Magnetic anisotropy

Figure 3.3: Comparison of the magnetic properties of (a) an FM/AFM system at a temperature T with 𝑇_𝐵 < 𝑇 < 𝑇_𝐶 and (d) the same system after field-cooling below the AFMs Neel temperature (with 𝑇 < 𝑇_𝐵 < 𝑇_𝐶). (b) The system shows a normal ferromagnetic hysteresis loop (c) an uniaxial anisotropy, indicated by a sin2𝜃-behavior of the torque measurements (e) after field cooling below T_𝐵, shows a hor-izontally shifted loop with increased coercivity (f) and an unidirectional anisotropy with a sin 𝜃-behavior of the torque measurements.

3.6 Magnetic anisotropy

Figure 3.4: Display of the angle between the magnetization M and the film surface normal.

Ferromagnetic materials, such as Fe, Co, or Ni present spontaneous magneti-zation below the Curie temperature. In reality, these materials show their magne-tization preferring some directions in space, which are called the easy axes. The direction of easy axis is observed to be dependent on the intrinsic symmetry of

crys-3.6. Magnetic anisotropy 26 talline structure and the shape of the sample. For example, in the latter, it might be parallel to the plane in thin film system. To discuss the mechanism of easy axis in detail, the magnetic anisotropy energy (MAE) is introduced as the energy dif-ference between two different magnetization axes. Since the MAE (𝐸_{𝑡𝑜𝑡𝑎𝑙}) depends on the orientation of the magnetization with respect to crystalline axes or its exter-nal shape, in a phenomenological model it can be decomposed into the crystalline anisotropy (𝐸_{𝑐𝑟𝑦𝑠𝑡𝑎𝑙}) and shape anisotropy (𝐸_{𝑠ℎ𝑎𝑝𝑒}). However, in the above discus-sion, the strain has been taken to be zero. If the strain does exist, it can induced magneto-elastic anisotropy (𝐸𝑚𝑎𝑔𝑛𝑒𝑡𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐). Therefore, from these different effects on the magnetic behavior, the total MAE can be expressed as :

𝐸_{𝑡𝑜𝑡𝑎𝑙} = 𝐸_{𝑐𝑟𝑦𝑠𝑡𝑎𝑙}+ 𝐸_{𝑠ℎ𝑎𝑝𝑒}+ 𝐸𝑚𝑎𝑔𝑛𝑒𝑡𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐

In the analysis of ultrathin film anisotropy, the MAE is defined as the energy dif-ference between the perpendicular and parallel to the film plane. It appears that, neglecting high order terms, a uniaxial description is often sufficient :

𝐸 = 𝐾_{𝑒𝑓 𝑓} sin²𝜃 = (𝐾_𝑉 + 2𝐾_𝑆

𝑡 ) sin²𝜃

E is the total energy per unit volume, 𝐾_{𝑒𝑓 𝑓} stands for the effective anisotropy energy including the contribution from various source and denotes the angle between the magnetization and the film surface, as shown in Fig. 3.4. The second order term 𝐾₂sin⁴𝜃 is usually very small. But in some cases, for example when the first order term vanishes, the second order term will become much more important than in usual. 𝐾_𝑆 indicates the contribution from the surface or interface per unit area.

Meanwhile, 𝐾_𝑉 denotes the contribution from the volume or bulk per unit volume.

The factor 2 of the surface term comes from the assumption that the contribution from the interface and surface are nearly identical, and this should be modified in some cases. Since the system prefers low energy, positive 𝐾_{𝑒𝑓 𝑓} describes the case of easy axis perpendicular to the film surface (𝜃 = 0) and negative 𝐾_{𝑒𝑓 𝑓} describes the case of easy axis parallel to the film surface ( 𝜃 = Π/2).

In Fig. 3.5 and Fig. 3.6, the plots of the product 𝐾_{𝑒𝑓 𝑓}𝑡 versus t are shown for the cases of Co/Cu(100) and Ni/Cu(100), where 2𝐾_𝑆 and 𝐾_𝑉 stand for the

3.6. Magnetic anisotropy 27

Figure 3.5: Effective magnetic anisotropy per unit area per Co layer versus the Co layer thickness.

Figure 3.6: Effective magnetic anisotropy per unit area per Ni layer versus the Ni layer thickness.

intercept at 𝑡 = 0 and the slope respectively. If 𝐾_𝑉 and 𝐾_𝑆 are of different signs, because 𝐾𝑆 decays with thickness as ¹_𝑡, 𝐾𝑒𝑓 𝑓 will change sign with the increasing of thickness, which results in the SRT. This spectacular behavior is found in many magnetic ultrathin film system, such as Co/Pt(111), Fe/Cu(100), Fe/Cu3Au(100), Ni/Cu(100) et al., and will be discussed later in this section. The magnetocrystalline anisotropy arises essentially from the spin-orbit coupling, but also, to lesser extent, from the dipolar interactions. The symmetry breaking on the surface and interface induces the magnetocrystalline surface anisotropy, which may be responsible for the perpendicular magnetization in several systems such as ultrathin films Fe/Cu(100), Co/Ag(100) etc. However, the sign of the magnetocrystalline surface anisotropy is strongly system dependent, thus resulting in different magnetic behavior. The shape anisotropy, which is also called the demagnetization energy, arises from the dipolar interaction. Because the dipolar interaction decrease slowly as a function of the distance 𝑟 (like _𝑟¹3), the dipolar field experienced by a given moment depends

3.6. Magnetic anisotropy 28 significantly on the moments located at the boundary of the sample, and this results in the shape anisotropy. In the case of ultrathin films, the volume shape anisotropy

𝐸_{𝑠ℎ𝑎𝑝𝑒}^𝑉 = −2𝜋𝑀_𝑉² sin²𝜃

where 𝑀_𝑉 is the saturated moment per unit volume. On the other hand the shape surface anisotropy contributes only weakly to the total surface anisotropy. For Fe, Co, and Ni, the volume shape anisotropy are larger than the volume magnetocrys-talline anisotropy. Therefore the shape anisotropy usually dominates the volume term (without strain), and the negative sign of it results in the magnetization lying in the film plane. Magnetostriction is the phenomenon that the shape of a ferromag-netic specimen changes during the process of magnetization. Inversely, if a stress is applied to a ferromagnetic specimen, the direction of the magnetization will also be affected through the magnetostriction. This strain induced MAE is called the magnetoelastic anisotropy. Because the magnetoelastic anisotropy comes from the strain induced change in the magnetocrystalline anisotropy, its physical origin is also the spin-orbit interaction. Particularly in ultrathin films, where considerable strain may result from the epitaxial growth of the film onto the substrate having a different lattice constance, the strain induced anisotropy plays a very important role.

Chapter 4

Experiment and Result

4.1 Experiment procedure

Figure 4.1: The flow chart of experiment procedure.

The thin film preparation and measurements were carried out in a ultrahigh vac-uum (UHV) chamber with the base pressure better than 2 × 10⁻¹⁰torr. After cycles of 2 𝑘𝑒𝑉 Ar⁺ sputtering and annealing, the clean substrate of Cu₃Au(001) with well-ordered c(2 × 2) superstructure and flat surface was obtained. 2.5 ML Fe were sequentially evaporated onto the substrate with the substrate temperature of 300 K (RT). During the evaporation, the pressure was better than 9 × 10⁻¹⁰ torr. The growth was monitored by medium energy electron diffraction (MEED) with a beam energy of 2 keV and the grazing angle of 1^∘. From the periodicity of MEED

oscil-29

4.2. Growth and Structure of Mn/Fe/Cu3Au(001) 30 lations, the deposition rate was calibrated precisely. Then Mn and Fe layers were deposited in turn over the Fe/Cu₃Au(001) films at RT. After the film growth was finished, we checked the composition by Auger electron spectroscopy which different signals come from different elements. The lateral crystalline structure was charac-terized at 300 K by low energy electron diffraction (LEED). In this experiment, a 4 grid rear view LEED was used to take the LEED images. Besides, from the LEED-I/V curves, the average vertical interlayer distance (d⊥) of the film was determined using the kinetic approximation. Magnetic properties of the films were detected by magneto-optical Kerr effect (MOKE). The MOKE measurement was performed in both longitudinal and polar geometries with the modulation and lock-in technique.

All the MOKE measurements of Fe/Mn/Fe trilayers were performed after a cooling process from 300 K to 195 K. A flow chart of this series of experiments is shown in Fig. 4.1.

4.2 Growth and Structure of Mn/Fe/Cu

Au(001)

Figure 4.2: MEED (0,0) spot intensity of Mn films grown on fcc-like Fe/Cu₃Au(001).

Fig. 4.2 shows the (0,0) spot MEED intensity for Mn grown on fcc-like Fe/Cu₃Au(001).

Mn grown on fcc-like Fe/Cu₃Au(001) at RT reveals apparent layer-by-layer growth even the thickness above 15 ML and the oscillation amplitude decreases gradually

4.2. Growth and Structure of Mn/Fe/Cu3Au(001) 31

Figure 4.3: Recorded intensity of MEED (0,0) and (¹₂,¹₂) spots for Mn films grown on Cu₃Au(001) at RT and LT (adapted from [8])

above 10 ML. Compared with Mn grown on Cu₃Au(001) without fcc-like Fe buffer layer, in Fig. 4.3 the MEED intensity of (0,0) spot for RT-grown Mn films also indicates layer-by-layer growth for 0 − 2 ML. After 2 ML, the oscillation amplitude is reduced and then gradually disappears after 6 − 7 ML. Obviously the number of oscillation of Mn grown on fcc-like Fe/Cu₃Au(001) is larger than that of Mn grown on Cu3Au(001). This points out that the growth of Mn films with fcc-like Fe buffer layer may be better than directly grown on Cu₃Au(001). Fig. 4.4 shows the LEED patterns of Cu3Au(001), 2.5 ML (fcc-like) Fe grown on Cu3Au(001) at RT and vari-ous Mn films grown on 2.5 ML (fcc-like) Fe/Cu₃Au(001)at RT. Fig. 4.4(a) exhibits the c(2 × 2) structure of Cu3Au(001). Fig. 4.4(b) the RT-grown 2.5 ML (fcc-like) Fe film reveals the p(1 × 1) LEED pattern. As shown in Fig. 4.4(c)-(g), the RT-grown Mn films appear the p(1 × 1) LEED pattern and the sharp p(1 × 1) LEED patterns exhibits the well-ordered crystalline structure. Figure 4.5 shows the LEED patterns of Cu3Au(001) and various Mn films grown at RT. Figure 4.5(a) exhibits the c(2×2) structure of Cu₃Au(001). 0.5 and 1 ML RT-Mn films reveal p(2 × 2) structure and for 5 ML, a transition to c(2 × 2) structure is observed. With the larger coverage of more than about 9 ML, the RT-Mn films always reveal the p(1 × 1) LEED pattern

4.2. Growth and Structure of Mn/Fe/Cu3Au(001) 32 as shown in Figs. 4.5(e)-(h).

Figure 4.4: LEED pattern of (a) Cu₃Au(001) (b) 2.5 ML (fcc-like) Fe grown on Cu₃Au(001) at RT (c) various thickness of Mn grown on 2.5 ML (fcc-like) Fe/Cu₃Au(001) at RT. All the images are taken at RT with the beam energy equiv-alent to 150 eV.

The LEED-I/V curves of (0,0) spot are also recorded for the analysis of interlayer distance (d⊥). Fig. 4.6 shows the LEED-I/V curves of RT-grown Mn films. The integers denote the order of the maximum conditions in Bragg interference. The indexed peak positions shift toward high energy both in RT-Mn films with increas-ing thickness. The shift toward high energy indicates a structural transition toward the smaller d⊥. Fig. 4.7 shows the d⊥ deduced from the LEED-I/V curves. Mn films with low coverage reveal the d⊥ almost the same as the substrate (Cu₃Au(001, d⊥=1.89 ˚𝐴). At 21.5 ML thickness, the d⊥ reduces to about 1.83 ˚𝐴. Since the LEED studies inform the coherence growth of Mn on Cu₃Au(001), the RT-grown Mn films are concluded to perform a structural transition from face-centered cubic (fcc) to a face-centered tetragonal (fct) and the critical thicknesses are ∼14 ML.

4.2. Growth and Structure of Mn/Fe/Cu3Au(001) 33

Figure 4.5: LEED patterns of RT-grown Mn/Cu₃Au(001) with various coverages.

All the images are taken at 100 K with the beam energy equivalent to 150 eV.

(adapted from [8])

Figure 4.6: LEED-IV of various thickness of Mn grown on 2.5 ML (fcc- like) Fe/Cu₃Au(001) at RT.

In comparison with RT-grown Mn/Cu₃Au(001), Figure. 4.8(a) shows Mn films with low coverage reveal a d⊥ almost the same as that of the substrate Cu3Au(001).

At a higher thickness, the d⊥is reduced to about 1.77 ˚𝐴. Since the coherence growth of Mn on Cu3Au(001), the Mn films are concluded to perform a structural transition

4.2. Growth and Structure of Mn/Fe/Cu3Au(001) 34

Figure 4.7: Vertical interlayer distance of various thickness of Mn grown on 2.5 ML (fcc-like) Fe/Cu₃Au(001) at RT.

Figure 4.8: Vertical interlayer distance of various thickness of Mn grown on 2.5 ML Fe/Cu₃Au(001) at RT. (adapted from [8])

from a face-centered cubic (fcc) to a face-centered tetragonal (fct) structure and the critical thicknesses are ∼12 ML.

4.3. Growth and Structure of Fe/Mn/Fe/Cu3Au(001) 35

4.3 Growth and Structure of Fe/Mn/Fe/Cu

Au(001)

Figure 4.9: (0,0) spot intensity of MEED of Fe grown on Mn/Fe/Cu₃Au(001).

Figure 4.10: LEED pattern of (a) 8 ML Fe (b) 10 ML Fe (c) 12 ML Fe (d) 14 ML Fe grown on 6 ML Mn/2.5 ML Fe/Cu₃Au(001) at RT.

Fig. 4.9 shows the MEED oscillation of Fe films deposited on various RT-Mn films and apparently Fe films grown on Mn/fcc-like Fe/Cu₃Au(001) is layer-by-layer growth. Fig. 4.10 shows the LEED patterns of various thickness of Fe films grown on 6 ML Mn/2.5 ML (fcc-like) Fe/Cu₃Au(001) at RT. The c(2 × 2) structure of the Fe films are supposed to be the superstructure on surface. The dash lines indicate the spot positions are almost the same which means epitaxial growth. Fig.

4.11(a)-(c) shows the LEED-I/V curves of RT-grown Fe films. Fig. 4.11(d) shows the fitting results of LEED I/V curves, the interlayer distance of Fe films grown on Mn/2.5 ML (fcc-like) Fe/Cu₃Au(001) is about 1.51 ˚𝐴 so that the crystalline

4.3. Growth and Structure of Fe/Mn/Fe/Cu3Au(001) 36

Figure 4.11: LEED-IV of various thickness of Fe grown on 6 ML Mn/2.5 ML Fe/Cu₃Au(001) at RT.

structure is body-centred tetragonal (bct) and apparently the vertical interlayer distance remains almost invariant in those coverages. Compared with Fe grown on Cu3Au(001) (Fig. 4.12), the vertical interlayer distance (d⊥) of Fe films is almost the same as the substrate (Cu₃Au(001), d⊥=1.89 ˚𝐴) at thickness lower than 3 ML and then performs a fcc-like to bcc-like structure transition. When the thickness of Fe films is larger than 7 ML, d⊥ is about 1.55 ˚𝐴. In our case, the d⊥ is almost the same as the substrate (Cu3Au(001)) for the fcc-like Fe buffer layer and the d⊥ is 1.51 ˚𝐴 for the top Fe overlayer.

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 37

Figure 4.12: Two different average vertical interlayer distances related to fcc-like (full circles) and bcc-like Fe films (open circles), respectively. adapted from [2]

4.4 Magnetic Properties of Fe/Mn/Fe/Cu

Au(001)

Coercivity enhancement phenomenon

Fe films grown on Mn/Fe/Cu₃Au(001) reveal different magnetic properties from those grown on Mn/Cu₃Au(001) at room temperature. In Fig. 4.13 the coercivity of magnetic hysteresis loop of 6.3 ML Fe/4.5 ML Mn/2.5 ML Fe/Cu₃Au(001) in perpendicular direction is greatly enhanced by the 2.5 ML fcc-like Fe buffer layer as compared with 6.3 ML Fe/4.5 ML Mn/Cu₃Au(001). The increase of H_𝐶 is intu-itively simple to understand. For an AFM (Mn) layer with small anisotropy, when the FM (Fe) layer rotates, it drags the AFM (Mn) layer spins irreversibly, hence increasing the FM (Fe) layer coercivity. In Fig. 4.14 the coercivity versus tempera-ture indicates two important results. One is the coercivity in perpendicular direction enhanced by 2.5 ML fcc-Fe buffer layer with perpendicular magnetization. The pos-sible explanation is that the perpendicular component of Mn layer spin configuration somehow ehanced by 2.5 ML fcc Fe buffer layer with perpendicular magnetization during growth. Thus the exchange coupling in perpendicular direction between Fe overlayer and Mn layer is enhanced, and the coercivity of the Fe overlayer is en-hanced. The other is that the exchange coupling of 6.3 ML Fe/4.5 ML Mn/2.5 ML Fe in perpendicular direction is larger than 6.3 ML/6.5 ML Mn. Generally

speak-4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 38

Figure 4.13: Hysteresis loops of 6.3 ML Fe/4.5 ML Mn/2.5 ML Fe/Cu₃Au(001) and 6.3 ML Fe/4.5 ML Mn/Cu₃Au(001). At 196 K coercivity is extraordinary enhanced caused by wetting layer effect.

ing, Mn layer with larger thickness results in larger exchange coupling between Fe overlyer and Mn layer. However the influence on excange coupling in perpendicular direction by fcc-like Fe buffer layer with perpendicular magnetization apparently remarkable.

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 39

Figure 4.14: Coercivity with respect to temperature. All the films were grown at 300 K.

Observation of thickness dependent SRT

The spin reorientation transition (SRT) phenomenon is an interesting subject in magnetism which describes the switch of magnetic easy axis. There are seveal different mechanism to induce SRT phenomenon. The thickness and temperature dependent spin reorientation transition of Fe/Mn/Fe/Cu₃Au(001) will be described.

In Fig. 4.15 hysteresis loops of n ML Fe/4 ML Mn/2.5 ML Fe/Cu3Au(001) was mea-sured at 195 K. When the thickness of Fe overlayer less than 7 ML, the coercivity gradually increased with thickness due to more ferromagnetic moments. Then the magnetic easy axis was switched from perpendicular direction to in-plane direction.

M𝑟 versus thickness curves (Fig. 4.16) also supports the same result. The reason why the magnetic easy axis aligns in different directions at different thickness is discussed in the following. When the thickness of top Fe layer is less than about 7 ML , the symmetry breaking on the surface induces perpendicular magnetization.

However, when the thickness of Fe overlayer is larger than about 7 ML, the vol-ume shape anisotropy which arises from the dipolar interaction forces the magnetic

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 40

Figure 4.15: Hysteresis loops of various coverage Fe grown on 4 ML Mn/2.5 ML Fe/Cu₃Au(001). The onset thickness for SRT is about 7 ML.

Figure 4.16: M_𝑟 versus thickness curves of n ML Fe/4 ML Mn/2.5 ML Fe/Cu₃Au(001). The transition region is 7 ML to 10 ML.

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 41 easy axis aligned in in-plane direction. In Fig. 4.17 hysteresis loop of 8 ML Fe/5 ML Mn/Cu₃Au(001) was measured only in in-plane direction at 195 K. When 2, 2.5, and 3 ML fcc-like Fe buffer layer was added individually between Mn film and Cu₃Au(001), the magnetic easy axis was switched from in-plane direction to perpen-dicular direction. The coercivity of those system with fcc-like Fe buffer layer seems almost the same.

Figure 4.17: Hysteresis loops of 8 ML Fe/5 ML Mn/n ML Fe/Cu₃Au(001). The magnetic easy axes switch from perpendicular direction to in-plane direction by fcc-like Fe buffer layers.

Observation of temperature dependent SRT

In Fig. 4.18 hysteresis loops of 10 ML Fe/6 ML Mn/2.5 ML Fe/Cu₃Au(001) were measured at different temperature. At lowest temperature (195 K), the magnetic easy axis lay in perpendicular direction. With rising temperature, the magnetic easy axis started to switching from perpendicular to in-plane direction which meant the exchange coupling in perpendicular direction decreses. The key factor of tempera-ture dependent SRT is the lattice vibration caused by rising temperatempera-ture. At low coverage region, symmetry breaking which dominates the perpendicular magnetiza-tion is easily disturbed by lattice vibramagnetiza-tion.

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 42

Figure 4.18: Hysteresis loops of 10 ML Fe/6 ML Mn/2.5 ML Fe/Cu₃Au(001) mea-sured at different temperature.

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 43 Overview of SRT

Figure 4.19: Hysteresis loops of m ML Fe/6 ML Mn/2.5 ML Fe/Cu₃Au(001) mea-sured at different temperature.

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 44

Figure 4.20: Hysteresis loops of m ML Fe/4 ML Mn/2.5 ML Fe/Cu₃Au(001) mea-sured at different temperature and 8 ML Fe/5 ML Mn/n ML Fe/Cu₃Au(001) mea-sured at 195 K.

4.4. Magnetic Properties of Fe/Mn/Fe/Cu3Au(001) 45

Figure 4.21: Hysteresis loops of m ML Fe/8 ML Mn/2.5 ML Fe/Cu₃Au(001) mea-sured at different temperature and overview of SRT with a magnetic phase diagram.

Chapter 5 Discussion

Mn/fcc-like Fe/Cu₃Au(001) and Mn/Cu₃Au(001)

From an intuitive aspect thin films grown on different substrate should appear differ-ent lattice orders but in our case Mn/fcc-like Fe/Cu₃Au(001) and Mn/Cu₃Au(001) present almost the same vertical interlayer distance. The thickness of the Fe buffer layer is 2.5 ML which means the vertical interlayer distance almost the same as the substrate Cu₃Au(001) (fcc, d_⊥= 1.89 ˚𝐴) (Fig. 5.1(a)). If the growth process is assumed to be epitaxial growth, although the interfaces are different, Mn films grown on fcc-like Fe/Cu₃Au(001) and Cu₃Au(001) should appear the similar lattice order. For Mn grown on Cu₃Au(001), Mn films with low coverage reveal a d⊥ al-most the same as that of the substrate Cu₃Au(001) (d_⊥= 1.89 ˚𝐴) and the d_⊥ is reduced to about 1.77 ˚𝐴 at a higher thickness. Since the LEED patterns indicates the coherence growth of Mn on Cu₃Au(001), the Mn films are concluded to perform a structural transition from a fcc to a fct structure and the critical thickness is about 12 ML (Fig. 5.1(b)). For Mn grown on fcc-like Fe/Cu₃Au(001), Mn films with low coverage reveal a d⊥about 1.91 ˚𝐴 and the d⊥ is reduced to about 1.83 ˚𝐴 at a higher thickness. The Mn films perform a structural transition from a fcc to a fct structure and the critical thickness is about 14 ML (Fig. 5.1(c)).

46

Chapter 5. Discussion 47

Figure 5.1: Comparison of interlayer distance between Mn/fcc-like Fe/Cu₃Au(001)

Figure 5.1: Comparison of interlayer distance between Mn/fcc-like Fe/Cu₃Au(001)