APPLIED PHYSICS LETTERS 89, 182503 共2006兲
Hyperfine splitting from magnetic boride domains embedded in Fe–Co–Ni–Al–B–Si alloy Hsin-Fu Kuo, Wei Chin, Tung-Wen Cheng, Wen-Kuang Hsu,a兲 and Jien-Wei Yeh Department of Materials and Engineering, National Tsing Hua University, 101, Section 2 Kuang Fu Road, Hsinchu 30013, Taiwan
共Received 31 July 2006; accepted 20 September 2006; published online 31 October 2006兲 Fe–Co–Ni–Al–B–Si alloy shows permeability at the gigahertz range and it is proposed that the underlying mechanism involves hyperfine splitting arising, from embedded boride domains. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2372746兴 Alloys made by equimolar mixtures of more than five elements have recently been developed and several unusual properties were discovered, including 共a兲 higher electrical resistivity 共10−6 – 10−7 ⍀ m兲, 共b兲 higher hardness 关Vickers hardness 共HV兲 = 700兴, 共c兲 higher wear resistance 共1.2– 1.6 m / mm3兲, 共d兲 higher thermal stability, and 共e兲 superior corrosion resistance, compared with ordinary alloys.1–5 The equimolar mixture promotes the degrees of freedom and materials tend to form an amorphous structure along with microprecipitates.2–4 This multiple element system has been termed as high entropy alloys 共HEAs兲 because its configurational entropy 共⌬Scon = 2.2R – 2.7R兲 is greater than that of ordinary alloys 共1.1R兲.3 According to previous studies, addition of boron to HEAs occasionally produces microprecipitates of borides and the material’s hardness thus increases from HV = 232 to HV= 736.6 In this work, we find that the permeability of Fe–Co–Ni–Al–B–Si alloy firstly decreases exponentially; it then increases significantly at gigahertz. Data reveal that the magnetic resonance at gigahertz involves the hyperfine structure arising from microprecipitates of magnetic borides. Fe–Co–Ni–Al–B, Fe–Co–Ni–Al–B–Si, and Fe–Co–Ni– Al–B–Si–Cr were studied, in comparison with boron-free Fe–Co–Ni–Al–Si–Cr and ferromagnetic Fe–Co–Ni. Samples were made by a standard arc-melting technique and elemental ratio in each HEA is equimolar 共e.g., 16.6 at. % for Fe–Co–Ni–Al–B–Si兲.4 As-made products were cut into films 共7 ⫻ 3 ⫻ 0.5 mm3兲 and sliced samples were measured by a constant magnetic field equipped with ac signal detector 共Permeance meter, PMF-3000, 0 – 3 GHz兲, x-ray diffraction 共XRD兲, electron probe x-ray microanalysis 共EPMA兲, superconducting quantum interference device 共SQUID兲 magnetometer, and electron paramagnetic resonance 共EPR兲. Figure 1共a兲 displays the permeability of HEAs in comparison with Fe–Co–Ni 共yellow兲 and all samples show an exponential decrease between 0 and 1.4 GHz. Surprisingly, a significant increase is present in Fe–Co–Ni–Al–B–Si 共red兲 above 1.4 GHz 共arrow兲 while others continuously level off. This outcome has been verified by repeated experiments. Permeability seen here for Fe–Co–Ni–Al–B–Si resembles tradeoff between domain wall motion resonance at low frequency and gyromagnetic coupling at high frequency, previously discussed by Dionne.7 The onset of angular resonance frequency for transverse permeability is at = ␥HK and is a兲
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limited at = ␥共HK + 4 M s兲, where ␥ is anisotropy constant= 2.78⫻ 106 Hz/ Oe, HK is coercivity, and M s is saturation magnetization. We find that hysteresis loops of Fe–Co–Ni–Al–Si–Cr, Fe–Co–Ni–Al–Si–Cr–B, Fe–Co–Ni– Al–B, and Fe–Co–Ni are similar and their coercivity is around 140– 160 Oe with saturation magnetization at 1000– 1200 Oe 共an example for Fe–Co–Ni–Al–Si–Cr–B is shown in the supplemental material兲. In contrast, the Fe–Co– Ni–Al–B–Si alloy shows smaller coercivity 共75 Oe兲 and higher saturation magnetization 关2500 Oe, Fig. 1共b兲兴, which is fairly unusual compared with other HEAs studied here. Firstly, although most HEAs with Fe 共or Co and Ni兲 behave as hard magnetic materials, saturation magnetization above 2000 Oe is not previously observed. Secondly, if one substitutes HK = 75 Oe and M s = 2000 Oe 关Fig 1共b兲兴 into the equation, the range appears to be 108 – 1010 Hz, namely, onset of angular resonance frequency for transverse permeability is lower than in Fig. 1共a兲 共arrow兲 by one order of magnitude. The gyromagnetic resonance at gigahertz has been observed
FIG. 1. 共Color online兲 共a兲 Permeability vs frequency for ternary alloy as well as HEAs, and 共b兲 hysteresis loop of Fe–Co–Ni–Al–B–Si.
0003-6951/2006/89共18兲/182503/3/$23.00 89, 182503-1 © 2006 American Institute of Physics Downloaded 21 Jun 2007 to 140.114.12.61. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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FIG. 2. 共Color online兲 X-ray diffraction profiles for Fe–Co–Ni–Al–B–Si alloy. Green lines denote bcc and dark lines are for tetragonal boride.
for thin permalloy films coupled with antiferromagnetic layers;8 however, we do not anticipate a similar effect for the current study because our samples are ferromagnetic in nature. Here we firstly focus on the origin of higher saturation magnetization seen in Fe–Co–Ni–Al–B–Si. According to the equation ⌬E / h = gB / h 共Hz兲, where ⌬E is energy difference between spins, g is Landé splitting factor,  is Bohr magnetron 共=9.273⫻ 10−24 J T−1兲, and B is magnetic field,9 if one inserts B = 1000 Oe and g = 2.0023 共free electron兲 into the equation, the ⌬E appears to be very small 共0.85 ⫻ 10−3 meV兲, indicating that spins have aligned before B = 1000 Oe. This outcome is obviously inconsistent with saturation magnetization at 2500 Oe 关Fig 1共b兲兴. Evidences provided by XRD, EPMA measurements, and calculation seem to suggest that higher saturation magnetization seen in Fe– Co–Ni–Al–B–Si probably originates from magnetic domains which broaden the distribution of spin directions. The Fe– Co–Ni–Al–B–Si alloy is a bcc structure with lattice constant ac of 0.29 nm, slightly greater than ␣-Fe by ⬃0.03– 0.05 nm 共Fig. 2兲. Additional reflections at 301, 321, and 411 correspond to tetragonal Fe3B,10 and the EPMA also confirms the presence of Fe–B enriched domains 共5 – 10 m兲 embedded in bcc matrix 共Fig. 3兲. XRD and EPMA did not detect enriched Fe–B domains in Fe–Co–Ni–Al–Si–Cr–B and Fe– Co–Ni–Al–B. Tetragonal domains embedded in bcc matrix imply large anisotropy energy for Fe–Co–Ni–Al–B–Si sample; for example, the Bloch wall energy of tetragonal Fe3B is 10– 20 ergs/ cm2 and its easy axis of magnetic symmetry lies along the c axis.11 The Wall energy of the bcc matrix is expected to be much lower than that of borides because the easy axis of magnetization for bcc structure usually lies along cubic edges and the corresponding wall energy is around 1 – 2 ergs/ cm2, e.g., the ␣-Fe along the 100 direction is 1 erg/ cm2. Here we estimate the anisotropy energy density of the bcc structure using the expression UK = K1关共␣1␣2兲2 + 共␣2␣3兲2 + 共␣3␣1兲2兴, where ␣n is cosine angle of magnetization in arbitrary direction with respect to the cubic edge and K1 is 4.2⫻ 105 ergs/ cm3 at room temperature.12 If one sets ␣ = 45° as upper limit the UK appears to be 3.1 ⫻ 105ergs/ cm3, which resembles ␣-Fe.12 In other words, the wall energy of the bcc matrix would approximate the ␣-Fe and higher saturation magnetization in Fe–Co–Ni–Al–B–Si alloy is truly attributed to large anisotropy energy. We now discuss the permeability increase at gigahartz from Fe–Co–Ni–Al–B–Si. Due to quenching of spin-orbit paramagnetic by electrostatic within the crystal lattice, the
FIG. 3. Elemental mapping of Fe–B enriched regions. 共a兲 Top panel for B and 共b兲 lower for Fe. Insert shows scanning electron microscopy image of embedded borides.
metals and alloys are usually weakly temperature dependent of spin susceptibility. HEAs are less atomic ordered and Coulomb field established within the crystal lattice is weaker; therefore resurrection of spin-orbit paramagnetic is expected. Our SQUID profiles truly show a clear temperature dependence of spin susceptibility 共m兲 for Fe–Co–Ni–Al–B, Fe–Co–Ni–Al–Si–Cr, and Fe–Co–Ni–Al–B–Si–Cr 共Fig. 4兲; the m of Fe–Co–Ni–Al–B–Si alloy 共red兲 is weakly temperature dependent, similar to ternary 共orange兲. At low temperature, the m of HEAs is the sum of spin paramagnetic and spin-orbit coupling; the latter decreases as temperature rises 共Fig. 4兲; the former dominates the magnetic property of HEAs at room temperature, which is consistent with EPR data. In our study, EPR profiles of Fe–Co–Ni–Al–B, Fe–Co– Ni–Al–B–Si–Cr, and Fe–Co–Ni–Al–Si–Cr are similar 共an example for Fe–Co–Ni–Al–B–Si–Cr is shown in the supplemental material兲 and are briefed as follows. Firstly, EPR
FIG. 4. 共Color online兲 SQUID data for ternary and HEAs; the field and zero-field cool profiles are overlapped, indicating a reversible process. Downloaded 21 Jun 2007 to 140.114.12.61. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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maining d electrons with Eg symmetry become available for hyperfine coupling with nuclei.15 This means that the circulating current must arise from paired 4s electrons of Fe; hence I = 1, consistent with a triplet state. Hyperfine coupling can resonate at the gigahertz range via rapid transition between paired spins 共↑↓兲 and parallel spins 共↓↓兲 under applied magnetic field, so-called electron nuclear double resonance process.13 This is supported by calculation as follows. According to Fig. 5, the triplet appears around 300– 1000 Oe and g value lies between 3 and 8 so adsorption frequency can be evaluated by substituting B = 300– 1000 Oe and g = 3 – 8 into the equation ⌬E / h = gB / h, which gives adsorption frequency around 1.2– 5 GHz, in good agreement with Fig. 1共a兲 共arrow兲. Selection of electromagnetic adsorption materials is largely determined by natural resonance frequency and materials with large anisotropic energy can promote resonance frequency to the gighertz range, e.g., ␣-Fe/ Fe3B / Y2O3.16 This work discovers that Fe–Co–Ni–Al–B–Si system contains microprecipitates of magnetic boride and its onset of magnetic resonance frequency appears at gigahertz, consistent with report.16,17 The authors thank the National Science Council of Taiwan 共NSC-95-2120-M-007-004兲 for financial support. FIG. 5. EPR profiles at different temperatures for Fe–Co–Ni–Al–B–Si. S. Ranganathan, Curr. Sci. 85, 1401 共2003兲. P.-K. Huang, J.-W. Yeh, T.-T. Shun, and S.-K. Chen, Adv. Eng. Mater. 6, 74 共2004兲. 3 C.-J. Tong, M.-R. Chen, S.-K. Chen, J.-W. Yeh, T.-T. Shun, S.-J. Lin, and S.-Y. Chang, Metall. Mater. Trans. A 36A, 1263 共2005兲. 4 J.-W. Yeh, S.-K. Chen, J.-Y. Gan, S.-J. Lin, T.-S. Chin, T.-T. Shun, C.-H. Tsau, and S.-Y. Chang, Metall. Mater. Trans. A 35A, 2533 共2004兲. 5 M. Jansen, Angew. Chem., Int. Ed. 41, 3746 共2002兲. 6 C.-Y. Hsu, J.-W. Yeh, S.-K. Chen, and T.-T. Shun, Metall. Mater. Trans. A 35A, 1465, 共2004兲. 7 G. F. Dionne, IEEE Trans. Magn. 39, 3121 共2003兲. 8 O. A. Cher, S. Queste, K. U. Barholz, and R. Mattheis, J. Appl. Phys. 93, 6668 共2003兲. 9 B. N. Banwell, Fundamentals of Molecular Spectroscopy, 3rd ed. 共McGraw-Hill, Maidenhead, England, 1983兲, Chap. 7, pp. 242–312. 10 JCPDS-ICDD File No. 39-1316. 11 L. D. Livington, J. Appl. Phys. 52, 2506 共1981兲. 12 C. Kittel, Introduction to Solid State Physics, 8th ed. 共Wiley, New York, 2005兲, Chap. 12, pp. 348–351. 13 K. A. Murphy and N. Hershkowitz, Phys. Rev. B 7, 23 共1973兲. 14 D. J. Joyner, O. Johnson, and D. M. Hercules, Phys. Rev. B 24, 3122 共1981兲. 15 B. W. Corb, R. C. O’Handley, and N. J. Grant, Phys. Rev. B 27, 636 共1983兲. 16 J. R. Liu, M. Itoh, and K. I. Machida, Appl. Phys. Lett. 83, 4017 共2003兲. 17 M. Matsumoto and Y. Miyata, J. Appl. Phys. 8, 5486 共1996兲. 1 2
band intensity significantly decreases with increasing temperature, indicating a reduction of spin concentration consistent with SQUID, and secondly, the band broadens towards the lower g-value region with increasing temperature, attributed to phase transition from spin-orbit interaction to spinspin coupling as temperature increases. For Fe–Co–Ni–Al– B–Si alloy a triplet is present between g = 3.450 and 6.822 at 4 K along with a broad adsorption of free electrons centered at g = 2.003 共Fig. 5兲. Resonance line separation of the triplet is ⬃200 Oe, which is similar to a hyperfine splitting previously observed in transition metal ions and borides.13 Hyperfine interaction occurs when an unpaired electron is very close to nuclei so spin instantly couples with circulating current around the nucleus, leading to spin splitting into 2I + 1 共I: nuclear spin兲 and variation of local electric quadrupole interaction.14 For Fe–Co–Ni–Al–B–Si alloy the hyperfine interaction probably arises from boride enriched regions because 共a兲 other HEAs 共i.e., boride-domain-free兲 do not show a triplet feature and 共b兲 the electronic configuration of Fe3B is such that 3d electrons with T2g symmetry hybridize with p orbit of B atoms to form nonmagnetic bonding and the re-
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