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Pt) multilayers with perpendicular magnetic anisotropy
Accepted Manuscript Research articles Ni thickness influence on magnetic properties (Co/Ni/Co/Pt) multilayers with perpendicular magnetic anisotropy R. Sbiaa, I.A. Al-Omari, M. Al Bahri, P.R. Kharel, M. Ranjbar, J. Åkerman, D.J. Sellmyer PII: DOI: Reference:
S0304-8853(17)30861-2 http://dx.doi.org/10.1016/j.jmmm.2017.06.054 MAGMA 62850
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
13 March 2017 27 May 2017 8 June 2017
Please cite this article as: R. Sbiaa, I.A. Al-Omari, M. Al Bahri, P.R. Kharel, M. Ranjbar, J. Åkerman, D.J. Sellmyer, Ni thickness influence on magnetic properties (Co/Ni/Co/Pt) multilayers with perpendicular magnetic anisotropy, Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/10.1016/j.jmmm.2017.06.054
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Ni thickness influence on magnetic properties (Co/Ni/Co/Pt) multilayers with perpendicular magnetic anisotropy R. Sbiaa,1* I. A. Al-Omari,1 M. Al Bahri,1 P. R. Kharel,2 M. Ranjbar,3 J. Åkerman3,4, and D. J. Sellmyer5 1
Department of Physics, Sultan Qaboos University, P.O. Box 36, PC 123, Muscat, Oman
2
Department of Physics, South Dakota State University, Brookings, SD 57007, USA
3
Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden
4
Materials and Nanophysics, School of ICT, KTH Royal Institute of Technology, Isafjordsg. 22, 16440
Kista, Sweden 5
Nebraska Center for Materials and Nanoscience, and Department of Physics and Astronomy,
University of Nebraska, Lincoln, NE 68588, USA
PACS 75.60.Ch– magnetic properties and materials
* Corresponding author: [email protected]
Abstract – We present a study of perpendicular magnetic anisotropy in [Co/Ni(t)/Co/Pt]×8 multilayers for use as free layers in magnetic tunnel junctions (MTJ) and spin valves. The thickness t of the Ni sub-layer was varied and the resulting magnetic properties were compared with (Co/Ni) and (Co/Pt) multilayers with the same number of repeats. As determined from magnetic force microscopy and magnetometry measurements, all multilayers exhibited a perpendicular magnetic anisotropy with an increase of saturation magnetization with thickness t. From the temperature dependence of the magnetization, well described by a Bloch law, we find that the spin-wave stiffness constant of the [Co/Ni(t)/Co/Pt]×8 multilayers is larger compared to (Co/Ni) multilayers. These multilayers could be the basis for spintronic devices where the reduction of total Pt content could help to reduce the damping constant while keeping the magnetic anisotropy energy relatively high. These are conflicting requirements needed for high performance magnetic memory devices.
1
1. Introduction−
Materials with strong perpendicular magnetic anisotropy (PMA) have
received a significant amount of interest in recent years because of their potential for highperformance magnetic memory [1−14]. For instance, the required electrical current for switching the magnetization of a soft layer in a magnetic tunnel junction with PMA by a spin transfer torque (STT) effect is much smaller than in the in-plane anisotropy case [4−7]. PMA materials are also beneficial for high storage density domain wall memory applications [15−24]. In spin torque oscillators, PMA free layers are also used both for zero-field operation [25,26] and for the realization of magnetic droplets [27−31]. Materials such as (Co/Pt), (Co/Pd) and (Co/Ni) multilayers have been intensively investigated as it is easy to adjust their magnetic properties by changing the thickness of the sub-layers and the number of bilayer repeats. Several reports have highlighted the drawback of (Co/Pd) or (Co/Pt) in terms of their higher damping constant (α) compared to that of (Co/Ni) multilayers [32−35]. It is known that the current required for magnetization switching by STT effect is proportional to the damping constant. On the other hand, (Co/Ni) multilayers suffer from their relatively low magnetic anisotropy energy which is an obstacle for reducing the device size due to thermal instability. In fact, a stability factor Ku/kBT should be larger than 40 for room temperature application and even 60 assuming T = 85 °C (Ku is the magnetic anisotropy energy, kB is Boltzmann constant and T is the temperature) [5]. To take advantage of the high anisotropy energy of (Co/Pd) or (Co/Pt) multilayers [36] and low damping constant of (Co/Ni) multilayers [37], we investigated a structure made of a combination of (Co/Ni/Co/Pt) multilayers. The additional layer of Pt in the multilayer is to improve the interface anisotropy energy while the existence of Ni is for improving the polarization and lowering the damping constant. In this paper, we investigate the temperature dependence of the magnetic properties of (Co/Ni/Co/Pt) multilayers. The focus was also on the understanding of the evolution of magnetic domains with Ni thickness and correlate it to saturation magnetization and spin wave stiffness.
2. Experiments
2
The samples have been deposition by DC-sputtering in high vacuum chamber on thermally oxidized silicon. The multilayer consists of [Co(0.3 nm)/Ni(t nm)/Co(0.3 nm)/Pt(0.8 nm)]×8 where Ni thickness was varied from 0.3 nm to 0.9 nm. Prior to the deposition of the multilayer 4 nm-thick Ta followed by 3 nm Pt were used as seedlayers similarly to our previous study [38]. The magnetic measurements were carried out using SQUID magnetometer in temperature range between 4.2 K and 300 K. To determine the direction of easy axis of the sample, the magnetic field was applied in both in-plane and out-of plane directions. The magnetic domain structures were performed by magnetic force microscopy at demagnetized state.
3. Results and discussions Fig. 1 shows the normalized room temperature magnetization as a function of the applied magnetic field H for samples with different Ni thickness. Fig. 1(a-d) are for cases when H is normal to film plane while Fig. 1(e-h) are for cases the magnetic field H is applied along the film plane. From these two geometries measurements, it can be clearly seen that all the samples exhibit a perpendicular magnetic anisotropy. The in-plane measurements (hard axis direction) reveal that the magnetization is rotating continuously until saturation. The low remanence magnetization shown in the left panels of Fig. 1 is mainly due to the high magnetostatic field as a result of the large number of repeats. This is similar to what was reported for other magnetic structures with perpendicular anisotropy such as L11−CoPt alloys [39] and for (Co/Ni) multilayers with large a repeat of bilayers [40]. Replacing a single Pt sublayer with Ni at different positions inside (Co/Pt) multilayer also resulted in loss of coercivity [41]. In our previous study on (Co/Pd) multilayers with perpendicular magnetic anisotropy, it was revealed that the hysteresis loop exhibit a bow-tie shape for large number of repeats [42]. This is the reason for the shift of nucleation field (HN) to positive value as revealed in (Co/Ni/Co/Pt) multilayers where the thickness of Ni layer was increased continuously (Fig. 1). A linear increase of HN with the thickness of Ni layer in the multilayer can be seen in Fig. 2. A nucleation field of 90 Oe was measured for the multilayer with 0.3 nm-thick Ni and increases to 390 Oe for 0.9 nm-thick Ni case, representing thus an increase of about 500 Oe/nm. From magnetometry measurements, the saturation magnetization MS at room temperature is also plotted in Fig. 2. A linear increase of MS with Ni thickness is observed with a value of 650 emu/cm3 for tNi = 0.3 nm to 790 emu/cm3 for tNi = 0.9 nm. Although the nucleation field is 3
positive for the four (Co/Ni/Co/Pt) multilayers, their magnetization is perpendicular to film plane as confirmed by the measurement of magnetization versus in-plane magnetic field, which shows a clear rotation of magnetization until saturation [Figs. 1(e−h)]. For better understanding of magnetization reversal, magnetic force microscopy was used
Fig. 1. Room temperature of the out-of plane (a−d) and in-plane (e−h) hysteresis loops for [Co(0.3nm)/Ni(t)/Co(0.3nm)/ Pt(0.8nm)]×8 with different thickness values. (a) and (e) for t = 0.3 nm, (b) and (f) for t = 0.5 nm, (c) and (g) for t = 0.7 nm and (d) and (h) for t =0.9 nm.
4
Fig. 2. Room temperature measurements of the nucleation field and saturation magnetization of [Co(0.3nm)/Ni(t)/Co(0.3nm)/Pt(0.8nm)]×8 multilayers for different Ni thickness t. The nucleation field HN can be fitted with a straight line with a slop of 500 Oe/nm.
to study magnetic domains in (Co/Ni/Co/Pt) multilayers. Firstly, each sample was demagnetized using and an ac magnetic field, which is initially at its maximum and reduced continuously to zero. Fig. 3 (a-d) show MFM images measured at demagnetized state for (Co/Ni/Co/Pt) multilayers with different Ni thickness values. The bottom panels of Fig. 3 are the corresponding simulated images obtained from micromagnetic simulation. The dynamics of the normalized magnetization m = (M/MS) of each multilayer is described by the LandauLifshitz-Gilbert equation:
= −( × ) + ( ×
)
(1)
In Eq. (1), γ, α and Heff are the gyromagnetic ratio, the Gilbert damping constant and the effective field, respectively. The effective field Heff includes the anisotropy field Hk, the exchange field Hex and the magnetostatic field Hmag. The simulated stable magnetic domains were obtained at remanence (without applied magnetic field). 5
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Fig. 3. Top panels are MFM images and bottom panels are the simulated at demagnetized states and for [Co/Ni(t)/Co/Pt] multilayers with different Ni thickness t. (a) t = 0.3 nm, (d) t = 0.5 nm, (e) t = 0.7 nm and (f) t = 0.9 nm. The images sizes are 5 µm by 5 µm.
Heff = Hk + Hex + Hmag
(2)
To obtain comparable simulated magnetic domains to experimental MFM images, we fixed MS to the values obtained by magnetometry measurements and Ku was varied (Tab. 1). The damping constant α for each sample was obtained from ferromagnetic resonance (FMR) [38]. The anisotropy energy Ku = (Hk MS /2) was the only parameter that was adjusted for better comparison between the calculated and measurement domain images. The obtained Ku values are reported in Tab. 1. The size of the images shown in Fig. 3 is 5µm by 5 µm. In the simulation, the cell size was fixed to 5 µm × 5 µm × t/2 nm. It can be clearly seen that the domain size decreases as the thickness of the Ni layer becomes larger consistent with an increasing magnetization. It is important to note that as tNi increases, a continuous reduction of domain size in the multilayers is observed. It is also worthy to notice that by increasing the thickness of Ni, the domains break in small portions. The values of Ku obtained from
6
micromagnetic simulation are slightly different from the experimental values measured using FMR method [38]. Tab. 1: The values of saturation magnetization MS, magnetic anisotropy energy Ku and damping constant α of (Co/Ni/Co/Pt)×8 multilayers with different Ni thickness. The values of Ku are taken from the best fit of MFM images to simulated magnetic domain structures while MS and α values are from magnetometry and FMR measurements, respectively.
Sample
α
MS
Ku
(emu/cm3)
(×106 erg/cm3)
S1
670
3.9
0.079
S2
700
4.4
0.073
S3
730
5.2
0.068
S4
790
5.2
0.060
Figure 4 (a) shows the measured temperature dependence of the saturation magnetization of the investigated samples. The measurements were performed with an external magnetic field of magnitude 20 kOe in a direction perpendicular to the films plane which is large enough to saturate the samples. MS can be described by Bloch's law [43−46]: MS(T) = MS0 (1− B T3/2)
(3)
where MS0 is the ground state magnetization and B is Bloch constant. From the fit of the values of MS versus temperature to Eq. (3), a constant value of B = 2×10−5 K−3/2 for all of samples was obtained. It is also found that MS0 is almost equal to the measured value at T = 4 K. From Fig. 4(b), it can be seen that Ku is linearly dependent on temperature for each value of tNi in the (Co/Ni/Co/Pt) multilayers. The decay of Ku with temperature is larger for thicker Ni sublayer. For 0.3 nm Ni in the multilayer, the decay rate is about 1.1×103 erg/cm3 K and becomes 1.8 ×103 erg/cm3K for 0.9 nm thick Ni. Equation (3) is valid for T < 0.5 Tc where Tc is Curie temperature of the ferromagnetic material. For T closer to Tc, the temperature dependence of saturation magnetization can be described by the power law equation [46]: 7
Fig. 4. The saturation magnetization (MS) as a function of temperature measured for [Co(0.3nm)/Ni(t)/Co(0.3nm)/Pt(0.8nm)]×8 multilayers with different Ni thickness t.
MS(T) = κ (1− )δ
(4)
κ is the proportionality factor and δ is a fitting parameter. From MFM images shown in Fig. 3, it was noticed that as Ni thickness increases the magnetic domains break in smaller regions at
8
the demagnetized state. We correlated between the intrinsic parameters of the multilayers and the spin-wave stiffness constant A through the expression [47]
Fig. 5. Saturation magnetization at 0 K and the spin wave stiffness constant as a function of Ni thickness in [Co(0.3nm)/Ni(t)/Co(0.3nm)/Pt(0.8nm)]×8 multilayers.
=
!"
#
$/&
(5)
where kB is Boltzman constant, µB is the Bohr magnetron, the Riemann-zeta function ξ(3/2) is equal to 2.216 and g-factor is fixed to 2.175. The parameters MS0 and B are determined from the fit of MS versus T to Eq. (3). As indicated above the (Co/Ni/Co/Pt) multilayers did not show any difference in both Block constant B and g-factor. Thus, the spin wave stiffness constant is inversely proportional to MS03/2. Fig. 5 is a plot of the ground state magnetization and the parameter A as a function of Ni thickness in (Co/Ni/Co/Pt) multilayer. It is clear that the increase of MS0 with Ni thickness is a consequence of the reduction of the wave stiffness constant which drops from 20.0×10−22 eV m2 at 0.3 nm-thick Ni to 17.6×10−22 eV m2 at 0.9 nm. These values remain larger that than for [Co(0.1 nm)/Ni(0.5 nm)]×5 multilayers reported by Posth et al. [46] which is itself larger than bulk Ni [48].
9
4. Conclusion Multilayers of (Co/Ni/Co/Pt) with different Ni thicknesses have been investigated using SQUID magnetometry measurements, magnetic force microscopy and micromagnetic formalism. From out-of plane and in-plane hysteresis loops, it was observed that all the samples exhibit a perpendicular magnetic anisotropy. The increase of nucleation field with Ni sublayer thickness was correlated to the reduction of domains size in the (Co/Ni/Co/Pt) multilayers. From micromagnetic simulation, magnetic domains were reduced and the best fit to MFM images was seen for materials properties closer to measured values. From temperature dependence of saturation magnetization MS, the Block’s constant B and spin wave stiffness constant A were determined. MS and A showed a strong dependence on Ni thickness which are themselves correlated to nucleation field and the observed magnetic domains features.
Acknowledgements R. Sbiaa would like to thank the Sultan Qaboos University for the financial support under Grant number IG/SCI/PHYS/14/09. Research at Nebraska by I.A.-O., P.R.K. and D.J.S. was supported by the United States Army Research Office under Award WF911NF-10-2-0099 and was performed in part in the Nebraska Nanoscale Facility, Nebraska Center for Materials and Nanoscience, which is supported by the National Science Foundation under Award NNCI: 1542182, and the Nebraska Research Initiative. Support from the Swedish Foundation for Strategic Research (SSF), the Swedish Research Council (VR), and the Knut and Alice Wallenberg foundation (KAW) is gratefully acknowledged. Johan Åkerman is a Royal Swedish Academy of Sciences Research Fellow supported by a grant from KAW.
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13
Highlights
• • • •
New material based on (Co/Ni/Co/Pt) multilayer with perpendicular magnetic anisotropy is investigated. The magnetic properties were investigated in (Co/Ni/Co/Pt) with different Ni thickness. Micromagnetic simulation was carried out to reproduce magnetic force microscopy images. From magnetometry measurements, micromagnetic simulation and temperature dependence of intrinsic properties (saturation magnetization and anisotropy energy), Block constant and spin wave stiffness were determined for each sample.
14
S0304-8853(17)30861-2 http://dx.doi.org/10.1016/j.jmmm.2017.06.054 MAGMA 62850
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
13 March 2017 27 May 2017 8 June 2017
Please cite this article as: R. Sbiaa, I.A. Al-Omari, M. Al Bahri, P.R. Kharel, M. Ranjbar, J. Åkerman, D.J. Sellmyer, Ni thickness influence on magnetic properties (Co/Ni/Co/Pt) multilayers with perpendicular magnetic anisotropy, Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/10.1016/j.jmmm.2017.06.054
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Ni thickness influence on magnetic properties (Co/Ni/Co/Pt) multilayers with perpendicular magnetic anisotropy R. Sbiaa,1* I. A. Al-Omari,1 M. Al Bahri,1 P. R. Kharel,2 M. Ranjbar,3 J. Åkerman3,4, and D. J. Sellmyer5 1
Department of Physics, Sultan Qaboos University, P.O. Box 36, PC 123, Muscat, Oman
2
Department of Physics, South Dakota State University, Brookings, SD 57007, USA
3
Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden
4
Materials and Nanophysics, School of ICT, KTH Royal Institute of Technology, Isafjordsg. 22, 16440
Kista, Sweden 5
Nebraska Center for Materials and Nanoscience, and Department of Physics and Astronomy,
University of Nebraska, Lincoln, NE 68588, USA
PACS 75.60.Ch– magnetic properties and materials
* Corresponding author: [email protected]
Abstract – We present a study of perpendicular magnetic anisotropy in [Co/Ni(t)/Co/Pt]×8 multilayers for use as free layers in magnetic tunnel junctions (MTJ) and spin valves. The thickness t of the Ni sub-layer was varied and the resulting magnetic properties were compared with (Co/Ni) and (Co/Pt) multilayers with the same number of repeats. As determined from magnetic force microscopy and magnetometry measurements, all multilayers exhibited a perpendicular magnetic anisotropy with an increase of saturation magnetization with thickness t. From the temperature dependence of the magnetization, well described by a Bloch law, we find that the spin-wave stiffness constant of the [Co/Ni(t)/Co/Pt]×8 multilayers is larger compared to (Co/Ni) multilayers. These multilayers could be the basis for spintronic devices where the reduction of total Pt content could help to reduce the damping constant while keeping the magnetic anisotropy energy relatively high. These are conflicting requirements needed for high performance magnetic memory devices.
1
1. Introduction−
Materials with strong perpendicular magnetic anisotropy (PMA) have
received a significant amount of interest in recent years because of their potential for highperformance magnetic memory [1−14]. For instance, the required electrical current for switching the magnetization of a soft layer in a magnetic tunnel junction with PMA by a spin transfer torque (STT) effect is much smaller than in the in-plane anisotropy case [4−7]. PMA materials are also beneficial for high storage density domain wall memory applications [15−24]. In spin torque oscillators, PMA free layers are also used both for zero-field operation [25,26] and for the realization of magnetic droplets [27−31]. Materials such as (Co/Pt), (Co/Pd) and (Co/Ni) multilayers have been intensively investigated as it is easy to adjust their magnetic properties by changing the thickness of the sub-layers and the number of bilayer repeats. Several reports have highlighted the drawback of (Co/Pd) or (Co/Pt) in terms of their higher damping constant (α) compared to that of (Co/Ni) multilayers [32−35]. It is known that the current required for magnetization switching by STT effect is proportional to the damping constant. On the other hand, (Co/Ni) multilayers suffer from their relatively low magnetic anisotropy energy which is an obstacle for reducing the device size due to thermal instability. In fact, a stability factor Ku/kBT should be larger than 40 for room temperature application and even 60 assuming T = 85 °C (Ku is the magnetic anisotropy energy, kB is Boltzmann constant and T is the temperature) [5]. To take advantage of the high anisotropy energy of (Co/Pd) or (Co/Pt) multilayers [36] and low damping constant of (Co/Ni) multilayers [37], we investigated a structure made of a combination of (Co/Ni/Co/Pt) multilayers. The additional layer of Pt in the multilayer is to improve the interface anisotropy energy while the existence of Ni is for improving the polarization and lowering the damping constant. In this paper, we investigate the temperature dependence of the magnetic properties of (Co/Ni/Co/Pt) multilayers. The focus was also on the understanding of the evolution of magnetic domains with Ni thickness and correlate it to saturation magnetization and spin wave stiffness.
2. Experiments
2
The samples have been deposition by DC-sputtering in high vacuum chamber on thermally oxidized silicon. The multilayer consists of [Co(0.3 nm)/Ni(t nm)/Co(0.3 nm)/Pt(0.8 nm)]×8 where Ni thickness was varied from 0.3 nm to 0.9 nm. Prior to the deposition of the multilayer 4 nm-thick Ta followed by 3 nm Pt were used as seedlayers similarly to our previous study [38]. The magnetic measurements were carried out using SQUID magnetometer in temperature range between 4.2 K and 300 K. To determine the direction of easy axis of the sample, the magnetic field was applied in both in-plane and out-of plane directions. The magnetic domain structures were performed by magnetic force microscopy at demagnetized state.
3. Results and discussions Fig. 1 shows the normalized room temperature magnetization as a function of the applied magnetic field H for samples with different Ni thickness. Fig. 1(a-d) are for cases when H is normal to film plane while Fig. 1(e-h) are for cases the magnetic field H is applied along the film plane. From these two geometries measurements, it can be clearly seen that all the samples exhibit a perpendicular magnetic anisotropy. The in-plane measurements (hard axis direction) reveal that the magnetization is rotating continuously until saturation. The low remanence magnetization shown in the left panels of Fig. 1 is mainly due to the high magnetostatic field as a result of the large number of repeats. This is similar to what was reported for other magnetic structures with perpendicular anisotropy such as L11−CoPt alloys [39] and for (Co/Ni) multilayers with large a repeat of bilayers [40]. Replacing a single Pt sublayer with Ni at different positions inside (Co/Pt) multilayer also resulted in loss of coercivity [41]. In our previous study on (Co/Pd) multilayers with perpendicular magnetic anisotropy, it was revealed that the hysteresis loop exhibit a bow-tie shape for large number of repeats [42]. This is the reason for the shift of nucleation field (HN) to positive value as revealed in (Co/Ni/Co/Pt) multilayers where the thickness of Ni layer was increased continuously (Fig. 1). A linear increase of HN with the thickness of Ni layer in the multilayer can be seen in Fig. 2. A nucleation field of 90 Oe was measured for the multilayer with 0.3 nm-thick Ni and increases to 390 Oe for 0.9 nm-thick Ni case, representing thus an increase of about 500 Oe/nm. From magnetometry measurements, the saturation magnetization MS at room temperature is also plotted in Fig. 2. A linear increase of MS with Ni thickness is observed with a value of 650 emu/cm3 for tNi = 0.3 nm to 790 emu/cm3 for tNi = 0.9 nm. Although the nucleation field is 3
positive for the four (Co/Ni/Co/Pt) multilayers, their magnetization is perpendicular to film plane as confirmed by the measurement of magnetization versus in-plane magnetic field, which shows a clear rotation of magnetization until saturation [Figs. 1(e−h)]. For better understanding of magnetization reversal, magnetic force microscopy was used
Fig. 1. Room temperature of the out-of plane (a−d) and in-plane (e−h) hysteresis loops for [Co(0.3nm)/Ni(t)/Co(0.3nm)/ Pt(0.8nm)]×8 with different thickness values. (a) and (e) for t = 0.3 nm, (b) and (f) for t = 0.5 nm, (c) and (g) for t = 0.7 nm and (d) and (h) for t =0.9 nm.
4
Fig. 2. Room temperature measurements of the nucleation field and saturation magnetization of [Co(0.3nm)/Ni(t)/Co(0.3nm)/Pt(0.8nm)]×8 multilayers for different Ni thickness t. The nucleation field HN can be fitted with a straight line with a slop of 500 Oe/nm.
to study magnetic domains in (Co/Ni/Co/Pt) multilayers. Firstly, each sample was demagnetized using and an ac magnetic field, which is initially at its maximum and reduced continuously to zero. Fig. 3 (a-d) show MFM images measured at demagnetized state for (Co/Ni/Co/Pt) multilayers with different Ni thickness values. The bottom panels of Fig. 3 are the corresponding simulated images obtained from micromagnetic simulation. The dynamics of the normalized magnetization m = (M/MS) of each multilayer is described by the LandauLifshitz-Gilbert equation:
= −( × ) + ( ×
)
(1)
In Eq. (1), γ, α and Heff are the gyromagnetic ratio, the Gilbert damping constant and the effective field, respectively. The effective field Heff includes the anisotropy field Hk, the exchange field Hex and the magnetostatic field Hmag. The simulated stable magnetic domains were obtained at remanence (without applied magnetic field). 5
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Fig. 3. Top panels are MFM images and bottom panels are the simulated at demagnetized states and for [Co/Ni(t)/Co/Pt] multilayers with different Ni thickness t. (a) t = 0.3 nm, (d) t = 0.5 nm, (e) t = 0.7 nm and (f) t = 0.9 nm. The images sizes are 5 µm by 5 µm.
Heff = Hk + Hex + Hmag
(2)
To obtain comparable simulated magnetic domains to experimental MFM images, we fixed MS to the values obtained by magnetometry measurements and Ku was varied (Tab. 1). The damping constant α for each sample was obtained from ferromagnetic resonance (FMR) [38]. The anisotropy energy Ku = (Hk MS /2) was the only parameter that was adjusted for better comparison between the calculated and measurement domain images. The obtained Ku values are reported in Tab. 1. The size of the images shown in Fig. 3 is 5µm by 5 µm. In the simulation, the cell size was fixed to 5 µm × 5 µm × t/2 nm. It can be clearly seen that the domain size decreases as the thickness of the Ni layer becomes larger consistent with an increasing magnetization. It is important to note that as tNi increases, a continuous reduction of domain size in the multilayers is observed. It is also worthy to notice that by increasing the thickness of Ni, the domains break in small portions. The values of Ku obtained from
6
micromagnetic simulation are slightly different from the experimental values measured using FMR method [38]. Tab. 1: The values of saturation magnetization MS, magnetic anisotropy energy Ku and damping constant α of (Co/Ni/Co/Pt)×8 multilayers with different Ni thickness. The values of Ku are taken from the best fit of MFM images to simulated magnetic domain structures while MS and α values are from magnetometry and FMR measurements, respectively.
Sample
α
MS
Ku
(emu/cm3)
(×106 erg/cm3)
S1
670
3.9
0.079
S2
700
4.4
0.073
S3
730
5.2
0.068
S4
790
5.2
0.060
Figure 4 (a) shows the measured temperature dependence of the saturation magnetization of the investigated samples. The measurements were performed with an external magnetic field of magnitude 20 kOe in a direction perpendicular to the films plane which is large enough to saturate the samples. MS can be described by Bloch's law [43−46]: MS(T) = MS0 (1− B T3/2)
(3)
where MS0 is the ground state magnetization and B is Bloch constant. From the fit of the values of MS versus temperature to Eq. (3), a constant value of B = 2×10−5 K−3/2 for all of samples was obtained. It is also found that MS0 is almost equal to the measured value at T = 4 K. From Fig. 4(b), it can be seen that Ku is linearly dependent on temperature for each value of tNi in the (Co/Ni/Co/Pt) multilayers. The decay of Ku with temperature is larger for thicker Ni sublayer. For 0.3 nm Ni in the multilayer, the decay rate is about 1.1×103 erg/cm3 K and becomes 1.8 ×103 erg/cm3K for 0.9 nm thick Ni. Equation (3) is valid for T < 0.5 Tc where Tc is Curie temperature of the ferromagnetic material. For T closer to Tc, the temperature dependence of saturation magnetization can be described by the power law equation [46]: 7
Fig. 4. The saturation magnetization (MS) as a function of temperature measured for [Co(0.3nm)/Ni(t)/Co(0.3nm)/Pt(0.8nm)]×8 multilayers with different Ni thickness t.
MS(T) = κ (1− )δ
(4)
κ is the proportionality factor and δ is a fitting parameter. From MFM images shown in Fig. 3, it was noticed that as Ni thickness increases the magnetic domains break in smaller regions at
8
the demagnetized state. We correlated between the intrinsic parameters of the multilayers and the spin-wave stiffness constant A through the expression [47]
Fig. 5. Saturation magnetization at 0 K and the spin wave stiffness constant as a function of Ni thickness in [Co(0.3nm)/Ni(t)/Co(0.3nm)/Pt(0.8nm)]×8 multilayers.
=
!"
#
$/&
(5)
where kB is Boltzman constant, µB is the Bohr magnetron, the Riemann-zeta function ξ(3/2) is equal to 2.216 and g-factor is fixed to 2.175. The parameters MS0 and B are determined from the fit of MS versus T to Eq. (3). As indicated above the (Co/Ni/Co/Pt) multilayers did not show any difference in both Block constant B and g-factor. Thus, the spin wave stiffness constant is inversely proportional to MS03/2. Fig. 5 is a plot of the ground state magnetization and the parameter A as a function of Ni thickness in (Co/Ni/Co/Pt) multilayer. It is clear that the increase of MS0 with Ni thickness is a consequence of the reduction of the wave stiffness constant which drops from 20.0×10−22 eV m2 at 0.3 nm-thick Ni to 17.6×10−22 eV m2 at 0.9 nm. These values remain larger that than for [Co(0.1 nm)/Ni(0.5 nm)]×5 multilayers reported by Posth et al. [46] which is itself larger than bulk Ni [48].
9
4. Conclusion Multilayers of (Co/Ni/Co/Pt) with different Ni thicknesses have been investigated using SQUID magnetometry measurements, magnetic force microscopy and micromagnetic formalism. From out-of plane and in-plane hysteresis loops, it was observed that all the samples exhibit a perpendicular magnetic anisotropy. The increase of nucleation field with Ni sublayer thickness was correlated to the reduction of domains size in the (Co/Ni/Co/Pt) multilayers. From micromagnetic simulation, magnetic domains were reduced and the best fit to MFM images was seen for materials properties closer to measured values. From temperature dependence of saturation magnetization MS, the Block’s constant B and spin wave stiffness constant A were determined. MS and A showed a strong dependence on Ni thickness which are themselves correlated to nucleation field and the observed magnetic domains features.
Acknowledgements R. Sbiaa would like to thank the Sultan Qaboos University for the financial support under Grant number IG/SCI/PHYS/14/09. Research at Nebraska by I.A.-O., P.R.K. and D.J.S. was supported by the United States Army Research Office under Award WF911NF-10-2-0099 and was performed in part in the Nebraska Nanoscale Facility, Nebraska Center for Materials and Nanoscience, which is supported by the National Science Foundation under Award NNCI: 1542182, and the Nebraska Research Initiative. Support from the Swedish Foundation for Strategic Research (SSF), the Swedish Research Council (VR), and the Knut and Alice Wallenberg foundation (KAW) is gratefully acknowledged. Johan Åkerman is a Royal Swedish Academy of Sciences Research Fellow supported by a grant from KAW.
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Highlights
• • • •
New material based on (Co/Ni/Co/Pt) multilayer with perpendicular magnetic anisotropy is investigated. The magnetic properties were investigated in (Co/Ni/Co/Pt) with different Ni thickness. Micromagnetic simulation was carried out to reproduce magnetic force microscopy images. From magnetometry measurements, micromagnetic simulation and temperature dependence of intrinsic properties (saturation magnetization and anisotropy energy), Block constant and spin wave stiffness were determined for each sample.
14