the thickness to about 450 nm, and a well-shaped $P$–$E$ loop is observed with saturated polarization of $\sim$ 60 µC$\cdot$cm$^{-2}$, as shown in Fig. 1(b). This is consistent with the previously reported epitaxial BFO film.[3] Furthermore, the asymmetry of the coercivity in the $P$–$E$ loop can be clearly observed, showing an obvious shift to a positive electric field. This imprint phenomenon has been commonly observed in BFO thin films, due to the different work functions of the top and bottom electrodes or strain gradient induced defect configurations.[20,21] To further confirm the ferroelectric nature of the 60-nm-thick BFO layer, the in-plane and out-of-plane domain patterns are observed by PFM. The bright regions in Fig. 1(c) show the domains with spontaneous polarization pointing upward, which is consistent with the shift of the $P$–$E$ loop. The much smaller area of bright regions indicates that the spontaneous polarization of the as-deposited BFO layer tends to be aligned downward. Thus, a larger positive electric field is needed to reverse the polarization of these domains, inducing the larger positive coercivity and the shift of the $P$–$E$ loop to the positive electric field. The in-plane domains are shown in Fig. 1(d). The nearly equal area of the contrast indicates equal in-plane domains, showing that there is no predominant alignment of the in-plane spontaneous polarization components.

Fig. 1. (a) XRD pattern, (b) $P$–$E$ loop, (c) out-of-plane domain, and (d) in-plane domain of the BFO layer on the STO (001) substrate. The peaks marked by stars in (a) are from the STO (001) substrate. The thickness of BFO layer in (b) is 450 nm with LaNiO$_{3}$ taken as the conductive bottom layer.

BFO is a G-type antiferromagnetic material, where the magnetic moments of Fe ions are coupled ferromagnetically within the pseudo-cubic (111) planes and antiferromagnetically between the neighboring planes. In the bulk, an additional long-range cycloidal magnetic modulation is superimposed on this antiferromagnetic order, resulting in a rotation of the spin axis with a long period of 62 nm.[22] However, in the epitaxial BFO films, collinear and cycloidal spin structures can be observed, depending on the strain states in the film. By using STO (001) substrates, the BFO tends to have a pseudo-tetragonal structure with a compressed in-plane lattice constant and elongated out-of-plane lattice constant, and the magnetic moments of Fe ions tend to be aligned along the [1$\bar{1}$0] pseudo-cubic direction in the film plane.[22] The field-dependent in-plane magnetization ($M$–$H$) curves are measured at 300 K. By subtracting the magnetic signal from the same batch of STO (001) substrates and the high field linear part, as shown in Fig. 2(a), the magnitude of the net magnetization is negligibly small, confirming the antiferromagnetic nature of the BFO layer. The field-dependent magnetic moment is measured, as shown in Fig. 2(b), for the treated STO (001) substrate at 300 K. The treated STO substrate is diamagnetic. The magnetoelectric coupling in BFO has been confirmed by the electrical manipulation of the exchange bias field with a NiFe layer using a 10% La substitution to suppress the leakage current.[7] According to SMR theory on the bilayer structure consisting of heavy metals (e.g., Pt, Ta, etc.) and antiferromagnetic materials, the modulation of the resistance depends on the relative orientation of the Néel vector ${\boldsymbol n}$ and current direction. However, in antiferromagnets with two antiferromagnetically coupled magnetic sublattices, the Néel vector rotates to be perpendicular to ${\boldsymbol H}$, in contrast to the same direction of magnetization with ${\boldsymbol H}$ in ferromagnets and ferrimagnets.[23] In a simple picture for single antiferromagnetic domain, the SMR can be expressed as \begin{equation} \Delta R\propto n_{\rm t}^{2}, \tag {1} \end{equation} where $n_{\rm t}$ is the transverse direction component of the Néel vector ${\boldsymbol n}$. Thus, a 90$^{\circ}$ shift can be observed, in contrast to the ferromagnets and ferrimagnets. The SMR in antiferromagnet is also called negative SMR.[23]

Fig. 2. (a) The in-plane $M$–$H$ curve of the BFO layer after the subtraction of the magnetic signal from the STO (001) substrate and the high field linear part. (b) The in-plane $M$–$H$ curve of the treated STO (001) substrate for the MR measurement.

Fig. 3. (a) Schematic of the angular-dependent MR measurement with current ${\boldsymbol J}_{\rm{e}}$ applied in the $x$ direction, and the notations of different rotations of the angle $\alpha$, $\beta$, and $\gamma$. [(b), (c)] Illustration of the $\alpha$, $\beta$, and $\gamma$ dependence of the MR curve for Pt/BFO and Pt/STO under an 80 kOe magnetic field at 300 K, respectively.

Figure 3(a) shows the measurement geometry and the definition of axes, with current ${\boldsymbol J}_{\rm{e}}$ (0.5 mA) in the $x$ axis, spin polarization ${\boldsymbol \sigma}$ in the $y$ axis, and film normal in the $z$ axis. The magnetic field ${\boldsymbol H}$ rotates in the $xy$ ($\alpha$ scan), $yz$ ($\beta$ scan), and $xz$ ($\gamma$ scan) planes from 0$^{\circ}$ to 360$^{\circ}$. The SMR ratio is defined as \begin{align} {\rm SMR~ratio}=\frac{\Delta R}{R_{\min}}=\frac{R_{\theta}-R_{\min}}{R_{\min}} , \tag {2} \end{align} where $R_{\theta}$ is the resistance at $\theta =\alpha,\, \beta,\, \gamma$, and $R_{\min}$ is the minimum resistance at $xy,\, yz,\, {\rm and}\, xz$, respectively. By rotating the field in the $xy$ plane, we consider that the variation in MR is dominated by SMR. As can be seen in Fig. 3(b), the resistance shows the minimum when the magnetic field is aligned parallel to the current, but the maximum when the magnetic field is aligned to be perpendicular to the current. This is consistent with the theory of SMR in antiferromagnets, but totally different in the SMR in ferromagnets and ferrimagnets, which shows the minimum with the magnetic field in the $y$ direction and the maximum with the magnetic field in the $x$ direction.[8] The other mechanisms might also contribute to the observed MR effect, such as Hanle magnetoresistance (HMR).[24] However, HMR can be excluded since its behavior is similar to the SMR in a ferromagnet.[25] In the $yz$ plane, the resistance is the minimum when the magnetic field is aligned in the $z$ direction, but is the maximum when the magnetic field is aligned in the $y$ direction. In contrast, when the magnetic field rotates in the $xz$ plane, the resistance exhibits the maximum with the magnetic field in the $z$ direction, but the minimum with the magnetic field in the $x$ direction. To understand this, the multidomain structure should be taken into consideration. It has been pointed out that the BFO film plane is the easy plane, and the Néel vector tends to be aligned in the film plane. Thus, the domain size tends to increase and a tendency to a single domain can be expected with the magnetic field rotating from the out-of-plane direction to the in-plane direction. Thus, when the magnetic field rotates in the $yz$ plane from the $z$ direction to the $y$ direction, more Néel vectors are aligned with the $x$ direction, and the resistance increases. When the magnetic field rotates in the $xz$ plane from the $z$ direction to the $x$ direction, more Néel vectors are aligned with the $y$ direction, and the resistance decreases.[23] To further confirm the SMR contribution from BFO and exclude the other possible contribution, such as ordinary magnetoresistance (OMR), a comparative sample with a Pt layer directly deposited on an STO (001) substrate is prepared. To exclude the possible contribution from any surface contaminations, the STO (001) substrate is treated by the standard method, and only diamagnetism is observed, as shown by the $M$–$H$ curve in Fig. 2(b).[17] As can be seen in Fig. 3(c), the MR behaviors with the magnetic field rotating in the $xy$ and $yz$ planes shows opposite trends to the SMR behavior in BFO, which can be attributed to the HMR in Pt.[25] When the magnetic field rotates in the $xz$ planes, significant MR can be observed, which can be attributed to the OMR in Pt.[12] However, both the values of HMR and OMR are much smaller than those in BFO, confirming the main SMR contribution in Pt/BFO. The thermal effect can also be safely excluded, since its value is estimated to be 3 orders smaller than the observed values. The field-dependent MR is measured with a fixed magnetic field aligned in the $x$, $y$, and $z$ directions, and the results are shown in Fig. 4. In contrast to the positive MR with magnetic field in the $x$ direction but negligibly small MR in the $y$ direction, the field-dependent MR of Pt/BFO exhibits positive MR in the $y$ direction, but is negligibly small in the $x$ direction.[15] This can be explained by that with increasing magnetic field in the $y$ direction, more domains with a Néel vector are aligned in the $x$ direction, leading to the increased resistance and positive MR.[23] The positive MR in the $z$ direction is due to the multidomain structure.[23] As can be seen in Fig. 3, the resistance increases when the magnetic field is rotated from the $z$ to $y$ direction, leading to the smaller positive MR in the $z$ direction. The SMR ratio can be calculated by \begin{align} \frac{\Delta R}{R_{\min}}\approx \theta_{{\rm SH,NM}}^{2}\frac{\frac{2{\lambda}_{{\rm NM}}^{\rm{2}}}{\sigma_{{\rm NM}}t_{{\rm NM}}}{\cdot} G_{\rm r}{\cdot} \tanh^{2}\frac{t_{{\rm NM}}}{2{\lambda}_{{\rm NM}}}}{1+\frac{2{\lambda}_{{\rm NM}}}{\sigma_{{\rm NM}}}{\cdot} G_{\rm r}{\cdot}\coth\frac{t_{\rm NM}}{{\lambda}_{{\rm NM}}}}, \tag {3} \end{align} where $\theta_{\scriptscriptstyle{\rm SH,NM}}$, $\sigma_{\scriptscriptstyle{\rm NM}}$, $\lambda_{\scriptscriptstyle{\rm NM}}$, and $t_{\scriptscriptstyle{\rm NM}}$ are the spin Hall angle, bulk conductivity, spin diffusion length, and thickness of the heavy metal layer (Pt), respectively.[14] Accordingly, the values of $\theta_{\rm{SH,Pt}}=0.1$, $\sigma_{\rm{Pt}}=2.5\times10^{6}\,{\Omega}^{-1}$$\cdot\rm{m}^{-1}$, $\lambda_{\rm{Pt}}=2.4$ nm, and $t_{\rm{Pt}}=5$ nm are used.[15] The spin mixing conductance $G_{\rm r}$ can be estimated to be $1.47\times {10}^{13}\,{\Omega}^{-1}$$\cdot\rm{m}^{-2}$, which is of the same order as that at the Pt/Bi$_{1.05}$La$_{0.05}$FeO$_{3}$ interface.[15] However, the smaller value of $G_{\rm r}$ at the Pt/BFOinterface indicates that the preparation parameters need optimization and the interface quality needs further improvement.

Fig. 4. MR curves of a Pt/BFO bilayer with the magnetic field fixed in the $x$, $y$, and $z$ directions measured at 300 K.

In summary, a bilayer structure of heavy metal Pt and multiferroic antiferromagnet BFO is prepared. The angular dependence of the MR behavior confirms the main contribution of SMR from the antiferromagnet BFO. This clearly demonstrates that the spin current can be effectively reflected at the Pt/BFO interface, and the spin mixing conductance $G_{\rm r}$ is calculated to be $1.47\times {10}^{13}$ ${\Omega}^{-1}\cdot$m$^{-2}$ at room temperature. Our results confirm that the antiferromagnetic structure in multiferroic materials can be transformed to electrical current directly by SMR, which opens a novel avenue of research in multiferroic spintronics. Acknowledgments. This work was supported by the National Key R&D Program of China (Grant No. 2022YFA1403602), the National Natural Science Foundation of China (Grant Nos. 51971109 and 52025012), the Fundamental Research Funds for the Central Universities (Grant No. 2242020k30039), and the open research fund of Key Laboratory of MEMS of Ministry of Education, Southeast University. Anpeng He is grateful to Professor Weiwei Lin and Miss Xiaona Di for technical assistance. References Why Are There so Few Magnetic Ferroelectrics?Multiferroicity: the coupling between magnetic and polarization ordersEpitaxial BiFeO₃ Multiferroic Thin Film HeterostructuresSpiral magnetic ordering in bismuth ferriteEffect of Nd dopant on magnetic and electric properties of BiFeO3 thin films prepared by metal organic deposition methodInterface Ferromagnetism and Orbital Reconstruction in

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