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Magnetic and electrical properties of Fe90Ta10 thin films
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
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Research articles
Magnetic and electrical properties of Fe90Ta10 thin films a
a
b
c
T d
Surabhi Shaji , Nikhil R. Mucha , A.K. Majumdar , Christian Binek , Abebe Kebede , ⁎ Dhananjay Kumara, a
Department of Mechanical Engineering, North Carolina A & T State University, Greensboro, NC 27411, USA Harish-Chandra Research Institute (HRI), Allahabad 211 019, India Department of Physics and Astronomy, University of Nebraska-Lincoln, NE 68588, USA d Department of Physics, North Carolina A & T State University, Greensboro, NC 27411, USA b c
A B S T R A C T
Fe90Ta10 (Fe-Ta) thin films, deposited using a pulsed laser deposition (PLD) method, have been found to exhibit characteristics of a soft ferromagnetic material with very low coercivities (1–10 mT) and saturation magnetization ~1.6 × 106 A/m. Our temperature dependent magnetization data at several fields (0.1–3 T) have conclusively detected the anharmonic term in the magnon dispersion relation. Moreover, the rigid-band model for metallic alloys can predict correctly the magnetic moment of ~2 µB as found by us from the above magnetization data of Fe90Ta10. We have also observed an Extraordinary Hall Effect (EHE) in these films. The extrinsic quantum mechanical side-jump mechanism as well as the intrinsic mechanism (due to the Berry phase curvatures) are responsible for the EHE varying here as the square of the electrical resistivity. Thus, our interpretation of the data at every stage is backed by theoretical considerations.
1. Introduction The rare-earth free magnetic composites, synthesized using small proportion of 5d elements such as W, Pt, Hf, and Zr and high proportion of ferromagnets such as Fe, Ni or Co, have shown significant promises as alternative candidates to rare-earth magnets [1,2]. Building on the interesting findings of our previous work on Fe-W (Ta) bulk materials [3], we have synthesized Fe90Ta10 thin films by a pulsed laser deposition method using arc-melted Fe90Ta10 alloy targets. The change of electronic structure of Fe (with 3d6 electronic configuration) due to Ta (with 5d3 electronic configuration) is expected to increase the spinorbit interactions [4]. These interactions play major role in electron transport phenomena such as Hall effect and magnetoresistance [4–11]. One of the interesting aspects of our studies has been the observation of Extraordinary Hall Effect (EHE) in the Fe90Ta10 thin films which makes them suitable for usage in magnetic field sensors, memory, or logic devices [2,4,9,12]. Ease of fabrication is an additional advantage of EHE based magnetic sensors. Among all the materials exhibiting EHE, Fe alloys have received much attention because of their wide range of material tunability and excellent magnetic properties. Alloys of iron are known to be ferromagnetic in general with strong magnetic anisotropy and improved corrosion resistance with respect to pure iron [4,13]. In the past few years, Fe alloys have also been widely studied for high density magnetic recording and shape memory applications. EHE in ultrathin films of ferromagnetic metallic alloys have exceptional efficiency as a tool for
⁎
magnetic characterization [9,10,12,14]. In this paper, we have studied magnetic properties along with EHE in Fe-Ta thin films. Addition of Ta to Fe is also known to make the resulting alloy one of the mechanically hardest materials among all the crystalline metals [15]. 2. Experimental details Fe-Ta thin films were deposited at room temperature on silicon (1 0 0) substrates. A multi-target pulsed laser deposition system was used for ablating Fe-Ta target. The total thickness of the Fe-Ta films was fixed by setting 20,000 pulses for each deposition. Other deposition parameters, such as chamber pressure, laser energy, and the substrate to target distance, were selected after optimization was carried out to determine the combination of parameters that gives the best quality film. The laser was operated at a pulse rate of 10 Hz with the energy of 380 mJ/pulse. The film was grown in a vacuum of the order of 10−7 Torr. The film thickness was measured to be 400 nm using optical profilometer. The magnetic properties of Fe-Ta systems were investigated using Vibrating Sample Magnetometer (VSM) and AC Transport measurements were done using Physical Property Measurement System (PPMS). Magnetization (M) versus field data (H) were recorded for both in-plane and out-of-plane fields. The correction of magnetization data was done by subtracting the substrate’s diamagnetic contributions from the overall magnetization data. The sample’s surface dimension for the in-plane and the out-of-plane M-H measurements were 4 mm × 3 mm and 2 mm × 2 mm respectively. The
Corresponding author. E-mail address: [email protected] (D. Kumar).
https://doi.org/10.1016/j.jmmm.2019.165446 Received 26 September 2018; Received in revised form 30 May 2019; Accepted 10 June 2019 Available online 19 June 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
S. Shaji, et al.
Fig. 1. ZFC magnetization curves at different applied fields between 0.1 and 3 T for Fe90Ta10 film on Si substrate.
sample size for the in-plane magnetization versus temperature measurements was 7 mm × 3 mm. 3. Results and discussion 3.1. Magnetic properties Fig. 1 shows the ZFC magnetization (M) vs. temperature (T) data at various fields. The magnetic field applied was parallel to the film plane during M−T measurements. All the M−T curves are convex upward indicating the ferromagnetic nature of the Fe-Ta film [10]. The temperature dependence of magnetization is explained using Bloch’s spin wave theory [6,15–17]. The dispersion relation of spin waves for k → 0 is given by
ε (k ) = gμB Hi + Dk 2 + Ek 4
Fig. 2. M(T) data fitted to Eq. (4) for two fields. Table 1 Values of χ2, correlation coefficient (R2), and the best-fit coefficients M (0), C, and D of Eq. (4).
(1)
where ε = energy of magnons or spin wave excitations. There is an energy gap in the magnon spectrum due to the internal field Hi that occurs in the first term of the above equation.
Hi = Happlied − NMs ,
(2)
where N is the demagnetization factor and Happlied is the external magnetic field. Since we have measured the in-plane magnetization of the film, N = 0 which makes the internal field equal to the applied external magnetic field, Hi = Happlied. The spontaneous magnetization due to spin wave excitation is expressed as 3
5
M (T ) = M (0) + AT 2 + BT 2 ,
M (0) (emu/cm3)
C (10−6 K−3/2)
D (10−8 K−5/2)
0.1 0.2 0.25 0.5 1 2 3 –
0.995 0.995 0.996 0.995 0.998 0.998 0.999
914.3 ± 0.4 918.7 ± 0.4 918.6 ± 0.4 918.3 ± 0.4 921.7 ± 0.2 920.5 ± 0.4 921 ± 1
−6.6 ± 0.5 −8 ± 0.5 −8.2 ± 0.4 −7.4 ± 0.5 −8.6 ± 0.3 −8 ± 0.3 −7.8 ± 0.2 −3.4 ± 0.2*
−1.1 ± 0.2 −0.6 ± 0.2 −0.5 ± 0.2 −0.7 ± 0.2 −0.4 ± 0.1 −0.5 ± 0.1 − 0.5 ± 0.1 −0.1 ± 0.1*
−(0.1 ± 0.1) × 10−8 K−5/2. The goodness of the fitting [19–21] is evident from the close-to-unity values of correlation coefficient, known as R2, tabulated in Table 1. Fig. 3 shows the magnetization (M) versus magnetic field (H) loops for Fe-Ta films at different temperatures in two orientations: (a) external magnetic field is parallel to the film surface (in-plane) and (b) external magnetic field is perpendicular to the film surface (out-ofplane). The staircase like shape of M−H loops in Fig. 3(b) is believed to be the manifestation of the coexistence of the predominantly amorphous and a small amount of crystalline FeTa phases, as evident from XRD spectrum (Fig. 5). The values of coercivity extracted from the M−H loops for in-plane and out-of-plane orientations are plotted in Fig. 4. The values of the in-plane coercivities are smaller than that of the out-of-plane coercivity almost by an order magnitude. The difference between the in-plane and out-of-plane coercivity values could be explained based on demagnetization factor [18]. The demagnetization factor in the in-plane case is N → 0 which makes magnetization easier as compared to the out-of-plane case where demagnetization factor, N → 1 making magnetization harder. Since the magnetization saturates
5/2
where M (0) = magnetization at 0 K. T and T terms come from the harmonic (k2) and the anharmonic (k4) terms in the spin wave dispersion relation respectively. Dividing both sides of Eq. (3) by M (0), we get
M (T ) − M (0) 3 5 = CT 2 + DT 2 M (0)
R2
* Pure Fe Sample [6].
(3) 3/2
Field (T)
(4)
M(T) data were fitted to Eq. (4) derived from spin wave theory. Shown in Fig. 2 are the fits for 0.1 T and 3 T. As seen in this figure, excellent fits were obtained for all fields (only 2 are shown) with correlation coefficients ranging from R2 = 0.999 for 3 T (highest field) and R2 = 0.995 for 0.1 T (lowest field). Moreover, even the T5/2 term could be found very convincingly. Table 1 shows the values of R2, M (0), C, and D at all 7 fields. The values of the coefficients C and D, obtained from the fits are in very good agreement with those obtained for pure Fe [6,18] which are C = −(3.4 ± 0.2) × 10−6 K−3/2 and D = 2
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
S. Shaji, et al.
Fig. 3. (a) In-plane and (b) Out-of-plane magnetization vs. field data extracted from M−H loops for Fe90Ta10 thin films on Si substrate till ± 10 mT and ± 60 mT, respectively.
at smaller fields in the case of in-plane orientation, the coercivity values will accordingly be smaller than in the case of out-of-plane orientation. The film shows soft ferromagnetic behavior as evident from the low coercivity values [22–25]. The low coercivities could be due to the amorphous nature of the film as supported by the XRD patterns of Fe-Ta thin film (Fig. 5). As seen in the XRD pattern, the peak due to Fe-Ta is low in intensity as well as very broad with full width at half maximum (FWHM) of more than two degrees. If Fe-Ta is truly amorphous, the electrical resistivity should be described by Ziman theory of liquid metals [26]. According to this theory, the temperature dependence of resistivity well below Debye temperature is expressed by,
ρ (T ) = ρ0 + aT 2
(6)
where ρo is residual resistivity and a is a constant. As seen in Fig. 6, a reasonably good fit to Eq. (6) was obtained for ρ (T) data from 10 to 100 K with a correlation coefficient of 0.990. Due to low addition of Ta, Fe-Ta film is expected to have Debye temperature similar to that of pure iron (470 K). The values of ρ0 (2.12 × 10−7 Ωm) obtained here for Fe-Ta is nearly an order of magnitude higher than that of Fe99Cr01 (Fe-Cr) bulk alloy (2.7 × 10−8 Ωm) [5]. Thus, based on the XRD and ρ (T) data analysis via Ziman theory, it can be conjectured that Fe-Ta films are predominantly amorphous.
Fig. 4. Coercivity vs. temperature for in-plane (blue) and out-of-plane (red) measurements. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. X-ray diffraction pattern of a Fe-Ta film on Si substrate.
Fig. 6. Electrical resistivity vs. temperature. Red points are the data points and the blue ones are the best-fitted points. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
S. Shaji, et al.
proposed by Berger, better known as the side-jump mechanism that is again a purely a quantum mechanical effect [8,12,34]. An electron wave packet, when approaching a central scattering potential, moves in a straight line through the periodic crystal both before and after the scattering. The spin-orbit interaction reduces the symmetry of the problem and produces a left-right asymmetry in the differential scattering cross-section with respect to the plane containing the electron spin and its velocity. This produces different scattering probability towards left and right. After interacting with the scattering potential, the electron wave packet can have two distinctly different trajectories: 1) The new trajectory might be at an angle to the old trajectory but meeting at the scattering centre. This effect is termed as the skew or the Smit asymmetric scattering (ħ/τEF < < 1). 2) The second possibility is that the new trajectory might be displaced by a finite transverse distance ‘Δ’ from its old trajectory. Both the trajectories, before and after collision, never meet each other; hence it is called the side-jump effect, as proposed by Berger. The side-jump effect is dominant when ħ/τEF is not small. The displacement ‘Δ’ has also been calculated using a shortrange impurity potential V(r) in addition to the spin-orbit interaction. The magnitude of Δ is calculated to be of the order of 10−10−10−11 m for band electrons and is independent of the range, strength, and nature (i.e., impurities, phonons, etc.) of the scattering potential. Here also Rs = bρ2 . So considering both classical and quantum cases one gets,
3.2. Extraordinary Hall effect The Hall resistivity in ferromagnetic metals and alloys in a polycrystalline form is given by
ρH = Ey / jx = R 0 B + μ0 Rs Ms
(7)
where R0 is the ordinary Hall constant (OHC), Rs is the extraordinary or spontaneous Hall constant, B is the magnetic induction, Ms is the saturation magnetization, µ0 is the permeability of the free space, and a is a material dependent constant [8–10,27,28]. Here, the first term represents the ordinary Hall effect which results from the Lorentz force acting on the moving charge carriers under the influence of an external magnetic field while the second term represents the extraordinary or the anomalous Hall effect (AHE) that is known to originate from the spin-orbit interaction present in a ferromagnet. The AHE has three components: an intrinsic scattering-free part and two extrinsic scattering-dependent parts. The intrinsic AHE is not very common. In the intrinsic regime, the AHE can often be understood in terms of the geometric concept of Berry phase and Berry curvature in momentum space. Berry phase is very similar to Bohm-Aharonv phase in real space [29]. The Berry-phase concept has established a link between the AHE and the topological nature of the Hall currents. New experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors have established the dominance of an intrinsic Berry-phaserelated AHE mechanism in metallic ferromagnets with moderate conductivity. In 1959, Yakir Aharonov and David Bohm predicted that the phase of a charged quantum particle moving around a loop in a magnetic field would acquire an additional phase of 2π times the number of magnetic flux quanta passing through any surface bounded by the loop. The Aharonov– Bohm effect has been confirmed in many experiments. In 1984 Michael Berry discovered a more general form of the Aharonov–Bohm effect by working in a general “parameter space” rather than real space. Berry predicted that the wavefunction of a particle can acquire a geometric phase when a parameter, such as the potential energy, is slowly varied before eventually returning to its original value. The geometric phase acquired by the particle is equal to the flux of a new field called the Berry curvature through the surface defined by this loop. One such dynamic effect is the anomalous Hall effect. In a recent reviews of modern physics [29], three broad regimes have been identified while surveying a large body of experimental data for diverse materials. First, a high conductivity regime where ρxx ≤ 1 µΩ cm, skew scattering dominates and ρxy is proportional to ρxx. Second, an intrinsic or scattering-independent good metal regime in which ρxy is roughly independent of ρxx (≈(1 − 100) µΩ cm). This dependence comes from a semiclassical treatment by a generalized Boltzmann equation taking into account the Berry curvature and coherent inter-band mixing effects due to band structure and disorder. Third, a bad metal regime where ρxx > 100 µΩ cm. In this situation, ρxy is proportional to ρxx2 coming from the side-jump mechanism. The two scattering dependent extrinsic mechanisms responsible for Rs are: (a) Classical Smit asymmetric scattering and (b) Non-classical transport (side-jump) [4,7,12,30,31]. Smit proposed the “asymmetric scattering” of magnetized conduction electrons by impurities [8,31–33]. In the presence of spin-orbit interaction in a ferromagnet, there is left-right asymmetry in the differential scattering cross-section about the j-B (x-z) plane. As a result, electrons tend to pile up on one side of the sample producing a Hall field along the y-axis. Boltzmann equation is correct to the lowest order in ħ/τEF, where τ is the relaxation time and EF is the Fermi energy [8]. For pure metals and dilute alloys at low temperatures ħ/τEF < < 1. When ħ/τEF is not small which is realized in concentrated and disordered alloys and high temperatures, Boltzmann transport is no more valid. In that situation, KarplusLuttinger-Kohn (KLK) gave a quantum mechanical transport theory yielding ρH as expressed in Eq. (7). A simple intuitive theory was
Rs = aρ + bρ,2
(8)
where ρ is the bulk resistivity and a and b are constants which are characteristics of the materials. The linear term in ρ is attributed to Smit asymmetric scattering or skew scattering of the charged carriers, derivable from the classical Boltzmann equation while the quadratic term in ρ is attributed to the side jump mechanism proposed by Berger [34]. Hall resistivity (ρH) versus the applied field (µoH) was measured in both positive and negative fields at different temperatures. We have shown the ρH versus µoH plots only for positive fields in Fig. 7 (B = µoH in the Hall geometry). Each plot consists of essentially two straight lines. The two straight lines cut at a point (called the technical saturation as shown in the inset of Fig. 7), whose ρH value is equal to the µoR1Ms (where R1 is the slope of the first straight line) and the B value is µoMs [35]. As we increase B from the origin and move along the first straight line (whose slope is R1), µoM keeps on increasing. Since M cannot change above saturation induction B beyond its spontaneous value of Ms, we get the second straight line starting from the B value of
Fig. 7. Hall resistivity (ρH) is plotted against external magnetic field (µoH) at different temperatures, all showing technical saturation around 2 T. The inset shows the schematic behavior of the Hall resistivity ρH, as a function of the magnetic induction B. µ0Ms is the spontaneous magnetization. 4
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
S. Shaji, et al.
because of the correlation coefficient is 0.985. Finally, we conclude that the extrinsic quantum mechanical sidejump mechanism as well as the intrinsic mechanism due to the Berry phase curvatures are responsible for the EHE varying here as the square of the electrical resistivity. An experimental method has been suggested to separate them by varying the film thickness following a recent work of Tian, Ye, and Jin [37] where they used both ρ(T) and the residual resistivity ρ(0) in the scaling fit. Their samples are thin films of Fe of thickness 93, 6.5, 4, 3, 2.5 and 1.5 nm with resistivities of ~10, 18, 25, 35, 45, and 65 µΩ cm, respectively. They find that all the three contributions (two extrinsic and one intrinsic) are of the same order in magnitude and so of equal importance. Our FeTa film has thickness of ~400 A with a resistivity of 20 µΩ cm. Following the work of Tian, Ye, and Jin, we plan to carry out Hall measurements on samples with different thicknesses and apply similar scaling laws to isolate the three contributions. The amount of side jump for free electrons is calculated using the Eq. (10) [34],
µoMs with a slope of R0 and µ0RsMs. The Hall coefficient R0 and µ0RsMs were found as the slope and the intercept of the linear portion of the Hall curves above the technical saturation field of 2 T by fitting ρH versus the µoH data to Eq. (7). It is interesting to note here that the Hall measurements could be used to roughly estimate the spontaneous magnetization of a material, here 2 T [35]. It is also the field needed to saturate M as found in our M−H measurements in the out of-plane configuration (inset of Fig. 3b). This value of 2 T for Fe-Ta sample compares very well with the spontaneous magnetization of 2.2 T for pure Fe. We observe that the drop in spontaneous magnetization (10%) is in the same ratio of 10% doping of Fe by Ta. The above magnetization value of 2 T of Fe90Ta10 could quantitatively be found from the rigid-band model as given below. The localized-moment theory of ferromagnetism breaks down in two aspects. The magnetic moment on each atom or ion should be the same in both the ferromagnetic and paramagnetic phases and its value should correspond to an integral multiple of μB. None of the above are observed experimentally. Hence there is a need of a band theory or collectiveelectron theory. In Fe, Ni, and Co, the Fermi energy lies in a region of overlapping 3d and 4 s bands. The rigid-band model assumes that the structures of the 3d and 4 s bands do not change markedly across the 3d series and so any differences in electronic structure are caused entirely by changes in the Fermi energy (EF). This is supported by detailed band structure calculations. According to band-structure studies [36], both theoretical and experimental, the density of states at EF is higher in Fe for the majority band electrons than that of the minority band electrons. In the present case of FeTa alloy, the electronic configuration of Fe is [Ar] 3d64s2 and that of Ta is [Xe] 4f145d34s2. Thus, our alloy has three fewer d-electrons per replacement of one Fe atom by one Ta atom. When the electrons are removed as Fe is replaced by Ta, they are first removed from the majority band due to their higher density of states and hence the magnetization decreases. Thus, the moment of the alloy should decrease by 3 × 0.1 = 0.3 µB for 10% alloy, i.e., 2.2–0.3 = 1.9 instead of 2.0 µB. So, the rigid band model holds even for a large difference in d electrons (3). Here also, we have a good quantitative agreement with theory. In Fig. 7, both R0 and Rs are found to be positive. The positive R0 implies that the effective conductivity of holes is more than that of electrons as in pure Fe. In Eq. (8), the first term, due to asymmetric scattering is very unlikely to contribute in Fe-Ta film since it’s resistivity (2.12 × 10−7 Ωm) is 2000 times that of pure Fe (≈1 × 10−10 Ωm)[5], where the most dominant contribution to Rs comes from the asymmetric scattering. So, we have left the asymmetric scattering term in the Eq. (8) and instead we have fitted Rs(T) data to
Rs = a + bρ2
Δy =
1 k 0 λc2 ≈ 3.7 × 10−16m 6
where k 0 =
2 × me εf ħ2 ħ me c
(10)
≈ 1.7 × 1010m−1 is the wave vector at the Fermi
≈ 3.6 × 10−13 is the rationalized Compton wavelevel and λ c = length, me is the mass of electron and c is the speed of light. We used εf = 11.1 eV as the Fermi energy of iron. Considering the band effects, there is an enhancement of ≈104 in the value of Δy. Hence, Δy ≈ 3.7 × 10−2Å , which is almost 1% of lattice parameter of iron, a = 2.86Å . Table 2 shows the values for ρ, R0 and Rs as a function of temperature. The value of Rs at 10 K is 7.4 × 10−9 Ωm/T in Fe-Ta which is 74 times larger than that of Rs in Fe99Cr01 (0.1 × 10−9 Ωm/T). The Ohmic resistivity of Fe-Cr (2.7 × 10−8Ωm at 4 K) and Fe-Ta (2.1 × 10−7 at 5 K) is in the ratio of 8:1 which justifies Rs ≈ ρ2 almost quantitatively (82 being close to 74) [5]. 4. Conclusions In summary, the Fe90Ta10 thin film gown on silicon (1 0 0) substrates were found to be structurally amorphous. The films have shown the characteristics of soft ferromagnets. Excellent magnetization versus temperature data at several fields fitted very well to the Bloch’s spin wave theory even with the T5/2 term along with the T3/2 term. The technical saturation of 2 T found from the ρH versus µ0H plot matches well with the saturation magnetization obtained from the M versus µ0H plot. Our calculated value of the magnetic moment, using the rigidband model, is in very good agreement with the above measured value even with a large valence difference of ΔZ = 3 between Fe and Ta. The anomalous Hall effect results suggest that the quantum mechanical side jump scattering well as the intrinsic scattering-independent mechanism are the most dominant contributors to the AHE. More experiments and modified scaling laws will be used to separate the two contributions. Small coercivity at all temperatures makes Fe-Ta thin films good candidates for applications like magnetic sensors, spin logic devices,
(9)
The fitting result is shown in Fig. 8. The fit seems reasonably good
Table 2 ρ, R0 and Rs as a function of temperature.
Fig. 8. Plot of Rs vs. ρ fitted to a + bρ2. 5
Temperature (K)
ρ (10−7 Ωm)
R0 (10−15 Ωm/T or m3/ C)
Rs (10−9 Ωm/T or m3/C)
5 10 50 100 150 200 250 300
2.1 2.12 2.13 2.19 2.29 2.35 2.43 2.57
2.6 ± 0.1 2.7 ± 0.1 2.6 ± 0.1 2.9 ± 0.1 2.8 ± 0.1 3 ± 0.1 2.9 ± 0.09 3.8 ± 0.1
7.44 7.43 6.67 6.58 7.63 8.26 9.0 10.5
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
S. Shaji, et al.
recording heads, etc. [16]
Acknowledgments
[17]
This work was supported by the National Science Foundation (NSF) through the Nebraska Materials Research Science and Engineering Center (MRSEC) (Grant No. DMR-1420645). We also like to thank NSFMRI (Grant No. CMMI-1040290) for Pulsed Laser Deposition facility at NCA&T State University.
[18] [19] [20]
Appendix A. Supplementary data [21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jmmm.2019.165446.
[22]
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6
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Research articles
Magnetic and electrical properties of Fe90Ta10 thin films a
a
b
c
T d
Surabhi Shaji , Nikhil R. Mucha , A.K. Majumdar , Christian Binek , Abebe Kebede , ⁎ Dhananjay Kumara, a
Department of Mechanical Engineering, North Carolina A & T State University, Greensboro, NC 27411, USA Harish-Chandra Research Institute (HRI), Allahabad 211 019, India Department of Physics and Astronomy, University of Nebraska-Lincoln, NE 68588, USA d Department of Physics, North Carolina A & T State University, Greensboro, NC 27411, USA b c
A B S T R A C T
Fe90Ta10 (Fe-Ta) thin films, deposited using a pulsed laser deposition (PLD) method, have been found to exhibit characteristics of a soft ferromagnetic material with very low coercivities (1–10 mT) and saturation magnetization ~1.6 × 106 A/m. Our temperature dependent magnetization data at several fields (0.1–3 T) have conclusively detected the anharmonic term in the magnon dispersion relation. Moreover, the rigid-band model for metallic alloys can predict correctly the magnetic moment of ~2 µB as found by us from the above magnetization data of Fe90Ta10. We have also observed an Extraordinary Hall Effect (EHE) in these films. The extrinsic quantum mechanical side-jump mechanism as well as the intrinsic mechanism (due to the Berry phase curvatures) are responsible for the EHE varying here as the square of the electrical resistivity. Thus, our interpretation of the data at every stage is backed by theoretical considerations.
1. Introduction The rare-earth free magnetic composites, synthesized using small proportion of 5d elements such as W, Pt, Hf, and Zr and high proportion of ferromagnets such as Fe, Ni or Co, have shown significant promises as alternative candidates to rare-earth magnets [1,2]. Building on the interesting findings of our previous work on Fe-W (Ta) bulk materials [3], we have synthesized Fe90Ta10 thin films by a pulsed laser deposition method using arc-melted Fe90Ta10 alloy targets. The change of electronic structure of Fe (with 3d6 electronic configuration) due to Ta (with 5d3 electronic configuration) is expected to increase the spinorbit interactions [4]. These interactions play major role in electron transport phenomena such as Hall effect and magnetoresistance [4–11]. One of the interesting aspects of our studies has been the observation of Extraordinary Hall Effect (EHE) in the Fe90Ta10 thin films which makes them suitable for usage in magnetic field sensors, memory, or logic devices [2,4,9,12]. Ease of fabrication is an additional advantage of EHE based magnetic sensors. Among all the materials exhibiting EHE, Fe alloys have received much attention because of their wide range of material tunability and excellent magnetic properties. Alloys of iron are known to be ferromagnetic in general with strong magnetic anisotropy and improved corrosion resistance with respect to pure iron [4,13]. In the past few years, Fe alloys have also been widely studied for high density magnetic recording and shape memory applications. EHE in ultrathin films of ferromagnetic metallic alloys have exceptional efficiency as a tool for
⁎
magnetic characterization [9,10,12,14]. In this paper, we have studied magnetic properties along with EHE in Fe-Ta thin films. Addition of Ta to Fe is also known to make the resulting alloy one of the mechanically hardest materials among all the crystalline metals [15]. 2. Experimental details Fe-Ta thin films were deposited at room temperature on silicon (1 0 0) substrates. A multi-target pulsed laser deposition system was used for ablating Fe-Ta target. The total thickness of the Fe-Ta films was fixed by setting 20,000 pulses for each deposition. Other deposition parameters, such as chamber pressure, laser energy, and the substrate to target distance, were selected after optimization was carried out to determine the combination of parameters that gives the best quality film. The laser was operated at a pulse rate of 10 Hz with the energy of 380 mJ/pulse. The film was grown in a vacuum of the order of 10−7 Torr. The film thickness was measured to be 400 nm using optical profilometer. The magnetic properties of Fe-Ta systems were investigated using Vibrating Sample Magnetometer (VSM) and AC Transport measurements were done using Physical Property Measurement System (PPMS). Magnetization (M) versus field data (H) were recorded for both in-plane and out-of-plane fields. The correction of magnetization data was done by subtracting the substrate’s diamagnetic contributions from the overall magnetization data. The sample’s surface dimension for the in-plane and the out-of-plane M-H measurements were 4 mm × 3 mm and 2 mm × 2 mm respectively. The
Corresponding author. E-mail address: [email protected] (D. Kumar).
https://doi.org/10.1016/j.jmmm.2019.165446 Received 26 September 2018; Received in revised form 30 May 2019; Accepted 10 June 2019 Available online 19 June 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
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Fig. 1. ZFC magnetization curves at different applied fields between 0.1 and 3 T for Fe90Ta10 film on Si substrate.
sample size for the in-plane magnetization versus temperature measurements was 7 mm × 3 mm. 3. Results and discussion 3.1. Magnetic properties Fig. 1 shows the ZFC magnetization (M) vs. temperature (T) data at various fields. The magnetic field applied was parallel to the film plane during M−T measurements. All the M−T curves are convex upward indicating the ferromagnetic nature of the Fe-Ta film [10]. The temperature dependence of magnetization is explained using Bloch’s spin wave theory [6,15–17]. The dispersion relation of spin waves for k → 0 is given by
ε (k ) = gμB Hi + Dk 2 + Ek 4
Fig. 2. M(T) data fitted to Eq. (4) for two fields. Table 1 Values of χ2, correlation coefficient (R2), and the best-fit coefficients M (0), C, and D of Eq. (4).
(1)
where ε = energy of magnons or spin wave excitations. There is an energy gap in the magnon spectrum due to the internal field Hi that occurs in the first term of the above equation.
Hi = Happlied − NMs ,
(2)
where N is the demagnetization factor and Happlied is the external magnetic field. Since we have measured the in-plane magnetization of the film, N = 0 which makes the internal field equal to the applied external magnetic field, Hi = Happlied. The spontaneous magnetization due to spin wave excitation is expressed as 3
5
M (T ) = M (0) + AT 2 + BT 2 ,
M (0) (emu/cm3)
C (10−6 K−3/2)
D (10−8 K−5/2)
0.1 0.2 0.25 0.5 1 2 3 –
0.995 0.995 0.996 0.995 0.998 0.998 0.999
914.3 ± 0.4 918.7 ± 0.4 918.6 ± 0.4 918.3 ± 0.4 921.7 ± 0.2 920.5 ± 0.4 921 ± 1
−6.6 ± 0.5 −8 ± 0.5 −8.2 ± 0.4 −7.4 ± 0.5 −8.6 ± 0.3 −8 ± 0.3 −7.8 ± 0.2 −3.4 ± 0.2*
−1.1 ± 0.2 −0.6 ± 0.2 −0.5 ± 0.2 −0.7 ± 0.2 −0.4 ± 0.1 −0.5 ± 0.1 − 0.5 ± 0.1 −0.1 ± 0.1*
−(0.1 ± 0.1) × 10−8 K−5/2. The goodness of the fitting [19–21] is evident from the close-to-unity values of correlation coefficient, known as R2, tabulated in Table 1. Fig. 3 shows the magnetization (M) versus magnetic field (H) loops for Fe-Ta films at different temperatures in two orientations: (a) external magnetic field is parallel to the film surface (in-plane) and (b) external magnetic field is perpendicular to the film surface (out-ofplane). The staircase like shape of M−H loops in Fig. 3(b) is believed to be the manifestation of the coexistence of the predominantly amorphous and a small amount of crystalline FeTa phases, as evident from XRD spectrum (Fig. 5). The values of coercivity extracted from the M−H loops for in-plane and out-of-plane orientations are plotted in Fig. 4. The values of the in-plane coercivities are smaller than that of the out-of-plane coercivity almost by an order magnitude. The difference between the in-plane and out-of-plane coercivity values could be explained based on demagnetization factor [18]. The demagnetization factor in the in-plane case is N → 0 which makes magnetization easier as compared to the out-of-plane case where demagnetization factor, N → 1 making magnetization harder. Since the magnetization saturates
5/2
where M (0) = magnetization at 0 K. T and T terms come from the harmonic (k2) and the anharmonic (k4) terms in the spin wave dispersion relation respectively. Dividing both sides of Eq. (3) by M (0), we get
M (T ) − M (0) 3 5 = CT 2 + DT 2 M (0)
R2
* Pure Fe Sample [6].
(3) 3/2
Field (T)
(4)
M(T) data were fitted to Eq. (4) derived from spin wave theory. Shown in Fig. 2 are the fits for 0.1 T and 3 T. As seen in this figure, excellent fits were obtained for all fields (only 2 are shown) with correlation coefficients ranging from R2 = 0.999 for 3 T (highest field) and R2 = 0.995 for 0.1 T (lowest field). Moreover, even the T5/2 term could be found very convincingly. Table 1 shows the values of R2, M (0), C, and D at all 7 fields. The values of the coefficients C and D, obtained from the fits are in very good agreement with those obtained for pure Fe [6,18] which are C = −(3.4 ± 0.2) × 10−6 K−3/2 and D = 2
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
S. Shaji, et al.
Fig. 3. (a) In-plane and (b) Out-of-plane magnetization vs. field data extracted from M−H loops for Fe90Ta10 thin films on Si substrate till ± 10 mT and ± 60 mT, respectively.
at smaller fields in the case of in-plane orientation, the coercivity values will accordingly be smaller than in the case of out-of-plane orientation. The film shows soft ferromagnetic behavior as evident from the low coercivity values [22–25]. The low coercivities could be due to the amorphous nature of the film as supported by the XRD patterns of Fe-Ta thin film (Fig. 5). As seen in the XRD pattern, the peak due to Fe-Ta is low in intensity as well as very broad with full width at half maximum (FWHM) of more than two degrees. If Fe-Ta is truly amorphous, the electrical resistivity should be described by Ziman theory of liquid metals [26]. According to this theory, the temperature dependence of resistivity well below Debye temperature is expressed by,
ρ (T ) = ρ0 + aT 2
(6)
where ρo is residual resistivity and a is a constant. As seen in Fig. 6, a reasonably good fit to Eq. (6) was obtained for ρ (T) data from 10 to 100 K with a correlation coefficient of 0.990. Due to low addition of Ta, Fe-Ta film is expected to have Debye temperature similar to that of pure iron (470 K). The values of ρ0 (2.12 × 10−7 Ωm) obtained here for Fe-Ta is nearly an order of magnitude higher than that of Fe99Cr01 (Fe-Cr) bulk alloy (2.7 × 10−8 Ωm) [5]. Thus, based on the XRD and ρ (T) data analysis via Ziman theory, it can be conjectured that Fe-Ta films are predominantly amorphous.
Fig. 4. Coercivity vs. temperature for in-plane (blue) and out-of-plane (red) measurements. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. X-ray diffraction pattern of a Fe-Ta film on Si substrate.
Fig. 6. Electrical resistivity vs. temperature. Red points are the data points and the blue ones are the best-fitted points. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
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proposed by Berger, better known as the side-jump mechanism that is again a purely a quantum mechanical effect [8,12,34]. An electron wave packet, when approaching a central scattering potential, moves in a straight line through the periodic crystal both before and after the scattering. The spin-orbit interaction reduces the symmetry of the problem and produces a left-right asymmetry in the differential scattering cross-section with respect to the plane containing the electron spin and its velocity. This produces different scattering probability towards left and right. After interacting with the scattering potential, the electron wave packet can have two distinctly different trajectories: 1) The new trajectory might be at an angle to the old trajectory but meeting at the scattering centre. This effect is termed as the skew or the Smit asymmetric scattering (ħ/τEF < < 1). 2) The second possibility is that the new trajectory might be displaced by a finite transverse distance ‘Δ’ from its old trajectory. Both the trajectories, before and after collision, never meet each other; hence it is called the side-jump effect, as proposed by Berger. The side-jump effect is dominant when ħ/τEF is not small. The displacement ‘Δ’ has also been calculated using a shortrange impurity potential V(r) in addition to the spin-orbit interaction. The magnitude of Δ is calculated to be of the order of 10−10−10−11 m for band electrons and is independent of the range, strength, and nature (i.e., impurities, phonons, etc.) of the scattering potential. Here also Rs = bρ2 . So considering both classical and quantum cases one gets,
3.2. Extraordinary Hall effect The Hall resistivity in ferromagnetic metals and alloys in a polycrystalline form is given by
ρH = Ey / jx = R 0 B + μ0 Rs Ms
(7)
where R0 is the ordinary Hall constant (OHC), Rs is the extraordinary or spontaneous Hall constant, B is the magnetic induction, Ms is the saturation magnetization, µ0 is the permeability of the free space, and a is a material dependent constant [8–10,27,28]. Here, the first term represents the ordinary Hall effect which results from the Lorentz force acting on the moving charge carriers under the influence of an external magnetic field while the second term represents the extraordinary or the anomalous Hall effect (AHE) that is known to originate from the spin-orbit interaction present in a ferromagnet. The AHE has three components: an intrinsic scattering-free part and two extrinsic scattering-dependent parts. The intrinsic AHE is not very common. In the intrinsic regime, the AHE can often be understood in terms of the geometric concept of Berry phase and Berry curvature in momentum space. Berry phase is very similar to Bohm-Aharonv phase in real space [29]. The Berry-phase concept has established a link between the AHE and the topological nature of the Hall currents. New experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors have established the dominance of an intrinsic Berry-phaserelated AHE mechanism in metallic ferromagnets with moderate conductivity. In 1959, Yakir Aharonov and David Bohm predicted that the phase of a charged quantum particle moving around a loop in a magnetic field would acquire an additional phase of 2π times the number of magnetic flux quanta passing through any surface bounded by the loop. The Aharonov– Bohm effect has been confirmed in many experiments. In 1984 Michael Berry discovered a more general form of the Aharonov–Bohm effect by working in a general “parameter space” rather than real space. Berry predicted that the wavefunction of a particle can acquire a geometric phase when a parameter, such as the potential energy, is slowly varied before eventually returning to its original value. The geometric phase acquired by the particle is equal to the flux of a new field called the Berry curvature through the surface defined by this loop. One such dynamic effect is the anomalous Hall effect. In a recent reviews of modern physics [29], three broad regimes have been identified while surveying a large body of experimental data for diverse materials. First, a high conductivity regime where ρxx ≤ 1 µΩ cm, skew scattering dominates and ρxy is proportional to ρxx. Second, an intrinsic or scattering-independent good metal regime in which ρxy is roughly independent of ρxx (≈(1 − 100) µΩ cm). This dependence comes from a semiclassical treatment by a generalized Boltzmann equation taking into account the Berry curvature and coherent inter-band mixing effects due to band structure and disorder. Third, a bad metal regime where ρxx > 100 µΩ cm. In this situation, ρxy is proportional to ρxx2 coming from the side-jump mechanism. The two scattering dependent extrinsic mechanisms responsible for Rs are: (a) Classical Smit asymmetric scattering and (b) Non-classical transport (side-jump) [4,7,12,30,31]. Smit proposed the “asymmetric scattering” of magnetized conduction electrons by impurities [8,31–33]. In the presence of spin-orbit interaction in a ferromagnet, there is left-right asymmetry in the differential scattering cross-section about the j-B (x-z) plane. As a result, electrons tend to pile up on one side of the sample producing a Hall field along the y-axis. Boltzmann equation is correct to the lowest order in ħ/τEF, where τ is the relaxation time and EF is the Fermi energy [8]. For pure metals and dilute alloys at low temperatures ħ/τEF < < 1. When ħ/τEF is not small which is realized in concentrated and disordered alloys and high temperatures, Boltzmann transport is no more valid. In that situation, KarplusLuttinger-Kohn (KLK) gave a quantum mechanical transport theory yielding ρH as expressed in Eq. (7). A simple intuitive theory was
Rs = aρ + bρ,2
(8)
where ρ is the bulk resistivity and a and b are constants which are characteristics of the materials. The linear term in ρ is attributed to Smit asymmetric scattering or skew scattering of the charged carriers, derivable from the classical Boltzmann equation while the quadratic term in ρ is attributed to the side jump mechanism proposed by Berger [34]. Hall resistivity (ρH) versus the applied field (µoH) was measured in both positive and negative fields at different temperatures. We have shown the ρH versus µoH plots only for positive fields in Fig. 7 (B = µoH in the Hall geometry). Each plot consists of essentially two straight lines. The two straight lines cut at a point (called the technical saturation as shown in the inset of Fig. 7), whose ρH value is equal to the µoR1Ms (where R1 is the slope of the first straight line) and the B value is µoMs [35]. As we increase B from the origin and move along the first straight line (whose slope is R1), µoM keeps on increasing. Since M cannot change above saturation induction B beyond its spontaneous value of Ms, we get the second straight line starting from the B value of
Fig. 7. Hall resistivity (ρH) is plotted against external magnetic field (µoH) at different temperatures, all showing technical saturation around 2 T. The inset shows the schematic behavior of the Hall resistivity ρH, as a function of the magnetic induction B. µ0Ms is the spontaneous magnetization. 4
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
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because of the correlation coefficient is 0.985. Finally, we conclude that the extrinsic quantum mechanical sidejump mechanism as well as the intrinsic mechanism due to the Berry phase curvatures are responsible for the EHE varying here as the square of the electrical resistivity. An experimental method has been suggested to separate them by varying the film thickness following a recent work of Tian, Ye, and Jin [37] where they used both ρ(T) and the residual resistivity ρ(0) in the scaling fit. Their samples are thin films of Fe of thickness 93, 6.5, 4, 3, 2.5 and 1.5 nm with resistivities of ~10, 18, 25, 35, 45, and 65 µΩ cm, respectively. They find that all the three contributions (two extrinsic and one intrinsic) are of the same order in magnitude and so of equal importance. Our FeTa film has thickness of ~400 A with a resistivity of 20 µΩ cm. Following the work of Tian, Ye, and Jin, we plan to carry out Hall measurements on samples with different thicknesses and apply similar scaling laws to isolate the three contributions. The amount of side jump for free electrons is calculated using the Eq. (10) [34],
µoMs with a slope of R0 and µ0RsMs. The Hall coefficient R0 and µ0RsMs were found as the slope and the intercept of the linear portion of the Hall curves above the technical saturation field of 2 T by fitting ρH versus the µoH data to Eq. (7). It is interesting to note here that the Hall measurements could be used to roughly estimate the spontaneous magnetization of a material, here 2 T [35]. It is also the field needed to saturate M as found in our M−H measurements in the out of-plane configuration (inset of Fig. 3b). This value of 2 T for Fe-Ta sample compares very well with the spontaneous magnetization of 2.2 T for pure Fe. We observe that the drop in spontaneous magnetization (10%) is in the same ratio of 10% doping of Fe by Ta. The above magnetization value of 2 T of Fe90Ta10 could quantitatively be found from the rigid-band model as given below. The localized-moment theory of ferromagnetism breaks down in two aspects. The magnetic moment on each atom or ion should be the same in both the ferromagnetic and paramagnetic phases and its value should correspond to an integral multiple of μB. None of the above are observed experimentally. Hence there is a need of a band theory or collectiveelectron theory. In Fe, Ni, and Co, the Fermi energy lies in a region of overlapping 3d and 4 s bands. The rigid-band model assumes that the structures of the 3d and 4 s bands do not change markedly across the 3d series and so any differences in electronic structure are caused entirely by changes in the Fermi energy (EF). This is supported by detailed band structure calculations. According to band-structure studies [36], both theoretical and experimental, the density of states at EF is higher in Fe for the majority band electrons than that of the minority band electrons. In the present case of FeTa alloy, the electronic configuration of Fe is [Ar] 3d64s2 and that of Ta is [Xe] 4f145d34s2. Thus, our alloy has three fewer d-electrons per replacement of one Fe atom by one Ta atom. When the electrons are removed as Fe is replaced by Ta, they are first removed from the majority band due to their higher density of states and hence the magnetization decreases. Thus, the moment of the alloy should decrease by 3 × 0.1 = 0.3 µB for 10% alloy, i.e., 2.2–0.3 = 1.9 instead of 2.0 µB. So, the rigid band model holds even for a large difference in d electrons (3). Here also, we have a good quantitative agreement with theory. In Fig. 7, both R0 and Rs are found to be positive. The positive R0 implies that the effective conductivity of holes is more than that of electrons as in pure Fe. In Eq. (8), the first term, due to asymmetric scattering is very unlikely to contribute in Fe-Ta film since it’s resistivity (2.12 × 10−7 Ωm) is 2000 times that of pure Fe (≈1 × 10−10 Ωm)[5], where the most dominant contribution to Rs comes from the asymmetric scattering. So, we have left the asymmetric scattering term in the Eq. (8) and instead we have fitted Rs(T) data to
Rs = a + bρ2
Δy =
1 k 0 λc2 ≈ 3.7 × 10−16m 6
where k 0 =
2 × me εf ħ2 ħ me c
(10)
≈ 1.7 × 1010m−1 is the wave vector at the Fermi
≈ 3.6 × 10−13 is the rationalized Compton wavelevel and λ c = length, me is the mass of electron and c is the speed of light. We used εf = 11.1 eV as the Fermi energy of iron. Considering the band effects, there is an enhancement of ≈104 in the value of Δy. Hence, Δy ≈ 3.7 × 10−2Å , which is almost 1% of lattice parameter of iron, a = 2.86Å . Table 2 shows the values for ρ, R0 and Rs as a function of temperature. The value of Rs at 10 K is 7.4 × 10−9 Ωm/T in Fe-Ta which is 74 times larger than that of Rs in Fe99Cr01 (0.1 × 10−9 Ωm/T). The Ohmic resistivity of Fe-Cr (2.7 × 10−8Ωm at 4 K) and Fe-Ta (2.1 × 10−7 at 5 K) is in the ratio of 8:1 which justifies Rs ≈ ρ2 almost quantitatively (82 being close to 74) [5]. 4. Conclusions In summary, the Fe90Ta10 thin film gown on silicon (1 0 0) substrates were found to be structurally amorphous. The films have shown the characteristics of soft ferromagnets. Excellent magnetization versus temperature data at several fields fitted very well to the Bloch’s spin wave theory even with the T5/2 term along with the T3/2 term. The technical saturation of 2 T found from the ρH versus µ0H plot matches well with the saturation magnetization obtained from the M versus µ0H plot. Our calculated value of the magnetic moment, using the rigidband model, is in very good agreement with the above measured value even with a large valence difference of ΔZ = 3 between Fe and Ta. The anomalous Hall effect results suggest that the quantum mechanical side jump scattering well as the intrinsic scattering-independent mechanism are the most dominant contributors to the AHE. More experiments and modified scaling laws will be used to separate the two contributions. Small coercivity at all temperatures makes Fe-Ta thin films good candidates for applications like magnetic sensors, spin logic devices,
(9)
The fitting result is shown in Fig. 8. The fit seems reasonably good
Table 2 ρ, R0 and Rs as a function of temperature.
Fig. 8. Plot of Rs vs. ρ fitted to a + bρ2. 5
Temperature (K)
ρ (10−7 Ωm)
R0 (10−15 Ωm/T or m3/ C)
Rs (10−9 Ωm/T or m3/C)
5 10 50 100 150 200 250 300
2.1 2.12 2.13 2.19 2.29 2.35 2.43 2.57
2.6 ± 0.1 2.7 ± 0.1 2.6 ± 0.1 2.9 ± 0.1 2.8 ± 0.1 3 ± 0.1 2.9 ± 0.09 3.8 ± 0.1
7.44 7.43 6.67 6.58 7.63 8.26 9.0 10.5
Journal of Magnetism and Magnetic Materials 489 (2019) 165446
S. Shaji, et al.
recording heads, etc. [16]
Acknowledgments
[17]
This work was supported by the National Science Foundation (NSF) through the Nebraska Materials Research Science and Engineering Center (MRSEC) (Grant No. DMR-1420645). We also like to thank NSFMRI (Grant No. CMMI-1040290) for Pulsed Laser Deposition facility at NCA&T State University.
[18] [19] [20]
Appendix A. Supplementary data [21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jmmm.2019.165446.
[22]
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