Research Article Performance Optimization of Spin …downloads.hindawi.com/journals/jnt/2016/8347280.pdfResearch Article Performance Optimization of Spin-Torque Microwave Detectors

Research ArticlePerformance Optimization of Spin-Torque MicrowaveDetectors with Material and Operational Parameters

X Li1 Y Zhou23 and Philip W T Pong1

1Department of Electrical and Electronic Engineering The University of Hong Kong Hong Kong2Department of Physics The University of Hong Kong Hong Kong3School of Electronics Science and Engineering Nanjing University Nanjing 210093 China

Correspondence should be addressed to Y Zhou yanzhouhkuhk and Philip W T Pong ppongeeehkuhk

Received 1 February 2016 Accepted 30 May 2016

Academic Editor Oded Millo

Copyright copy 2016 X Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Sensitivity bandwidth and noise equivalent power (NEP) are important indicators of the performance of microwave detectorsThe previous reports on spin-torque microwave detectors (STMDs) have proposed various approaches to increase the sensitivityHowever the effects of these methods on the other two indicators remain unclear In this work macrospin simulation is developedto evaluate how the performance can be optimized through changing the material (tilt angle of reference-layer magnetization) andoperational parameters (the direction of magnetic field and working temperature) The study on the effect of magnetic field revealsthat the driving force behind the performance tuning is the effective field and the equilibrium angle between the magnetizationof the free layer and that of the reference layer The material that offers the optimal tilt angle in reference-layer magnetization isdetermined The sensitivity can be further increased by changing the direction of the applied magnetic field and the operationtemperature Although the optimized sensitivity is accompanied by a reduction in bandwidth or an increase in NEP a balanceamong these performance indicators can be reached through optimal tuning of the corresponding influencing parameters

1 Introduction

Spintronics is an emerging field of research on the interactionbetween the spin of electrons and the magnetization ofmagneticmaterialsThe discovery of giantmagnetoresistance(GMR) effect for which Fert [1] and Grunberg [2] wereawarded the 2007 Nobel Prize has proved that the spin ofelectrons can be polarized by the magnetization of magneticmaterials Meanwhile the spin current is also capable ofaltering the magnetization of the ferromagnetic material [34] through the spin-transfer torque (STT) effect [5 6] Thisobservation has led to the development of spin-torque oscilla-tors [7 8] which can change direct current into frequency-tunable microwave signal It was later shown that whenmicrowave current flows through a magnetic tunnel junction(MTJ) nanopillar a rectified DC voltage (119881mix) is generatedrevealing its potential application as spin-torque microwavedetectors (STMDs) [9]

Sensitivity bandwidth andnoise equivalent power (NEP)are three important performance indicators for STMDs

Through adjusting the magnitude of the magnetic field (119867)the working frequency of STMDs (119891

119875) can be tuned to match

that of the incident microwave to achieve the largest DCoutput The sensitivity is defined as the ratio of the peak DCvoltage to the incidentmicrowave powerThe bandwidth is anevaluation of the range of achievable119891

119875within a certain range

of 119867 NEP on the other hand is a parameter reflecting theminimum detection power defined by noise power spectrumdensity over sensitivity Although the three indicators are allimportant for a microwave detector most of the scientificefforts are devoted to the optimization of sensitivity sincecompetitive sensitivity is the prerequisite for industrial appli-cation [10]Theprevious publications reported increased sen-sitivity through applying DC bias [11] optimizing the orien-tation of in-plane (IP) and out-of-plane (OOP)magnetic field[10 12 13] and adjusting the IP shift angle of reference-layermagnetization [14] All these optimizations have resulted inthe record high sensitivity of over 14000mVmW undertilted magnetic field [15] and 75400mVmW under zeromagnetic field [16] Although these reported sensitivities far

Hindawi Publishing CorporationJournal of NanotechnologyVolume 2016 Article ID 8347280 11 pageshttpdxdoiorg10115520168347280

2 Journal of Nanotechnology

y

H

x

y

z

x

z

Iac times Vmix

120575H

120579H

120575F

120579FHk

m

sin (2120587ft)120573M

(a)

50 55 60 65 70 75minus02

00

02

04

SimulationFitted

LorentzAnti-Lorentz

f (GHz)

Vm

ix(120583

V)

VDCfR

H = minus10mT 120573 = 45∘

fP

M

(b)

f (GHz)1 2 3 4 5 6 7

minus4

minus2

0

2

4

Frequency bandwidth

Vm

ix(m

V)

minus10mTminus60mT

= 45∘120573M

(c)

Figure 1 (a) AC is injected into an STMD under magnetic field (119867) applied at (120579119867 120575119867) and the free-layer magnetization (120579

119865 120575119865) precesses

around its equilibrium (b) a typical 119881mix-119891 spectrum can be decomposed into a Lorentz peak and an anti-Lorentz curve (c) frequencybandwidth is defined as frequency gap of 119891

119875at 1205830119867 = minus10mT and minus60mT

exceed that of the existing Schottky diode detector the effectsof these approaches on bandwidth and NEP are seldommen-tioned On the other hand the number of reports aiming atextending the bandwidth or reducing the NEP is small It hasbeen shown that the bandwidth can be extended through theintroduction of reference layer with tiltedmagnetization [17]It has also been shown that the minimum detection power ofan STMD can be reduced through working at cryogenic tem-peratures [18] A comprehensive investigation on how thesethree performance indicators are influenced by the material

or operational parameters is required to extend the under-standing in the behavior of STMDsThe outcome of this workis beneficial for optimizing the performance of STMDs

2 Modeling and Computational Details

The device under investigation is a 200 times 100 nm2 ellipticalMTJ nanopillar with reference-layermagnetization (M) tiltedout of plane by 120573M (Figure 1(a))119867 is applied at 3D directiondefined by the polar (120579

119867) and azimuthal (120575

119867) angles In

Journal of Nanotechnology 3

a coordinate system where the 119909-axis is perpendicular to thethin-film plane and the 119911-axis is parallel to the magnetic easyaxis the unit vector of M and free-layer magnetization (m)can be written as

= (cos120573M 0 sin120573M)

= (sin 120579119865cos 120575119865 sin 120579119865sin 120575119865 cos 120579

119865)

(1)

Microwave current 119868(119905) = 119868ac sin(2120587119891119905) with 119868ac = 10 120583A and119891 = 01ndash10GHz is injected into the MTJ and a steady-stateoscillation in m is excited by the STT of spin current Timeevolution of m(120579

119865(119905) 120575119865(119905)) can be obtained by numerically

solving the Landau-Lifshitz-Gilbert equation

119889

119889119905= minus120574 times [

997888119867eff + therm (119905)] + 120572 times

119889

119889119905minus 120574

sdot119868 (119905) ℎ

41205871198901205830119872119904119881

sdot119875

1 + 1198752 cos (120593 (119905))[ times ( times ) + 119887

119891 times ]

(2)

where 120574 = 176GHzT represents the gyromagnetic ratio 120572 =001 the Gilbert damping parameter 119881 the volume of freelayer 119890 the charge of an electron and 120583

0the vacuummagnetic

permeability 119867eff is the effective field comprised of externalfield IP anisotropy field (119867

119896) and demagnetization field

(119867119889) defined respectively by

119867119896= 1198731199091205830119872119878 (3)

119867119889asymp 1205830119872119878 (4)

where119873119909= 0016 is the demagnetization factor in the 119909-axis

120593(119905) is the time-dependent angle betweenM andm

cos120593 (119905) = sdot

= sin 120579119865 (119905) sdot cos 120575119865 (119905) sdot cos120573M + cos 120579

119865 (119905)

sdot sin120573M

(5)

The contribution of field-like STT is considered and 119887119891= 01

is its ratio to the IP torque [19] The thermal fluctuation term(therm(119905)) is introduced as in [20]

therm (119905) = (119905) radic120572

1 + 12057222119896119861119879

1205741205830119872119878119881 (6)

where (119905) is a random vector whose components are nor-mally distributed random numbers with mean of 0 and vari-ance of 1 The temperature dependence of polarization ratio(119875) parallel resistance (119877

119875) antiparallel resistance (119877AP) and

saturation magnetization (119872119878) are expressed respectively as

119875 (119879) = 119875 (0) times (1 minus 12057811987932

) (7)

119877119875 (119879) =

119877 (0) times (1 minus 120594119879)

1 + 119875 (119879)2

(8)

119877AP (119879) =119877 (0) times (1 minus 120594119879)

1 minus 119875 (119879)2

(9)

119872119878 (119879) = 119872

119878 (0) times (1 minus119879

119879119862

)

120591

(10)

where119875(0) = 0385 120578 = 17times 10minus5 Kminus32119877(0) = 800Ω 120594 = 765times 10minus4 Kminus1119872

119878(0) = 13 times 106 Am 120591 = 04 and 119879

119862= 1300K

The oscillation of m results in the changing resistance ofthe MTJ

119877 (119905) = [119877minus1AP + 119877minus1

119875

2minus

119877minus1119875

minus 119877minus1AP2

cos120593 (119905)]

minus1

(11)

The changing resistance is thus mixed with the alternatingcurrent generating a mixing voltage (119881mix) on the MTJdefined as the average voltage over one period

119881mix =int1199050+1119891

1199050

119868 (119905) sdot 119877 (119905) 119889119905

1119891 (12)

A typical 119881mix-119891 spectrum can be decomposed into a sym-metric Lorentz peak contributed by the IP STT and ananti-Lorentz curve resulted from the field-like torque [21](Figure 1(b))

119881mix = 1198601198682

119877119865+ 1198611198682

119877119865[

1

1 + ((119891 minus 119891119877) 120590)2

minus 119862119891 minus 119891119877

120590

1

1 + ((119891 minus 119891119877) 120590)2]

(13)

where119891119877and 120590 are the frequency and line-width of the ferro-

magnetic resonant (FMR) peak respectively119860 and119861 are con-stants related to the nonlinearity of junction resistance while119862 is related to the content of field-like STT This combinedcontribution has resulted in a peak and a valley at either sideof 119891119877in the 119881mix-119891 spectrum If the IP STT is dominating

more symmetric curve will be observed and 119891119875approaches

119891119877 On the other hand if the proportion of field-like STT

is higher the curve will be more dispersed and the resonantpeak shifts away from119891

119877The output DC voltage (119881DC) is cal-

culated as the voltage difference between the peak and valleyin the 119881mix-119891 spectrum Considering the microwave reflec-tion caused by impedance mismatch the sensitivity and NEP[15] can be calculated from

Sensitivity =119881DC

(18) (((119877 + 1198850)2sdot 1198682ac) 1198850)

(14)

NEP =noise

sensitivity

= radic8120587120572

119875 (119879)2

119872119878 (119879)

120583119861

1198811198850

ℎ1198902(119877 + 119885

0

1198850

)

2

119896119861119879radic120590

(15)

where 119877 is the average junction resistance and 1198850= 50Ω is

the characteristic impedance of the transmission lines


In this work one material parameter (120573M) and two oper-ational parameters (the orientation of magnetic field and thetemperature) are selected as the influencing parameters foroptimizing detector performance Firstly the reliance of 119891

119877

sensitivity and NEP on 119867 is analyzed to explore the mecha-nism for the performance tuning Later on the suitable mate-rial for reference layer is suggested based on optimal 120573M forhighest sensitivity The influence of operational parameters(the orientation of magnetic field and temperature) is subse-quently studied Finally the approaches to achieve optimizedperformance in STMDs are discussed

3 Simulation Results

31 Magnitude of Magnetic Field (H) Since 119891119875and 119881DC of

STMDs are primarily influenced by 119867 the voltage responseunder different 119867 is firstly studied to explore the mecha-nism for the changes in 119891

119875 sensitivity and NEP In these

simulations M is tilted OOP (120573M = 40∘) while the magneticfield is applied in the hard plane (120575

119867= 40∘) (Figure 2(a))

The contour plots of 119881mix-119891 spectra when 1205830119867 is changed

from minus10mT to minus150mT are shown in Figure 2(b) 119891119877and

119891119875are shown in Figure 2(c) 119891

119877tends to decrease with 119867

when 1205830119867 lt minus64mT but increase with 119867 thereafter This 119867

dependence of FMR frequency [22 23] and line-width [24]can be explained by the following model

119891119877=

120574

2120587radic119867eff119861119898 =

120574

2120587radic119867eff (119867eff + 120583

0119872119878) (16)

120590 asymp minus120572120574 (21003816100381610038161003816119867eff

1003816100381610038161003816 + 119867119888) (17)

where119867eff is the effective field represented by

119867eff = 119867 minus 119867an (18)

where 119867an represents the anisotropy field The V-shaperelation between 119891

119877and 119867 resulted from the competition

between the external magnetic field and the anisotropy fieldWhen 120583

0119867 = minus64mT the free-layer anisotropy is overcome

by the external magnetic field resulting in minimum 119867effand thus minimum119891

119877 according to (16) At larger 119867 119867eff

increases with 119867 resulting in increasing 119891119877 The field

dependence of 119891119875is nearly the same as that of 119891

119877 This

constant frequency gap between 119891119875and 119891

119877is contributed

by the constant ratio between IP and field-like STT Sincethe range of 119891

119875is constrained by the range of 119867 the fre-

quency bandwidth mentioned in the following is calculatedas the bandwidth of 119891

119875when the 120583

0119867 is changed from

minus10mT to minus60mT For example a bandwidth of 46GHz isachieved in this situation (119891

119877decreasing monotonously from

62GHz at minus10mT to 16GHz at minus60mT) 120590 shares similar119867 dependence with 119891

119877(Figure 2(d)) since it is proportional

to the magnitude of 119867eff according to (17) It should benoted that highest sensitivity 127mVmW is achieved withthe minimum frequency (Figure 2(e)) This can be explained

by an analytical model proposed byWang et al [10] The119881DCof an STMDs can be expressed as

119881DC =119877AP minus 119877

119875

119877119875

120583119861

2119890 (119872119878119860) 120590

119875

1 + 11987521198772

119877119875119877AP

1198682ac8119877

sdot sin2120593

(19)

When 1205830119867 = minus64mT the free-layer magnetization is satu-

rated in the direction of the hard-plane magnetic field [25]so the angle (120593) between m and M reaches 90∘ This resultsin maximum 119877 according to (11) As 120590 also reaches theminimum the 119881DC and the sensitivity are thus expected toarrive at the maximum Meanwhile the calculated NEP inFigure 2(f) presents similar reliance on 119867 as the line-widthThis is because NEP is proportional to the square root of 120590as inferred from (15) In the following investigation 120583

0119867 =

minus60mT is used since it is beneficial for high sensitivity andlowNEPThe above analysis has revealed that themechanismin the tuning of119891

119877120590 sensitivity andNEP can all be explained

through analyzing the changes in119867eff and 120593 Similarly it canbe inferred that through tuning the material and operationalparameters of STMDs changes in 119867eff and 120593 can also beinduced The altered performance indicators shown belowcan also be analyzed with the same model

32 Tilt Angle of Reference Layer OOP anisotropy is reportedin CoPt [26] or CoNi [27] multilayers and annealed singlelayers [28] 120573M can be carefully tuned through adoptingreference-layer materials with different OOP anisotropy Theangular dependence of sensitivity bandwidth and NEP isanalyzed to explore an optimal 120573MThe direction of magneticfield is applied at 120579

119867= 90∘ and 120575

119867= 40∘ while 120573M is changed

from 0∘ to 180∘The contour plots of119881mix-119891 spectra simulatedat different 120573M are shown in Figure 3(a) Observed 119891

119877and

120590 present only slight changes at various 120573M (Figures 3(b)and 3(c)) This indicates that the STMD works at free-layerresonation mode so the resonant frequency is immune tothe changes in the reference layer Since the magnetic field isapplied in the 119909minus119910 plane the119891

119877and 120590 are roughly symmetric

when the IP component of M is parallel (120573M lt 90∘) andantiparallel (120573M gt 90∘) to the 119911 direction However angulardependent and asymmetric119891

119875is observed in Figure 3(b)The

larger frequency difference between 119891119877and 119891

119875when M is

tilted by 10∘ndash80∘ or 10∘ndash170∘ indicates that the119881mix-119891 relation-ship is dominated by the field-like STTThe asymmetry is dueto the different contribution of STT (positive when 120573M lt 90∘negative when 120573M gt 90∘)The resulting frequency bandwidthreaches maximum when 120573M = 75∘ (Figure 3(d)) This isconsistent with our previous simulation results that the band-width can be extended by optimizing 120573M [17] However sincevery narrow119867 range (50mT) is used in this work the changesin the bandwidth are also relatively small Apart from band-width the sensitivity and NEP are also angular dependentThe sensitivity reaches maximum when 120573M = sim45∘ and sim135∘(Figure 3(e)) This is because largest 120593 at these angles resultsin large 119881DC according to (19) The calculated NEP presents atrend to slightly decrease at larger 120573M in Figure 3(f) Consid-ering that 120590 is nearly constant the low NEP is contributed by


H

x

y

z

120575H

M

120573M

(a)f

(GH

z)

10

8

6

4

2

6

4

2

1205830H (mT)minus150 minus100 minus50

Vmix (120583V)

0

minus2

minus4

(b)

minus140 minus120 minus100 minus80 minus60 minus40 minus200

2

4

6

8

10

1205830H (mT)

fR

fP

fRf

P(G

Hz)

(c)

00

02

04

06

08

minus140 minus120 minus100 minus80 minus60 minus40 minus201205830H (mT)

120590 (G

Hz)

(d)

0

50

100

150

Sens

itivi

ty (m

Vm

W)


(e)

05

10

15

20

25

30


NEP

(10minus10

WH

z05

)

(f)

Figure 2 (a) Schematic of alignment between119867 andM (b)119881mix-119891 spectra (c) FMR frequency (119891119877) and peak frequency (119891

119875) (d) line-width

(e) sensitivity and (f) NEP when the magnitude of magnetic field is changed from minus10mT to minus150mT


f (G

Hz)

4

2

0

minus2

3

25

2

15

10 50 100 150

Vmix (120583V)

(deg)120573M

(a)

15

16

17

18

19

20

0 30 60 90 120 150 180

fRf

P(G

Hz)

fR

fP

(deg)120573M

(b)

016

018

020

022

Line

wid

th (G

Hz)

0 30 60 90 120 150 180(deg)120573M

(c)

42

44

46

48Ba

ndw

idth

(GH

z)

0 30 60 90 120 150 180(deg)120573M

(d)

0 30 60 90 120 150 1800

20

40

60

80

Sens

itivi

ty (m

Vm

W)

(deg)120573M

(e)

10

12

14

16

18

0 30 60 90 120 150 180(deg)

NEP

(10minus10

WH

z05

)

120573M

(f)

Figure 3 (a) The contour plots of 119881mix-119891 spectra (b) 119891119877and 119891

119875 (c) line-width (d) bandwidth (e) sensitivity and (f) NEP as a function of

120573M when 1205830119867 = minus60mT is applied at 120579

119867= 90∘ and 120575

119867= 40∘


the relatively lower junction resistance at larger 120573M From theabove analysis we can infer that optimal 120573M is 45∘ or 135∘where highest sensitivity can be achieved while the band-width and NEP are only slightly influenced In the followingdiscussion 120573M = 45∘ is used Materials such as L1

0(101) FePt

is suggested as the reference layer to achieve120573M = 45∘ [29 30]

33 Orientation of OOP Magnetic Field The direction ofmagnetic field can be changed to achieve the preferredperformance in STMDs In this investigation the directionof minus60mTmagnetic field is changed within the range of 120579

119867=

0∘ndash90∘ and 120575119867= 10∘ndash90∘ (Figure 4(a)) Higher 119891

119877is observed

at smaller 120579119867(Figure 4(b)) due to the higher effective field

when the magnetic field is applied IP The angular depen-dence of bandwidth in Figure 4(c) is roughly consistent withthat of 119891

119877at 1205830119867 = minus60mT because in most cases higher

119891119875and 119891

119877occur at larger 119867 However when 120579

119867approaches

90∘ and 120575119867

is small very narrow bandwidth is observedThis is consistent with our experimental observations thatwhen the magnetic field is nearly perpendicular to plane 119891

119875-

tunability by 119867 is much reduced (not shown in this paper)Similar to Figure 2 the narrow line-width (Figure 4(d))coexists with low 119891

119877because they have similar reliance on

119867eff from (16) and (18) Small 120590 at larger 120579119867

also resultsin the highest sensitivity (Figure 4(e)) and smallest NEP(Figure 4(f)) when 120579

119867= 90∘ and 120575

119867= 40∘ These results have

indicated a contradiction between high sensitivity and widebandwidthwhen choosing the optimal field angle larger 120579

119867is

beneficial for high sensitivity and low NEP but it also resultsin a reduction in bandwidth widest bandwidth over 10GHzcan be achievedwhen 120579

119867= 0∘ while it comeswith a drawback

of low sensitivity below 10mVmW and high NEP over 3 times

10minus10WHz05 Nevertheless these results have shown that theperformance of STMDs can be tailored in a wide range bychanging the orientation of magnetic field

34 Working Temperature The above investigations haveshown that the highest sensitivity can be achieved when thereference-layer magnetization is tilted by 120573M = 45∘ and themagnetic field is applied at 120579

119867= 90∘ and 120575

119867= 40∘ Based on

this optimized alignment the working temperature is furtherstudied as another influencing parameter to tune the STMDperformanceThe contour plots of119881mix-119891 spectra when tem-perature changes from 5K to 380K are shown in Figure 5(a)Calculated 119891

119877increases monotonously with decreasing tem-

perature (Figure 5(b)) which resulted from increasing 119867effcontributed by higher 119872

119878at low temperature 119891

119875at 1205830119867 =

minus60mT also changes from 34GHz to 04GHz as temper-ature increases from 5K to 380K In contrast 119891

119875at 1205830119867

= minus10mT presents much smaller temperature dependencewhich decreases from 7GHz to 61 GHzwithin the same tem-perature range As a result the frequency bandwidth shownin Figure 5(c) increases with temperature from 36GHz to57GHz Decreasing 119891

119877at high temperature results in nar-

rower line-width shown in Figure 5(d) It is noted that the cal-culated sensitivity increases with temperature (Figure 5(e))which contradicts with the previous simulation report [18]The reasons for this temperature dependence can be inter-preted as follows Firstly 119872

119878 119875 and 120590 increase at lower

temperature Secondly equilibrium 120593 under 1205830119867 = minus60mT

is reduced at lower temperature due to the higher anisotropyThirdly the higher resistance at low temperature results inhigher microwave reflection coefficient leading to smaller119868ac when constant microwave power is applied All thesereduction effects at lower temperature have overwhelmedthe increasing effect brought by higher TMR ratio so areduction in 119881DC and sensitivity is expected with decreasingtemperature according to (19) The calculated NEP increaseswith temperature as shown in Figure 5(f) This is reasonablesince the level of noise is expected to increase at higher tem-perature As such increasing the working temperature is ben-eficial for increasing the sensitivity and frequency bandwidthHowever a drawback of increased NEP is accompanied

4 Discussion

Based on the above analysis the approaches for optimizingthe performance of STMDs can be inferred The sensitivitycan be optimized while maintaining bandwidth and NEPnearly unchanged by adopting a reference layer tilted at 120573M =45∘ However the attempt to further improve the sensitivitythrough changing the direction of magnetic field or workingtemperature is accompanied by a reduction in bandwidthor an increase in NEP Fortunately through the combinedmanipulation of the two operational parameters a balanceamong the sensitivity bandwidth and NEP can be achievedbased on the specific applications In a situation where highsensitivity is needed themagnetic field can be applied at 120579

119867=

90∘ and 120575119867= 40∘ to achieve the peak sensitivityThe resulting

reduction in bandwidth can be partially compensated byincreasing the working temperature which also contributesto higher sensitivity Meanwhile the resulting high NEP isalso reduced at the optimized orientation of magnetic fieldSimilarly when awide-band STMD is preferred small 120579

119867can

be used to achieve wide bandwidth and the loss of sensitivitycan be made up by increasing temperature These resultsreveal a new degree of freedom in tailoring the performanceof STMDs Through altering the operational parameters theregime of the applications of STMDs is remarkably extended

5 Conclusions

In summary the influencing parameters on the performanceof STMDs are evaluated through macrospin simulationThe alignment between 119867 and M is optimized and thetemperature dependence of sensitivity bandwidth and NEPare investigated The V-shape reliance of 119891

119877and 120590 on 119867

is interpreted through evaluating 119867eff and 120593 When M istilted OOP by 120573M = 45∘ highest sensitivity can be achievedwhile the bandwidth and line-width exhibit small angulardependence Higher sensitivity and lower NEP are observedwhen the direction of magnetic field approaches the hardplane (120579

119867= 90∘) due to larger 120593 and smaller 120590 However the

high sensitivity is accompanied by a reduction in bandwidthHigher working temperature results in higher sensitivity andwide bandwidth at the cost of increased NEP Although theaccomplishment of optimized sensitivity bandwidth andNEP by one single approach is not yet possible these results


H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

Sensitivity (mVmW) 60

50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80

NEP (10minus10 WHz05)

3

25

2

15

1

(f)

Figure 4 (a) Schematic of OOPmagnetic field (b) 119891119877 (c) bandwidth (d) line-width (e) sensitivity and (f) NEP as a function of orientation

angles of magnetic field (1205830119867 = minus60mT)


100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)

Figure 5 (a)The contour plots of119881mix-119891 spectra the temperature dependence of (b) 119891119877and 119891

119875 (c) bandwidth (d) line-width (e) sensitivity

and (f) NEP when 120573M = 45∘ 1205830119867 = minus60mT 120579

119867= 90∘ and 120575

119867= 40∘


provide insight for balancing these three performance param-eters of STMDs through tuning the direction of magneticfield and the working temperature The outcome of this workenables designing STMDs based on specific requirements onsensitivity bandwidth or NEP

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is supported in part by the Seed Funding Programfor Basic Research and Small Project Funding Program fromtheUniversity of HongKong ITF Tier 3 funding (ITS20314ITS10413 and ITS21414) RGC-GRF grant (HKU 17210014andHKU704911P) Innovation andTechnology Fund Intern-ship Programme (InP18214) and University Grants Com-mittee of Hong Kong (Contract no AoEP-0408)

References

[1] A Fert ldquoNobel lecture origin development and future ofspintronicsrdquo Reviews of Modern Physics vol 80 no 4 pp 1517ndash1530 2008

[2] P A Grunberg ldquoNobel lecture From spin waves to giantmagnetoresistance and beyondrdquoReviews ofModern Physics vol80 no 4 pp 1531ndash1540 2008

[3] E B Myers D C Ralph J A Katine R N Louie and R ABuhrman ldquoCurrent-induced switching of domains in magneticmultilayer devicesrdquo Science vol 285 no 5429 pp 867ndash8701999

[4] J Z Sun ldquoCurrent-drivenmagnetic switching in manganite tri-layer junctionsrdquo Journal of Magnetism and Magnetic Materialsvol 202 no 1 pp 157ndash162 1999

[5] J Z Sun and D C Ralph ldquoMagnetoresistance and spin-transfertorque in magnetic tunnel junctionsrdquo Journal of Magnetism andMagnetic Materials vol 320 no 7 pp 1227ndash1237 2008

[6] D C Ralph Y-T Cui L Q Liu T Moriyama C Wang andR A Buhrman ldquoSpin-transfer torque in nanoscale magneticdevicesrdquo Philosophical Transactions of the Royal Society AMathematical Physical and Engineering Sciences vol 369 no1951 pp 3617ndash3630 2011

[7] S I Klselev J C Sankey I N Krivorotov et al ldquoMicrowaveoscillations of a nanomagnet driven by a spin-polarized cur-rentrdquo Nature vol 425 no 6956 pp 380ndash383 2003

[8] W H Rippard M R Pufall S Kaka S E Russek and T JSilva ldquoDirect-current induced dynamics in Co

90Fe10Ni80Fe20

point contactsrdquo Physical Review Letters vol 92 no 2 ArticleID 027201 4 pages 2004

[9] A A Tulapurkar Y Suzuki A Fukushima et al ldquoSpin-torquediode effect in magnetic tunnel junctionsrdquo Nature vol 438 no7066 pp 339ndash342 2005

[10] C Wang Y-T Cui J Z Sun J A Katine R A Buhrman andD C Ralph ldquoSensitivity of spin-torque diodes for frequency-tunable resonant microwave detectionrdquo Journal of AppliedPhysics vol 106 no 5 Article ID 053905 2009

[11] CWang Y-T Cui J Z Sun J A Katine R A Buhrman andDC Ralph ldquoBias and angular dependence of spin-transfer torque

in magnetic tunnel junctionsrdquo Physical Review B vol 79 no 22Article ID 224416 2009

[12] T Taniguchi and H Imamura ldquoDependence of spin torquediode voltage on applied field directionrdquo Journal of AppliedPhysics vol 114 no 5 Article ID 053903 2013

[13] X Li C Zheng Y Zhou H Kubota S Yuasa and PW T PongldquoSpin-torque diode with tunable sensitivity and bandwidth byout-of-planemagnetic fieldrdquoApplied Physics Letters vol 108 no23 Article ID 232407 2016

[14] T Taniguchi and H Imamura ldquoMaximizing spin torquediode voltage by optimizing magnetization alignmentrdquo AppliedPhysics Express vol 6 no 5 Article ID 053002 2013

[15] S Miwa S Ishibashi H Tomita et al ldquoHighly sensitivenanoscale spin-torque dioderdquo Nature Materials vol 13 no 1pp 50ndash56 2014

[16] B Fang M Carpentieri X Hao et al ldquoGiant spin-torquediode sensitivity in the absence of bias magnetic fieldrdquo NatureCommunications vol 7 p 11259 2016

[17] T Zeng Y Zhou K W Lin P T Lai and P W T Pong ldquoSpin-torque diode-based radio-frequency detector by utilizing tiltedfixed-layer magnetization and in-plane free-layer magnetiza-tionrdquo IEEE Transactions on Magnetics vol 51 no 11 2015

[18] O V Prokopenko E Bankowski T Meitzler V S Tiberkevichand A N Slavin ldquoInfluence of temperature on the performanceof a spin-torque microwave detectorrdquo IEEE Transactions onMagnetics vol 48 no 11 pp 3807ndash3810 2012

[19] J Zhu J A Katine G E Rowlands et al ldquoVoltage-induced fer-romagnetic resonance in magnetic tunnel junctionsrdquo PhysicalReview Letters vol 108 no 19 Article ID 197203 2012

[20] J Park G E Rowlands O J Lee D C Ralph and R ABuhrman ldquoMacrospin modeling of sub-ns pulse switching ofperpendicularly magnetized free layer via spin-orbit torques forcryogenic memory applicationsrdquo Applied Physics Letters vol105 no 10 Article ID 102404 2014

[21] J C Sankey Y-T Cui J Z Sun J C Slonczewski R ABuhrman and D C Ralph ldquoMeasurement of the spin-transfer-torque vector inmagnetic tunnel junctionsrdquoNature Physics vol4 no 1 pp 67ndash71 2008

[22] C Kittel ldquoOn the theory of ferromagnetic resonance absorp-tionrdquo Physical Review vol 73 no 2 pp 155ndash161 1948

[23] C Kittel ldquoInterpretation of anomalous larmor frequencies inferromagnetic resonance experimentrdquo Physical Review vol 71no 4 pp 270ndash271 1947

[24] S Ishibashi K Ando T Seki et al ldquoHigh spin-torque diodesensitivity in CoFeBMgOCoFeB magnetic tunnel junctionsunder DC bias currentsrdquo IEEE Transactions on Magnetics vol47 no 10 pp 3373ndash3376 2011

[25] Z Zeng K H Cheung H W Jiang et al ldquoEvolution of spin-wave modes in magnetic tunnel junction nanopillarsrdquo PhysicalReview BmdashCondensed Matter andMaterials Physics vol 82 no10 Article ID 100410 2010

[26] B Carvello C Ducruet B Rodmacq et al ldquoSizable room-temperaturemagnetoresistance in cobalt basedmagnetic tunneljunctions with out-of-plane anisotropyrdquoApplied Physics Lettersvol 92 no 10 Article ID 102508 2008

[27] T Moriyama T J Gudmundsen P Y Huang et al ldquoTunnelmagnetoresistance and spin torque switching in MgO-basedmagnetic tunnel junctions with a CoNi multilayer electroderdquoApplied Physics Letters vol 97 no 7 Article ID 072513 2010

[28] W X Wang Y Yang H Naganuma Y Ando R C Yuand X F Han ldquoThe perpendicular anisotropy of Co

40Fe40B20


sandwiched between Ta and MgO layers and its application inCoFeBMgOCoFeB tunnel junctionrdquo Applied Physics Lettersvol 99 no 1 Article ID 012502 2011

[29] Y Zhou C L Zha S Bonetti J Persson and J AkermanldquoMicrowave generation of tilted-polarizer spin torque oscilla-torrdquo Journal of Applied Physics vol 105 no 7 Article ID 07D1162009

[30] Y Zhou C L Zha S Bonetti J Persson and J Akerman ldquoSpin-torque oscillator with tilted fixed layer magnetizationrdquo AppliedPhysics Letters vol 92 no 26 Article ID 262508 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


y

H

x

y

z

x

z

Iac times Vmix

120575H

120579H

120575F

120579FHk

m

sin (2120587ft)120573M

(a)

50 55 60 65 70 75minus02

00

02

04

SimulationFitted

LorentzAnti-Lorentz

f (GHz)

Vm

ix(120583

V)

VDCfR

H = minus10mT 120573 = 45∘

fP

M

(b)

f (GHz)1 2 3 4 5 6 7

minus4

minus2

0

2

4

Frequency bandwidth

Vm

ix(m

V)

minus10mTminus60mT

= 45∘120573M

(c)

Figure 1 (a) AC is injected into an STMD under magnetic field (119867) applied at (120579119867 120575119867) and the free-layer magnetization (120579

119865 120575119865) precesses

around its equilibrium (b) a typical 119881mix-119891 spectrum can be decomposed into a Lorentz peak and an anti-Lorentz curve (c) frequencybandwidth is defined as frequency gap of 119891

119875at 1205830119867 = minus10mT and minus60mT

exceed that of the existing Schottky diode detector the effectsof these approaches on bandwidth and NEP are seldommen-tioned On the other hand the number of reports aiming atextending the bandwidth or reducing the NEP is small It hasbeen shown that the bandwidth can be extended through theintroduction of reference layer with tiltedmagnetization [17]It has also been shown that the minimum detection power ofan STMD can be reduced through working at cryogenic tem-peratures [18] A comprehensive investigation on how thesethree performance indicators are influenced by the material

or operational parameters is required to extend the under-standing in the behavior of STMDsThe outcome of this workis beneficial for optimizing the performance of STMDs

2 Modeling and Computational Details

The device under investigation is a 200 times 100 nm2 ellipticalMTJ nanopillar with reference-layermagnetization (M) tiltedout of plane by 120573M (Figure 1(a))119867 is applied at 3D directiondefined by the polar (120579

119867) and azimuthal (120575

119867) angles In



= (cos120573M 0 sin120573M)


119865)

(1)




119889

119889119905= minus120574 times [

997888119867eff + therm (119905)] + 120572 times

119889

119889119905minus 120574

sdot119868 (119905) ℎ

41205871198901205830119872119904119881

sdot119875

1 + 1198752 cos (120593 (119905))[ times ( times ) + 119887

119891 times ]

(2)


0the vacuummagnetic




119867119896= 1198731199091205830119872119878 (3)

119867119889asymp 1205830119872119878 (4)



cos120593 (119905) = sdot


119865 (119905)

sdot sin120573M

(5)



therm (119905) = (119905) radic120572

1 + 12057222119896119861119879

1205741205830119872119878119881 (6)




119875 (119879) = 119875 (0) times (1 minus 12057811987932

) (7)

119877119875 (119879) =

119877 (0) times (1 minus 120594119879)

1 + 119875 (119879)2

(8)

119877AP (119879) =119877 (0) times (1 minus 120594119879)

1 minus 119875 (119879)2

(9)

119872119878 (119879) = 119872

119878 (0) times (1 minus119879

119879119862

)

120591

(10)


119878(0) = 13 times 106 Am 120591 = 04 and 119879

119862= 1300K


119877 (119905) = [119877minus1AP + 119877minus1

119875

2minus

119877minus1119875


cos120593 (119905)]

minus1

(11)


119881mix =int1199050+1119891

1199050

119868 (119905) sdot 119877 (119905) 119889119905

1119891 (12)


119881mix = 1198601198682

119877119865+ 1198611198682

119877119865[

1

1 + ((119891 minus 119891119877) 120590)2

minus 119862119891 minus 119891119877

120590

1

1 + ((119891 minus 119891119877) 120590)2]

(13)









(18) (((119877 + 1198850)2sdot 1198682ac) 1198850)

(14)

NEP =noise

sensitivity

= radic8120587120572

119875 (119879)2

119872119878 (119879)

120583119861

1198811198850

ℎ1198902(119877 + 119885

0

1198850

)

2

119896119861119879radic120590

(15)





119877







119867= 40∘) (Figure 2(a))







119891119877=

120574

2120587radic119867eff119861119898 =

120574

2120587radic119867eff (119867eff + 120583

0119872119878) (16)

120590 asymp minus120572120574 (21003816100381610038161003816119867eff

1003816100381610038161003816 + 119867119888) (17)


119867eff = 119867 minus 119867an (18)









119877 This






119875when the 120583








119881DC =119877AP minus 119877

119875

119877119875

120583119861

2119890 (119872119878119860) 120590

119875

1 + 11987521198772

119877119875119877AP

1198682ac8119877

sdot sin2120593

(19)



0119867 =





119867= 90∘ and 120575



119877and






119875when M is



H

x

y

z

120575H

M

120573M

(a)f

(GH

z)

10

8

6

4

2

6

4

2


Vmix (120583V)

0

minus2

minus4

(b)


2

4

6

8

10

1205830H (mT)

fR

fP

fRf

P(G

Hz)

(c)

00

02

04

06

08


120590 (G

Hz)

(d)

0

50

100

150

Sens

itivi

ty (m

Vm

W)


(e)

05

10

15

20

25

30


NEP

(10minus10

WH

z05

)

(f)





f (G

Hz)

4

2

0

minus2

3

25

2

15

10 50 100 150

Vmix (120583V)

(deg)120573M

(a)

15

16

17

18

19

20

0 30 60 90 120 150 180

fRf

P(G

Hz)

fR

fP

(deg)120573M

(b)

016

018

020

022

Line

wid

th (G

Hz)

0 30 60 90 120 150 180(deg)120573M

(c)

42

44

46

48Ba

ndw

idth

(GH

z)

0 30 60 90 120 150 180(deg)120573M

(d)

0 30 60 90 120 150 1800

20

40

60

80

Sens

itivi

ty (m

Vm

W)

(deg)120573M

(e)

10

12

14

16

18

0 30 60 90 120 150 180(deg)

NEP

(10minus10

WH

z05

)

120573M

(f)




119867= 90∘ and 120575

119867= 40∘



0(101) FePt



119867=


119877is observed




119891119875and 119891


119867approaches

90∘ and 120575119867


119875-





119867= 90∘ and 120575



119867is






119867= 90∘ and 120575

119867= 40∘ Based on





119875at 1205830119867 =


119875at 1205830119867







4 Discussion


119867=



119867can


5 Conclusions


119877and 120590 on 119867





H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80


50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80


3

25

2

15

1

(f)




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





= (cos120573M 0 sin120573M)


119865)

(1)




119889

119889119905= minus120574 times [

997888119867eff + therm (119905)] + 120572 times

119889

119889119905minus 120574

sdot119868 (119905) ℎ

41205871198901205830119872119904119881

sdot119875

1 + 1198752 cos (120593 (119905))[ times ( times ) + 119887

119891 times ]

(2)


0the vacuummagnetic




119867119896= 1198731199091205830119872119878 (3)

119867119889asymp 1205830119872119878 (4)



cos120593 (119905) = sdot


119865 (119905)

sdot sin120573M

(5)



therm (119905) = (119905) radic120572

1 + 12057222119896119861119879

1205741205830119872119878119881 (6)




119875 (119879) = 119875 (0) times (1 minus 12057811987932

) (7)

119877119875 (119879) =

119877 (0) times (1 minus 120594119879)

1 + 119875 (119879)2

(8)

119877AP (119879) =119877 (0) times (1 minus 120594119879)

1 minus 119875 (119879)2

(9)

119872119878 (119879) = 119872

119878 (0) times (1 minus119879

119879119862

)

120591

(10)


119878(0) = 13 times 106 Am 120591 = 04 and 119879

119862= 1300K


119877 (119905) = [119877minus1AP + 119877minus1

119875

2minus

119877minus1119875


cos120593 (119905)]

minus1

(11)


119881mix =int1199050+1119891

1199050

119868 (119905) sdot 119877 (119905) 119889119905

1119891 (12)


119881mix = 1198601198682

119877119865+ 1198611198682

119877119865[

1

1 + ((119891 minus 119891119877) 120590)2

minus 119862119891 minus 119891119877

120590

1

1 + ((119891 minus 119891119877) 120590)2]

(13)









(18) (((119877 + 1198850)2sdot 1198682ac) 1198850)

(14)

NEP =noise

sensitivity

= radic8120587120572

119875 (119879)2

119872119878 (119879)

120583119861

1198811198850

ℎ1198902(119877 + 119885

0

1198850

)

2

119896119861119879radic120590

(15)





119877







119867= 40∘) (Figure 2(a))







119891119877=

120574

2120587radic119867eff119861119898 =

120574

2120587radic119867eff (119867eff + 120583

0119872119878) (16)

120590 asymp minus120572120574 (21003816100381610038161003816119867eff

1003816100381610038161003816 + 119867119888) (17)


119867eff = 119867 minus 119867an (18)









119877 This






119875when the 120583








119881DC =119877AP minus 119877

119875

119877119875

120583119861

2119890 (119872119878119860) 120590

119875

1 + 11987521198772

119877119875119877AP

1198682ac8119877

sdot sin2120593

(19)



0119867 =





119867= 90∘ and 120575



119877and






119875when M is



H

x

y

z

120575H

M

120573M

(a)f

(GH

z)

10

8

6

4

2

6

4

2


Vmix (120583V)

0

minus2

minus4

(b)


2

4

6

8

10

1205830H (mT)

fR

fP

fRf

P(G

Hz)

(c)

00

02

04

06

08


120590 (G

Hz)

(d)

0

50

100

150

Sens

itivi

ty (m

Vm

W)


(e)

05

10

15

20

25

30


NEP

(10minus10

WH

z05

)

(f)





f (G

Hz)

4

2

0

minus2

3

25

2

15

10 50 100 150

Vmix (120583V)

(deg)120573M

(a)

15

16

17

18

19

20

0 30 60 90 120 150 180

fRf

P(G

Hz)

fR

fP

(deg)120573M

(b)

016

018

020

022

Line

wid

th (G

Hz)

0 30 60 90 120 150 180(deg)120573M

(c)

42

44

46

48Ba

ndw

idth

(GH

z)

0 30 60 90 120 150 180(deg)120573M

(d)

0 30 60 90 120 150 1800

20

40

60

80

Sens

itivi

ty (m

Vm

W)

(deg)120573M

(e)

10

12

14

16

18

0 30 60 90 120 150 180(deg)

NEP

(10minus10

WH

z05

)

120573M

(f)




119867= 90∘ and 120575

119867= 40∘



0(101) FePt



119867=


119877is observed




119891119875and 119891


119867approaches

90∘ and 120575119867


119875-





119867= 90∘ and 120575



119867is






119867= 90∘ and 120575

119867= 40∘ Based on





119875at 1205830119867 =


119875at 1205830119867







4 Discussion


119867=



119867can


5 Conclusions


119877and 120590 on 119867





H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80


50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80


3

25

2

15

1

(f)




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





119877







119867= 40∘) (Figure 2(a))







119891119877=

120574

2120587radic119867eff119861119898 =

120574

2120587radic119867eff (119867eff + 120583

0119872119878) (16)

120590 asymp minus120572120574 (21003816100381610038161003816119867eff

1003816100381610038161003816 + 119867119888) (17)


119867eff = 119867 minus 119867an (18)









119877 This






119875when the 120583








119881DC =119877AP minus 119877

119875

119877119875

120583119861

2119890 (119872119878119860) 120590

119875

1 + 11987521198772

119877119875119877AP

1198682ac8119877

sdot sin2120593

(19)



0119867 =





119867= 90∘ and 120575



119877and






119875when M is



H

x

y

z

120575H

M

120573M

(a)f

(GH

z)

10

8

6

4

2

6

4

2


Vmix (120583V)

0

minus2

minus4

(b)


2

4

6

8

10

1205830H (mT)

fR

fP

fRf

P(G

Hz)

(c)

00

02

04

06

08


120590 (G

Hz)

(d)

0

50

100

150

Sens

itivi

ty (m

Vm

W)


(e)

05

10

15

20

25

30


NEP

(10minus10

WH

z05

)

(f)





f (G

Hz)

4

2

0

minus2

3

25

2

15

10 50 100 150

Vmix (120583V)

(deg)120573M

(a)

15

16

17

18

19

20

0 30 60 90 120 150 180

fRf

P(G

Hz)

fR

fP

(deg)120573M

(b)

016

018

020

022

Line

wid

th (G

Hz)

0 30 60 90 120 150 180(deg)120573M

(c)

42

44

46

48Ba

ndw

idth

(GH

z)

0 30 60 90 120 150 180(deg)120573M

(d)

0 30 60 90 120 150 1800

20

40

60

80

Sens

itivi

ty (m

Vm

W)

(deg)120573M

(e)

10

12

14

16

18

0 30 60 90 120 150 180(deg)

NEP

(10minus10

WH

z05

)

120573M

(f)




119867= 90∘ and 120575

119867= 40∘



0(101) FePt



119867=


119877is observed




119891119875and 119891


119867approaches

90∘ and 120575119867


119875-





119867= 90∘ and 120575



119867is






119867= 90∘ and 120575

119867= 40∘ Based on





119875at 1205830119867 =


119875at 1205830119867







4 Discussion


119867=



119867can


5 Conclusions


119877and 120590 on 119867





H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80


50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80


3

25

2

15

1

(f)




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




H

x

y

z

120575H

M

120573M

(a)f

(GH

z)

10

8

6

4

2

6

4

2


Vmix (120583V)

0

minus2

minus4

(b)


2

4

6

8

10

1205830H (mT)

fR

fP

fRf

P(G

Hz)

(c)

00

02

04

06

08


120590 (G

Hz)

(d)

0

50

100

150

Sens

itivi

ty (m

Vm

W)


(e)

05

10

15

20

25

30


NEP

(10minus10

WH

z05

)

(f)





f (G

Hz)

4

2

0

minus2

3

25

2

15

10 50 100 150

Vmix (120583V)

(deg)120573M

(a)

15

16

17

18

19

20

0 30 60 90 120 150 180

fRf

P(G

Hz)

fR

fP

(deg)120573M

(b)

016

018

020

022

Line

wid

th (G

Hz)

0 30 60 90 120 150 180(deg)120573M

(c)

42

44

46

48Ba

ndw

idth

(GH

z)

0 30 60 90 120 150 180(deg)120573M

(d)

0 30 60 90 120 150 1800

20

40

60

80

Sens

itivi

ty (m

Vm

W)

(deg)120573M

(e)

10

12

14

16

18

0 30 60 90 120 150 180(deg)

NEP

(10minus10

WH

z05

)

120573M

(f)




119867= 90∘ and 120575

119867= 40∘



0(101) FePt



119867=


119877is observed




119891119875and 119891


119867approaches

90∘ and 120575119867


119875-





119867= 90∘ and 120575



119867is






119867= 90∘ and 120575

119867= 40∘ Based on





119875at 1205830119867 =


119875at 1205830119867







4 Discussion


119867=



119867can


5 Conclusions


119877and 120590 on 119867





H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80


50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80


3

25

2

15

1

(f)




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




f (G

Hz)

4

2

0

minus2

3

25

2

15

10 50 100 150

Vmix (120583V)

(deg)120573M

(a)

15

16

17

18

19

20

0 30 60 90 120 150 180

fRf

P(G

Hz)

fR

fP

(deg)120573M

(b)

016

018

020

022

Line

wid

th (G

Hz)

0 30 60 90 120 150 180(deg)120573M

(c)

42

44

46

48Ba

ndw

idth

(GH

z)

0 30 60 90 120 150 180(deg)120573M

(d)

0 30 60 90 120 150 1800

20

40

60

80

Sens

itivi

ty (m

Vm

W)

(deg)120573M

(e)

10

12

14

16

18

0 30 60 90 120 150 180(deg)

NEP

(10minus10

WH

z05

)

120573M

(f)




119867= 90∘ and 120575

119867= 40∘



0(101) FePt



119867=


119877is observed




119891119875and 119891


119867approaches

90∘ and 120575119867


119875-





119867= 90∘ and 120575



119867is






119867= 90∘ and 120575

119867= 40∘ Based on





119875at 1205830119867 =


119875at 1205830119867







4 Discussion


119867=



119867can


5 Conclusions


119877and 120590 on 119867





H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80


50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80


3

25

2

15

1

(f)




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





0(101) FePt



119867=


119877is observed




119891119875and 119891


119867approaches

90∘ and 120575119867


119875-





119867= 90∘ and 120575



119867is






119867= 90∘ and 120575

119867= 40∘ Based on





119875at 1205830119867 =


119875at 1205830119867







4 Discussion


119867=



119867can


5 Conclusions


119877and 120590 on 119867





H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80


50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80


3

25

2

15

1

(f)




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




H

x

y

z

120575H

120579H

M

120573M

(a)120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

fR (GHz)10

8

6

4

2

(b)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80

10

8

6

4

2

Bandwidth (GHz)

(c)

120575H

(deg

)80

60

40

20

120579H (deg)0 20 40 60 80

120590 (GHz) 08

06

04

02

(d)

120575H

(deg

)

80

60

40

20

120579H (deg)0 20 40 60 80


50

40

30

20

10

(e)

120575H

(deg

)

80

60

40

20

120579H (deg)20 40 60 80


3

25

2

15

1

(f)




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




100 200 300

5

4

3

2

1

f (G

Hz)

8

6

4

2

0

minus2

minus4

minus6

Temperature (K)

Vmix (120583V)

(a)

0 100 200 300 4000

1

2

3

4

5

Temperature (K)

fRf

P(G

Hz)

fR

fP

(b)

30

35

40

45

50

55

60

Band

wid

th (G

Hz)

0 100 200 300 400Temperature (K)

(c)

016

017

018

019

020

021Li

ne w

idth

(GH

z)

0 100 200 300 400Temperature (K)

(d)

50

100

150

200

Sens

itivi

ty (m

Vm

W)

0 100 200 300 400Temperature (K)

(e)

00

04

08

12

16

20

0 100 200 300 400Temperature (K)

NEP

(10minus11

WH

z05

)

(f)




119867= 90∘ and 120575

119867= 40∘



Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Competing Interests


Acknowledgments


References









90Fe10Ni80Fe20























40Fe40B20












CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials














CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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