In-situ studies of magnetostriction in TbxHo1-xFe1.9Mn0.1 Laves compounds

Journal Pre-proofs In-situ studies of magnetostriction in TbxHo1-xFe1.9Mn0.1 Laves compounds M.K. Wang, J.J. Liu, Q.L. Ding, Y. Xiao, R.B. Jiao, Z.B. Pan, W.X. Xia, J.P. Liu PII: DOI: Reference:

S0304-8853(19)33669-8 https://doi.org/10.1016/j.jmmm.2020.166422 MAGMA 166422

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Journal of Magnetism and Magnetic Materials

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22 October 2019 12 December 2019 7 January 2020

Please cite this article as: M.K. Wang, J.J. Liu, Q.L. Ding, Y. Xiao, R.B. Jiao, Z.B. Pan, W.X. Xia, J.P. Liu, In-situ studies of magnetostriction in TbxHo1-xFe1.9Mn0.1 Laves compounds, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166422

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In-situ studies of magnetostriction in TbxHo1-xFe1.9Mn0.1 Laves compounds M. K. Wang1, 2, J. J. Liu1, *, Q. L. Ding1, Y. Xiao2, R. B. Jiao2, Z. B. Pan1, W. X. Xia2,*, J. P. Liu2,3 1

Faculty of Materials Science & Chemical Engineering, Ningbo University, Ningbo 315211, China 2

Ningbo Institute of Materials Technology & Engineering, Chinese Academy of Sciences, Ningbo 315201, China 3

Department of Physics, University of Texas at Arlington, Arlington, TX 76019, USA Abstract The

magnetic

domain

structure

and

magnetostrictive

properties

of

TbxHo1-xFe1.9Mn0.1compounds have been investigated by in-situ Lorentz transmission electron microscopy (LTEM). The magnetocrystalline anisotropy compensation has been realized to be around x = 0.12 based on the easy magnetization direction (EMD) and by evaluating magnetocrystalline anisotropy constant K1, magnetization and magnetostriction. The EMD at room temperature rotates from the <100> axis for x ≤ 0.10 to <111> axis for x ≥ 0.12, which is detected directly by electronic holography technique. The magnetic domain wall movements were observed by in-situ magnetic field LTEM, and the critical magnetic field Hcr decreases continuously from 100 Oe for the Tb-rich side of x = 0.16 to 60 Oe for the Tb-poor side of x = 0.12, owing to the decrease in magnetocrystalline anisotropy subjected by anisotropy compensation. A high low-field magnetostriction (a~200 ppm at 1 kOe) is achieved at the critical magnetocrystalline anisotropy compensation point of x = 0.12. This work helps to understand the correlation between magnetocrystalline anisotropy, magnetization process, magnetic domain wall motion and magnetostriction in the C15 Laves phase system.

*

Corresponding author.

E-mail address: [email protected] and [email protected] 1

Keywords: Cubic Laves phase, Easy magnetization direction, Magnetostriction, Magnetocrystalline anisotropy, Magnetic domains.

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1. Introduction The C15 Laves phase RFe2 (R = rare earth) compounds have drawn constant interest to develop high performance magnetostrictive materials due to the magnetomechanical effect converting electrical energy to mechanical one [1,2]. To date, TbFe2 possesses the largest linear anisotropy magnetostriction at room temperature (RT), where the large spontaneous magnetostriction coefficient λ111 (λ111>>λ100, λ111~2400 ppm) is caused by the structure distortion from cubic to rhombohedral one when cooling down to below its Curie temperature, simultaneously accompanied by the easy magnetization direction (EMD) lying along <111> axis [3-7]. However, TbFe2 also exhibits a large magnetocrystalline anisotropy, which leads to hard magnetic properties and appears as a hindrance for certain applications in acoustic transducers, sensors and actuators, etc. Thus, it is needed to minimize the anisotropy while still maintaining a large magnetostriction. The pseudobinary (Tb,R’)Fe2 compounds were designed by composition anisotropy compensation between Tb and R’ with different anisotropy sign and EMD, i.e., the sign is negative for TbFe2 while positive for DyFe2 (or HoFe2), as well as the EMD for TbFe2 and DyFe2 (or HoFe2) lies towards <111> and <100> axis, respectively [1]. Anisotropy can be adjusted in TbxDy1-xFe2 (or TbxHo1-xFe2) system by tailoring the composition ratio between Tb and Dy/Ho elements, subsequently the anisotropy compensation would be achieved in the morphotropic phase boundary (MPB), which separates a rhombohedral phase on the TbFe2 side with <111> EMD and a tetragonal phase on the DyFe2 (or HoFe2) side with <100> EMD. Consequently, Terfenol-D

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(Tb0.27Dy0.73Fe2) and Tb0.15Ho0.85Fe2 with the compositions near MPB region are developed as excellent magnetostrictive materials contributing large magnetostriction at low switching magnetic field [5,6]. Recently, the anisotropy compensation characteristic in Mn-doped TbxHo1-xFe2 system was evaluated by taking into account the EMD, Mössbauer spectra and magnetostriction, indicating that EMD transition is crucial for the realization of good magnetoelastic properties [7,8]. The EMD is detected by X-ray diffraction on magnetic-field aligned powders, that is, the strongest (222) peak, accompanied with the other <111>-type peaks with strengthened intensity, corresponds to <111> EMD, while the strongest (800) peak associates with <100> EMD [9-12]. However, if the magnetocrystalline anisotropy near MPB, in the case of <111>EMD, is so small that the curing field in sample preparation process is insufficient to provide the torque to rotate the crystallites to align their easy axis, which might be mistaken as the <311> EMD[13,14]. Another shortcoming of this XRD method performing on field-aligned powders was to consider all the powders as single domain particles, while the grain size about 100 μm cannot ensure the single crystal and the intensity of (311) peak in polycrystalline (multidomain) state is strongest. These indicated that the proof for anisotropy compensation based on EMD is not very sufficient. In this work, the EMD of TbxHo1-xFe1.9Mn0.1 compounds was straightforwardly determined by electron holography (EH) technique, offering the more conclusive evidence on EMD compared to previous research. As a Joule-type magnetostriction, the linear anisotropic magnetostriction in RFe2

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system is the result of magnetic domain wall movement and domain rotation with the action of external magnetic field [15,16]. In this work, the dynamic magnetic domain structure was observed with in-situ magnetic field Lorentz transmission electron microscopy (LTEM), in order to elucidate the effect of magnetization process on magnetostriction. The findings in this work help to understand the correlation between magnetostriction, magnetocrystalline anisotropy, EMD, magnetization process for RFe2 Laves phase system. 2. Experimental Polycrystalline samples of TbxHo1-xFe1.9Mn0.1 (0.08 ≤ x ≤ 0.16) were prepared by arc-melting the constituent metals in a magneto-controlled arc furnace under an argon atmosphere [8]. The homogenized process was performed in tube furnace filled with high-purity argon for 7 days with the annealing temperature of 900 oC [8,17]. X-ray diffraction (XRD) was performed at room temperature (RT) with Cu-Kα radiation, which shows that all prepared samples crystallize in a single C15-type cubic Laves phase. The magnetization at RT was measured by a superconducting quantum interference devices (SQUID) magnetometer at fields up to 50 kOe. The magnetostrictive properties, the two magnetostriction  and  either parallel or perpendicular to the applied field up to 13 kOe, were measured with zero applied pre-stress at RT by using a standard strain-gauge technique. Magnetic domain walls were studied by LTEM (with a JEOL TEM JEM-2100F). This TEM has a special objective lens that reduces the magnetic field at the sample position by less than 5 Oe, and the microscope is mounted with a JEOL platinum wire biprism. It also has a

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special sample holder, setting a small electromagnet at the clamped sample that can provide a horizontal magnetic field of 0 to 500 Oe [18,19]. 3. Results and discussion The magnetic-field dependence of the initial magnetization at RT for the TbxHo1-xFe1.9Mn0.1 compounds is shown in Fig.1(a). It is obvious that all the magnetization is close to saturation when the applied field increases above 20 kOe, while the tendency of saturation varies slightly with composition x due to the difference in magnetic anisotropy. One can see that the sample around x = 0.12 tends to saturate faster than the others, inferring its relatively low anisotropy resulted from the compensation in anisotropy between Tb3+ and Ho3+ ions, which is similar to the magnetization curves measured by the vibrating sample magnetometer (VSM) [8]. To quantitatively

characterize

the

variation

of

anisotropy,

the

first-order

magnetocrystalline anisotropy constant K1 was estimated by simulating the M–H curves using the law of approach to saturation [15] M  M S (1 

a b  2 ) p H H H

(1)

and the relation

b

8 K12 1050 2 M s 2

(2)

where MS is saturation magnetization, a and b are constants, χp is the susceptibility of the paramagnetic (parallel) magnetization process, μ0 is the permeability of free space. The composition dependence of K1, obtained by fitting the data at the magnetic fields in the range of 30-60 kOe, is shown in Fig.1 (b). As expected, K1 increases with increasing Tb content with x > 0.12, while K1 increases with increasing Ho content 6

with x < 0.12, appearing a minimum value at x = 0.12. This result infers that Tb contributes an opposite role in magnetocrystalline anisotropy as compared with Ho, and the magnetocrystalline anisotropy compensation can be achieved around x = 0.12. Taking account of the K1 sign negative for TbFe2, proposed by Clark [1], the K1 sign for HoFe2 should be positive. Thus, the curve K1-x is modified and shown in Fig.1(c). It is evident that K1 appears zero around the composition of x = 0.12. Since the positive sign of K1 corresponds to EMD<100> axis, while the negative sign of K1 with EMD<111> axis [1], it is reasonable that K1 for TbxHo1-xFe1.9Mn0.1 compounds should change its sign across the anisotropy compensation point, accompanied by the EMD changing from <100> to <111> axis with increasing Tb contents. One can speculate that the good magnetostrictive properties can be achieved around x = 0.12, especially for the TbFe2 side with <111> EMD, which possesses low anisotropy and a large spontaneous magnetostriction λ111 originating from the distortion of cubic to rhombohedral symmetry. The magnetostriction measurements of the TbxHo1-xFe1.9Mn0.1 alloys were performed in a static state. Fig. 2(a) represents the magnetic field dependence of the linear anisotropic magnetostriction a (= –) at RT and its low-field curves in the scale of 1.5 kOe are shown in Fig. 2(c) for clarity. It is evident that a for x = 0.12 presents the larger value at the relatively low fields less than 1 kOe, even though its saturation magnetostriction S is less than those of Tb-rich sides of x > 0.12 [8]. Simultaneously, the tendency to saturation is much easier than the others, indicating the lowest anisotropy, which is in consistence with the previous reports on

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the anisotropy compensation between Tb3+ and Ho3+ ions for the pseudobinary (Tb,Ho,R)(Fe,M) 2 Laves alloy systems [20-22]. This result is further proved by the composition dependence of the ratio a/K1, plotted in Fig. 2(b), which exhibits a peak around x = 0.12 at different fields from 0.5 to 13 kOe. To quantitatively characterize the rate of approach to saturation, the magnetostriction parameter a0 as a function of composition x is shown in Fig. 2(d), which was estimated from an approximate approach for the saturation relation as [20]

a ( H )  0 s (1 

a0 ) H

(3)

where 0S is the saturation value for a, the magnetic field H is applied at the range of 6 to 13 kOe. Obviously, the a0-X curve shows a pronounced minimum near x = 0.12 around which the anisotropy is compensated. This critical compensation point is shifted to Tb-poor side compared to Mn-free (Tb,Ho)Fe2 counterparts, showing a higher performance [22,23]. It is noted that a high low-field magnetostriction (a~200 ppm at 1 kOe) is achieved at the critical point of x = 0.12. It is well established that the spontaneous magnetization direction of magnetic domain in ferromagnet should be along the EMD due to the lowest magnetocrystalline anisotropy energy [24]. Besides, the evolution of domain structure under external field is strongly related to the magnetostriction. Consequently, the characterization of domain structure by LTEM is indispensable to understand the mechanism of magnetostriction. As examples of three samples, x = 0.12 with lowest anisotropy, x = 0.16 with negative K1 and x = 0.1 with positive K1 were selected for Lorentz TEM observation. Fig. 3(b) is the bright field image of x = 0.12 with selected area electron

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diffraction pattern (SAED) in the inset showing the TEM specimen plane is (110). Fig. 3(a) is the under-focused Fresnel Lorentz image where dark and bright domain walls are indicated by the blue arrows, corresponding to the magnetic domain walls due to the reflection of election beams subjected to the Lorentz forces of adjacent magnetic domains on both sides of the wall [25]. In the over-focused image with Fig.3(c) the “bright” wall becomes “dark” and vice versa. To detect the magnetization direction in situ, the domain structure was further characterized by EH experiment, and the reconstructed phase image in red dotted box in Fig. 3(c) is shown in Fig. 3(d) [26]. The tangential direction and density of the lines (Fig. 3(d)) represent the direction and strength of the magnetic flux density, respectively [27]. The domain wall position was marked by white dashed line and the directions of magnetization in the domains are indicated by red arrows [28]. It is clearly exhibited that the angle between two magnetization directions is about 71°. Fig. 3(j) illustrates the crystal structure (Fd3m), where the white and red lines are [111] and [100] directions, respectively [28,29]. If the crystalline is observed along the <110> direction as shown in Fig. 3(e), the <111> and <111> directions form an angle of 71°[30], which is in good agreement with the experimental results (Fig. 3(d)) because of the identical crystalline orientation. The magnetization directions (red arrows in Fig. 3(d)) are exactly along <111> and <111> directions. The similar experiment was carried out for x = 0.16 and, as shown in Fig. 3(f)-(i) (In order to increase the legibility, the domain wall position is enhanced by dotted lines, more detailed in Fig. S1), the EMD is confirmed to be along [111] directions. Therefore, one can know that though the

9

anisotropy compensation point is around x = 0.12, the EMDs are along [111] directions for x ≥ 0.12. For comparison, the results of sample x = 0.10 are shown in Fig. 3(k)-(n). The TEM specimen was prepared to make the specimen plane in (100) as exhibited by the SAED in inset of Fig. 3(l), the magnetization directions in domains point <400> and <004> directions and form 90° domain wall (Fig. 3(n)), which well coincides with the projection model (Fig. 3(o)). It is clear that for x = 0.10 sample with positive K1 the EMD are along <100> directions and 90° domain walls are formed [31]. It can be seen from above, the EMD at RT is observed to be <100> axis for x  0.10 and <111> axis for x ≥ 0.12. Considering the facts that both EMD and K1 sign are different for the two sides of composition compensation point, as an example, we perform two samples of x = 0.12 and 0.16 here, of which the K1 signs and the EMDs are unified. To compare the influence of K1 on the evolution of domains, in-situ observation was performed under low magnetic fields by LTEM [32,33]. Fig. 4 shows the results of x = 0.12 sample where the magnetization directions are indicated by red arrows according to the EH analysis. The magnetic field is applied along <111> direction as indicated by yellow arrow in Fig. 4(a) (the same image as Fig. 3(a)). When the field increases from 0 to 50 Oe, no movement of domain walls are observed. The domain walls A1 and A2 begin to move with the field increasing to be 60 Oe, as shown in Fig. 4(b), where A1 and A2 move to the bottom right. When the field further increases to be 200 Oe and 500 Oe, A1 and A2 gradually move to the lower right side (Fig. 4(c), (d)). As a result, the domain area with the

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magnetization direction same to the magnetic field increases. In-situ observation for x = 0.16 was carried out and the results are shown in Fig. 5. The domain wall B1 and B2 remain unchanged until the magnetic field increases to be 100 Oe (Fig. 5(b)) and, when the field increases to be 500 Oe (Fig. 5(d)), the two domain walls become closer to make the domain with the same direction as the field increases. Thus, two points can be drawn, one is that the magnetization process is mainly determined by the domain wall displacement in low field; another is that the fields required to move the domain wall are different, i.e., the critical magnetic field Hcr increases continuously from 60 Oe for x = 0.12 to 100 Oe for x = 0.16, which is consistent with the strength variation of anisotropic constant K1. In thermal demagnetization, domains and domain walls are generated to minimize the energy of the system. When an external magnetic field is applied, magnetization will overcome its anisotropic energy barrier to turn towards the field direction[34]. Therefore, a lower anisotropy sample needs a smaller field to rotate its magnetization, that is why in current TbxHo1-x1Fe1.9Mn0.1 sample of x = 0.12 with the anisotropy compensation, shows the best low-field magnetostriction characteristics. 4. Conclusion In summary, the domain wall structure, EMD and magnetostriction of the pseudobinary TbxHo1-xFe1.9Mn0.1 alloys have been investigated. The EMD at RT is observed to be <100> axis for x ≤ 0.10 and <111> axis for x ≥ 0.12 by means of EH technique. The in-situ study of the magnetic domain structure more intuitively observes the difference in the driving field of the magnetic domain wall motion due to

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the difference in anisotropy caused by the composition compensation. The magnetic domain walls movement were observed by in-situ magnetic field LTEM, and the critical magnetic field Hcr decreases continuously from 100 Oe for the Tb-rich side of x = 0.16 to 60 Oe for the Tb-poor side of x = 0.12, owing to the decrease in magnetocrystalline

anisotropy

subjected

by

anisotropy

compensation.

Magnetocrystalline anisotropy compensation can be achieved in the pseudobinary TbxHo1-xFe1.9Mn0.1 alloy system around the critical composition point of x = 0.12. The Tb0.12Ho0.88Fe1.9Mn0.1 compound has good magnetoelastic properties (e.g., low magnetic anisotropy, high low-field magnetostriction a~200 ppm at 1 kOe). These results directly prove that the reduction of the magnetocrystalline anisotropy caused by the composition compensation between rare earths in Laves phase system, subsequently reduce the critical driving-field. These results further understand the correlation between magnetocrystalline anisotropy, magnetization process, magnetic domain wall motion and magnetostriction in rare-earth giant magnetostrictive materials. Supplementary material See supplementary material for the unprocessed image taken directly from the LTEM, showing typical Fresnel images for TbxHo1-xFe1.9Mn0.1 alloys. Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 50801039), Zhejiang Province (Y18E010005), Ningbo City (2019A610167), K.C. Wong Magna Fund in Ningbo University, and K. C. Wong Education

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Foundation (No. rczx0800).

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Figure Captions Fig.1. (a) Magnetic field dependence of magnetization, (b) composition dependence of

the

first-order

magnetocrystalline

anisotropy

constant

K1

for

the

TbxHo1-xFe1.9Mn0.1 alloys indicated in absolute value and (c) is the actual value. Fig.2. (a) Magnetic field dependence of magnetostriction a (=–), (b) Composition dependence of the ratio λa/Kl at variant magnetic fields, (c) Low-field region for magnetostriction in (a), and (d) the parameter a0 for the TbxHo0.9-xFe1.9Mn0.1 alloys. Fig.3. (a)-(c) are Lorentz Fresnel images for x = 0.12 sample at under-, just- and over-focus states, respectively. (d) is the reconstructed phase image in red dotted box in (c). (f)-(i) and (k)-(n) are the corresponding images for x = 0.16 and x = 0.10 samples, respectively. (j) illustrates the crystal pseudocubic structure, and (e) and (o) are the projected planes along <110> and <100> directions, respectively. Fig. 4. In-situ domain observation under magnetic field of x = 0.12 sample (red and yellow arrows indicate the directions of magnetization and field, respectively). Fig. 5. In-situ domain observation under magnetic field of x = 0.16 sample (red and yellow arrows indicate the directions of magnetization and field, respectively).

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Author Statement The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The manuscript has not been published elsewhere and no conflict of interest exits. All authors have read and approved this version of the article, and due care has been taken to ensure the integrity of the work.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Highlights Title: In-situ studies of magnetostriction in TbxHo1-xFe1.9Mn0.1 Laves compounds

> Direct experimental evidence for EMD is obtained by electron holography technique. > In-situ studies of magnetic domain and magnetostriction by magnetic field-LTEM. > Anisotropy compensation and a high low-field magnetostriction are obtained. >

Correlation

between

magnetic

anisotropy,

magnetostriction.

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domain

wall

motion

and