Inverted Hysteresis Loops in the Fe73.5Cu1Nb3Si13.5B9 Alloy With Small Coercivity

The phenomenon of inverted hysteresis loop has been observed in many materials for the past decades. However, the physical origin of the inverted hysteresis loop has long been debated. Here, we report the completely inverted hysteresis loop with a clockwise cycle in the soft-magnetic nanocrystalline Fe73.5Cu1Nb3Si13.5B9 alloy and amorphous Fe73.5Cu1Nb3Si13.5B9 alloy at room temperature. The negative remanence and positive coercivity were observed in the descending branch of magnetization curve when the scan field range was above 1 KOe. By comparing the results with that of the standard Pd sample, we found that the net coercivities of the nanocrystalline Fe73.5Cu1Nb3Si13.5B9 alloy and standard Pd sample are almost equal for the different scanning field ranges. Therefore, it is confirmed that the phenomenon of completely inverted hysteresis loop is caused by the remanence of superconducting magnet rather than the structural inhomogeneity effects. Our results suggest that special care should be taken during the measurement of hysteresis loops using MPMS 3, especially for the materials with small coercivity.


INTRODUCTION
Hysteresis loops are important for studying the properties of magnetic materials and often take a variety of different forms, which strongly depend on the chemical composition, the size of the magnetic materials, temperature, etc. Two important parameters to characterize the hysteresis loop are the remanence M r and the coercive field H c , respectively. Normally, the remanence and coercive field retain positive and negative values for the descending branch of the hysteresis loop. The positive remanence refers to the magnetization of the sample after a large magnetic field is applied. The coercivity is the reverse magnetic field to make the remanence value zero. Unlike common hysteresis loop with a counter clockwise cycle, the inverted hysteresis loop with negative remanence has a clockwise cycle and has been observed in many magnetic systems (Takanashi et al., 1993;Aharoni, 1994;Oshea and Alsharif, 1994;Ohkoshi et al., 2001;Wu et al., 2001;Kim et al., 2006;Demirtas et al., 2007;Van Tho et al., 2008;Ziese et al., 2010;Demirci et al., 2020;Ghising et al., 2020;Soldatov et al., 2020;Kumar et al., 2021) over the past decades.
In a multilayer films material, the inverted hysteresis loops were observed in Co/Pt/Gd/Pt multilayers by Takanashi et al., 1993, who considered that the origin of the inverted hysteresis loop is the interfacial exchange coupling. The phenomenon was also observed in Co/Mn/Co multilayers (Wu et al., 2001) and La 0.7 Sr 0.3 MnO 3 /SrRuO 3 superlattices with ultrathin individual layers (Ziese et al., 2010;Song et al., 2013). In addition, Esho reported the inverted hysteresis loops with negative remanence in a sputtered Gd-Co alloy (Esho, 1976), and several models that are based on structural inhomogeneity effects have been proposed (Lutes et al., 1977;Togami, 1978). However, the anomalous hysteresis loop has also been reported on simple homogeneous systems, like pyrochlore compound Nd 2 Hf 2 O 7 and nanoparticles EuS NPs (Gu et al., 2014;Opherden et al., 2018), and it has been attributed to the competition of two anisotropies (Takanashi et al., 1993;Geshev et al., 1998;Valvidares et al., 2002;Yoon Jae and Lim, 2011). Despite the number of previous studies, the physical origin of the inverted hysteresis loop remains controversial.
Iron-based amorphous/nanocrystalline alloys have attracted considerable interests for many years since they exhibit superior magnetic softness (Fish, 1990). Among them, the nanocrystalline Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy with a inhomogeneous structure, known as Finemet, is a frequently studied alloy owing to its high saturation magnetization M s and low coercivity H c (Hofmann et al., 1992;Polak et al., 1994;Gorria et al., 1996;Hofmann and Kronmüller, 1996;Barquín et al., 1998). The magnetic softness of the nanocrystalline Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy mainly arises from the dispersion of ultrafine α-Fe(Si) grains in an amorphous matrix which reduces the effective magnetic anisotropy (Alleg et al., 2013).
In this study, we present the observation of completely inverted hysteresis loop with negative remanence in amorphous and nanocrystalline Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloys at room temperature. By comparing with the results of magnetization curve of standard Pd sample under the same conditions, we find that the net coercivities of the nanocrystalline Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy and standard Pd sample are almost equal for the different scanning field ranges. In contrast to previous studies, we confirm the presence of the inverse hysteresis loops in Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloys is due to the remanence of superconducting magnet rather than the structural inhomogeneity effects. This may clarify the controversy about the physical origin of the inverse hysteresis loops observed in magnetic materials with small coercivity.

EXPERIMENTAL METHODS
Amorphous ribbons of the Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy were prepared by the spinning wheel technique on a single copper roller. Nanocrystalline alloys were obtained by means of thermal treatments of amorphous compounds of Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 at 813 K for 30 min in vacuum (Fujii et al., 2008), which is higher than crystallization temperature. The details were reported elsewhere (Ayers et al., 1998). The identification of amorphous and crystalline phases was measured by an X-ray (Cu Kα) diffraction technique at room temperature. The microstructure observation and selected area electron diffraction (ED) of the as-quenched and annealed alloys were studied using the FEI Talos F200X transmission electron microscope (TEM). A vibrating sample magnetometer (VSM) with Magnetic Property Measurement System 3 (MPMS 3 Quantum Design) was employed to measure magnetization (M) versus applied magnetic field (H) using the conventional sequence for different scan field ranges from ± 0.1 to ± 70 KOe. All measurements were carried out at 300 K, and the applied H was in the plane of the ribbons. The specimen and magnet were demagnetized in an oscillation mode at 350 K before each measurement.

RESULTS AND DISCUSSIONS
The phase of Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 ribbons was identified by X-ray diffraction using a diffractometer with Cu-Kα radiation in the 2θ angular range of 25-80°at a scanning rate of 0.2°/s, as shown in Figure 1A. The diffractogram of the as-quenched sample shows a halo pattern typical for amorphous alloys. As a comparison, the X-ray diffraction pattern of the annealed sample shows the presence of a crystalline α-Fe solid-solution phase and an amorphous rest phase, and no other phases, except α-Fe(Si), were recognized from the XRD profiles, which is consistent with previous related reports (Zhang et al., 1998;Gorria et al., 2001;Majumdar and Akhtar, 2005). In order to further characterize the morphology and microstructure of the two ribbons, transmission electron microscope tests were carried out, and the results are shown in Figure 1B,D. transmission electron microscope observation of the as-quenched Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 ribbon confirmed that the microstructure of the sample is very uniform. The high-resolution TEM (HRTEM) image ( Figure 1B) shows a homogeneous material with no crystal lattice. Also, there is no trace of crystalline reflections in the associated fast Fourier transform (FFT) pattern. These factors indicated that the as-quenched ribbon is fully amorphous. Figures 1C,D show the TEM microstructure images of the annealed Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 sample at different magnifications. The dark field image ( Figure 1C) demonstrates that there are a lot of nanoparticles with a size around 20 nm in the annealed samples. The selected electron diffraction pattern exhibited diffraction rings for the (1 1 0) and (2 0 0) of α-Fe phase, as proved in the inset of Figure 1C. The HRTEM image of annealed ribbons demonstrated nanoparticles with a size around 20 nm embedded in an amorphous matrix, as shown in Figure 1D. The FFT pattern associated with Figure 1D reveals polycrystalline diffraction ring and a diffuse amorphous ring. The microstructures identified by TEM were a good agreement with XRD analysis results.
Magnetic hysteresis measurements using the following procedure for different scan field ranges H FR from ± 0.1 to ± 70 KOe were carried out at 300 K. For each H FR , the data were obtained in the conventional sequence: 0 →+ H FR →− H FR (descending branch) →+ H FR (ascending branch). In addition, the magnet was demagnetized in oscillation mode from 7 T at 350 K to eliminate remanence in the sample and magnet before each measurement. Figure 2 shows a series of normalized magnetization loops of the annealed Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 sample, which are enlarged near the central portion for a clearer understanding. The full loop measured in corresponding field ranges is shown in Supplementary Figure S1.
In Figure 2A, we observed clearly the phenomenon of inverted hysteresis loop with obvious negative remanence for H FR 3000 Oe. The arrows stuck to the curve indicate the switching direction of the magnetic field. The inverted hysteresis loop with negative remanence presents a clockwise loop, which is an obvious contrast to the normal hysteresis loop with positive remanence and anticlockwise cycle. The coercivities are 12.86 Oe and −9.67 Oe for descending (H des C ) and ascending (H asc C ) branches, respectively. The net coercivity, defined as H c H asc C −H des C , is −22.53 Oe. However, the magnetization curve has no hysteresis behavior and almost overlaps for different H FR at low scan fields ( ≤ 500 Oe). Meanwhile, the inversion phenomenon of hysteresis loop was absent, as can be seen from Figure 2B. Furthermore, the magnetization curves at other higher scan field ranges ( ≥ 1,000 Oe) are displayed in Figure 2C,E. The behavior of inverted hysteresis loop begins to be observed and the corresponding coercivity values, including H des C and H asc C , are very small when the scan field range is 1,000 Oe, as shown in Figure 2C. With the increase of the scan field range, the phenomenon of inverted hysteresis loop becomes clearer and the coercivity increases gradually. When the scan field is above 50 KOe, the magnetization curves almost overlap and the coercivity is nearly constant ( ≈ 72 Oe). The results of hysteresis loops for the Fe-based amorphous samples also showed similar results with that of the nanocrystalline samples (see Supplementary Figure S2). This indicated that the origin of the inverted hysteresis loop may not arise from the structural inhomogeneities in amorphous alloys, as proposed in previous reports (Esho, 1976;Tsujimoto and Sakurai, 1983;Oshea and Alsharif, 1994;Yan and Xu, 1996;Gu et al., 2014).
Since standard Pd sample is a paramagnetic material, the magnetization curve should be a straight line that passes through the origin and has no hysteresis. In order to further investigate the underlying origin for the inverted hysteresis loop in our specimens, the hysteresis loops of standard Pd sample were also measured following the same procedure as that of Finemet alloys at 300 K. Figure 3 shows the M(H) loops enlarged near the origin for different scanning field ranges of standard Pd sample, and the full loops measured in corresponding field ranges is in the inset. We can see clearly that the inverted hysteresis loop is absent at low scan fields ( ≤ 500 Oe), as  shown in Figure 3A. While for higher scan field ranges ( ≥ 1,000 Oe), the loops are inverted (see Figures 3B,C). When the H FR 3000 Oe, the coercivities are 11 Oe and −11.3 Oe for descending (H des C ) and ascending (H asc C ) branches, respectively. The net coercivity H c is −22.3 Oe, which is very close to the results of our alloy sample.
For comparison, the net coercivity H c of annealed sample and standard Pd sample is plotted as a function of scan field ranges H FR in Figure 4. The net coercivity is almost zero when the applied magnetic field range is less than 1,000 Oe. However, the net coercivity increases rapidly when the magnetic field range is higher than 1,000 Oe, and it almost saturates with maximum field of 50 KOe. The H c1 , defined as the net coercivity difference between the annealed sample and Pd sample, is only several Oe.
Because standard Pd sample is a paramagnetic material, the deviation between the magnetization curve and the origin can reflect the remanence of the superconducting magnet, which is caused by the vortex pinning. It can be seen from Figure 3 that when the applied magnetic field is greater than 1 KOe and then the magnetic field is removed, the superconducting magnet will have a negative remanence, and this negative remanence will increase with the increase of the applied magnetic field, even if the vibration degaussing treatment is carried out in an oscillation mode from 7T before each measurement. It indicates that the measurement results of the magnetization curve may have errors for the samples with net coercivity less than tens of Oe, which should not be ignored, when the applied magnetic field is more than 1,000 Oe. To further verify our inference, we also performed the magnetic measurement on the AlNiCo alloy with a large coercivity ∼1,300 Oe using the same sequence, which is much larger than the remanence of superconducting magnet after applying a large magnetic field and then removing it. The magnetization curve of the AlNiCo alloy at 300 K represents the normal hysteresis loop with coercivity of 1,333 Oe for the H FR 7 T (see Supplementary Figure S3 for more details). Additionally, we noted that the exchange bias |H EB | is almost equal to the coercivity |H des C | or |H asc C | for the inverted hysteresis loop at the same temperature. Therefore, the previously reported exchange bias (Maity et al., 2017;Ghising et al., 2020)) may also be caused by the remanence of superconducting magnet.

CONCLUSIONS
In conclusion, the hysteresis loop inversion was observed in the nanocrystalline Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy ribbons and amorphous Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy ribbons at room temperature. We prove that the phenomenon of completely inverted hysteresis loop is caused by the remanence of superconducting magnet rather than the inhomogeneity effects. We emphasize that there are slight differences in remanence for different MPMS 3 devices. Our results indicate that the results of the magnetization curve may have errors for the samples with net coercivity less than tens of Oe, which should not be ignored, when the applied magnetic field is more than 1,000 Oe using MPMS 3.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.

AUTHOR CONTRIBUTIONS
PPS performed experiments and wrote the manuscript; YTW performed the data analysis; BAS conceived the data and wrote the manuscript.