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Temperature dependence of spin-torque driven ferromagnetic resonance in MgO-based magnetic tunnel junction with a perpendicularly free layer
Accepted Manuscript Research articles Temperature dependence of spin-torque driven ferromagnetic resonance in MgO-based magnetic tunnel junction with a perpendicularly free layer Xiao Wang, Jiafeng Feng, Peng Guo, H.X. Wei, X.F. Han, B. Fang, Z.M. Zeng PII: DOI: Reference:
S0304-8853(17)30961-7 http://dx.doi.org/10.1016/j.jmmm.2017.07.075 MAGMA 63006
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
22 March 2017 19 June 2017 21 July 2017
Please cite this article as: X. Wang, J. Feng, P. Guo, H.X. Wei, X.F. Han, B. Fang, Z.M. Zeng, Temperature dependence of spin-torque driven ferromagnetic resonance in MgO-based magnetic tunnel junction with a perpendicularly free layer, Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/10.1016/ j.jmmm.2017.07.075
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.
Temperature dependence of spin-torque driven ferromagnetic resonance in MgO-based magnetic tunnel junction with a perpendicularly free layer Xiao Wang,1 Jiafeng Feng,1∗ Peng Guo,1 H. X. Wei,1∗ X. F. Han1, B. Fang2, and Z. M. Zeng2 1
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese
Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China. 2
Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-tech and
Nano-bionics, Chinese Academy of Sciences, Ruoshui Road 398, Suzhou 215123, China
Abstract We report the temperature dependence of the spin-torque (ST) driven ferromagnetic resonance in MgO-based magnetic tunnel junction (MTJ) nanopillars with a perpendicularly free layer and an in-plane reference layer. From the evolution of the resonance frequency with magnetic field, we clearly identify the free-layer resonance mode and reference-layer mode. For the reference layer, we demonstrate a monotonic increase in resonance frequency and the effective damping with decreasing temperature, which suggests the saturated magnetization of the reference layer is dominant. However, for the free layer, the frequency and damping exhibit almost no change with temperature, indicating that the perpendicular magnetic anisotropy plays an important role in magnetization dynamics of the free layer.
1
A spin-polarized DC current via spin-torque (ST) effect1,2 can generate microwave oscillations in nanometer-sized magnetic multilayers, 3,4 such as magnetic tunnel junctions (MTJs). The microwave oscillations caused by magnetization dynamics normally occur at high frequencies in the GHz range.1,2 On the interplay between magnetization dynamics and the spin-dependent transport, a microwave alternating power (or current) to the magnetic multilayers can lead to a measureable DC voltage due to the ST effect,5 which results in a STdriven ferromagnetic resonance (ST-FMR). The ST-FMR technique can be used to study magnetic anisotropy, damping, or ST interactions in the magnetic multilayers5-14, or enables a new type of nanoscale diode (ST diode).15
Recently, MTJs with a perpendicular magnetic anisotropy in combination of high tunnel magnetoresistance and high thermal stability were demonstrated to be a promising candidate for ST magnetic random access memory,16,17 or ST nano-scaled oscillators.18-21 In such systems, the perpendicular anisotropy plays an important role in determining the magnetization dynamics. Here, we report on temperature dependence of magnetization dynamics in such system by using the ST-FMR technique. The precession oscillation modes of both free and reference layers at high frequency have been identified under a microwave power. The relation between microwave oscillation (resonance frequency, linewidth) and the saturated magnetization, anisotropy field and damping factor are discussed for both free and reference layers at different temperatures.
The MTJ consists of a main structure of PtMn (15)/Co70Fe30 (2.3)/Ru (0.85)/Co40Fe40B20 (2.4) (in-plane magnetized CoFeB, reference layer)/ MgO (1.0)/ Co20Fe60B20 (1.1)
2
(perpendicular magnetized CoFeB, free layer) (thicknesses in nm) was deposited by a sputtering system. Then the MTJ nanopillars with a diameter of 60 nm [Fig. 1 (a)] were fabricated using electron-beam lithography and ion milling techniques. The measurement circuit setup of ST-FMR [Fig. 1 (a)] is similar to that described in Ref. 9. A constant microwave power (0 dBm) was applied to the MTJ nanopillar device through a bias Tee and the DC voltage produced across the device was recorded by a vector network analyzer. A baseline taken without any microwave power as subtracted from the measured spectral data. During the measurement, magnetic field H was applied in the film plane and the magnetic configurations between free and reference layers are shown in Fig. 1 (b). The angle of the free layer deviating from z - axis is defined as ϕ, while the angle between the reference layer and the field direction is marked as θ , which is set to 25° at zero magnetic field in our work.
Figure 2 shows the nanopillar resistance R as a function of the in-plane magnetic field H at 140 K. Its resistance-area (RA) value is 30 Ωµm2 in the parallel state, which is relatively larger than that in previous work18 but still excites a DC voltage under a microwave alternating power as shown below. In the range from -1000 Oe to + 1000Oe, the MTJ nanopillar shows a roughly linear response of resistances, suggesting that the magnetization of the free layer gradually change as magnetic field increases. The evolution of magnetic configurations between free layer and reference layer are presented in Figure 2. Similar behaviors in R - H curves have also been observed in other temperatures. In a MTJ the resistance depends on the relative orientation (β ) between free and reference layers:
[(1+cosβ)
+ (1-cosβ )
(β ) =
], where RP and RAP are the parallel and antiparallel resistances
when β = 0° and 180°, respectively. The fitting of R-H curve with this angle dependence 3
yields RAP = 20.15k Ω and RP = 10.67 kΩ, respectively. From here, we can estimate the β values at different fields, which determine the magnetic configurations between the free and reference layers. For example, as given in Fig. 2, β = 111° at H = -1 kOe. Moreover, the field position for β = 90° is about 190 Oe at 140 K, which indicates a dipolar stray-field coupling Hcoupling between free and reference layers exists in our MTJ nanopillar. The values of Hcoupling extracted from the R - H curves at different temperatures are given in the insert of Fig. 2, which changes from 70 Oe at 300 K to 211 Oe at 100 K. The positive Hcoupling in our case suggests that the free and reference layers couple ferromagnetically.22
For our MTJ nanopillar with a perpendicularly free layer and an in-plane reference layer, it is feasible to produce a nonzero ST effect under a microwave power because the magnetizations of free and reference layers are always misaligned unless they are absolutely in the parallel and antiparallel configurations. The nonzero ST under a microwave power can excite high frequency procession in the magnetization of either the free or reference layer (or both). To simplify the analysis, we focus on ST-FMR study in the field range of -1kOe ∼ -3kOe, where the perpendicularly free layer almost remains in-plane. In this field range, the high frequency precession modes arouse from both the free and reference layers were identified.
Figure 3 displays the representative ST-FMR spectra at different magnetic fields at 100 K. The maximum of DC voltage is 1.5mV, which is relatively low compared to that (17mV) given previously.23 Two obvious resonance peaks (fr1 and fr2) are found: the higher frequency precession arises from the reference layer while the lower frequency precession is from the
4
free layer. Moreover, the line shape of DC voltage signals at fr1 and fr2 is not symmetric, which can be described by a combined symmetric and antisymmetric Lorenztian of the
( )/∆
form = ( )/∆ − ( ) /∆ with fr and ∆0 as resonance frequency and linewidth.
By fit the DC voltage, fr and ∆0 at different fields and temperatures can be obtained, as shown in Fig. 4, Fig. 5 (b) and their inserts. In addition, the |B/A| ratio in our case is in the range from 1/3 to 3/2 with magnetic field, which might suggest the “effective field” component of spin torque perpendicular to the magnetizations of both free and reference layers may make the contribution to the antisymmetric component of the ST-FMR line shape in our case.5 To study the magnetic properties of both free and reference layers, we select fr1 = fr2 =
[ − ( − !" ) cos φ],
(1)
(( + * )( + * + !"−+,, )
(2)
to study fr1, fr2 versus H at different temperatures, here is Landé g factor, -. is Bohr magneton, h is Plank’s constant, / and !" are the perpendicular magnetic anisotropy field and the saturated magnetization of free layer, * and !"−+,, are the in-plane anisotropy field and effective saturated magnetization of the reference layer, respectively. As an example, the field dependence of fr1 and fr2 at 100 K is given in the insert of Fig. 4 (a). By fitting the fr1, fr2 versus H curves, one obtains factor, ( / − 4π !" ) cos 2 of the free layer, the in-plane anisotropy field * and !"−+,, of the reference layer, respectively. The solid lines as shown in the insert of Fig. 4 (a) are the fitted results, which match the experimental data of fr1 and fr2 versus H well. Furthermore, we obtain the same value of (1.12) for both fr1 and fr2 versus H at all measured temperatures, and the in-plane 3 is fixed to 50 Oe during the fit. 5
All the fit data of ( − 4π !" ) cos 2 and !"−+,, from 100 K to 300 K are given in Fig. 4 (a). To check !"−+,, of the in-plane reference layer, we use Block’s Law ;
8
!"−+,, (K) = !"−+,, (0)[1 − 79∗ : ] to describe its temperature dependence. By fitting !"−+,, versus T as given by the black solid curve in Fig. 4 (a), we obtain the spontaneous magnetization at 0 K [ !"−+,, (0)] is 1.84 Tesla (1468 emu/cc), and T ∗ is 1373 K. The fitted !"−+,, (0) and T ∗ in our case are comparable to those observed in the Fe-riched thin CoFeB with a perpendicular anisotropy,24 which are 1457 emu/cc and 1120 K, indicating that high-quality CoFeB with different magnetic anisotropy has similar intrinsic magnetic properties. To further check !"−+,, , the fit values of , 3 and !"−+,, are used to calculate the fr2 – T curve at different magnetic fields: fr2 =
(( + * + =>?@ABCD )( + * + =>?@ABCD + !"−+,, ).
(3)
Here =>?@ABCD is added in the formula of fr2. As examples, the calculated results of fr2 at -1.2 kOe and -1.6 kOe are shown in Fig. 4 (b), and one can see the calculated values of fr2 at different fields are close to the experimental data especially at low temperatures, which also suggests the fitted and !"−+,, are reasonable. The deviation of the calculated fr2 at high temperature might be due to the temperature effect of critical current density variation.22 As shown in Fig. 4 (b), one may see the fit values of ( / − 4π !" ) cos φ of the perpendicular free layer are small and remain almost unchangeable from 100 K to 300 K, which suggests fr1 has weak temperature dependence. Similar to the fr2 case shown in Fig. 4 (b), the solid lines of the calculated fr1 using the formula
[ − ( / − 4π !" ) cos 2] almost follow the
experimental data of fr1 at H = -1.2 kOe and -1.8 kOe, which again suggests that the fit values of and ( / − 4π !" ) cos φ are reasonable. The calculated fr1 at other magnetic fields 6
also follows the experimental data well. In this work, the aim to use the format of ( / − 4π !" ) cos 2 as a whole mainly gives an intuitive description of the fr1 – T curves. Moreover, there is a critical value for 2 if we set / = 0. If using the effective !" data in Ref. 24, the critical value for 2 is 89.3° ± 0.05° at different magnetic fields in the temperature range of 100 K - 300 K. Finally, we discuss the effective damping factor of free and reference layers varying with temperature. As shown before, ∆0 can be obtained by fitting the line shape of DC voltage as given in Fig. 3. As examples, the fitted data of ∆01 of the free layer at -1.2 kOe and ∆02 of the reference layer at -1 kOe as a function of temperature are given in the insert of Fig. 5. From the fitted ∆0, one can see both ∆01 and ∆02 have a roughly linear response with temperature, but ∆01 decreases and ∆02 increases by decreasing temperature. This suggests fr2 and ∆02 have normal temperature dependence, while fr1 and ∆01 have abnormal one. For simplicity, we use the formula of the Gilbert damping factor to describe the damping factor in our case. The linewidth due to pure FMR effect follows ∆01(02) = E+,,(+,,)
!"+,,,25 here E+,,
is the effective Gilbert damping factor of the free layer, and E+,, is that of the reference layer. To estimate the effective damping factors (E) of the free and reference layers, we use the fitted !"+,, data of the in-plane reference layer, while reference to the effective !" for the free layer from Ref. 24. The estimated E+,, and E+,, are shown in Fig.5. E+,, of the reference layer increases gradually by decreasing temperature, which has a similar change with temperature compared to the previous reports for a perpendicular Fe-riched CoFeB26 and for an in-plane NiFe/CoFe bilayers.27 The value of E+,, at 300 K is about 0.01, which is comparable to that of CoFeB11,12,28 or Py alloy13. However, if one 7
considers the spin torque effect, the damping factor E should be variable some.13 Moreover, the damping factor should also vary with the angles (ϕ, β, and θ in our case).11 Compared to E+,, , a different temperature dependence of E+,, is observed for the free layer, which might be due to the suppressed / and !" when the free layer remains in-plane. However, the free layer is still active because a small damping factor has been obtained compared to that of the reference layer, and the large DC voltage for the free layer as shown in Fig. 3 can also prove this point. In conclusion, MgO MTJ nanopillars with a perpendicular free layer and an in-plane reference layer have been fabricated and their temperature dependence of the microwave oscillation at high frequency under ST-FMR effect has been systematically investigated. The related
parameters,
such
as
the
effective
!"
of
in-plane
reference
layer,
( − 4π M" )cosϕ of the perpendicular free layer, and the damping factor of both free and reference layers, have been obtained in the temperature range from 300 K to 100 K. The values of !" and ( / − 4π !" )cosϕ at 300 K are 1.66 Tesla and 180 Oe, while the effective damping factors of both free and reference layers at 300 K are 0.0057 and 0.01, respectively. The effective damping factor of the reference layer shows normal temperature dependence, while that of the free layer remains almost unchangeable with temperature due to the suppressed and !" when the free layer remains in-plane. From our work, one may find MgO MTJ stack with a perpendicular free layer and an in-plane reference layer is good candidate for studying the microwave oscillation at high frequency using the ST-FMR effect.
Acknowledgements
The work was supported by the National Natural Science Foundation [NSFC, Grant Nos. 8
11434014, 11674373 and 51401236], Youth Innovation Promotion Association of Chinese Academy of Sciences (No.2017010).
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Figure Captions
Figure1 (a) The schematic ST-FMR circuit setup and cross-sectional view of the MTJ structure. (b) The magnetic configurations of free and reference layers when applying an in plane magnetic field H. The x- y-, and z- axes and the angles ϕ, θ, and β are defined, which 11
are the angle ϕ of the free layer deviating from z - axis, θ between the reference layer and the field direction, and β between the reference and free layers.
Figure 2 The field dependence of pillar resistance at 140 K. The relative orientation of magnetic moments of the free (blue color) and reference (black color) layers are given. The insert shows the dipolar coupling field Hcoupling as a function of temperature obtained from the R - H curves at different temperatures, where the angle β between the free and reference layers is absolutely 90°.
Figure 3 Signals of DC voltage due to the ST-FMR effect at 100 K. There are two main precession peaks, which are responsible for the free and reference layers, respectively. The dash lines are guide to eye.
Figure 4 The temperature dependence of (a) fitted in-plane effective µ0Ms-eff and perpendicular ( − 4π !" )cosϕ and (b) resonance frequencies of free and reference layers at different fields. The insert in (a) shows the field dependence of oscillation frequencies fr1 and fr2 at 100 K. The solid lines in (a) and in the insert are the fitted results and the solid lines in (b) are the calculated results.
Figure 5 The temperature dependence of the effective damping factor of free (α1-eff) and reference (α2-eff) layers. The insert shows the fitted linewidth of free (∆01) and reference (∆02), which are taken at -1.2 kOe and -1 kOe. The solid and dash lines are guide to eye.
12
13
14
15
16
17
This work reports the spin-torque driven ferromagnetic resonance in MgO magnetic tunnel junction nanopillars with a perpendicularly free layer and an in-plane reference layer Both free and reference layers precess at high frequencies under a microwave power and their saturated magnetization, anisotropy field and damping factor have been studied at different temperatures.
18
S0304-8853(17)30961-7 http://dx.doi.org/10.1016/j.jmmm.2017.07.075 MAGMA 63006
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
22 March 2017 19 June 2017 21 July 2017
Please cite this article as: X. Wang, J. Feng, P. Guo, H.X. Wei, X.F. Han, B. Fang, Z.M. Zeng, Temperature dependence of spin-torque driven ferromagnetic resonance in MgO-based magnetic tunnel junction with a perpendicularly free layer, Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/10.1016/ j.jmmm.2017.07.075
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.
Temperature dependence of spin-torque driven ferromagnetic resonance in MgO-based magnetic tunnel junction with a perpendicularly free layer Xiao Wang,1 Jiafeng Feng,1∗ Peng Guo,1 H. X. Wei,1∗ X. F. Han1, B. Fang2, and Z. M. Zeng2 1
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese
Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China. 2
Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-tech and
Nano-bionics, Chinese Academy of Sciences, Ruoshui Road 398, Suzhou 215123, China
Abstract We report the temperature dependence of the spin-torque (ST) driven ferromagnetic resonance in MgO-based magnetic tunnel junction (MTJ) nanopillars with a perpendicularly free layer and an in-plane reference layer. From the evolution of the resonance frequency with magnetic field, we clearly identify the free-layer resonance mode and reference-layer mode. For the reference layer, we demonstrate a monotonic increase in resonance frequency and the effective damping with decreasing temperature, which suggests the saturated magnetization of the reference layer is dominant. However, for the free layer, the frequency and damping exhibit almost no change with temperature, indicating that the perpendicular magnetic anisotropy plays an important role in magnetization dynamics of the free layer.
1
A spin-polarized DC current via spin-torque (ST) effect1,2 can generate microwave oscillations in nanometer-sized magnetic multilayers, 3,4 such as magnetic tunnel junctions (MTJs). The microwave oscillations caused by magnetization dynamics normally occur at high frequencies in the GHz range.1,2 On the interplay between magnetization dynamics and the spin-dependent transport, a microwave alternating power (or current) to the magnetic multilayers can lead to a measureable DC voltage due to the ST effect,5 which results in a STdriven ferromagnetic resonance (ST-FMR). The ST-FMR technique can be used to study magnetic anisotropy, damping, or ST interactions in the magnetic multilayers5-14, or enables a new type of nanoscale diode (ST diode).15
Recently, MTJs with a perpendicular magnetic anisotropy in combination of high tunnel magnetoresistance and high thermal stability were demonstrated to be a promising candidate for ST magnetic random access memory,16,17 or ST nano-scaled oscillators.18-21 In such systems, the perpendicular anisotropy plays an important role in determining the magnetization dynamics. Here, we report on temperature dependence of magnetization dynamics in such system by using the ST-FMR technique. The precession oscillation modes of both free and reference layers at high frequency have been identified under a microwave power. The relation between microwave oscillation (resonance frequency, linewidth) and the saturated magnetization, anisotropy field and damping factor are discussed for both free and reference layers at different temperatures.
The MTJ consists of a main structure of PtMn (15)/Co70Fe30 (2.3)/Ru (0.85)/Co40Fe40B20 (2.4) (in-plane magnetized CoFeB, reference layer)/ MgO (1.0)/ Co20Fe60B20 (1.1)
2
(perpendicular magnetized CoFeB, free layer) (thicknesses in nm) was deposited by a sputtering system. Then the MTJ nanopillars with a diameter of 60 nm [Fig. 1 (a)] were fabricated using electron-beam lithography and ion milling techniques. The measurement circuit setup of ST-FMR [Fig. 1 (a)] is similar to that described in Ref. 9. A constant microwave power (0 dBm) was applied to the MTJ nanopillar device through a bias Tee and the DC voltage produced across the device was recorded by a vector network analyzer. A baseline taken without any microwave power as subtracted from the measured spectral data. During the measurement, magnetic field H was applied in the film plane and the magnetic configurations between free and reference layers are shown in Fig. 1 (b). The angle of the free layer deviating from z - axis is defined as ϕ, while the angle between the reference layer and the field direction is marked as θ , which is set to 25° at zero magnetic field in our work.
Figure 2 shows the nanopillar resistance R as a function of the in-plane magnetic field H at 140 K. Its resistance-area (RA) value is 30 Ωµm2 in the parallel state, which is relatively larger than that in previous work18 but still excites a DC voltage under a microwave alternating power as shown below. In the range from -1000 Oe to + 1000Oe, the MTJ nanopillar shows a roughly linear response of resistances, suggesting that the magnetization of the free layer gradually change as magnetic field increases. The evolution of magnetic configurations between free layer and reference layer are presented in Figure 2. Similar behaviors in R - H curves have also been observed in other temperatures. In a MTJ the resistance depends on the relative orientation (β ) between free and reference layers:
[(1+cosβ)
+ (1-cosβ )
(β ) =
], where RP and RAP are the parallel and antiparallel resistances
when β = 0° and 180°, respectively. The fitting of R-H curve with this angle dependence 3
yields RAP = 20.15k Ω and RP = 10.67 kΩ, respectively. From here, we can estimate the β values at different fields, which determine the magnetic configurations between the free and reference layers. For example, as given in Fig. 2, β = 111° at H = -1 kOe. Moreover, the field position for β = 90° is about 190 Oe at 140 K, which indicates a dipolar stray-field coupling Hcoupling between free and reference layers exists in our MTJ nanopillar. The values of Hcoupling extracted from the R - H curves at different temperatures are given in the insert of Fig. 2, which changes from 70 Oe at 300 K to 211 Oe at 100 K. The positive Hcoupling in our case suggests that the free and reference layers couple ferromagnetically.22
For our MTJ nanopillar with a perpendicularly free layer and an in-plane reference layer, it is feasible to produce a nonzero ST effect under a microwave power because the magnetizations of free and reference layers are always misaligned unless they are absolutely in the parallel and antiparallel configurations. The nonzero ST under a microwave power can excite high frequency procession in the magnetization of either the free or reference layer (or both). To simplify the analysis, we focus on ST-FMR study in the field range of -1kOe ∼ -3kOe, where the perpendicularly free layer almost remains in-plane. In this field range, the high frequency precession modes arouse from both the free and reference layers were identified.
Figure 3 displays the representative ST-FMR spectra at different magnetic fields at 100 K. The maximum of DC voltage is 1.5mV, which is relatively low compared to that (17mV) given previously.23 Two obvious resonance peaks (fr1 and fr2) are found: the higher frequency precession arises from the reference layer while the lower frequency precession is from the
4
free layer. Moreover, the line shape of DC voltage signals at fr1 and fr2 is not symmetric, which can be described by a combined symmetric and antisymmetric Lorenztian of the
( )/∆
form = ( )/∆ − ( ) /∆ with fr and ∆0 as resonance frequency and linewidth.
By fit the DC voltage, fr and ∆0 at different fields and temperatures can be obtained, as shown in Fig. 4, Fig. 5 (b) and their inserts. In addition, the |B/A| ratio in our case is in the range from 1/3 to 3/2 with magnetic field, which might suggest the “effective field” component of spin torque perpendicular to the magnetizations of both free and reference layers may make the contribution to the antisymmetric component of the ST-FMR line shape in our case.5 To study the magnetic properties of both free and reference layers, we select fr1 = fr2 =
[ − ( − !" ) cos φ],
(1)
(( + * )( + * + !"−+,, )
(2)
to study fr1, fr2 versus H at different temperatures, here is Landé g factor, -. is Bohr magneton, h is Plank’s constant, / and !" are the perpendicular magnetic anisotropy field and the saturated magnetization of free layer, * and !"−+,, are the in-plane anisotropy field and effective saturated magnetization of the reference layer, respectively. As an example, the field dependence of fr1 and fr2 at 100 K is given in the insert of Fig. 4 (a). By fitting the fr1, fr2 versus H curves, one obtains factor, ( / − 4π !" ) cos 2 of the free layer, the in-plane anisotropy field * and !"−+,, of the reference layer, respectively. The solid lines as shown in the insert of Fig. 4 (a) are the fitted results, which match the experimental data of fr1 and fr2 versus H well. Furthermore, we obtain the same value of (1.12) for both fr1 and fr2 versus H at all measured temperatures, and the in-plane 3 is fixed to 50 Oe during the fit. 5
All the fit data of ( − 4π !" ) cos 2 and !"−+,, from 100 K to 300 K are given in Fig. 4 (a). To check !"−+,, of the in-plane reference layer, we use Block’s Law ;
8
!"−+,, (K) = !"−+,, (0)[1 − 79∗ : ] to describe its temperature dependence. By fitting !"−+,, versus T as given by the black solid curve in Fig. 4 (a), we obtain the spontaneous magnetization at 0 K [ !"−+,, (0)] is 1.84 Tesla (1468 emu/cc), and T ∗ is 1373 K. The fitted !"−+,, (0) and T ∗ in our case are comparable to those observed in the Fe-riched thin CoFeB with a perpendicular anisotropy,24 which are 1457 emu/cc and 1120 K, indicating that high-quality CoFeB with different magnetic anisotropy has similar intrinsic magnetic properties. To further check !"−+,, , the fit values of , 3 and !"−+,, are used to calculate the fr2 – T curve at different magnetic fields: fr2 =
(( + * + =>?@ABCD )( + * + =>?@ABCD + !"−+,, ).
(3)
Here =>?@ABCD is added in the formula of fr2. As examples, the calculated results of fr2 at -1.2 kOe and -1.6 kOe are shown in Fig. 4 (b), and one can see the calculated values of fr2 at different fields are close to the experimental data especially at low temperatures, which also suggests the fitted and !"−+,, are reasonable. The deviation of the calculated fr2 at high temperature might be due to the temperature effect of critical current density variation.22 As shown in Fig. 4 (b), one may see the fit values of ( / − 4π !" ) cos φ of the perpendicular free layer are small and remain almost unchangeable from 100 K to 300 K, which suggests fr1 has weak temperature dependence. Similar to the fr2 case shown in Fig. 4 (b), the solid lines of the calculated fr1 using the formula
[ − ( / − 4π !" ) cos 2] almost follow the
experimental data of fr1 at H = -1.2 kOe and -1.8 kOe, which again suggests that the fit values of and ( / − 4π !" ) cos φ are reasonable. The calculated fr1 at other magnetic fields 6
also follows the experimental data well. In this work, the aim to use the format of ( / − 4π !" ) cos 2 as a whole mainly gives an intuitive description of the fr1 – T curves. Moreover, there is a critical value for 2 if we set / = 0. If using the effective !" data in Ref. 24, the critical value for 2 is 89.3° ± 0.05° at different magnetic fields in the temperature range of 100 K - 300 K. Finally, we discuss the effective damping factor of free and reference layers varying with temperature. As shown before, ∆0 can be obtained by fitting the line shape of DC voltage as given in Fig. 3. As examples, the fitted data of ∆01 of the free layer at -1.2 kOe and ∆02 of the reference layer at -1 kOe as a function of temperature are given in the insert of Fig. 5. From the fitted ∆0, one can see both ∆01 and ∆02 have a roughly linear response with temperature, but ∆01 decreases and ∆02 increases by decreasing temperature. This suggests fr2 and ∆02 have normal temperature dependence, while fr1 and ∆01 have abnormal one. For simplicity, we use the formula of the Gilbert damping factor to describe the damping factor in our case. The linewidth due to pure FMR effect follows ∆01(02) = E+,,(+,,)
!"+,,,25 here E+,,
is the effective Gilbert damping factor of the free layer, and E+,, is that of the reference layer. To estimate the effective damping factors (E) of the free and reference layers, we use the fitted !"+,, data of the in-plane reference layer, while reference to the effective !" for the free layer from Ref. 24. The estimated E+,, and E+,, are shown in Fig.5. E+,, of the reference layer increases gradually by decreasing temperature, which has a similar change with temperature compared to the previous reports for a perpendicular Fe-riched CoFeB26 and for an in-plane NiFe/CoFe bilayers.27 The value of E+,, at 300 K is about 0.01, which is comparable to that of CoFeB11,12,28 or Py alloy13. However, if one 7
considers the spin torque effect, the damping factor E should be variable some.13 Moreover, the damping factor should also vary with the angles (ϕ, β, and θ in our case).11 Compared to E+,, , a different temperature dependence of E+,, is observed for the free layer, which might be due to the suppressed / and !" when the free layer remains in-plane. However, the free layer is still active because a small damping factor has been obtained compared to that of the reference layer, and the large DC voltage for the free layer as shown in Fig. 3 can also prove this point. In conclusion, MgO MTJ nanopillars with a perpendicular free layer and an in-plane reference layer have been fabricated and their temperature dependence of the microwave oscillation at high frequency under ST-FMR effect has been systematically investigated. The related
parameters,
such
as
the
effective
!"
of
in-plane
reference
layer,
( − 4π M" )cosϕ of the perpendicular free layer, and the damping factor of both free and reference layers, have been obtained in the temperature range from 300 K to 100 K. The values of !" and ( / − 4π !" )cosϕ at 300 K are 1.66 Tesla and 180 Oe, while the effective damping factors of both free and reference layers at 300 K are 0.0057 and 0.01, respectively. The effective damping factor of the reference layer shows normal temperature dependence, while that of the free layer remains almost unchangeable with temperature due to the suppressed and !" when the free layer remains in-plane. From our work, one may find MgO MTJ stack with a perpendicular free layer and an in-plane reference layer is good candidate for studying the microwave oscillation at high frequency using the ST-FMR effect.
Acknowledgements
The work was supported by the National Natural Science Foundation [NSFC, Grant Nos. 8
11434014, 11674373 and 51401236], Youth Innovation Promotion Association of Chinese Academy of Sciences (No.2017010).
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Figure Captions
Figure1 (a) The schematic ST-FMR circuit setup and cross-sectional view of the MTJ structure. (b) The magnetic configurations of free and reference layers when applying an in plane magnetic field H. The x- y-, and z- axes and the angles ϕ, θ, and β are defined, which 11
are the angle ϕ of the free layer deviating from z - axis, θ between the reference layer and the field direction, and β between the reference and free layers.
Figure 2 The field dependence of pillar resistance at 140 K. The relative orientation of magnetic moments of the free (blue color) and reference (black color) layers are given. The insert shows the dipolar coupling field Hcoupling as a function of temperature obtained from the R - H curves at different temperatures, where the angle β between the free and reference layers is absolutely 90°.
Figure 3 Signals of DC voltage due to the ST-FMR effect at 100 K. There are two main precession peaks, which are responsible for the free and reference layers, respectively. The dash lines are guide to eye.
Figure 4 The temperature dependence of (a) fitted in-plane effective µ0Ms-eff and perpendicular ( − 4π !" )cosϕ and (b) resonance frequencies of free and reference layers at different fields. The insert in (a) shows the field dependence of oscillation frequencies fr1 and fr2 at 100 K. The solid lines in (a) and in the insert are the fitted results and the solid lines in (b) are the calculated results.
Figure 5 The temperature dependence of the effective damping factor of free (α1-eff) and reference (α2-eff) layers. The insert shows the fitted linewidth of free (∆01) and reference (∆02), which are taken at -1.2 kOe and -1 kOe. The solid and dash lines are guide to eye.
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15
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This work reports the spin-torque driven ferromagnetic resonance in MgO magnetic tunnel junction nanopillars with a perpendicularly free layer and an in-plane reference layer Both free and reference layers precess at high frequencies under a microwave power and their saturated magnetization, anisotropy field and damping factor have been studied at different temperatures.
18