- Email: [email protected]
Giant exchange bias effect with low-coercivity in YbBaCo4O7
Journal of Alloys and Compounds 753 (2018) 329e332
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Giant exchange bias effect with low-coercivity in YbBaCo4O7 K. Dey a, b, S. Majumdar a, S. Giri a, * a b
Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032, India S.B.S.S. Mahavidyalaya, Goaltore, 721128, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 January 2018 Received in revised form 13 April 2018 Accepted 18 April 2018 Available online 21 April 2018
We observe significant exchange-bias effect below 76 K in antiferromagnetic YbBaCo4O7. Exchangebias field (HE ) is 10 kOe for 50 kOe cooling-field (Hcool ) at 4 K. The HE increases considerably with Hcool associated with the nominal increase of coercivity ðHC Þ. Low HC provides high value of HE =HC ( 15) at 4 K. High HE =HC ratio and nominal increase of HC are appealing. The results suggest robust EB effect associated with the minimal occurrence of inhomogeneous micro-domains, which is potential for the applications. Magnetic phase separation between antiferromagnetic components with k1 ¼ (0, 0, 0) and k2 ¼ (1/2, 0, 0) propagation vectors of the Pbn21 space group is correlated with the exchange-bias effect. © 2018 Elsevier B.V. All rights reserved.
Keywords: Geometric frustration lattice Kagome Antiferromagnetic ordering Exchange bias effect
1. Introduction The exchange bias (EB) effect is a six decade old phenomenon which was first observed in the Co/CoO nanoparticles having coreshell structure [1]. The conventional EB effect is manifested through the shift in the magnetic hysteresis loop when the material el temperature in a static magnetic field for is cooled through the Ne a combination of ferromagnetic (FM) and antiferromagnetic (AFM) substances [1e8]. After the discovery of EB in a classic combination of FM/AFM substances, this has also been explored in diverse combinations of magnetic substances, which creates intricacy for understanding the EB phenomenon. In the last decade EB effect has also been observed in the chemically single phase alloys and compounds [9]. Despite of the extensive studies of EB effect in plenty of systems, the origin of loop shift is not yet completely understood because of complex interface mechanism. Nevertheless, observation of EB effect is important for the fundamental interests, because it confirms microscopic magnetic phase separation in a chemically single phase compound, which can be simply probed from the bulk magnetization studies [10e12]. The EB effect is also significant for the technological applications such as data storage products, spintronic devices, permanent magnets [2e4,13]. The compound of our interest belongs to the 114-type rare earth (R) cobaltite family with formula RBaCo4O7. The RBaCo4O7 attracts
* Corresponding author. E-mail address: [email protected] (S. Giri). https://doi.org/10.1016/j.jallcom.2018.04.205 0925-8388/© 2018 Elsevier B.V. All rights reserved.
special attention for the geometric magnetic frustration, where Co ions residing in CoO4 tetrahedra form an alternate stacking layers of and triangular lattices along the crystallographic c axis Kagome [14]. The compound YbBaCo4O7 revealed a first-order transition to an orthorhombic structure with Pbn21 space group from the trigonal P31c space group around 175 K [15]. It has been suggested that the significant number of under-bonded Ba2þ site in the high temperature phase gave rise to the structural transition around 175 K. This structural instability was found to be associated with the strong softening of Young modulus [16]. Significant oxygen storage capacity has been tested for YbBaCo4O7 [17]. The effects of Pb doping on the thermoelectric properties were investigated for Yb1xPbxBaCo4O7, where the Pb doping led to the decrease of electrical resistivity as well as Seebeck coefficient [18]. The neutron diffraction studies have been performed on YbBaCo4O7, proposing that, the symmetry lowering attributed to the structural transition around 175 K led to the release of geometric magnetic frustration. As a result of it, an AFM long range ordering developed below 76 K with two propagation vectors, k1 ¼ (0, 0, 0) and k2 ¼ (1/2, 0, 0) of the Pbn21 space group [15]. The k1 ¼ (0, 0, 0) propagation vector has also been observed for isostructural YBaCo4O7 [19]. Thus k2 ¼ (1/2, 0, 0) propagation vector was suggested from a contribution of rare earth moment, although the complete magnetic structure is yet to be determined. In order to probe the nature of magnetic ordering, further magnetization studies are performed. Our careful observation reveals the evident signature of giant EB effects in YbBaCo4O7. The value of EB field ðHE Þ is 10 kOe for 50 kOe cooling field ðHcool Þ. The
330
K. Dey et al. / Journal of Alloys and Compounds 753 (2018) 329e332
Fig. 1. (a) Rietveld refinement of x-ray powder diffraction patterns (red symbols) at 300 K, (b) atomic arrangements fitted in a P31c space group. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
large HE without any doping is unique [20]. Large value of HE =HC ratio ( 15) is observed. High HE =HC ratio associated with the small value of HC in YbBaCo4O7 is unique and indicates that the unidirectional anisotropy involves minimal occurrence of inhomogeneous micro-domains due to field cooling process. Unlike usual consequences, the comparatively homogeneous domains and interfaces involving EB effect are attractive for searching potential spintronic materials. As proposed by the neutron results the magnetic phases involving antiferromagnetic k1 ¼ (0, 0, 0) and k2 ¼ (1/ 2, 0, 0) propagation vectors are suggested to be engaged with the observed EB effect. 2. Experimental details The polycrystalline compound YbBaCo4O7 is prepared using solid state reaction by mixing stoichiometric ratios of the Yb2O3, BaCO3 and Co3O4 [21]. Transmission electron microscopy (TEM) is carried out by using a JEOL TEM, 2010 microscope. The crystalline phase is identified by the powder x-ray diffraction patterns (XRD) using a BRUKER axs (Model: 8D - ADVANCE) diffractometer with a CuKa radiation source. The magnetization (M) is measured using a commercial superconducting magnetometer of UK Cryogenics. Thermal variation of resistivity is recorded using a commercial physical property measurement system (PPMS-II) of Quantum Design. 3. Experimental results and discussions Fig. 1(a) depicts the x-ray powder diffraction pattern at 300 K. Rietveld refinement is done using P31c space group. The refined pattern is shown by the continuous curve. The Rietveld fitting
seems to be quite satisfactory as revealed by the blue difference plot and the small values of the parameters, Rw (%) (4.06), Rwp (%) (2.12), and s (1.91). The values of refined lattice parameters are a ¼ 6.2693(2) and c ¼ 10.2310(3) [14,15]. As obtained from the refinement the Co ions residing at the CoO4 tetrahedra associated with other atoms are depicted in Fig. 1(b). In Fig. 2(a) high resolution TEM image shows the lattice fringes. We note that the planes extend up to the edge of the particle. The value of interplanar spacing is 5.45 Å, which corresponds to the (100) plane, as also confirmed from the x-ray diffraction pattern. The results of the element mapping of Co, Yb, and Ba are displayed in Fig. 2(cee), respectively for a selected area of the sample as also displayed in Fig. 2(b). The homogeneous distribution of the elements confirms homogeneity of the chemical phase. Temperature (T) variation of zero-field cooled (ZFC) and fieldcooled (FC) magnetization curves measured with a 20 kOe magnetic field are depicted in Fig. 3(a). The ZFC curve deviates from the FC curve around 76 K ðTN Þ, at which a long range antiferromagnetic (AFM) order was confirmed from the neutron diffraction study [15,21]. A step-like feature is observed below 180 K in MðTÞ, which is highlighted in Fig. 3(b). The evident signature of thermal hysteresis is consistent with the first order transition [15]. Thermal hysteresis associated with the similar step-like feature is also observed below 180 K in the resistivity ½rðTÞ recorded in zerofield, as depicted in Fig. 3(c). The evident signatures point to the structural coupling to the MðTÞ and rðTÞ. These results are significant, because these structural signatures confirm the O7 oxygen stoichiometry in YbBaCo4O7 [21]. Inverse of the susceptibility (c1 ) is depicted with temperature in the inset of Fig. 3(a). The straight line exhibits the Curie-Weiss fit with paramagnetic moment (meff ) and Curie-Weiss temperature to be 7.0 mB /formula unit and 305 K, respectively. The experimentally obtained meff value is below the full moment value considering the high-spin moment of Yb3þ and Co2þ. The results are consistent with that proposed coexistence of major Co2þ and minor Co3þ ions in YbBaCo4O7 [21]. We note that the value of q=TN is 3.8, proposing considerable magnetic frustration. This is consistent with the coexistence of magnetically and triangular lattice arrangements formed by frustrated kagome the AFM Co ions. A non-linear magnetic hysteresis loop with coercivity ðHC Þ of 505 Oe is observed at 4 K, which does not show any saturating trend at 80 kOe. When the sample is cooled in a static magnetic field from 300 K, the considerable shift of the magnetic hysteresis is observed at 4 K. The shift is positive for negative Hcool and negative for positive Hcool , which is a typical manifestation of the conventional EB effect. An example of both the positive and negative shifts at 4 K is depicted in Fig. 4(a) for Hcool ¼ ± 10 kOe. Central portions of the loops are further highlighted in Fig. 4(b). From the shift of the
Fig. 2. (a) High resolution TEM image, element mapping analysis of (b) a portion of sample, for (c) Co, (d) Yb, (e) Ba.
K. Dey et al. / Journal of Alloys and Compounds 753 (2018) 329e332
Fig. 3. (a) Thermal variation of ZFC-FC magnetization (M). Inset shows inverse of the susceptibility ðc1 Þ with T. Thermal hysteresis of (b) MðTÞ and (c) resistivity, rðTÞ shown in the high temperature region.
Fig. 4. (a) Shifts of the magnetic hysteresis loops at 4 K after cooling in ± 10 kOe. Inset shows the dM=dH H curve at 4 K. (b) Central portions of the loop are highlighted.
hysteresis loop one can obtain exchange bias field ðHE Þ defined as HE ¼ ðH1 þ H2 Þ=2, where H1 and H2 are the left and right coercive fields, respectively. In order to avoid experimental artifact due to minor loop effect and confirm genuine occurrence of EB effect, different suggestions have been recently proposed in recent reports [22e25]. We perform first order derivative of the magnetization (dM=dH) of the magnetic hysteresis loop with respect to magnetic field (H). Inset of Fig. 4(a) depicts the dM=dH H plot in the
331
negative field regime. The plot demonstrates that ascending and descending dM=dH curves meet above 30 kOe pointing absence of minor loop effect, as suggested in Ref. [26]. In case of YbBaCo4O7 magnetic phase separation between long range ordered AFM components with K1 ¼ (0 0 0) and K2 ¼ (1/2 0 0) propagation vectors has been proposed by the neutron diffraction studies, where second component involves the rare earth moment [15]. Thus we suggest that the exchange coupling between magnetic phases associated with the rare earth component and non-rare earth component causes the EB effect. The value of HE increases with Hcool at 4 K and indicates a saturating trend at Hcool ¼ 50 kOe, as depicted in Fig. 5(a). The value of HE is considerable as 9.6 kOe. The value is comparable to the results reported in natural minerals [27], double perovskite La1.5Sr0.5CoMnO6 [28], Pr doped YCrO3 [29], NdMnO3 [30], LaCr0.85Mn0.15O3 [31], YbCr2O4 [32], La1/3Sr2/3FeO3 [34], double perovskite Sr2YbRuO6 [33], NiMnSn Heusler alloys [35]. Although large value of HE is observed, the value is still smaller than the highest value of HE ( 30 kOe) for Mn-Pt-Ga Heusler alloy [36]. We note that the HE increases with increasing Hcool , which is associated with the similar increase of HC , as commonly observed for exchange biased systems. Unusually, the increase of HC is very small in the current observation. Here, the HC is increased to 635 Oe from 505 Oe for Hcool ¼ 50 kOe, as depicted in the inset of Fig. 5(a). This small increase of HC provides large HE =HC ratio for Hcool ¼ 50 kOe at 4 K. Intriguingly, the HE =HC ratio in the current observation is remarkably high as 15, which is nearly 20 times larger than the ratio for Mn-Pt-Ga Heusler alloy, exhibiting highest reported value of HE [36]. The high value of HE =HC in the current investigation is unique in oxides, which has also been recently observed in the rare earth-transition metal inter-metallic compounds, YMn12xFex [37] and Ni50Mn35In15 Heusler alloy [38]. Large HE =HC ratio is significant, which confirms that the large HC is not a primary for obtaining large EB effect. In general, the observation of EB in the FC process is associated with the large coercivity enhancement, which appears commonly due to the appearance of inhomogeneous microstructures [39]. In contrast to the usual consequences, minimal occurrence of inhomogeneous microstructures is fascinating in the current observation. The origin of this exceptional results further need to be investigated both theoretically and experimentally. Asymmetric vertical shift at the saturation of magnetization is typically defined as EB
Fig. 5. The Hcool dependence of (a) HE and (b) ME at 4 K. Inset of (a) shows Hcool dependence of HC at 4 K. T dependence of (c) HE , (d) HC , (e) HE =HC , and (f) ME for Hcool ¼ 50 kOe. Inset of (c) depicts the fit using a phenomenological exponential curve.
332
K. Dey et al. / Journal of Alloys and Compounds 753 (2018) 329e332
magnetization ðME Þ [9]. Since the magnetization curve does not saturate at 80 kOe, the ME is determined to be at ± 80 kOe as 1.35 emu/g, which is also high. We observe the similar Hcool dependence of ME at 4 K, as depicted in Fig. 5(b). Thermal variation of HE is depicted in Fig. 5(c). Inset of the figure depicts the fit using a phenomenological exponential curve as HE ðTÞ ¼ HE0 exp½T=T0 , where HE0 is the EB field at 0 K and T0 is a constant. The straight line does not fit with the data above TN . The fit below TN provides HE0 ¼ 10.07 kOe. The sharp fall of HE is observed initially, followed by a slow decrease with increasing T, and finally vanishes close to TN . Initial sharp fall is associated with the change in anisotropy, as depicted by the non-monotonous change of HC ðTÞ in Fig. 5(d). The HC ðTÞ exhibits a maximum, then it decreases systematically with increasing T, and nearly vanishes close to TN . Importantly, the HC ðTÞ recorded after zero-field cooling and field-cooling at 50 kOe nearly follow similar T dependence. The plot of HE =HC ratio with T is depicted in Fig. 5(e), exhibiting that, the ratio falls sharply with increasing temperature and becomes very small at 20 K, around which a maximum in HC ðTÞ is observed. Thermal variation of ME is depicted in Fig. 5(f), exhibiting similar thermal dependence of HE ðTÞ. 4. Conclusion In conclusion, large EB effect is observed in antiferromagnetic YbBaCo4O7 compound. The values of HE and ME are high as 10 kOe and 1.35 emu/g, respectively for Hcool ¼ 50 kOe, which decrease with increasing temperature and nearly vanishes close to 76 K. The HE is found to increase with increasing Hcool , which is associated with the small increase of coercivity. The small increase of coercivity and high HE =HC ratio suggest the unique homogeneous nature of EB effect. The exchange coupling between magnetic phases associated with the rare earth moment and non-rare earth moment is suggested for occurrence of EB effect in YbBaCo4O7. Acknowledgment One of the authors (S.G.) wishes to thank SERB (Project No. SR/ S2/CMP-029/2003), India for the financial support. References [1] W.H. Meiklejohn, C.P. Bean, New magnetic anisotropy, Phys. Rev. 102 (1956) 1413. [2] J. Nogues, J. Sort, V. Langlais, V. Skumryev, S. Surinach, J.S. Munoz, M.D. Baro, Exchange bias in nanostructures, Phys. Rep. 422 (2005) 65. [3] J. Nogues, J. Sort, V. Langlais, V. Skumryev, S. Surinach, J.S. Munoz, M.D. Baro, Exchange bias in ferromagnetic nanoparticles embedded in an antiferromagnetic matrix, Int. J. Nanotechnol. 2 (2005) 23e42. [4] J. Nogues, I.K. Schuller, Exchange bias, J. Magn. Magn. Mater. 192 (1999) 203e232. [5] R.L. Stamps, Mechanisms for exchange bias, J. Phys. D Appl. Phys. 33 (2000) R247. [6] O. Iglesias, A. Labarta, X. Batlle, Exchange bias phenomenology and models of core/shell nanoparticles, J. Nanosci. Nanotechnol. 8 (2008) 2761e2780. [7] P.K. Manna, S.M. Yusuf, Two interface effects: exchange bias and magnetic proximity, Phys. Rep. 535 (2014) 61e99. [8] S. Das, M. Patra, S. Majumdar, S. Giri, Exchange bias effect at the irregular interfaces between Co and CoO nanostructures, J. Alloys Compd. 488 (2009) 27e30. [9] S. Giri, M. Patra, S. Majumdar, Exchange bias effect in alloys and compounds, J. Phys. Condens. Mater. 23 (2011), 073201. [10] M. Thakur, M. Patra, K. De, S. Majumdar, S. Giri, Particle size dependent exchange bias and cluster-glass states in LaMn0.7Fe0.3O3, J. Phys. Condens. Matter 20 (2008), 195215. [11] M. Patra, M. Thakur, S. Majumdar, S. Giri, The exchange bias effect in phase separated Nd1xSrxCoO3 at the spontaneous ferromagnetic/ferrimagnetic interface, J. Phys. Condens. Matter 21 (2009), 236004. [12] M. Patra, S. Majumdar, S. Giri, Grain size effect on the magnetic cluster-glass
properties of La0.88Sr0.12CoO3, J. Phys. Condens. Matter 22 (2010), 116001. s, [13] V. Skumryev, S. Stoyanov, Y. Zhang, G. hadjipanayis, D. Givord, J. Nogue Beating the superparamagnetic limit with exchange bias, Nature (London) 423 (2003) 850e853. [14] W. Wong-Ng, W. Xie, Y. Yan, G. Liu, J. Kaduk, E. Thomas, T. Tritt, Structural and thermoelectric properties of BaRCo4O7 (R¼Dy, Ho, Er, Tm, Yb, and Lu, J. Appl. Phys. 110 (2011), 113706. [15] A. Huq, J.F. Mitchell, H. Zheng, L.C. Chapon, P.G. Radaelli, K.S. Knight, antiferroP.W. Stephens, Structural and magnetic properties of the kagome magnet YbBaCo4O7, J. Solid State Chem. 179 (2006) 1136. [16] Z.A. Kazei, V.V. Snegirev, A.S. Andreenko, L.P. Kozeeva, Anomalies in the Young modulus at structural phase transitions in rare-earth cobaltites RBaCo4O7 (R ¼ Y, Tm-Lu), J. Exp. Theor. Phys. 113 (2011) 245. [17] S. Kadota, M. Karppinen, T. Motohashi, H. Yamauchi, R-Site substitution effect on the oxygen-storage capability of RBaCo4O7þd, Chem. Mater. 20 (2008) 6378e6381. [18] Y. Chen, R. Ma, K. Wang, F. Gao, X. Hu, H. Song, Thermoelectric properties of hole-doped Yb1xPbxBaCo4O7þd ceramics, Int. J. Mod. Phys. B 29 (2015), 1550082. [19] L.C. Chapon, P.G. Radaelli, H. Zheng, J.F. Mitchell, Competing magnetic in system YBaCo4O7, Phys. Rev. B 74 (2006), teractions in the extended kagome 172401. [20] B. Koteswararao, T. Chakrabarty, T. Basu, B.K. Hazra, P.V. Srinivasarao, P.L. Paulose, S. Srinath, Large spontaneous exchange bias in a weak ferromagnet Pb6Ni9(TeO)65, Sci. Rep. 7 (2017) 8300. bert, V. Pralong, J. Hejtmanek, [21] A. Maignan, V. Caignaert, D. Pelloquin, S. He D. Khomskii, Spin, charge, and lattice coupling in triangular and Kagome sublattices of CoO4 tetrahedra: YbBaCo4O7þd (d¼0, 1), Phys. Rev. B 74 (2006), 165110. [22] J. Geshev, Comment on ’Particle size dependent exchange bias and clusterglass states in LaMn0.7Fe0.3O3, J. Phys. Condens. Matter 21 (2009), 078001. [23] M. Patra, M. Thakur, K. De, S. Majumdar, S. Giri, Reply to comment on ‘Particle size dependent exchange bias and cluster-glass states in LaMn0.7Fe0.3O3’, J. Phys. Condens. Matter 21 (2009), 078002. n, F. Palacio, [24] N.J.O. Silva, V.S. Amaral, A. Urtizberea, R. Bustamante, A. Milla Iglesias, A. Labarta, Shifted loops and E. Kampert, U. Zeitler, S. de Brion, O. coercivity from field-imprinted high-energy barriers in ferritin and ferrihydrite nanoparticles, Phys. Rev. B 84 (2011), 104427. [25] X.K. Zhang, J.J. Yuan, Y.M. Xie, Y. Yu, F.G. Kuang, H.J. Yu, X.R. Zhu, H. Shen, Phase coexistence and exchange-bias effect in LiMn2O4 nanorods, Phys. Rev. B 97 (2018), 104405. [26] A. Harres, M. Mikhov, V. Skumryev, A.M.H. de Andrade, J.E. Schmidt, J. Geshev, Criteria for saturated magnetization loop, J. Magn. Magn. Mater. 402 (2016) 76. [27] S.A. Mcenroe, B. Carter-Stiglitz, R.J. Harrison, P. Robinson, K. Fabian, C. Mccammon, Magnetic exchange bias of more than 1 Tesla in a natural mineral intergrowth, Nat. Nanotechnol. 2 (2007) 631. [28] J. Krishna Murthy, A. Venimadhav, Giant zero field cooled spontaneous exchange bias effect in phase separated La1.5Sr0.5CoMnO6, Appl. Phys. Lett. 103 (2013), 252410. [29] D. Deng, J. Zheng, D. Yu, B. Wang, D. Sun, M. Avdeev, Z. Feng, C. Jing, B. Lu, W. Ren, S. Cao, J. Zhang, Cooling field tuned magnetic phase transition and exchange bias-like effect in Y0.9Pr0.1CrO3, Appl. Phys. Lett. 107 (2015), 102404. [30] F. Hong, Z. Cheng, J. Wang, X. Wang, S. Dou, Positive and negative exchange bias effects in the simple perovskite manganite NdMnO3, Appl. Phys. Lett. 101 (2012), 102411. [31] T. Bora, S. Ravi, Sign reversal of magnetization and exchange bias field in LaCr0.85Mn0.15O3, Appl. Phys. Lett. 114 (2013), 183902. [32] Y. Sun, J.-Z. Cong, Y.-S. Chai, L.-Q. Yan, Y.-L. Zhao, S.-G. Wang, W. Ning, Y.H. Zhang, Giant exchange bias in a single-phase magnet with two magnetic sublattices, Appl. Phys. Lett. 102 (2013), 172406. [33] R.P. Singh, C.V. Tomy, A.K. Grover, Observation of tunable exchange bias in Sr2YbRuO6, Appl. Phys. Lett. 97 (2010), 182505. Iglesias, [34] Sk Sabyasachi, M. Patra, S. Majumdar, S. Giri, S. Das, V.S. Amaral, O. W. Borghols, T. Chatterji, Glassy magnetic phase driven by short-range charge and magnetic ordering in nanocrystalline La1/3Sr2/3FeO3d: magnetization, €ssbauer, and polarized neutron studies, Phys. Rev. B 86 (2012), 104416. Mo [35] H.C. Xuan, Q.Q. Cao, C.L. Zhang, S.C. Ma, S.Y. Chen, D.H. Wang, Y.W. Du, Large exchange bias field in the Ni-Mn-Sn Heusler alloys with high content of Mn, Appl. Phys. Lett. 96 (2010), 202502. [36] A.K. Nayak, M. Nicklas, S. Chadov, P. Khuntia, C. Shekhar, A. Kalache, M. Baenitz, Y. Skourski, V.K. Guduru, A. Puri, U. Zeitler, J.M.D. Coey, C. Felser, Nat. Mater. 14 (2015) 679. [37] L.T. Coutrim, E.M. Bittar, F. Stavale, F. Garcia, E. Baggio-Saitovitch, M. Abbate, R.J.O. Mossanek, H.P. Martins, D. Tobia, P.G. Pagliuso, L. Bufaical, Compensation temperatures and exchange bias in La1.5Ca0.5CoIrO6, Phys. Rev. B 93 (2016), 174406. [38] C. Jing, J. Chen, Z. Li, Y. Qiao, B. Kang, S. Cao, J. Zhang, Exchange bias behavior and inverse magnetocaloric effect in Ni50Mn35In15 Heusler alloy, J. Alloys Compd. 475 (2009) 1e4. [39] M.D. Stiles, R.D. McMichael, Coercivity in exchange-bias bilayers, Phys. Rev. B 63 (2001), 064405.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Giant exchange bias effect with low-coercivity in YbBaCo4O7 K. Dey a, b, S. Majumdar a, S. Giri a, * a b
Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032, India S.B.S.S. Mahavidyalaya, Goaltore, 721128, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 January 2018 Received in revised form 13 April 2018 Accepted 18 April 2018 Available online 21 April 2018
We observe significant exchange-bias effect below 76 K in antiferromagnetic YbBaCo4O7. Exchangebias field (HE ) is 10 kOe for 50 kOe cooling-field (Hcool ) at 4 K. The HE increases considerably with Hcool associated with the nominal increase of coercivity ðHC Þ. Low HC provides high value of HE =HC ( 15) at 4 K. High HE =HC ratio and nominal increase of HC are appealing. The results suggest robust EB effect associated with the minimal occurrence of inhomogeneous micro-domains, which is potential for the applications. Magnetic phase separation between antiferromagnetic components with k1 ¼ (0, 0, 0) and k2 ¼ (1/2, 0, 0) propagation vectors of the Pbn21 space group is correlated with the exchange-bias effect. © 2018 Elsevier B.V. All rights reserved.
Keywords: Geometric frustration lattice Kagome Antiferromagnetic ordering Exchange bias effect
1. Introduction The exchange bias (EB) effect is a six decade old phenomenon which was first observed in the Co/CoO nanoparticles having coreshell structure [1]. The conventional EB effect is manifested through the shift in the magnetic hysteresis loop when the material el temperature in a static magnetic field for is cooled through the Ne a combination of ferromagnetic (FM) and antiferromagnetic (AFM) substances [1e8]. After the discovery of EB in a classic combination of FM/AFM substances, this has also been explored in diverse combinations of magnetic substances, which creates intricacy for understanding the EB phenomenon. In the last decade EB effect has also been observed in the chemically single phase alloys and compounds [9]. Despite of the extensive studies of EB effect in plenty of systems, the origin of loop shift is not yet completely understood because of complex interface mechanism. Nevertheless, observation of EB effect is important for the fundamental interests, because it confirms microscopic magnetic phase separation in a chemically single phase compound, which can be simply probed from the bulk magnetization studies [10e12]. The EB effect is also significant for the technological applications such as data storage products, spintronic devices, permanent magnets [2e4,13]. The compound of our interest belongs to the 114-type rare earth (R) cobaltite family with formula RBaCo4O7. The RBaCo4O7 attracts
* Corresponding author. E-mail address: [email protected] (S. Giri). https://doi.org/10.1016/j.jallcom.2018.04.205 0925-8388/© 2018 Elsevier B.V. All rights reserved.
special attention for the geometric magnetic frustration, where Co ions residing in CoO4 tetrahedra form an alternate stacking layers of and triangular lattices along the crystallographic c axis Kagome [14]. The compound YbBaCo4O7 revealed a first-order transition to an orthorhombic structure with Pbn21 space group from the trigonal P31c space group around 175 K [15]. It has been suggested that the significant number of under-bonded Ba2þ site in the high temperature phase gave rise to the structural transition around 175 K. This structural instability was found to be associated with the strong softening of Young modulus [16]. Significant oxygen storage capacity has been tested for YbBaCo4O7 [17]. The effects of Pb doping on the thermoelectric properties were investigated for Yb1xPbxBaCo4O7, where the Pb doping led to the decrease of electrical resistivity as well as Seebeck coefficient [18]. The neutron diffraction studies have been performed on YbBaCo4O7, proposing that, the symmetry lowering attributed to the structural transition around 175 K led to the release of geometric magnetic frustration. As a result of it, an AFM long range ordering developed below 76 K with two propagation vectors, k1 ¼ (0, 0, 0) and k2 ¼ (1/2, 0, 0) of the Pbn21 space group [15]. The k1 ¼ (0, 0, 0) propagation vector has also been observed for isostructural YBaCo4O7 [19]. Thus k2 ¼ (1/2, 0, 0) propagation vector was suggested from a contribution of rare earth moment, although the complete magnetic structure is yet to be determined. In order to probe the nature of magnetic ordering, further magnetization studies are performed. Our careful observation reveals the evident signature of giant EB effects in YbBaCo4O7. The value of EB field ðHE Þ is 10 kOe for 50 kOe cooling field ðHcool Þ. The
330
K. Dey et al. / Journal of Alloys and Compounds 753 (2018) 329e332
Fig. 1. (a) Rietveld refinement of x-ray powder diffraction patterns (red symbols) at 300 K, (b) atomic arrangements fitted in a P31c space group. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
large HE without any doping is unique [20]. Large value of HE =HC ratio ( 15) is observed. High HE =HC ratio associated with the small value of HC in YbBaCo4O7 is unique and indicates that the unidirectional anisotropy involves minimal occurrence of inhomogeneous micro-domains due to field cooling process. Unlike usual consequences, the comparatively homogeneous domains and interfaces involving EB effect are attractive for searching potential spintronic materials. As proposed by the neutron results the magnetic phases involving antiferromagnetic k1 ¼ (0, 0, 0) and k2 ¼ (1/ 2, 0, 0) propagation vectors are suggested to be engaged with the observed EB effect. 2. Experimental details The polycrystalline compound YbBaCo4O7 is prepared using solid state reaction by mixing stoichiometric ratios of the Yb2O3, BaCO3 and Co3O4 [21]. Transmission electron microscopy (TEM) is carried out by using a JEOL TEM, 2010 microscope. The crystalline phase is identified by the powder x-ray diffraction patterns (XRD) using a BRUKER axs (Model: 8D - ADVANCE) diffractometer with a CuKa radiation source. The magnetization (M) is measured using a commercial superconducting magnetometer of UK Cryogenics. Thermal variation of resistivity is recorded using a commercial physical property measurement system (PPMS-II) of Quantum Design. 3. Experimental results and discussions Fig. 1(a) depicts the x-ray powder diffraction pattern at 300 K. Rietveld refinement is done using P31c space group. The refined pattern is shown by the continuous curve. The Rietveld fitting
seems to be quite satisfactory as revealed by the blue difference plot and the small values of the parameters, Rw (%) (4.06), Rwp (%) (2.12), and s (1.91). The values of refined lattice parameters are a ¼ 6.2693(2) and c ¼ 10.2310(3) [14,15]. As obtained from the refinement the Co ions residing at the CoO4 tetrahedra associated with other atoms are depicted in Fig. 1(b). In Fig. 2(a) high resolution TEM image shows the lattice fringes. We note that the planes extend up to the edge of the particle. The value of interplanar spacing is 5.45 Å, which corresponds to the (100) plane, as also confirmed from the x-ray diffraction pattern. The results of the element mapping of Co, Yb, and Ba are displayed in Fig. 2(cee), respectively for a selected area of the sample as also displayed in Fig. 2(b). The homogeneous distribution of the elements confirms homogeneity of the chemical phase. Temperature (T) variation of zero-field cooled (ZFC) and fieldcooled (FC) magnetization curves measured with a 20 kOe magnetic field are depicted in Fig. 3(a). The ZFC curve deviates from the FC curve around 76 K ðTN Þ, at which a long range antiferromagnetic (AFM) order was confirmed from the neutron diffraction study [15,21]. A step-like feature is observed below 180 K in MðTÞ, which is highlighted in Fig. 3(b). The evident signature of thermal hysteresis is consistent with the first order transition [15]. Thermal hysteresis associated with the similar step-like feature is also observed below 180 K in the resistivity ½rðTÞ recorded in zerofield, as depicted in Fig. 3(c). The evident signatures point to the structural coupling to the MðTÞ and rðTÞ. These results are significant, because these structural signatures confirm the O7 oxygen stoichiometry in YbBaCo4O7 [21]. Inverse of the susceptibility (c1 ) is depicted with temperature in the inset of Fig. 3(a). The straight line exhibits the Curie-Weiss fit with paramagnetic moment (meff ) and Curie-Weiss temperature to be 7.0 mB /formula unit and 305 K, respectively. The experimentally obtained meff value is below the full moment value considering the high-spin moment of Yb3þ and Co2þ. The results are consistent with that proposed coexistence of major Co2þ and minor Co3þ ions in YbBaCo4O7 [21]. We note that the value of q=TN is 3.8, proposing considerable magnetic frustration. This is consistent with the coexistence of magnetically and triangular lattice arrangements formed by frustrated kagome the AFM Co ions. A non-linear magnetic hysteresis loop with coercivity ðHC Þ of 505 Oe is observed at 4 K, which does not show any saturating trend at 80 kOe. When the sample is cooled in a static magnetic field from 300 K, the considerable shift of the magnetic hysteresis is observed at 4 K. The shift is positive for negative Hcool and negative for positive Hcool , which is a typical manifestation of the conventional EB effect. An example of both the positive and negative shifts at 4 K is depicted in Fig. 4(a) for Hcool ¼ ± 10 kOe. Central portions of the loops are further highlighted in Fig. 4(b). From the shift of the
Fig. 2. (a) High resolution TEM image, element mapping analysis of (b) a portion of sample, for (c) Co, (d) Yb, (e) Ba.
K. Dey et al. / Journal of Alloys and Compounds 753 (2018) 329e332
Fig. 3. (a) Thermal variation of ZFC-FC magnetization (M). Inset shows inverse of the susceptibility ðc1 Þ with T. Thermal hysteresis of (b) MðTÞ and (c) resistivity, rðTÞ shown in the high temperature region.
Fig. 4. (a) Shifts of the magnetic hysteresis loops at 4 K after cooling in ± 10 kOe. Inset shows the dM=dH H curve at 4 K. (b) Central portions of the loop are highlighted.
hysteresis loop one can obtain exchange bias field ðHE Þ defined as HE ¼ ðH1 þ H2 Þ=2, where H1 and H2 are the left and right coercive fields, respectively. In order to avoid experimental artifact due to minor loop effect and confirm genuine occurrence of EB effect, different suggestions have been recently proposed in recent reports [22e25]. We perform first order derivative of the magnetization (dM=dH) of the magnetic hysteresis loop with respect to magnetic field (H). Inset of Fig. 4(a) depicts the dM=dH H plot in the
331
negative field regime. The plot demonstrates that ascending and descending dM=dH curves meet above 30 kOe pointing absence of minor loop effect, as suggested in Ref. [26]. In case of YbBaCo4O7 magnetic phase separation between long range ordered AFM components with K1 ¼ (0 0 0) and K2 ¼ (1/2 0 0) propagation vectors has been proposed by the neutron diffraction studies, where second component involves the rare earth moment [15]. Thus we suggest that the exchange coupling between magnetic phases associated with the rare earth component and non-rare earth component causes the EB effect. The value of HE increases with Hcool at 4 K and indicates a saturating trend at Hcool ¼ 50 kOe, as depicted in Fig. 5(a). The value of HE is considerable as 9.6 kOe. The value is comparable to the results reported in natural minerals [27], double perovskite La1.5Sr0.5CoMnO6 [28], Pr doped YCrO3 [29], NdMnO3 [30], LaCr0.85Mn0.15O3 [31], YbCr2O4 [32], La1/3Sr2/3FeO3 [34], double perovskite Sr2YbRuO6 [33], NiMnSn Heusler alloys [35]. Although large value of HE is observed, the value is still smaller than the highest value of HE ( 30 kOe) for Mn-Pt-Ga Heusler alloy [36]. We note that the HE increases with increasing Hcool , which is associated with the similar increase of HC , as commonly observed for exchange biased systems. Unusually, the increase of HC is very small in the current observation. Here, the HC is increased to 635 Oe from 505 Oe for Hcool ¼ 50 kOe, as depicted in the inset of Fig. 5(a). This small increase of HC provides large HE =HC ratio for Hcool ¼ 50 kOe at 4 K. Intriguingly, the HE =HC ratio in the current observation is remarkably high as 15, which is nearly 20 times larger than the ratio for Mn-Pt-Ga Heusler alloy, exhibiting highest reported value of HE [36]. The high value of HE =HC in the current investigation is unique in oxides, which has also been recently observed in the rare earth-transition metal inter-metallic compounds, YMn12xFex [37] and Ni50Mn35In15 Heusler alloy [38]. Large HE =HC ratio is significant, which confirms that the large HC is not a primary for obtaining large EB effect. In general, the observation of EB in the FC process is associated with the large coercivity enhancement, which appears commonly due to the appearance of inhomogeneous microstructures [39]. In contrast to the usual consequences, minimal occurrence of inhomogeneous microstructures is fascinating in the current observation. The origin of this exceptional results further need to be investigated both theoretically and experimentally. Asymmetric vertical shift at the saturation of magnetization is typically defined as EB
Fig. 5. The Hcool dependence of (a) HE and (b) ME at 4 K. Inset of (a) shows Hcool dependence of HC at 4 K. T dependence of (c) HE , (d) HC , (e) HE =HC , and (f) ME for Hcool ¼ 50 kOe. Inset of (c) depicts the fit using a phenomenological exponential curve.
332
K. Dey et al. / Journal of Alloys and Compounds 753 (2018) 329e332
magnetization ðME Þ [9]. Since the magnetization curve does not saturate at 80 kOe, the ME is determined to be at ± 80 kOe as 1.35 emu/g, which is also high. We observe the similar Hcool dependence of ME at 4 K, as depicted in Fig. 5(b). Thermal variation of HE is depicted in Fig. 5(c). Inset of the figure depicts the fit using a phenomenological exponential curve as HE ðTÞ ¼ HE0 exp½T=T0 , where HE0 is the EB field at 0 K and T0 is a constant. The straight line does not fit with the data above TN . The fit below TN provides HE0 ¼ 10.07 kOe. The sharp fall of HE is observed initially, followed by a slow decrease with increasing T, and finally vanishes close to TN . Initial sharp fall is associated with the change in anisotropy, as depicted by the non-monotonous change of HC ðTÞ in Fig. 5(d). The HC ðTÞ exhibits a maximum, then it decreases systematically with increasing T, and nearly vanishes close to TN . Importantly, the HC ðTÞ recorded after zero-field cooling and field-cooling at 50 kOe nearly follow similar T dependence. The plot of HE =HC ratio with T is depicted in Fig. 5(e), exhibiting that, the ratio falls sharply with increasing temperature and becomes very small at 20 K, around which a maximum in HC ðTÞ is observed. Thermal variation of ME is depicted in Fig. 5(f), exhibiting similar thermal dependence of HE ðTÞ. 4. Conclusion In conclusion, large EB effect is observed in antiferromagnetic YbBaCo4O7 compound. The values of HE and ME are high as 10 kOe and 1.35 emu/g, respectively for Hcool ¼ 50 kOe, which decrease with increasing temperature and nearly vanishes close to 76 K. The HE is found to increase with increasing Hcool , which is associated with the small increase of coercivity. The small increase of coercivity and high HE =HC ratio suggest the unique homogeneous nature of EB effect. The exchange coupling between magnetic phases associated with the rare earth moment and non-rare earth moment is suggested for occurrence of EB effect in YbBaCo4O7. Acknowledgment One of the authors (S.G.) wishes to thank SERB (Project No. SR/ S2/CMP-029/2003), India for the financial support. References [1] W.H. Meiklejohn, C.P. Bean, New magnetic anisotropy, Phys. Rev. 102 (1956) 1413. [2] J. Nogues, J. Sort, V. Langlais, V. Skumryev, S. Surinach, J.S. Munoz, M.D. Baro, Exchange bias in nanostructures, Phys. Rep. 422 (2005) 65. [3] J. Nogues, J. Sort, V. Langlais, V. Skumryev, S. Surinach, J.S. Munoz, M.D. Baro, Exchange bias in ferromagnetic nanoparticles embedded in an antiferromagnetic matrix, Int. J. Nanotechnol. 2 (2005) 23e42. [4] J. Nogues, I.K. Schuller, Exchange bias, J. Magn. Magn. Mater. 192 (1999) 203e232. [5] R.L. Stamps, Mechanisms for exchange bias, J. Phys. D Appl. Phys. 33 (2000) R247. [6] O. Iglesias, A. Labarta, X. Batlle, Exchange bias phenomenology and models of core/shell nanoparticles, J. Nanosci. Nanotechnol. 8 (2008) 2761e2780. [7] P.K. Manna, S.M. Yusuf, Two interface effects: exchange bias and magnetic proximity, Phys. Rep. 535 (2014) 61e99. [8] S. Das, M. Patra, S. Majumdar, S. Giri, Exchange bias effect at the irregular interfaces between Co and CoO nanostructures, J. Alloys Compd. 488 (2009) 27e30. [9] S. Giri, M. Patra, S. Majumdar, Exchange bias effect in alloys and compounds, J. Phys. Condens. Mater. 23 (2011), 073201. [10] M. Thakur, M. Patra, K. De, S. Majumdar, S. Giri, Particle size dependent exchange bias and cluster-glass states in LaMn0.7Fe0.3O3, J. Phys. Condens. Matter 20 (2008), 195215. [11] M. Patra, M. Thakur, S. Majumdar, S. Giri, The exchange bias effect in phase separated Nd1xSrxCoO3 at the spontaneous ferromagnetic/ferrimagnetic interface, J. Phys. Condens. Matter 21 (2009), 236004. [12] M. Patra, S. Majumdar, S. Giri, Grain size effect on the magnetic cluster-glass
properties of La0.88Sr0.12CoO3, J. Phys. Condens. Matter 22 (2010), 116001. s, [13] V. Skumryev, S. Stoyanov, Y. Zhang, G. hadjipanayis, D. Givord, J. Nogue Beating the superparamagnetic limit with exchange bias, Nature (London) 423 (2003) 850e853. [14] W. Wong-Ng, W. Xie, Y. Yan, G. Liu, J. Kaduk, E. Thomas, T. Tritt, Structural and thermoelectric properties of BaRCo4O7 (R¼Dy, Ho, Er, Tm, Yb, and Lu, J. Appl. Phys. 110 (2011), 113706. [15] A. Huq, J.F. Mitchell, H. Zheng, L.C. Chapon, P.G. Radaelli, K.S. Knight, antiferroP.W. Stephens, Structural and magnetic properties of the kagome magnet YbBaCo4O7, J. Solid State Chem. 179 (2006) 1136. [16] Z.A. Kazei, V.V. Snegirev, A.S. Andreenko, L.P. Kozeeva, Anomalies in the Young modulus at structural phase transitions in rare-earth cobaltites RBaCo4O7 (R ¼ Y, Tm-Lu), J. Exp. Theor. Phys. 113 (2011) 245. [17] S. Kadota, M. Karppinen, T. Motohashi, H. Yamauchi, R-Site substitution effect on the oxygen-storage capability of RBaCo4O7þd, Chem. Mater. 20 (2008) 6378e6381. [18] Y. Chen, R. Ma, K. Wang, F. Gao, X. Hu, H. Song, Thermoelectric properties of hole-doped Yb1xPbxBaCo4O7þd ceramics, Int. J. Mod. Phys. B 29 (2015), 1550082. [19] L.C. Chapon, P.G. Radaelli, H. Zheng, J.F. Mitchell, Competing magnetic in system YBaCo4O7, Phys. Rev. B 74 (2006), teractions in the extended kagome 172401. [20] B. Koteswararao, T. Chakrabarty, T. Basu, B.K. Hazra, P.V. Srinivasarao, P.L. Paulose, S. Srinath, Large spontaneous exchange bias in a weak ferromagnet Pb6Ni9(TeO)65, Sci. Rep. 7 (2017) 8300. bert, V. Pralong, J. Hejtmanek, [21] A. Maignan, V. Caignaert, D. Pelloquin, S. He D. Khomskii, Spin, charge, and lattice coupling in triangular and Kagome sublattices of CoO4 tetrahedra: YbBaCo4O7þd (d¼0, 1), Phys. Rev. B 74 (2006), 165110. [22] J. Geshev, Comment on ’Particle size dependent exchange bias and clusterglass states in LaMn0.7Fe0.3O3, J. Phys. Condens. Matter 21 (2009), 078001. [23] M. Patra, M. Thakur, K. De, S. Majumdar, S. Giri, Reply to comment on ‘Particle size dependent exchange bias and cluster-glass states in LaMn0.7Fe0.3O3’, J. Phys. Condens. Matter 21 (2009), 078002. n, F. Palacio, [24] N.J.O. Silva, V.S. Amaral, A. Urtizberea, R. Bustamante, A. Milla Iglesias, A. Labarta, Shifted loops and E. Kampert, U. Zeitler, S. de Brion, O. coercivity from field-imprinted high-energy barriers in ferritin and ferrihydrite nanoparticles, Phys. Rev. B 84 (2011), 104427. [25] X.K. Zhang, J.J. Yuan, Y.M. Xie, Y. Yu, F.G. Kuang, H.J. Yu, X.R. Zhu, H. Shen, Phase coexistence and exchange-bias effect in LiMn2O4 nanorods, Phys. Rev. B 97 (2018), 104405. [26] A. Harres, M. Mikhov, V. Skumryev, A.M.H. de Andrade, J.E. Schmidt, J. Geshev, Criteria for saturated magnetization loop, J. Magn. Magn. Mater. 402 (2016) 76. [27] S.A. Mcenroe, B. Carter-Stiglitz, R.J. Harrison, P. Robinson, K. Fabian, C. Mccammon, Magnetic exchange bias of more than 1 Tesla in a natural mineral intergrowth, Nat. Nanotechnol. 2 (2007) 631. [28] J. Krishna Murthy, A. Venimadhav, Giant zero field cooled spontaneous exchange bias effect in phase separated La1.5Sr0.5CoMnO6, Appl. Phys. Lett. 103 (2013), 252410. [29] D. Deng, J. Zheng, D. Yu, B. Wang, D. Sun, M. Avdeev, Z. Feng, C. Jing, B. Lu, W. Ren, S. Cao, J. Zhang, Cooling field tuned magnetic phase transition and exchange bias-like effect in Y0.9Pr0.1CrO3, Appl. Phys. Lett. 107 (2015), 102404. [30] F. Hong, Z. Cheng, J. Wang, X. Wang, S. Dou, Positive and negative exchange bias effects in the simple perovskite manganite NdMnO3, Appl. Phys. Lett. 101 (2012), 102411. [31] T. Bora, S. Ravi, Sign reversal of magnetization and exchange bias field in LaCr0.85Mn0.15O3, Appl. Phys. Lett. 114 (2013), 183902. [32] Y. Sun, J.-Z. Cong, Y.-S. Chai, L.-Q. Yan, Y.-L. Zhao, S.-G. Wang, W. Ning, Y.H. Zhang, Giant exchange bias in a single-phase magnet with two magnetic sublattices, Appl. Phys. Lett. 102 (2013), 172406. [33] R.P. Singh, C.V. Tomy, A.K. Grover, Observation of tunable exchange bias in Sr2YbRuO6, Appl. Phys. Lett. 97 (2010), 182505. Iglesias, [34] Sk Sabyasachi, M. Patra, S. Majumdar, S. Giri, S. Das, V.S. Amaral, O. W. Borghols, T. Chatterji, Glassy magnetic phase driven by short-range charge and magnetic ordering in nanocrystalline La1/3Sr2/3FeO3d: magnetization, €ssbauer, and polarized neutron studies, Phys. Rev. B 86 (2012), 104416. Mo [35] H.C. Xuan, Q.Q. Cao, C.L. Zhang, S.C. Ma, S.Y. Chen, D.H. Wang, Y.W. Du, Large exchange bias field in the Ni-Mn-Sn Heusler alloys with high content of Mn, Appl. Phys. Lett. 96 (2010), 202502. [36] A.K. Nayak, M. Nicklas, S. Chadov, P. Khuntia, C. Shekhar, A. Kalache, M. Baenitz, Y. Skourski, V.K. Guduru, A. Puri, U. Zeitler, J.M.D. Coey, C. Felser, Nat. Mater. 14 (2015) 679. [37] L.T. Coutrim, E.M. Bittar, F. Stavale, F. Garcia, E. Baggio-Saitovitch, M. Abbate, R.J.O. Mossanek, H.P. Martins, D. Tobia, P.G. Pagliuso, L. Bufaical, Compensation temperatures and exchange bias in La1.5Ca0.5CoIrO6, Phys. Rev. B 93 (2016), 174406. [38] C. Jing, J. Chen, Z. Li, Y. Qiao, B. Kang, S. Cao, J. Zhang, Exchange bias behavior and inverse magnetocaloric effect in Ni50Mn35In15 Heusler alloy, J. Alloys Compd. 475 (2009) 1e4. [39] M.D. Stiles, R.D. McMichael, Coercivity in exchange-bias bilayers, Phys. Rev. B 63 (2001), 064405.