DSpace at VNU: The contribution of the exchange biased field direction in multilayer thin films to planar Hall resistance

Original Paper phys stat sol (b) 244, No 12, 4431 – 4434 (2007) / DOI 10.1002/pssb.200777309 The contribution of the exchange biased field direction in multilayer thin films to planar Hall resistance Tran Quang Hung1, Pham Hong Quang2, Nguyen Trung Thanh1, Oh Sunjong1, Bharat Bajaj1, and Kim CheolGi*,1 Department of Materials Science and Engineering, Chungnam National University, 220 Gung-Dong, Yu-Seong Gu, Daejeon 305-764, Korea Cryogenic Laboratory, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam Received May 2007, revised 19 September 2007, accepted 11 October 22007 Published online 12 December 2007 PACS 75.47.–m, 75.70.Cn Recently, planar Hall effect (PHE) has been widely pursued due to its application potential for biosensors Planar Hall sensor is based on the anisotropy magnetoresistance and exhibits many advantages, such as large signal-to-noise ratio at low frequencies and high sensitivity at low applied field The planar Hall resistance (PHR) curve in multilayer thin films with spinvalve structure has pre-eminent sensitivity when compared to single layer and bilayer thin films In this work, we report a model for PHR calculation that includes the behaviour of single domain basic structure in the external magnetic field Our results show a qualitative dependence between PHR curves and the angle (β) between the exchange biased field direction and the easy axis of the free layer As the β increases the sensitivity of the PHR curves also increases Further, it is shown that our calculation helps to determine the exchange biased field direction © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim Introduction The spinvalve multilayer has received much attention in recent years due to its vast potential for readheads in hard disk and magnetic tape applications [1–3] Other applications have been envisaged, including biosensors, directional sensors and magnetic random access memories [4] In these applications, the key property of the spinvalve is the relatively large change in resistance that can be obtained under low applied fields at room temperature In earlier magnetic read-head systems, magnetic stray fields were used to be detected using simple permalloy-based (single layer) sensors by exploiting the anisotropic magnetoresistive (AMR) effect Though these structures provide better signal-to-noise ratio, they provide only ≈ 2% change in resistance; thus, they are unsuitable to provide satisfactory sensitivity to detect the rapidly varying weak magnetic stray fields of the present recording media Subsequently, spin valve structures based on giant magnetoresistance (GMR) have been reported to be providing large resistance changes by about 10–20% However, the signal-to-noise ratio of GMR spin valves is relatively small leaving scope for erroneous detection of the stray fields Recently, on the other hand, the planar Hall effect (PHE) in spin valves has been emerged as a better sensitive technique to detect small deviations in the magnetization from the current direction with much less background signal; thus useful for probing magnetization reversal and domain structure in small size magnetic systems [5] Nguyen Dau et al demonstrated the advantage of PHE measurements in reducing the temperature drift by at least four orders of magnitude, and hence there is considerable increase in the * Corresponding author: e-mail: cgkim@cnu.ac.kr © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim 4432 Tran Quang Hung et al.: Contribution of the exchange biased field direction in multilayer thin films resolution of magnetoresistive sensors [6] Further, the PHE has been additionally found to be more effective for magnetic micro and nanobead detection [7] as the signal to noise ratios in these sensors are also higher by several orders compared to others [8] Thus, we develop and report here a model for planar Hall resistance (PHR) calculation while taking into account of the effect of a canted pinning field in spinvalve multilayers Theoretical background Ohm’s law, in general, expresses the symmetry of the Hall and Magnetoresistance effects In this discussion the electric field inside an isotropic material is related to the current density by Ohm’s law [9] E = ρ J (1) In general, ρ is a tensor given by ρ^ ( H ) - ρH ( H ) ρH ( H ) ρ^ ( H ) 0 0 (2) ρ // ( H ) for H parallel to the z direction Here ρ┴ (ρ//) is the resistivity in a direction perpendicular (parallel) to the H field (which, in the case of a ferromagnet, is replaced by the magnetization) and ρH is the Hall resistivity All the components of the resistivity tensor depends on the magnitude of H Ohm’s law can be rewritten as follows: E = h( J h)[ ρ - ρ ] + ρ J + ρ h ¥ J // ^ ^ H (3) where h is a unit vector in the direction of the applied field for a ferromagnet, the magnetization In Eq (3), it is shown that the spontaneous magnetoresistivity is a function of the relative direction of M and J Normally, the PHE or PHR in magnetic conductors occurs when the resistivity depends on the angle between the direction of current density J and the magnetization M, known as the anisotropic magnetoresistive (AMR) effect When M makes an angle θ with J, the AMR effect is described by magnetization reversal of the single domain as following; Ex = j ρ ^ + j ( ρ // - ρ ^ ) cos θ , E y = j ( ρ // - ρ ^ )sin θ cosθ , (4) where the transverse induced-voltage related to Ey in Eq (3) is called by PHR voltage, and it is revealed when anisotropy of resistivitive exists In order to understand the PHR curves theoretically in magnetic layers, a model which is based on magnetic density energy was used Commonly it is assumed that in spin valve structure the exchange coupling with antiferromagnetic (AFM) layer results in a single domain behavior in the ferromagnetic (FM) layer In spin valve structure, the reversal of FM films could be treated by the Stoner-Wohlfarth model [9, 10] The magnetic energy per unit of FM layers can be written as follows: E = - H p M s t p cos( β - θ p ) + K up t p sin θ p - M sp t p H cos(α - θ p ) + K uf t f sin θ f (5) - M sf t f H cos(α - θ f ) - J cos(θ f - θ p ) Here, the tf and tp; θf and θp; Kuf and Kup; Msf and Msp, are thickness; the angles between magnetization and easy axis direction; the effective anisotropy constants; and the saturation magnetization of the free and pinned layers, respectively Hp is the pinned field (exchange biased field that is induced from interaction between AFM and FM layers [11]), J is the interlayer coupling, α is the measurement angle between © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim www.pss-b.com Original Paper phys stat sol (b) 244, No 12 (2007) 4433 external magnetic field and easy axis, and the β is the angle between the exchange biased field direction and the easy axis of the free layer During calculations, the exchange biased field between the pinned FM layer and AFM layer in the spin valve structure is assumed strong enough to assign a zero angle for θp and a maximum variation (0180°) for θf on external magnetic field reversals In the Stoner-Wohlfarth model, energy term can be rewritten as follows [12]: E = K u t sin θ - M s tH cos(α - θ ) - J cos( β - θ ), (6) nπ ( -1) n + arcsin(V ( H ) / Vmax ) , 2 n = 0, ± 1, (7) where the Vmax is the maximum PHR voltage and the value of n should be chosen to keep the continuous existence of θ(H) From Eqs (6) and (4), the PHR profile can be calculated theoretically as shown in Fig under the condition that the energy E is minimum Results and discussion In our calculation, when β in Eq (7) is varied from up to 90 degrees, the theoretical calculation of PHR profiles is shown in Fig The PHE curves based on this model were obtained by numerical calculation Once the angles (α, β) and applied field H are chosen, the energy E can be computed for the angles (α, β) from Eq (7), and the angles (α0, β0) for which energy E is a minimum can be found Then the PHE voltages can be obtained from Eq (6) Figure shows that when the β value is positive (the exchange biased field rotates in plane in an anticlockwise direction), the PHR curves shift towards the negative direction of the applied magnetic field as β increases and vice versa From Fig we can also calculate numerically the sensitivity of PHR curves corresponding to different β values: 0o, 15o, 30o, 60o and 90o The change of sensitivity is given in Table below www.pss-b.com H (Oe) Fig The calculated profile of PHR based on Ohm’s law and Stoner-Wohlfarth model PHR (Ω) θ (H ) = PHR (mΩ) where J is interlayer coupling between pinned and free layers In this calculation, it is also assumed that the magnetization distribution of ferromagnetic layer is in a single domain state as a function of external applied magnetic field In this case, the angle between magnetization and induced unidirectional anisotropy of ferromagnetic layer can be obtained from measured PHR voltage as follows: β = 0o β = 15o β = 30o β = 60o β = 90o H (Oe) Fig PHR curves depend on the β values © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim 4434 Tran Quang Hung et al.: Contribution of the exchange biased field direction in multilayer thin films Table The sensitivity of PHR with several values of β beta (o) sensitivity (µΩ/Oe) 1.6 15 1.8 30 2.1 60 3.4 90 5.7 During our experiment, we fabricated multilayer spinvalve thin films Ta(5)/NiFe(6)/Cu(3)/NiFe(3)/IrMn(15)/Ta(5) (nm) in 100 (Oe) applied magnetic field The experimental PHR curve (dot line) of 3ì3 àm2 junction and fitting curve (solid line) of selected sample is given in Fig In numerical calculation, we use the values, Ku = 2×103 erg/cm3, Ms = 800 emu/cm3, J = 10-3 erg/cm2, Hk = 2Ku/Ms and R0 = (ρ// - ρ┴)/t = 44 µΩ By changing β value of the calculation we found that the experimental curve and fitting curve are in good concurrence at β = 19o This means that the exchange bias field of selected sample has some deviation from the longitudinal axis of the sample due to the demagnetization field and interlayer coupling Conclusions PHR (Ω) From Table the sensitivity of PHR increases when the angle between the exchange biased field direction and the easy axis of free layer β increases, the sensitivity changes quite large amount when β changes from 0o up to 90o This shows that the sensitivity of PHR sensor increases when the exchange bias field direction tilts at an angle of the longitudinal axis • Experiment curve Fitting curve with β = 19o H (Oe) Fig Experiment PHR curves and fitting curve with =19o of 3ì3 àm2 junction of selected sample A model to calculate the sensitivity of PHR versus external magnetic field dependence on the β value of multilayer spinvalve structures has been proposed It is shown that increasing angle (β) between the exchange biased field direction and the easy axis of the free layer not only steady shifts the experimental PHR curve towards the magnetic field axis but also increases the sensitivity of the PHR curve The best fitting of calculations with the experimental curve amply demonstrates that our work provides a good tool to determine the direction of exchange bias field of multilayer spinvalve structures, which is immensely helpful for fabricating PHR sensors Acknowledgements This work was supported by KOSEF through ReCAMM, MIC under project number A11000601-0033 and project number QG-06-03 References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] M N Baibich et al., Phys Rev Lett 61, 2472 (1988) A Moser et al., J Phys D, Appl Phys 35, R157 (2002) K.-M H Lenssen, A E M de Vierman, and J J T M Donkers, J Appl Phys 81, 4915 (1997) D D Tang, P K Wang, V S Speriosu, and S Le, IEEE Trans Magn 31, 3206 (1995) Z Q Lu, G Pan, and W Y Lai, J Appl Phys 90, 1414 (2001) F Nguyen Van Dau, A Schuhl, J R Childress, and M Sussiau, Sens Actuators A 53, 256 (1996) L Ejsing et al., Appl Phys Lett 84, 4729 (2004) B H Miller and D Dahlberg, Appl Phys Lett 69, 3932 (1996) R C O’Handley, Modern Magnetic Materials: Principles and Applications (John Wiley & Sons, Inc., 2000) Z Q Lu and G Pan, Appl Phys Lett 80, 3156 (2002) J Nogués and I K Schuller, J Magn Magn Mater 192, 203 (1999) N T Thanh et al., J Magn Magn Mater 304, e84 (2006) © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim www.pss-b.com ... while taking into account of the effect of a canted pinning field in spinvalve multilayers Theoretical background Ohm’s law, in general, expresses the symmetry of the Hall and Magnetoresistance... magnetic field and easy axis, and the β is the angle between the exchange biased field direction and the easy axis of the free layer During calculations, the exchange biased field between the pinned... unit vector in the direction of the applied field for a ferromagnet, the magnetization In Eq (3), it is shown that the spontaneous magnetoresistivity is a function of the relative direction of M