鎳鈀多層膜中的自旋霍爾效應與磁鄰近效應

全文

(1)國立師範大學理學院物理研究所碩士論文 Graduate Institute of Physics, College of Science National Normal University Master Thesis. 鎳鈀多層膜中的自旋霍爾效應與磁鄰近效應 Spin Hall Magnetoresistance and Proximity Effect in the Pd/Ni multilayers. 高銘儀 Ming-Yi Kao. 指導教授：李尚凡. 博士. 蔡志申. 博士. Advisor：Dr. Shang-Fan Lee Dr. Jyh-Shen Tsay 中華民國一○四年七月 July, 2015.

(2) 摘要磁性材料的電阻率會隨著磁場與電流的夾角不同而改變；例如在鐵、鈷、鎳等純元素金屬中，磁場平行於電流方向時其電阻會大於磁場垂直於電流方向的電阻，此效應稱為異向性磁阻(Anisotropy Magnetoresistance, AMR)；當材料是薄膜形式時，在磁場垂直於電流方向部分，又可以分為垂直於膜面(Perpendicular)以及平行於膜面(Transverse)兩種，因為幾何尺寸效應，平行於膜面的電阻率會大於垂直於膜面的電阻率。近幾年的研究中，曾經在釔鐵石榴石(yttrium iron garnet, YIG) 上長 Pt 發現了縱向電阻率與垂直於膜面電阻率大於平行於膜面電阻率 (. )的現象，與以往的異向性磁阻現象不同。為了解釋這樣的現象，有. 兩種不同的方式被提出：其一是因為 Pt 很接近 Stoner 準則，因此 Pt 會被誘導出磁性，而 Pt 層的磁阻貢獻便會產生這樣的現象，稱之為混合式磁阻(Hybrid MR) 或是磁鄰近效應磁阻(Proximity MR)，而另一種理論則是認為因為 Pt 會因為自旋霍爾效應產生自旋流，自旋流會因為磁性層的磁矩方向不同而在介面上穿透或反射，因此影響電阻率，這樣的行為稱為自旋霍爾效應磁阻 (Spin Hall Magnetoresistance)。我們實驗室過去發現了在 Pt/Ni 以及 Pd/Ni 的多層膜結構中，有. 的異常現象，在此研究中確認此現象必須在 Ni 層夠薄，以及 Pd. 夠厚的情形才會發生，並且此結果跟溫度是相關的；此外將樣品退火過後也發生了異常. 的行為，當材料改變為 Ta/Ni 作為對照組時，行為與傳統異. 向性磁阻一致；根據數據，這些異常的結果，是同時跟自旋霍爾效應磁阻以及磁鄰近效應磁阻有關的。關鍵字: 自旋霍爾效應，磁鄰近效應，磁阻. I.

(3) Abstract Metallic ferromagnetic materials exhibit anisotropic magnetoresistance (AMR) effect. For Fe, Co, and Ni, the resistivity measured with current parallel to the applied magnetic field is larger than that with current perpendicular to the applied magnetic field. In thin-film forms, two configurations could be distinguished for current perpendicular to the applied field. One is field in the film plane (transverse MR, TMR), and the other is field perpendicular to the plane (perpendicular MR, PMR). In singlecomposition films, such as Co or Ni films, the effect of longitudinal ML (LMR) is larger than that of TMR, and then the effect of TMR is larger than that of PMR due to ‘Geometric Size Effect’. In recent researches, unusual resistivity in the Pt/yttrium iron garnet (YIG) structure has been reported. The resistivity in the Pt/YIG structure is in the sequence of. . Two different theories were proposed to explain this. result. The one called the Hybrid MR is that the Pt acquires induced magnetization by YIG layer. The other one called spin Hall MR is that the Pd layer generates spin currents by the spin Hall effect, and the spin current reflects or transmits according the magnetization direction in the YIG layer. In our previous studies, we found that in the Pd/Ni and Pt/Ni multilayer structure. In this study, we found that this result is both thickness and temperature dependent. According to our experiment data, we conclude that this result is associated with the Hybrid MR and the spin Hall magnetoresistance concurrently.. Key word: spin Hall effect, proximity effect, magnetoresistance. II.

(4) Contents Abstract(in Chinese) ...................................................................................................... I Abstract(in English) ...................................................................................................... II Contents ....................................................................................................................... III. List of Figures ............................................................................ V List of Tables .............................................................................. X Chapter 1 ........................................................................................................................ 1 Chapter 2 ........................................................................................................................ 5 2.1 General Background ........................................................................................................ 5. 2.1.1 Introduction to Magnetoresistance ................................................................ 5 2.1.2 Anisotropic magnetoresistance (AMR) ........................................................ 5 2.1.3 Giant magnetoresistance (GMR) .................................................................. 7 2.2 Anomalous Hall Effect (AHE) ........................................................................................ 9 2.3 Spin Hall Effect (SHE) .................................................................................................. 11 2.4 Spin transfer torque ....................................................................................................... 13 2.5 Stoner criterion .............................................................................................................. 14. CHAPTER 3 ................................................................................................................ 16 3.1 Optical lithography ........................................................................................................ 16 3.2 Electron beam lithography ............................................................................................ 17 3.3 Sputtering system .......................................................................................................... 19 3.4 Four-probe method ........................................................................................................ 21 3.5 Atomic force microscopy .............................................................................................. 22. Chapter 4 ...................................................................................................................... 27 Chapter 5 ...................................................................................................................... 33 5.1 Resistance measurements in multilayers sample with rotating angle ............................ 34 5.2 Measurements with variable Pd thickness ..................................................................... 40 III.

(5) 5.3 Resistance measurement with varying temperature and rotating field ....................... 45 5.4 Canting angle measurement .......................................................................................... 48 5.5 Anomalous Hall effect measurement ............................................................................ 54 5.6 Measurements after annealing ....................................................................................... 60 5.7 Measurement with inserted Au layer ............................................................................. 65 5.8 MR measurement with changed sample geometry ........................................................ 67 5.9 Ta/Ni multilayer measurement ...................................................................................... 69 5.10 AFM surface structure ................................................................................................. 72. Chapter 6 ...................................................................................................................... 74 Chapter 7 ...................................................................................................................... 78 Reference ..................................................................................................................... 79. List of Figures. Figure 2.1 Magnetoresistance of three Fe/Cr superlattices at 4.2 K .............................. 8 Figure 2.2 Spin valve GMR structure. ........................................................................... 9 Figure 2.3 Schematic figures for right skew-scattering (SS) and left side-jump mechanisms .................................................................................................................. 11 Figure 2.4 Schematic figures for Spin Hall Effect ....................................................... 12 Fig.2.5 Schematic illustration of spin transfer torque.[24] .......................................... 13 Figure 3.1 Left: geometrical pattern of the pad. Right: enlargement of the central part of pad. .......................................................................................................................... 16 IV.

(6) Figure 3.2 The procedure of the making pattern film by a standard lift-off process using electron beam lithography. ................................................................................. 18 Figure 3.3 Sputtering system 1. This system includes four sputtering guns, an ion source, and a pumping system. .................................................................................... 20 Figure 3.4 Sputtering system 2. This system includes two sputtering guns, an ion source, and a pumping system. .................................................................................... 20 Figure 3.5 Schematic for four probe measurement ...................................................... 22 Figure 3.6 Block diagram of atomic force microscope using beam deflection detection. As the cantilever is displaced via its interaction with the surface, so too will the reflection of the laser beam be displaced on the surface of the photodiode. ......... 23 3.6 Schematic illustration of PPMS ............................................................................. 25 Figure 3.7 the Horizontal & Vertical Sample Rotators (from PPMS Horizontal rotator manual) ........................................................................................................................ 25 Figure 3.8 Schematic illustration of persistent switch ................................................. 26 Figure 4.1 MR ratio versus the thickness of Co........................................................... 27 Figure 4.2 The scan direction of the sample and the Hybrid MR ................................ 29 Figure 4.3 Schematic for SMR [15] ............................................................................. 30 Figure 4.4 the MR and AHE results of Pt(3nm)/SiO2(7% Fe) and Pt/YIGBB .............. 31 Figure 4.5 Field dependence of the (a) Hall resistance RH at different temperatures, (b) R∥ and RT for Pt3 nm/Au2 nm/YIG. Insert of (a) shows the temperature dependence of the anomalous Hall resistance RAHE for Pt3 nm/Au2 nm/YIG. Field dependence of the (c) Hall resistance RH at different temperatures, (d) R∥ and RT for Pt3 nm/Au6 nm/YIG .................................................................................................... 32 Figure 5.1.1 sample geometry...................................................................................... 33 Figure 5.1.2 Schematic illustration of field rotation .................................................... 34 Figure 5.1.3 Angular dependence measurement of saturation resistance in the multilayers sample with fixed Pd thickness and changing Ni thickness. .................... 35 Figure 5.1.5 The figure of polar axes from Figure 5.1.4 ............................................. 36. V.

(7) Figure 5.1.6 Resistance measurement with variable temperature in LP rotation of the sample Pd4.8nm/(Ni5nm/Pd4.8nm)20/Si ..................................................................... 38 Figure 5.2.1 the resistance measurement in LP rotation and the MR results of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si ............................................................................... 40 Figure 5.2.2 the resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si........................................................... 41 Figure 5.2.3 the resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd4.8nm/(Ni1.6nm/Pd4.8nm)20/Si........................................................... 41 Figure 5.2.4 the resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd6nm/(Ni1.6nm/Pd6nm)20/Si................................................................. 42 Figure 5.2.5 the resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd7.2nm/(Ni1.6nm/Pd7.2nm)20/Si........................................................... 42 Figure 5.2.6 the resistance measurement in LP rotation and the MR results at 10K of the Pd8.4nm/(Ni1.6nm/Pd8.4nm)20/Si ......................................................................... 43 Figure 5.2.7 ∆ρ/ρ versus the thickness of Pd , the black line P-L means that the perpendicular megnetoresistance(PMR) minus longitudinal magnetoresistance(LMR) and than divided by the perpendicular megnetoresistance(PMR), same method were used in red line and black line...................................................................................... 43 Figure 5.3.1 Resistance measurement in LP rotation with variable temperature of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si sample .................................................................. 45 Figure 5.3.2 Resistance measurement in LP rotation with variable temperature of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si sample .................................................................. 46 Figure 5.3.3 Resistance measurement in TP rotation with variable temperature of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si sample .................................................................. 46 Figure 5.3.4 The ∆ρ/ρ of the LP and TP rotation versus temperature. Red line means that perpendicular resistance(PMR) minus longitudinal resistance(LMR) and than divided by the perpendicularresistance(PMR). Black means that perpendicular resistance(PMR) minus transverse resistance(TMR) and than divided by the perpendicular resistance(PMR) .................................................................................... 46 Figure 5.4.1 Schematic illustration of canting angle determination.[27] .................... 48 VI.

(8) Figure 5.4.2 Magnetic anisotropy versus angle [27].................................................... 49 Figure 5.4.3 ∆R versus field angle for different field changes [27]............................ 50 Figure 5.4.4 the 10K resistance measurement with field rotating in LP plane of the Pd6nm/(Ni1.6nm/Pd6nm)20/Si ..................................................................................... 51 Figure 5.4.5 ∆R versus field angle of the Pd6nm/(Ni1.6nm/Pd6nm)20/Si (θC = 73) ...................................................................................................................................... 51 Figure 5.4.6 ∆R versus field angle of the Pd8.4nm/(Ni1.6nm/Pd8.4nm)20/Si (field in LP plane) ...................................................................................................................... 52 Figure 5.4.7 ∆R versus field angle of the Pd8.4nm/(Ni1.6nm/Pd8.4nm)20/Si (field in TP plane) ...................................................................................................................... 52 Figure 5.5.1 anomalous Hall effect with the applied field rotate in the LP and the Sine fit at 300K of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si .................................................. 56 Figure 5.5.2 anomalous Hall effect with the applied field rotate in the LP and the Sine fit at 10K of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si .................................................... 56 Figure 5.5.3 anomalous Hall effect with the applied field rotate in the LP and the Sine fit at 300K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si .................................................. 57 Figure 5.5.4 anomalous Hall effect with the applied field rotate in the LP and the Sine fit at 10K of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si .................................................... 57 Figure 5.5.5 anomalous Hall effect with the applied field rotate in the TP and the Sine fit at 300K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si .................................................. 58 Figure 5.5.6 anomalous Hall effect with the applied field rotate in the TP and the Sine fit at 10K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si .................................................... 58 Figure 5.5.7 anomalous Hall effect with the applied field rotate in the TP plane under varying temperature and the Sine fit of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si .......... 58 Figure 5.5.8 anomalous Hall effect at 10K and 300K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si ............................................................................... 59 Figure 5.5.9 anomalous Hall effect with field at longitudinal direction at 10K and 300K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si........................................................... 59 Figure 5.5.10 Hall resistance versus temperature with applied field at longitudinal and perpendicular direction of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si .............................. 59 VII.

(9) Figure 5.6.1 Resistance versus field angle and MR after annealing with applied field at transverse direction .................................................................................................. 61 Figure 5.6.2 Resistance versus field angle and MR after annealing with applied field at longitudinal direction ............................................................................................... 61 Figure 5.6.3 Resistance versus field angle and MR before annealing ......................... 61 Figure 5.6.4 After annealing with field at longitudinal direction, the canting angle is about 73 degree. ........................................................................................................... 62 Figure 5.6.5 After annealing with field at transverse direction, the canting angle is about 70 degree. ........................................................................................................... 62 Figure 5.6.6 Anomalous Hall effect after annealing with field rotating in the LP plane (the left one is 300K, the right one is 10K).................................................................. 63 Figure 5.6.7Anomalous Hall effect after annealing with field rotating in the TP plane (10K). ........................................................................................................................... 63 Figure 5.6.9 AHE and PHE after annealing with applied field at longitudinal direction (the left one is 300K the right is 10K). ........................................................................ 64 Figure 5.6.10 AHE and PHE after annealing with applied field at transverse direction(10K). ............................................................................................................. 64 Figure 5.7.1 Pd4.8nm/(Au1nm/Ni1.6nm/Au1nm/Pd4.8nm)20/Si ...................... 65 (the left one is 300K the right is 10K) ......................................................................... 65 Figure 5.7.2 resistance measurement with varying field angle of the Pd4.8nm/(Au1nm/Ni1.6nm/Au1nm/Pd4.8nm)20/Si ............................................. 65 Figure 5.7.3 MR of the Pd4.8nm/(Au1nm/Ni1.6nm/Au3nm/Pd4.8nm)20/Si (the left one is 300K the right is 10K)................................................................................. 65 Figure 5.7.4 resistance measurement with varying field angle of the Pd4.8nm/(Au1nm/Ni1.6nm/Au3nm/Pd4.8nm)20/Si ............................................. 65 Figure 5.8.1 resistance measurement with varying field angle of the Pd4.8nm/(Ni1.6nm/Pd4.8nm)20/Si (From top to down are 300K,150k,10K respectively) ................................................................................................................. 67 Figure 5.8.2 MR at 10K of the Pd4.8nm/(Ni1.6nm/Pd4.8nm)20/Si ........................ 67 VIII.

(10) Figure 5.9.1 resistance measurement with varying field angle of theTa4.8nm/(Ni1.6nm/Ta4.8nm)20/Si(the left one is 300K the right is 10K) ......... 69 Figure 5.9.2 MR measurement at 10k of the Ta4.8nm/(Ni1.6nm/Ta4.8nm)20/Si ... 69 Figure 5.9.3 measure the canting angle of the Ta4.8nm/(Ni1.6nm/Ta4.8nm)20/Si . 70 Figure 5.9.4 AHE with varying field angle at 10k of the Ta4.8nm/(Ni1.6nm/ Ta4.8nm)20/Si(the left one is field in LP plane, the right one is field in LT plane ) . 70 Figure 5.9.5 AHE at 10K of the Ta4.8nm/(Ni1.6nm/Ta4.8nm)20/Si ....................... 70 Figure 5.10.1 AFM measurement of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si ......... 72 Figure5.10.2 AFM measurement of the Pd4.8nm/(Ni1.6nm/Pd4.8nm)20/Si .......... 73. IX.

(11) Lis of Tables Table 2.1 Stoner criterion of materials mentioned in this study……………………15. X.

(12) Chapter 1. Introduction Thousands of years ago, people already used magnet to identify directions. The long history eventually opened the window for the application of magnetic materials and the Magnetism research. In the Nineteenth century, the magnetic materials were applied on motor, which started the second industrial Revolution. As we know, an electron is an elementary particle carries two distinct attributes, one is “charge” and the other is “spin”. Magnetism originates from the “spin” and orbital angular momenta which is the reason why individual atoms contains local magnetic moment. There is an exchange coupling between one atom’s magnetic moment and the neighboring atoms. The Heisenberg model describes the energy between two spins ⃗⃗⃗1 ∙ ⃗⃗⃗ (magnetic moments) S1 and S2 as E = −D𝑆 𝑆2 , where D is a coupling constant. If this coupling constant has negative sign, the magnetic moment are aligned anti-parallel to reach minimum energy. For example, anti-ferromagnet is this kind of materials. In contrast, if the sign changes, magnetic moments are aligned parallel which is the socalled ferromagnet. Before the discovery of giant magnetoresistance (GMR) in 19880, lots of theoretical investigations on the charges and spins of electrons were considered but little experimental results showed the correlation between these two attributes: charge and spin. Magnetoresistance (MR)[1] is a term widely used to mean the change in the electric resistivity due to the presence of a magnetic field. Ferromagnetic materials with metallic conductance exhibit the anisotropic magnetoresistance (AMR) effect [2]. When the sample is placed in an external magnetic field, its conductance depends on the current direction and the magnetization. Normally the resistivity measured with 1.

(13) current parallel to the applied magnetic field is larger than the one with current perpendicular to the applied field. In thin films, current perpendicular to the applied field can be separated into two directions. One is field in the thin film plane (transverse MR, TMR), the other is field perpendicular to the plane (PMR). In single ferromagnet Co and Ni films, LMR is larger than TMR, then larger than PMR due to “Geometric Size Effect” (𝜌𝐿 > 𝜌𝑇 > 𝜌𝑃 ).[3][4][5] AMR is regarded to originate from spin–orbit interactions. The change of resistance (MR ratio) due to the AMR effect is fairly small, a few percent for Ni80Fe20 alloy (permalloy) at room temperature, but this phenomenon is very useful in technical applications. In 1980s, two independent research groups discovered that magnetic layered structure showed considerably large magnetoresistance. They are Peter Grünberg’s group and Albert Fert and his colleagues. Grünberg [6] and his group were investigating the magnetic properties of Fe/Cr/Fe sandwich systems. They measured the magnetic behavior of the two Fe layers by changing the thickness of Cr spacer layers. They are seeking to clarify the role of the Cr layer inserted in between Fe layers initially and found that neighboring Fe layers aligned antiparallelly with certain Cr thicknesses. Real “giant” magnetoresistance was first observed in Fe/Cr multilayers by the group of Fert in 1988 [9] . They were interested in the crucial behavior of the interlayer coupling in the Fe/Cr/Fe structure found by Grünberg’s group and intended to utilize the role of interlayer coupling in a multilayered structure. They growed multilayers of the form (Fe/Cr)n where n could be as high as 60. The Fert’s group saw a magnetizationdependent change of resistance of up to 50%, whereas the German group saw a 10% difference at most, as result of Fert’s use of many more layers and interfaces than Grünberg’s. Although A. Fert showed a much higher MR ratio than P. Grunberg, the underlying physical concepts were identical in both cases. 2.

(14) The mechanism of the GMR was phenomenologically explained rather soon after the discovery by considering the spin-dependent scattering of conduction electrons. The scattering probability for conduction electrons at the interfaces between the ferromagnetic and normal metal layers should depend on the spin direction, up or down. When a multilayer with a specific normal layer thickness was grown and resulted in spontaneously antiparallel aligned ferromagnetic layers, the up and down spin electrons had the same scattering probability. With an applied saturation magnetic field, the magnetization in different layers were aligned to the field direction. The electrons at the interface scatter more if their spin was anti-parallel to the general direction of magnetization than those parallel to the direction of magnetization. Those electrons with spin parallel to the magnetization thus showed short circuit effect and the total resistance was smaller at saturation. The semi-classical theory based on Boltzmann diffusion equation was given by Valet and Fert[7]. After the discovery of GMR, similar system which two ferromagnetic layers are separated by an insulating material has been constructed. This kind of experiment is called Tunnelling Magnetoresistance(TMR). TMR was first discovered in 1975 in Fe/Ge/Co junctions at 4.2 K. TMR has not attract much attention because the variation in resistance value is smaller than 1% at room temperature and the results are difficult to reproduce. Moodera and coworkers reported reliable Al2O3 based tunnel junctions and TMR values in the order of 10% at room temperature[8] . Tunnel barriers of crystalline magnesium oxide (MgO) have been developed recently. Researchers have succeeded in making Fe/MgO/Fe junctions that reach over 200% TMR ratio at room temperature. MTJs comprise two ferromagnets separated by a thin insulator. The electrons can tunnel from one ferromagnet to the other due to the thin nature, about 1 to 3 nm, of the insulating layer. Such behavior opposes the laws of classical physics, making TMR a quantum mechanical phenomenon. 3.

(15) In AMR, the resistivity shown the 𝜌𝐿 > 𝜌𝑇 > 𝜌𝑃 relation. However, in recent years the resistivity relation show some different relations. In 2011, Oepon’s group constructed Pt/Co/Pt trilayer structures and discovered the 𝜌𝐿 > 𝜌𝑃 > 𝜌𝑇 . This result defied the Geometric Size Effect (GSE) in the single ferromagnetic thin film. They called this phenomenon anisotropic interface magnetoresistance (AIMR). [10] In 2012, C. L. Chien’s group measured the magnetoresistance in the Pt/YIG structure. They found that Pt/YIG exhibited a new type of MR with unique characteristics that were very different from those of other known MR phenomena. The results is 𝜌𝐿 ≅ 𝜌𝑃 > 𝜌𝑇 . In our previous work, we observed the unusual magnetoresistance in Ni/Pd and Ni/Pt multilayers, 𝜌𝑃 was larger than 𝜌𝐿 (𝜌𝑃 > 𝜌𝐿 > 𝜌𝑇 ) which has yet been discovered. In the samples with numbers of bilayer larger than 20, Pd thickness larger than 3 nm, and Ni thickness thinner than 2nm, we observed regular AMR behavior at 300 K and the unusual magnetoresistance at 10 K. The transition temperature was around 100 K. We also fabricated Current perpendicular plane (CPP) Ni/Pd multilayer sample, but there were no unusual magnetoresistance transition in the CPP samples. Besides, in Anomalous Hall effect measurement, there were no relation between unusual magnetoresistance and perpendicular magnetic anisotropy. According to our data, we thought the unusual magnetoresistance is caused by the interface, there might be some different mechanism of magnetic origin to cause it. In order to clarify the underlying physical meanings of our results, I fabricated samples with the geometry 800 nm wide and 20 micron long, and did a series of experiment to understand the mechanism of our results. I try to establish a model to describe the mechanism.. 4.

(16) Chapter 2. 2.1 General Background 2.1.1 Introduction to Magnetoresistance External field can influence the resistivity, including the electric field and magnetic field. The external field deflects the path of the current and cause the increase of resistance. When an electron begins to orbit around the magnetic field, it does not contribute to the current density until it is scattered. After scattering, it begins its next cyclotron orbit, with an initial velocity biased toward the applied field[16]. MR means that the value of the electrical resistance will be changed when an external magnetic field is applied. Ordinary MR is caused by the effect of the classical Lorentz force. The MR increases when the probability of collision between the electron and the heavy-ion nuclear increases with increased moving path. The MR ratio is defined as the ratio of the change in resistance when the field is applied to the resistance at zero, as follows, MR ratio= (RH-R0) / R0 =ΔR / R If the magnetic field increases the resistivity, it is referred to as positive MR. If the resistance value decreases, it results in a negative MR effect.. 2.1.2 Anisotropic magnetoresistance (AMR) The AMR of a magnetic material means that the resistance is dependent on the angle between the measuring current and the magnetization of materials when an external field is applied. AMR is originated from a larger probability of s-d scattering of electrons with different direction of the magnetic field. 5. In most cases, when the.

(17) applied filed direction is parallel to the direction of current, the resistance (Rparallel) increases with the applied field, whereas when the current flows perpendicular to the direction of the magnetic field, the resistance (Rperpendicular) decreases with the applied field. The effect is small but has significant application value. The origin of AMR lies in the spin-orbit coupling [17]. When the magnetization direction is perpendicular to the current direction, the scattering cross-section is decreased compared with the zero-field case, whereas when the magnetization direction is parallel to the current direction, the scattering cross-section is increased compared with the zero-field case. A phenomenological theory of AMR is introduced as follows. Let the magnetization M is in the z-direction, and the angle between magnetization M and the current J isθ. The relationship between the electric field E and the current J can be written down as the following equation: 𝐸𝑥 𝜌⊥ (𝐸𝑦 )=(𝜌𝐻 0 𝐸𝑧. 𝜌𝐻 𝜌⊥ 0. 𝐽𝑥 0 0 ) (𝐽𝑦 ) 𝜌∥ 𝐽𝑧. The 𝜌𝐻 in the equation above is the Hall resistivity, and the 𝜌⊥ and the 𝜌∥ are the resistivity when the current flows perpendicular and parallel to the direction of the ⃗ ∙ J/E 2 between the electric field magnetic field, respectively. Using the relation ρ=E and the current to express the total resistivity, we obtain ρ = ρ + (ρ − ρ ) cos2 θ ⊥. ∥. ⊥. When the samples are polycrystalline, it should be averaged over the angle to give ρ = ρ + (ρ − ρ ) ∕ 3 ≡ ̅̅̅ ρ ⊥. ∥. ⊥. When H ∥ M, ρ = 𝜌∥ andH⊥ M, ρ = 𝜌⊥ , one may define the MR ratio as △ ρ ρ∥ − ρ⊥ = ̅̅̅ ̅̅̅ ρ ρ 6.

(18) 2.1.3 Giant magnetoresistance (GMR) The GMR phenomenon was discovered in 1988 in Fe/Cr/Fe trilayers [6]. It was simultaneously but independently discovered by Baibich et al. in Fe/Cr multilayers [9]. Data from the original paper of Fert’s group are shown in Figure 2.1. The MR ratio in the GMR is much larger than other known MR before such as AMR. In GMR effect, the spin polarized current can be controlled by the parallel or antiparallel arrangement of the magnetization in the multilayer. This can be viewed as the origin of Spintronics. Magnetic coupling effect can be observed in thin film structures which are constructed by the ferromagnet and normal metal multilayers. Without any applied field, the directions of magnetization of adjacent FM layers can be spontaneously coupled antiparallelly due to anti-ferromagnetic coupling through the normal metal layers, resulting in high-resistance. While an external magnetic field is applied, the magnetizations of all FM layers are rotated into the parallel state, leading to lower magnetic scattering, and less resistance. The coupling through the normal metal layer, which is a modified RKKY nature, depends on the band structure and can be oscillatory from antiparallel to parallel for several periods from 0.5 to 5 nm. The effect is exploited commercially by, e.g., manufactures of hard disk drives.. 7.

(19) Figure 2.1 Magnetoresistance of three Fe/Cr superlattices at 4.2 K. The current and the applied field are along the same (110) axis in the plane of the layers[9]. There is an alternative name, the spin valve effect. As the Figure 2.2 shown, it is a trilayer structure contains the top and down FM electrode layers and the thin nonferromagnetic spacer layer inserted between two FM layers. There is no RKKY coupling inside this structure so that when the applied field is low, the direction of magnetization of adjacent FM layers should not be antiparallel. However, we can change the switching behaviors by regulating the thickness of two FM layers. With different thickness of two layers, their coercive should be different, too. Thus, parallel and anti-parallel alignment can be achieved. Normally, the resistance is higher in the anti-parallel case. Research on spin valves is focused on increasing the MR ratio by practical methods such as enhancing the resistance between individual layers interfacial resistance or use half-metallic layers inserted into the spin valve structure. The magnetic properties of nanostructures are dominated by surface and interface effects due to the high local ratio of atoms as compared to the bulk. To maximize the GMR ratio and yield 8.

(20) high performance from the spin valve, it is important to determine the optimal resistance and polarization of the interface between the layers. The configuration that currently yields the highest GMR is the current-perpendicular-to-plane (CPP) spin valve device.. Figure 2.2 Spin valve GMR structure.[by wiki]. 2.2 Anomalous Hall Effect (AHE) Before introducing the Anomalous Hall Effect, we must consider the spin orbital interaction first. Spin orbital interaction is a relativistic effect and the corresponding Hamiltonian is given by 𝐻𝑆𝑂 = −. 𝑒ℏ 𝑒 𝑑𝑉 (𝜎 ∙ [𝐸 × 𝑃]) ≅ ( )(𝑠 ∙ 𝑙) 4𝑚2 𝑐 2 2𝑚2 𝑐 2 𝑟𝑑𝑟. , where c is the light velocity, E is an electric field induced by a potential gradient dV/dr , 9.

(21) 𝜎 is the Pauli matrix and l is the orbital angular momentum. The spin orbital interaction can be separated into two parts, extrinsic SOI caused by impurity potentials and intrinsic SOI caused by intrinsic material structure. The Hall effect was discovered in 1879 by Edwin Hall [20]. He found that the path of the current can be deflected under external magnetic field, thus, has the charge accumulation at the edge of the sample. This is the so-called “ordinary” Hall effect in which the electrons are deflected into the direction of Eext ×Hext due to the Lorentz force. In ferromagnets, the Hall effect consists of two contributions, the ordinary Hall effect and the “anomalous” Hall effect [21][22] being proportional not to Hext but to the magnetization M of the ferromagnet. The Hall resistivity ρ. 𝐻. is thus given as 𝜌𝐻 =. 𝑅0 𝐻 + 4𝜋𝑅𝑆 𝑀. The first and second terms are the ordinary and anomalous Hall effect, respectively. Coefficients 𝑅0 and 𝑅𝑆 are called as ordinary and anomalous Hall coefficient, respectively. In ferromagnetic materials, 𝑅0 is usually much smaller than 𝑅𝑆 so that it can be ignored. In experiments, with increasing Hext, 𝜌𝐻 changes rapidly at first, and then tends to increase in proportion to H. The initial rapid change in 𝜌𝐻 is dominated by the alignment of the domain magnetization. After the alignment of the domain magnetization, 𝜌𝐻 changes in proportional to Hext. The constant increment gives the value of R0, and the extrapolated value of 𝜌𝐻 to Hext=0 gives the value of 4πRsM. To explain the extrinsic mechanisms of the Anomalous Hall Effect, skew-scattering and side-jump have been employed.. 10.

(22) Figure 2.3 Schematic figures for right skew-scattering (SS) and left side-jump mechanisms In SS mechanism, the spin up and spin down electrons are scattered into opposite directions as shown in Figure 2.3. On the other hand, in SJ mechanism, there occurs a displacement of the electron path as shown in Figure 2.3. In ferromagnets, the number of the spin up and spin down are not equal at the Fermi level, which makes the spin up and spin down charge Hall currents asymmetric and produces the spin polarization current at the transverse direction which is proportional to the spin polarization, that is, magnetization.. 2.3 Spin Hall Effect (SHE) As mentioned in the Anomalous Hall Effect, the extrinsic AHE appears due to spindependent scattering. The spin up and spin down electrons are scattered into opposite directions, resulting in spin-up and spin-down charge Hall currents along the perpendicular direction of current direction. The intrinsic spin imbalance makes the two charge Hall currents asymmetric and produces a Hall voltage in ferromagnetic materials. For non-magnets, the spin up and spin down remains to separate into opposite directions due to spin scattering. However, the number of spin up and spin down electrons are equal, so that the number of electrons at the two sides of the sample are equal. This causes no Hall voltage but the pure spin current at the direction perpendicular to the 11.

(23) charge current. The pure spin current originate from this mechanism is called Spin Hall Effect (SHE). SHE is shown in Figure 2.4 When the spin Hall current is originated from scattering of electrons by impurity potentials with SO interaction, the effect may be called “extrinsic” SHE.. Figure 2.4 Schematic figures for Spin Hall Effect[23] The SHE does not accompany a Hall voltage, we cannot measure the spin current easily by conventional electrical measurement. However, the spin polarization at opposite edge should be different even without the applied magnetic fields. The first evidence of SHE is measure by optically detecting the spin accumulation at the sample edge. Kato et al [23] spatially resolved the Kerr rotation of the reflected light from n-type bulk GaAs and InGaAs samples and found accumulation of opposite spins at the two edges of the sample.. 12.

(24) 2.4 Spin transfer torque When spins are injected from one ferromagnetic layer (FM1) into another ferromagnetic layer (FM2), this spin injection gives rise to a torque on the FM layers. As a result, one of the FM layers will switch its magnetization direction, as shown in Fig.2.5. A typical device consists of two ferromagnetic layers (FM1 and FM2) and a non-magnetic layer (NM1) inserted as the spacer layer. When current is passed through this device, the electrons are first polarized by the FM1 and then injected into the FM2 through the NM1. The spins of the injected electrons interact with the spins in the ferromagnetic layers by exchange interaction and exert torque. If the spin density is large enough, the exerting torque can reverse the magnetization in FM2 or continuous precession is excited.. Fig.2.5 Schematic illustration of spin transfer torque.[24]. To simplify the problem, let us imagine an electron system in which the conduction electrons (s orbital) and the electrons that dominating local magnetic moments (d orbital) interact with each other through exchange interactions. The exchange interaction (s–d exchange interaction) conserves the total spin angular momentum. Therefore, a decrease in the s-orbital angular momentum equals the increase in the d-orbital angular 13.

(25) momentum. In the magnetic multilayer, if the spin angular momentum of a conduction electron changes because of the s–d interaction during transport through the FM2 layer, this amount of angular momentum should be transferred to the d-electrons in the FM2 layer. As the following equation shows: 𝑑𝑠⃗⃗⃗⃗2 𝑑𝑡. = 𝑗1𝑠 -𝑗2𝑠. , where 𝑠2 is the total angular momentum in the FM2. The spin currents 𝑗1𝑠 and 𝑗2𝑠 are obtained by integrating the spin current density flowing in NM1 and NM2 over the cross-sectional area of the multilayer. Since FM2 is very thin, we neglect the spin–orbit interaction in FM2. The equation above indicates that a torque can be exerted on the local angular momentum as a result of spin transfer from the conduction electrons. This type of torque, is called the “spin-transfer torque”.. 2.5 Stoner criterion Stoner criterion is used to determine whether a material is ferromagnetic or not. If the Stoner criterion is satisfied, the material is ferromagnetic. If it is close but not satisfied, the material may acquire an induced magnetization by the proximity of other ferromagnetic material. Stoner criterion is expressed as , where I is the Stoner exchange parameter and D(EF) is the density of states at the Fermi energy. The following table is the Stoner criterion of materials mentioned in this study. 14.

(26) Table 2.1 Stoner criterion of materials mentioned in this study [29]. 15.

(27) CHAPTER 3 Experimental facilities and measurement methods 3.1 Optical lithography Optical lithography was used to make the electrode for the electronic transport measurement. After making the electrodes on the Si substrate, we use e-beam lithography to define the microscale and nanoscale sample geometry. Optical lithography refers to a lithographic process that uses visible or ultraviolet light to form patterns on the photoresist through printing. The advantage of the optical lithography is fast and having the larger printing sample size. In optical lithography procedure, the substrate is covered with a photoresist by spin coating. The photoresist used in our case is S1813. After coated on the substrate, the photoresist is exposed by the visible or ultraviolet light. The photo mask, composed of glass or quartz, are usually used to cover areas of photoresist layers that shouldn’t get exposed to light. After exposure, the substrate was put into a developer solution, MF319, to produce a resist pattern on the substrate. The Ti 10 nm and Au 50nm were deposited on the resist pattern. Finally, we used remover PG to remove the photoresist and the film upon it.. Figure 3.1 Left: geometrical pattern of the pad. Right: enlargement of the central part of pad. 16.

(28) 3.2 Electron beam lithography For the sample fabrication process, the optical lithography is restricted by the optical diffraction limit because the wavelength of the incident light is too long so that it is hard to fabricate nanoscale samples. Recently, the electron-beam lithography is the main technique for fabricating nano-scaled samples. Here, our samples were fabricated by a standard lift-off process using electron-beam lithography. The sample fabrication procedure combined electron-beam lithography and a standard lift-off technique as illustrated in Fig. 3.2. (a) We prepare a clean Si substrate coated with an insulator layer SiO2. (b) The electron resist, polymethyl methacrylate (PMMA 4A), is covered onto substrate by spin coating method with 4000 rpm for 25 sec and then baked by a hot plate at 135 °C for 1 hour. (c) The electron resist is exposed by the electron beam. (d) Exposed PMMA is developed using the methylisobutyl ketone (MIBK) first with developing time 1 m and then put into isopropyl alcohol +(IPA) for 30 s. (e) After development, resist pattern was produced. (f) Film deposition. (g) Liftoff. By using Ultrasonic Cleaner with the remover, acetone, the resist and the film upon are removed. (h) Pattern is transferred onto the wafer.. 17.

(29) PMMA. Substrate. Spin coating PMMA Electron beam. After development. PMMA. Substrate. Exposure using the electron beam. Evaporating metals. MIBK:IPA. Acetone PMMA. Development using MIBK/IPA. Substrate. Lift-off using acetone Substrate. Figure 3.2 The procedure of the making pattern film by a standard lift-off process using electron beam lithography. 18.

(30) 3.3 Sputtering system. Samples were deposited by two different sputtering chambers to avoid that our abnormal magnetoresistance is due to the sputtering system problem. In the sputtering system 1, four dc/rf sputtering guns and an ion source are included, as shown in Fig. 3.3. This system is evacuated using a mechanical pump and a turbo-molecular pump. We use mechanical pump to rough pump to 0.02torr to avoid damaging the flabellum of the turbo pump. The base pressure can be achieved is less than. 7×10-7 Torr with. turbo-molecular pump. The working pressure is 1.2×10-3 Torr with Ar inlet.. The second sputtering system has two dc/rf sputtering guns and an ion source, is evacuated using a cryopump which provided a high pumping power equipped with no oil vapor contamination. The system is first roughly pumped to 0.02 torr with a mechanical pump to avoid the cryopump to absorb too much gas molecules. The base pressure can be achieved is less than 2×10-7 torr with the cryopump. The sputtering gas comes from a cylinder of ultrahigh purity Ar (99.999%), as Figure 3.4 shows.. 19.

(31) Figure 3.3 Sputtering system 1. This system includes four sputtering guns, an ion source, and a pumping system.. Figure 3.4 Sputtering system 2. This system includes two sputtering guns, an ion source, and a pumping system.. 20.

(32) 3.4 Four-probe method To determine the value of a resistance, we may connect two leads to an Ohmmeter and read off the value. However, if the resistance we are trying to measure is very small. A voltage source may damage your sample due to the high current density induced Joule heat. To avoid the problem mentioned above, we often determines the resistance of a sample by passing through a fixed current I, measuring the resulting voltage drop ΔV, and performing the division to get R = ΔV/I. This might be a direct current, or it might be an alternating current. The constant-current circuit allows us to determine the sample resistance with a very small current, eliminating the possibility of damage to the sample, especially for an ultrafine wire. However, the sample resistance might be so small that the resistance of the leads running to the sample might be significant by comparison. A related problem is that of contact resistance. The four-probe method is the most common way to separate out the resistivity of conducting materials. As shown in Figure 3.5, two of the probes are used for applied current source and the other two probes are used to measure voltage. By separating the current contacts from the voltage contacts we are able to distinguish the sample resistance from that of the contacts and connecting wires. If the voltmeter has an infinite input impedance, no current will flow through the voltage contacts, and the measured voltage drop V is across the portion of the sample that is between the two voltage contacts.. 21.

(33) Figure 3.5 Schematic for four probe measurement. 3.5 Atomic force microscopy Atomic force microscopy (AFM) probes the surface of a sample with a sharp tip, a couple of microns long and often less than 100Å in diameter. The resolution of AFM is usually 100 times better than the optical diffraction limit. The tip is located at the free end of a cantilever that is 100 to 200 μm long. The tip will bend or reflect when it is scanned through the sample surface. There is an incident light injected to the cantilever that will be reflected. We can detect the reflected light angle to determine the sample surface topography indirectly, as Figure 3.6 shows. Several forces typically contribute to the deflection of an AFM cantilever. An inter-atomic force known as van der Waals’ is most commonly associated with AFM. Compare to other microscopy, such as optical microscope and an electronic microscope, the major advantage of AFM is that it has no lens and beam irradiation. Therefore, the resolution will not be limited by the diffraction limit.. 22.

(34) Figure 3.6 Block diagram of atomic force microscope using beam deflection detection. As the cantilever is displaced via its interaction with the surface, so too will the reflection of the laser beam be displaced on the surface of the photodiode. (By wiki). 23.

(35) All of the CIP resistivity measurements in our study were performed in the Quantum Design Inc. physical property measurement system (PPMS). The PPMS can provide an experimental environment in the temperature range of 1.9 to 400 K and magnetic field of 9T by low noise bi-polar power supply. In the DC Resistivity option, the current range is from 5 nA to 5 mA and voltage sensitivity is 20 nV. Moreover, the option of AC Transport measurement system (ACT) contains a precision current source and voltage detector providing four different types of automated, electrical transport measurements: AC resistivity, five-wire Hall effect, I-V curve, and critical current.. 24.

(36) 3.6 Schematic illustration of PPMS The sample is first put on the Horizontal & Vertical Sample Rotators, and the rotators is inserted in the sample chamber. The sample chamber can be pumped to 15 torr to avoid thermal drift effect. The sample chamber is put in the vacuum flask which is equipped with liquid He to lower the temperature. Next to the sample, there is a thermal circuit to raise the temperature. The thermal circuit is controlled by the PID circuit.. Figure 3.7 the Horizontal & Vertical Sample Rotators (from PPMS Horizontal rotator manual). 25.

(37) The magnet current can control the field induced by the superconducting magnet coil. The current flow into the superconducting magnet coil is controlled by a well-designed persistent switch. As Figure 3.8 shows, the left one is superconducting magnet coil, the middle is the heater, and the right one is power supply.. Figure 3.8 Schematic illustration of persistent switch. 26.

(38) Chapter 4 In 2011, Oepon’s group constructed Pt/Co/Pt trilayer structures and discovered that when the current passed through the sample, which was parallel to the interface, the resistivity had an abnormal result when the field was rotate in the plane perpendicular to the current direction. That is the resistivity of field perpendicular to the plane (Perpendicular MR, PMR) was larger than the one with field parallel the plane (Transverse MR). This result defied the Geometric Size Effect (GSE) in the single ferromagnetic thin film. As Figure 4.1 shows, they changed the thickness of Co in the Pt/Co/Pt structure and discovered that the MR ratio increased with the increasing Co thickness when the Co thickness was thinner than 7nm. But when the Co thickness was larger than 7nm, the MR ratio decreased with the trend of 1/tco. They considered this particular magnetoresistance phenomenon to be unrelated to the inner part of Co layer. Therefore, this phenomenon was due to the Pt/Co interface contribution. They called this phenomenon anisotropic interface magnetoresistance (AIMR). [10]. Figure 4.1 MR ratio versus the thickness of Co [10]. 27.

(39) In the last decade, there have seen growing interest on research in spintronics such as Spin Hall Effect (SHE)[11][12], spin Seeback Effect (SSE)[14] and spin pumping Effect [13]. Take Spin Hall Effect for example, SHE can convert a charge current in a nonmagnetic metal, which has strong spin-orbit coupling (SOC), into a pure spin current in the transverse direction. Although this spin current cannot easily be detected by usual electrical measurement method, it can be detected by some pure spin detectors. When passes through materials with strong SOC, the spin current converts into charge current resulting in charge accumulation in the transverse direction and a voltage drop, which can be detected easily. Pt is the most popular pure spin detector due to its large SOC. Pt/YIG (yttrium iron garnet, Y3Fe5O12) bilayers have been widely investigated due to the essential roles mentioned above. In 2012, C. L. Chien’s group measured the magnetoresistance in the Pt/YIG structure. They found that Pt/YIG exhibited a new type of MR with unique characteristics that were very different from those of other known MR phenomena, as shown in Figure 4.2. Pt/YIG shows a pronounced MR (Longitudinal MR equal to Perpendicular MR, both were larger than Transverse MR). As we know, Pt is a normal metal with no ferromagnetic characteristics, and YIG is an insulator. Therefore Pt and YIG should not show MR phenomenon individually. Because Pt is a material which is close to the Stoner Criterion, it will acquire induced magnetization by YIG layer and causes the MR effect. Pt is a well-known material with strong spin orbital coupling (SOC) and has usually been used as a spin current detector. In the emerging spintronic research, the relation between magnetic proximity effect (MPE) and pure spin current detector must be examined carefully.. 28.

(40) Figure 4.2 The scan direction of the sample and the Hybrid MR [?].. E. Saitoh’s group from Japan proposed a different aspect to explain the abnormal magnetoresistance in the Pt/YIG structure. They published Spin Hall magnetoresistance theory in Physic Review Letter in 2013. In their theory, the charge current pass through the Pt layer will be converted into a pure spin current in the transverse direction. With spin-angular-momentum exchange between magnetization M in YIG and conductionelectron spin polarization in Pt, Spin-flip scattering is activated when the spin direction of spin current and M are not collinear. Some part of the spin current is then absorbed by the magnetization as a spin-transfer torque even at an interface to a magnetic insulator and the spin current reflection is suppressed. This absorption is maximized if M is perpendicular to the spin direction and zero if parallel. When the absorption is zero, the reflected spin current will be converted into charge current due to the inverse Spin Hall effect (ISHE), which enhances the conductivity. Conductivity enhancement due to SHE and ISHE is expected to be maximized (minimized) when M is in transverse (longitudinal and perpendicular) direction. The Pt film resistance is therefore affected by the magnetization direction in YIG, giving rise to the spin Hall magnetoresistance (SMR)[15].. 29.

(41) Figure 4.3 Schematic for SMR [15]. To further investigate the physical origin of hybrid magnetoresistance, C. L. Chien’s group did two measurements on the altered YIG surface and use SiO2(7% Fe) to replace the YIG in 2014[26]. The altered YIG surface called the YIGBB greatly reduces the spin-mixing conductance at the Pt/YIG interface, thus, blocking the spin current transmission. In SiO2(7% Fe) sample, the concentration of the Fe is too low to be ferromagnetic, but it still contains Fe composition so that the SiO2(7% Fe) still can simulate the MPE but without spin current. Interesting results shown in Figure 4.4, Pt(3nm)/SiO2(7% Fe) exhibits very similar MR behavior to that of Pt/YIGBB at all fields. However, the Pt(3nm)/SiO2(7% Fe) and Pt/YIGBB show different results to that of conventional Pt/YIG at small field. The Pt(3nm)/SiO2(7% Fe) and Pt/YIGBB show the same angular dependence as that of Pt(3nm)/YIG. All of them exhibit (cos 𝜃)2 angular dependence in the ϕxy scan and θyz scan with saturation field. Hence, they claim that in the Pt/YIG sample, the SMR influences the results at small field while the MPE dominates at high field.. 30.

(42) Figure 4.4 the MR and AHE results of Pt(3nm)/SiO2(7% Fe) and Pt/YIGBB. [26]. Au is a material used as a spin current detector with a relatively long spin diffusion length. Besides, Au is far from the stoner criteria so that it couldn’t have magnetization induced by the YIG. Therefore, if the Au is inserted into the Pt/YIG, the MPE will diminish but the spin Hall magnetoresistance should survive. C. L. Chien’s group did the experiment as mention above. Interesting results were obtained as shown in Figure 4.5.. 31.

(43) Figure 4.5 Field dependence of the (a) Hall resistance RH at different temperatures, (b) R∥ and RT for Pt3 nm/Au2 nm/YIG. Insert of (a) shows the temperature dependence of the anomalous Hall resistance RAHE for Pt3 nm/Au2 nm/YIG. Field dependence of the (c) Hall resistance RH at different temperatures, (d) R∥ and RT for Pt3 nm/Au6 nm/YIG. [26] In the Pt(3nm)/Au(2nm)/YIG sample, the AHE results still show the negative AHE signals which means that the MPE still exists in this sample. The AHE signal is increasing with decreasing temperature which agrees with the MPE model. Although the AHE signals are smaller than that of Pt(3nm)/YIG, the inserted Au layer is still too thin to eliminate the MPE. As a result, the MR ratio of Pt(3nm)/Au(2nm)/YIG increases with increasing field similar to the Pt(3nm)/YIG results. In the Pt(3nm)/Au(6nm)/YIG, the MPE is obstructed, shows only ordinary Hall effect signals but without AHE. The MR ratio of Pt(3nm)/Au(6nm)/YIG decreases with increasing field. This is the intrinsic spin current related MR without the MPE.. 32.

(44) Chapter 5 Sample parameters The samples were deposited by sputter deposition, the sample geometry is like a key which is defined by the e-beam lithography. The samples were measured by the standard four probe measurement. We can measure the Hall voltage by using the electrode VH and Vb at transverse direction.. Figure 5.1.1 sample geometry. 33.

(45) 5.1 Resistance measurements in multilayers sample with rotating angle We fix the magnetic field direction and change the sample direction by using the PPMS Horizontal & Vertical Sample Rotators. The field we applied was 3T which is larger than the saturation field. The rotation is from field parallel to the sample plane to field perpendicular to plane. When the field is parallel to plane, it can be divided into two direction, current parallel to field (longitudinal) and current perpendicular to field (transverse). Hence, the rotating direction can be divided into three parts, the field is rotating from transverse to perpendicular (TP rotation), the field is rotating from longitudinal to perpendicular (LP rotation), and the field is rotating from longitudinal to transverse (LT rotation) directions, as shown in the Figures below. (a). (b). Figure 5.1.2 Schematic illustration of field rotation 34.

(46) In MR measurement, we applied the field at three directions, longitudinal, transverse and perpendicular. To exclude the thermal disturbance effect we measured the resistance at the temperature 10K. In the Section 5.1, we fix the Pd layer thickness at 4.8nm, and change the thickness of the Ni layers. The number of bilayer is 20 in my samples. We measure the angular dependence of resistance at 10K and 300K respectively. The results are shown in Figure 5.1.3.. t=5nm. t=1.6nm. t=5nm. t=1.6nm. Figure 5.1.3 Angular dependence measurement of saturation resistance in the multilayers sample with fixed Pd thickness and changing Ni thickness. 35.

(47) To elaborate the figures above more clearly, we take the 10K measurement data and plot in polar axes. The 0 degree and 180 degree represent the field parallel and antiparallel to the current direction (Longitudinal), respectively, and the 90 degree and 270 degree represent the field perpendicular to the plane.. Figure 5.1.5 The figure of polar axes from Figure 5.1.4 36.

(48) As shown in Figure 5.1.5, there are interesting results. When the Ni thickness decreases from 12nm to 1.6 nm, the angular dependence of saturation resistance shows totally different behavior. When Ni thickness is 12.5nm, the AMR effect dominates because most part of the sample is Ni. Hence, the results only show the Ni contribution, the Pd contribution is too small to be observed. But when Ni thickness decreases to 5nm which is approximately equal to the Pd thickness, the resistance behavior at 10K shows bi-axial anisotropy where the maximum ρ occur when θ=45 ° between the perpendicular and longitudinal direction. Interesting results as shown in Figure 5.1.4, the 300K measurement of the Ni 5nm sample shows only AMR behavior. When the thickness of Ni decreases to only 1.6nm, we can observe an abnormal phenomenon, that is, the resistivity with field in perpendicular direction is larger than the field in longitudinal direction. This abnormal magnetoresistance has yet been discovered. What’s worthy to talk about is that this phenomenon can be observed whether the temperature is 10K or 300K. However the phenomenon in 10K measurement is more notable. Besides, because of the different behavior in 10K and 300K of the tni=5nm sample, we do the measurement with variable temperature.. 37.

(49) Figure 5.1.6 Resistance measurement with variable temperature in LP rotation of the sample Pd4.8nm/(Ni5nm/Pd4.8nm)20/Si. 38.

(50) As shown in Figure5.1.5, we measure the angular dependence of resistance with variable Ni thickness, when the Ni thickness is thick enough compared to the Pd thickness, the results show conventional AMR as we expected. With decreasing Ni thickness, the abnormal magnetoresistance phenomenon appears gradually. The MR behavior of the tNi=5nm sample show bi-axial anisotropy. These results can prove that the AMR and our new MR exist concurrently. Whether the AMR or our new MR dominates depends on the thickness of Ni. Besides, as shown in Figure 5.1.6, we can observe the new MR phenomenon increases with decreasing temperature while the AMR is almost the same with decreasing temperature. In the measurement of rotating angle, some data show the difference of the resistance due to the thermal drift.. 39.

(51) 5.2 Measurements with variable Pd thickness We can observe abnormal magnetoresistance in the tNi=1.6nm sample whether the temperature is 10K or 300K except the measurement at 300k of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si . Hence, we focused on the tNi=1.6nm sample with variable Pd thickness.. Figure 5.2.1 Resistance measurement in LP rotation and the MR results of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si.. 40.

(52) Figure 5.2.2Resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si.. Figure 5.2.3 Resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd4.8nm/(Ni1.6nm/Pd4.8nm)20/Si.. 41.

(53) Figure 5.2.4 Resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd6nm/(Ni1.6nm/Pd6nm)20/Si.. Figure 5.2.5 Resistance measurement in LP rotation and the MR results at 10K and 300K of the Pd7.2nm/(Ni1.6nm/Pd7.2nm)20/Si.. 42.

(54) Figure 5.2.6 Resistance measurement in LP rotation and the MR results at 10K of the Pd8.4nm/(Ni1.6nm/Pd8.4nm)20/Si.. Figure 5.2.7 ∆ρ/ρ versus the thickness of Pd , the black line P-L means that the perpendicular resistance (PMR) minus longitudinal resistance (LMR) and then divided by the perpendicular resistance (PMR), same method were used in red line and black line.. 43.

(55) As shown in Figures 5.2.1, to Figure 5.2.3, we measure the MR at 300K with variable Pd thickness. The results show that the resistance decreases with increasing magnetic field. This result is due to the decreasing of the spin disorder scattering with increasing field and some thermal disturbance. For MR measurement at 10K, as shown in Figures 5.2.1 to 5.2.6, the resistance is almost constant when the field is large enough. Hence we focus on the 10K measurement. In the data shown above, we can observe the abnormal magnetoresistance in all sample whether the temperature is 10K or 300K except the measurement of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si sample at 300K. This transition. of. the. MR. results. between. 10K. and. 300K. of. the. Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si sample may due to the Pd have the induced magnetization and the Curie temperature of this induced magnetization for 2.4 nm Pd is between 10 and 300 K. In this series of sample, we can see the new MR phenomenon increases with decreasing temperature. I consider this phenomenon is due to the increase of the spin diffusion length with decreasing temperature. Detailed discussion will be given in Section 5.6. Besides, we can observe the giant magnetoresistance (GMR) occur when the Pd thickness is thick enough. But whether the GMR occur, the new MR phenomenon still exists. In Figure 5.2.7, we show that the new MR phenomenon is prominent when the Pd thickness is 6 to 8.4 nm. Hence, we consider this new MR is due to not only the interlayer contribution but also the bulk contribution from Pd.. 44.

(56) 5.3. Resistance measurement with varying temperature. and rotating field. Figure 5.3.1 Resistance measurement in LP rotation with variable temperature of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si sample. 45.

(57) Figure 5.3.2 Resistance measurement in LP rotation with variable temperature of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si sample.. Figure 5.3.3 Resistance measurement in TP rotation with variable temperature of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si sample.. Figure 5.3.4 The ∆ρ/ρ of the LP and TP rotation versus temperature. Red line means that perpendicular resistance (PMR) minus longitudinal resistance (LMR) and then divided by the perpendicular resistance (PMR). Black means that perpendicular resistance (PMR) minus transverse resistance (TMR) and then divided by the perpendicular resistance(PMR).. 46.

(58) Figure 5.3.5 Color coded ∆ρ/ρ in LP rotation of Pd2.4nm/ (𝑁𝑖1.6𝑛𝑚/ 𝑃𝑑2.4𝑛𝑚)20 /𝑆𝑖 sample.. 圖 5.3.6 Color coded ∆ρ/ρin LP rotation of Pd3.6nm/(𝑁𝑖1.6𝑛𝑚/𝑃𝑑3.6𝑛𝑚)20 /𝑆𝑖 sample. 47.

(59) 5.4 Canting angle measurement. Figure 5.4.1 Schematic illustration of canting angle determination.[27]. The canting angle means that when there is no external field acting on the magnetization, the magnetization will lie on the energy minimum state which has an angle to the perpendicular axis, as shown in Figure 5.4.1. When the external field increases, the magnetization will be aligned from the easy axis to the applied field direction. If the external field is high enough to maintain a single-domain state but not sufficient to completely align the magnetization in field direction, the magnetization will lie at the angle between canting angle and the applied field direction. As we know, the resistance of the ferromagnetic materials depends on the magnetization direction, hence, there is a method that allows a very accurate and unambiguous determination of the canting angle via magnetoresistance measurements indirectly.. 48.

(60) Figure 5.4.2 Magnetic anisotropy versus angle [27].. H. P. Oepen’s group presented in the Journal of Applied Physics in 2013[27] a method that allow us to measure the canting angle via electrical measurement. The free-energy density for a system in an external field can be approximated by the anisotropy constants,K1,eff and K2 and the Zeeman energy. The equation can be described as below. From Figure 5.4.2, when the field strength along the normal is reduced, the magnetization cannot overcome the high energy barrier at 0 degree and 90 degree, hence, the field aligned cone is populated. In order to determine the canting angle of the strongly canted sample, magnetotransport measurements are proposed. If the applied field is strong enough to saturate the magnetization, the magnetization will be aligned to the field direction, if not, with varying field magnitudes, reducing the field strength from the saturation, the field aligned cone angle will move toward the canting 49.

(61) angle gradually. Therefore, in the magnetotransport measurements, the resistance will be changed by the field strength. If we measure the resistance with rotating field angle, there will be some difference between the resistance with saturation field and unsaturation field. One then take the difference between two of them and plot ∆R versus field angle. If at some angle, ∆R is zero, it means that this angle is the canting angle. That is because if the applied field is at the canting angle, the magnetization will be aligned to the field direction whether the field is strong enough to reach saturation or not. See Figure 5.4.3.. Figure 5.4.3 ∆R versus field angle for different field changes [27] 50.

(62) Figure 5.4.4 the 10K resistance measurement with field rotating in LP plane of the Pd6nm/(Ni1.6nm/Pd6nm)20/Si.. Figure 5.4.5 ∆R versus field angle of the Pd6nm/(Ni1.6nm/Pd6nm)20/Si (𝜃𝐶 = 73). 51.

(63) Figure 5.4.6 ∆R versus field angle of the Pd8.4nm/(Ni1.6nm/Pd8.4nm)20/Si (field in LP plane).. Figure 5.4.7 ∆R versus field angle of the Pd8.4nm/(Ni1.6nm/Pd8.4nm)20/Si (field in TP plane).. 52.

(64) As shown in Figures 5.4.5, 5.4.6, and 5.4.7, we can find that the canting angle is about 70~75 degree to the plane normal. These results can be caused by four reasons. First, the Ni thickness is thin enough so that the easy axis can lie at the angle between in plane and out of plane. In our sample, no perpendicular magnetic anisotropy was found. Secondly, because our thin film structure is deposited by sputtering, in which depositing time is short, hence, the thin film structure may form the corrugated plane instead of smooth plane. Thirdly, in the Pd/Ni multilayers structure, the Pd is the material near the stoner criteria so that the Pd layer may have magnetization which is induced by the Ni layer. If the magnetization direction of the Pd layer is not collinear with that of the Ni layer, it may cause the canting angle. Lastly, the Pd layer is the material which have strong spin orbital interaction, when the adjacent layer is ferromagnetic material, the Dzyaloshinskii-Moriya interaction (DMI) effect may occur. Hence, form the corrugated magnetization. The canting angle results are all the same in all the samples, even in the samples after annealing.. 53.

(65) 5.5 Anomalous Hall effect measurement We measure the anomalous Hall effect with the applied field rotated in the LP and TP plane. In our measurement, the current flow is defined as the X direction, the applied field is defined as the Z direction, and we measure the Hall voltage in the Y direction. The voltage signal is proportional to the Z component of the magnetization, as the equation below. 𝜌𝐻 = 𝑅𝐻 𝐵 + 𝑅𝑆 4𝜋𝑀 , where B is the applied field, M is the magnetization，𝑅𝐻 、𝑅𝑆 are Hall coefficient and anomalous Hall coefficient, respectively. In ferromagnetic materials, the 𝑅𝐻 is small enough to be ignored. Hence, 𝜌𝐻 ≈ 𝑅𝑆 4𝜋𝑀 ∝ M. We measure the anomalous Hall effect with the applied field rotate in the LP plane of the. If the field is rotated in the LP plane, the Hall voltage should proportional to the Z component of the magnetization which is the perpendicular projection of the magnetization. Thus, this value should correspond to the Sine function. However, the experiment results are out of our expectation, as shown in Figures 5.5.1 to 5.5.4. In the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si and Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si samples,when the applied field is in the longitudinal direction, the voltage signal is nonzero. This nonzero voltage signal is more notable at low temperature. We consider that there is a Z component of the magnetization, when the applied field is in the longitudinal direction. This Z component of the magnetization in the Pd2.4nm sample is directed away from the substrate, while in the Pd3.6nm sample is directed into the substrate. This Z component of the magnetization may be caused by the contribution of the magnetization of the Pd layer induced by the Ni layer, or the DMI contribution in the Pd/Ni interlayers. Worth to mention is that this nonzero voltage breaks the spatial symmetry. 54.

(66) However, whether this phenomenon originates from the anti-symmetry of the DMI or from other reasons is discussed below. Although in the Hall effect measurement, the voltage between two leads wouldn’t be completely perpendicular to the current direction and might cause the normal resistance contribution. However, the difference between the Sine fit and experiment data is 10 times larger than the normal resistance with field rotated out of plane .Hence, this results is not from the experimental deviation. Besides, this phenomenon is notable in 10K similar to our abnormal magnetoresistance. Therefore, there is some relation between two of them. When measuring the Hall Effect with field rotating in the TP plane, as shown in Figures 5.5.5 to 5.5.7, we find interesting results that the Sine function fits well to the data. Hence, when we applied the field at transverse direction, there is no z component of the magnetization. But this cannot prove that there is no induced magnetization in the Pd layer. As shown in Figure 5.5.8, when measuring the anomalous Hall Effect with varying field at Z direction, we can observe the results as the equation describes above. As shown in Figure 5.5.9, the huge peak in the Hall measurement with varying field at longitudinal direction is due to the experimental error in voltage. As shown in Figure 5.5.10, when measuring the Hall Effect with varying temperature, the signal decreases with decreasing temperature in the temperature range 200K to 300K, while the signal increases with decreasing temperature in the temperature range 10K to 200K. But whether these results come from the RT signal or the magnetization contribution needs further investigation.. 55.

(67) Figure 5.5.1 anomalous Hall effect with the applied field rotate in the LP and the Sine fit at 300K of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si. Figure 5.5.2 anomalous Hall effect with the applied field rotate in the LP and the Sine 56.

(68) fit at 10K of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si.. Figure 5.5.3 anomalous Hall effect with the applied field rotate in the LP and the Sine fit at 300K of the Pd3.6nm/(Ni1.6nm/Pd3.6nm)20/Si.. Figure 5.5.4 anomalous Hall effect with the applied field rotate in the LP and the Sine fit at 10K of the Pd2.4nm/(Ni1.6nm/Pd2.4nm)20/Si. 57.