The Inverted Hysteresis Loops and Exchange Bias Effects in Amorphous/Nanocrystalline Fe 72 Cu 1 V 4 Si 15 B 8 Ribbons at Room Temperature

: Тhe influence of thermally induced microstructural transformations on magnetic properties of Fe 72 Cu 1 V4Si 15 B 8 ribbon with combined amorphous/nanocrystalline structure is presented. The experiments showed that thermally induced structural changes are in correlation with the appearance of magnetic hysteresis, i.e. with inverted hysteresis loops (IHL) and exchange bias (EB) effects. It was found that the ratio of surface to volume of a ribbon sample have an influence on hysteresis loop appearance. The inverted hysteresis loops were observed for the 1.5 mm wide and 55 μm thick alloy samples shorter than 10 mm, but for the samples longer than 10 mm hysteresis loops were normal. With an increase of annealing temperature, a shift of the hysteresis loops measured at room temperature was noticed. The highest positive exchange bias field Heb was observed for the sample annealed at 723 K, together with the lowest magnetic field at which the changes from inverted to normal hysteresis loop occurred. Annealing at the temperature of 823 K resulted in negative Heb.


Introduction
The nanocrystalline iron based alloys obtained from the starting amorphous precursors prepared by rapidly quenching technology are interesting topics in the field of the alloy research since they have excellent soft magnetic properties [1][2][3][4]. Moreover, in comparison with other iron based systems prepared by sintering technology [5][6][7][8], amorphous Fe-based ribbons have competitive functional properties. The Fe-Cu-M-Si-B (M = Cr, V, Mo, Nb, Ta, W) "FINEMET" type аlloys with amorphous/nanocrystalline structure have been the subject of numerous scientific studies [9][10][11][12][13]. By selecting M-element different nanostructures were obtained. The experiments indicate that the best soft magnetic properties were attained in the alloys with the optimum α-Fe (Si) nanocrystalline grain size, which can be evolved by controlled annealing of the starting amorphous structure.
A recent investigation of thermally induced structural transformations of Fe 72 Cu 1 V 4 Si 15 B 8 alloy with combined amorphous/nanocrystalline structure showed that

Inverted hysteresis loops effect
The study of magnetic hysteresis loops in ferromagnetic thin films where IHL was observed [15][16][17], is based on the assumption that there is a uniaxial anisotropy in the longitudinal direction which is mostly explained by the Stoner-Wohlfarth model [18]. An extended explanation was given by Arrot who studied ultra-thin magnetic films and found certain similarities in the magnetic properties of thin films with the nanoparticle systems [19,20]. According to Arrot [20], thin film is like a single domain particle in the direction normal to the plane of the film.
Examining the METGLAS 2605SC alloy in the form of a plate, Tejedor et al. discovered different magnetization processes on the surface relative to the bulk of a material [21]. The origin of this behavior reflects different influences of demagnetization field on the surface and bulk of the ribbon. In some stages of the magnetizing process, vectors of the magnetization in surface M SF and in bulk M BL are oriented in opposite directions that can be followed by the appearance of IHL.
Shalyguina et al. found different magnetic properties on the surface and in the volume of heterogeneous (nanocrystalline/amorphous) Fe 81 Nb 7 B 12 ribbons prepared by a melt spinning method [22]. Changes of the magnetic properties induced by annealing are more pronounced in the vicinity of the surface than in the bulk of the alloy. Also, it was found that there different magnetic properties were indicated on the two sides of the ribbon due to the differences in residual stresses on the wheel side and the free side of the ribbon during production, as well as due to the differences in a surface morphology of these two sides. The IHL in the near-surface layers of this Fe 81 Nb 7 B 12 heterogeneous system is explained by a twophase model, according to which two dissimilar phases (magnetically hard at the surface and magnetically soft in the volume) with uniaxial magnetic anisotropy exhibit antiferromagnetic exchange interaction.
Furthermore, IHL was found in the homogeneous EuS NP nanoparticle system. This is explained by the presence of a magnetically hard component formed by surface atoms and magnetic soft component which was created by atoms in the core of the nanoparticle system [23]. IHL was also observed in other magnetically non-homogeneous structures, where this phenomenon has been explained by the coexistence of a magnetically soft and magnetically hard component [24][25][26][27][28].
The total magnetic energy (per unit volume) of the two-phase model, according to the Stoner-Wohlfarth model, in the systems where IHL effect was observed, can be described by equation [23]: Е = K h ·sin 2 β h + K s · sin 2 β so -М h · H·cos(β hθ) -М s · H· cos(β sθ) -Ј·М h · М s · cos(β hβ s ) (1) where: K h -the anisotropy constant of the hard component (that can be obtained from 2·K h /M = H c ) ; K s -the anisotropy constant of the soft component; М h -magnetization of the hard component; М s -magnetization of the soft component; H-magnetic field; β h -the angle between М h and the easy axis of the hard component; β s -the angle between М s and the easy axis of the hard component; βs 0 -the angle between М s and the easy axis of the soft component; θ-the angle between the applied field and the easy axis of the hard component and J -antiferromagnetic exchange coupling constant. The first two terms which present the uniaxial magnetic anisotropy energy are followed by two terms that present an expression for energy achieved by applying the external magnetic field (Zeeman energy). The last term presents the exchange interaction between the magnetically soft and hard components.
The total magnetization of the system can be given by [22]: Fig. 1 shows a model of the inverted hysteresis loop of the ribbon, which consists of two components (magnetically softer in the bulk and magnetically harder on the surface). Ascending and descending branches of the major hysteresis loop are obtained by the sum of magnetization of components according to equation (2). The saturation magnetization is significantly higher for the magnetically softer component, and therefore, exchange-coupled soft-hard biphasic system exhibit IHL effect.

Exchange bias effect
Meiklejohn and Bean discovered the Exchange bias effect in 1956 [29] and named it with the new type of magnetic anisotropy (hysteresis loop shifts away from the H = 0). The effect was found on fine particles of cobalt which were made by electrodeposition of cobalt into mercury. The electrodeposition of cobalt was followed by oxidization in order to produce cobaltous oxide shell. During cooling, CoO at the Neel temperature (293 K) has transition from the paramagnetic to the antiferromagnetic state and the system is characterized by the interaction of ferromagnetic Co and antiferromagnetic CoO. If saturating magnetic field is applied during cooling to 77 K, hysteresis loop shifts to the left, i.e. a negative EB effect (NEB) occurs. A positive EB (PEB) was found in the FeF 2 -Fe bilayer system [30], which was obtained by applying a large magnetic field during cooling through the Neel temperature. Therefore, the EB effect is explained by the existence of an antiferromagnetic exchange between the various magnetic components resulting in a shift of the hysteresis loop. The effect was first found in a combination of ferromagnetic/antiferromagnetic (FM/AFM) system [29]. However, the combinations of antiferromagnetic/ferrimagnetic (AFM/ferri), and ferromagnetic/ferrimagnetic (FM/ferri) components were later examined [31]. In the combination of a soft/hard Fe/Co spring magnet system prepared by pinning magnetic field influence, PEB is observed even at the room temperature [32]. Extensive theoretical background supported by experimental results on exchange bias/exchange anisotropy was published [33][34][35][36].
The magnetic energy (per unit area) of two-phase model regarding the real Meiklejohn and Bean model where EB was observed can be described by equation [37]: where М F -saturation magnetization of the ferromagnetic component, Hmagnetic field, αthe angle between the magnetic moment of the antiferromagnetic component М AF and easy axis, β -the angle between the magnetic moment of the ferromagnetic component М F and easy axis, θ*-the angle between the magnetic field H and easy axis, K AF and K F are magnetic anisotropy coefficient of the antiferromagnetic and ferromagnetic components respectively, t F and t AF are thicknesses of the ferromagnetic and antiferromagnetic components respectively, and Ј eb -exchange energy between ferromagnetic and antiferromagnetic components. The first two terms represent uniaxial magnetic anisotropy energy; the next term is an expression for Zeeman energy, while the last term represents an expression for the antiferromagnetic exchange. For an ideal model (α = 0) the antiferromagnetic anisotropy energy disappears and energy is expressed by the next equation: The coercive field is calculated from the intersection points of the hysteresis loop with H axis (H c1 and H c2 ). The coercivity H c of the loop and the loop displacement H eb can be calculated according to the following equations [37]: For both models (S-W and M-B), it is inherent that the total magnetization energy is made of: (i) -the energy of anisotropy, (ii) -Zeeman energy and (iii) -the energy of antiferromagnetic exchange.
The aim of this research is to investigate the influence of thermally induced structural changes on magnetic properties of Fe 72 Cu 1 V 4 Si 15 B 8 ribbons and therefore on the inverted hysteresis loops (IHL) and the exchange bias (EB) effects that appeared. The evolution of amorphous/nanocrystalline structure accompanied with the appearance of EB effect as well as the influence of sample length on IHL effect, was studied. The investigated FeCuVSiB alloy ribbons possess curious properties as a magnetoimpedance MI -sensing element [38].

Materials and Experimental Procedures
This research paper aims to analyze the ribbons of metastable alloy Fe 72 Cu 1 V 4 Si 15 B 8 , with a thickness of about 55 μm and width of 1.5 mm obtained by melt-spinning method.
X-ray diffraction patterns were recorded using a Rigaku SmartLab diffractometer with a Cu Kα radiation source at room temperature. The obtained XRD patterns were analyzed by means of the Maud software [39] and databases PDF-2 [40] and ICSD [41]. The observed crystalline phases were identified according to the cards No. PDF#35-0519, PDF#75-1062 and ICSD#54786. Williamson-Hall method [42] was applied to get the values of average crystallite size.
Magnetic measurements were performed at room temperature by a Faraday balance as well as by SQUID device. In both cases, the orientation of the applied magnetic field was parallel to the length of the ribbon.
The Faraday balance was used to observe the dependence of the normalized magnetization M (H ex )/M max for the as-cast alloy samples of different lengths 4 mm, 6 mm, 10 mm, 15 mm , 20 mm and 29 mm. Sample thickness and width were the same for all studied samples (55 μm and 1.5 mm, respectively). External magnetic field H ex varied from 0 to 10.695 kA/m with the step of 0.345 kA/m. The magnetic force (F) was measured by analytical balance OHAUS, model EP4102CM with 10 -6 N sensitivity.
The change of magnetic force ΔF (H ex ) = Δm (H ex ) • g was obtained under the external magnetic field influence on the ribbon sample and normalized magnetization was defined by: where Δm max = m (H max ) -m (0) is measured at H max = 10.695 kA/m. The static hysteresis loops were measured at room temperature with an MPMS-XL5 Quantum Design SQUID device, in the magnetic field intensity up to 5032 Oe (400.434 kA/m) in both directions. The measurement was performed with increasing measuring step: from zero the step was 10 Oe (0.796 kA/m) but after magnetic saturation (above 300 Oe) the step was 500 Oe (39.789 kA/m). Measurements were performed on a 6 mm long as-cast sample and samples annealed at different temperatures 723, 773 and 823 K, for one hour.

Structural analysis
The as-cast sample of the Fe 72 Cu 1 V 4 Si 15 B 8 alloy contains both amorphous and crystalline phases, as indicated by the broad halo and narrow diffraction peaks in XRD patterns given in Fig. 3a. Thermal treatment of the alloy at different temperatures for 60 min provokes structural transformations starting from 723 K [14], see Tab. I.
Tab. I Phases present in the as-cast and thermally treated alloy samples [14]. Besides the changes in weight fraction of the phases already present in the as-cast alloy, after annealing at 723 K Fe 2 B phase also begins to crystallize. The Fe 23 B 6 phase completely disappears at higher annealing temperatures (T an ≥ 823 K), so that in an entirely crystalline alloy only α-Fe (Si) and Fe 2 B phases can be found. The average crystallite size of the α-Fe (Si) exhibits weak changes up to annealing temperature of 823 K (see Fig. 3b). Higher annealing temperatures stimulate a sudden growth, which can be correlated with the presence of vanadium in the alloy [9,14].

Magnetic measurements by a Faraday balance
It is generally considered that, the ferromagnetic thin ribbons, exhibit a different magnetic behavior in the near-surface layer and in the bulk of the ribbon [21,22]. The influence of the length of the as-cast Fe 72 Cu 1 V 4 Si 15 B 8 ribbon samples on its magnetic properties was analyzed using a Faraday balance. The length differences change the surfaceto-volume ratio of the sample, influencing the magnetization changes. This method was used to observe the trend of hysteresis loop changes in the vicinity of saturation (magnetic field up to the 10.7 kA/m).
In Fig. 4, the diagrams а), b) and c) show the IHL trend for the ribbon length of 4 mm, 6 mm, and 10 mm. This behavior was not found for the samples longer than 10 mm (Fig.  4d, 4e, 4f). For samples of 6 mm and 10 mm length, points when the hysteresis loop changes from normal to inverted trend were observed (for instance 6.7 kA/m is the intersection of descending and ascending curves of 10 mm sample). Faraday's method has unequivocally shown that the inverted hysteresis loops of the investigated Fe 72 Cu 1 V 4 Si 15 B 8 samples are dependent upon the length of the ribbons. The change of the length of the ribbons is followed by the changes of surface to volume ratio of a ribbon and therefore by the changes of magnetic energy (the last term in equation (1) antiferromagnetic exchange interaction between the surface layer and the bulk; surface layer as a magnetically harder component and bulk as a magnetically softer component [21][22][23]).

SQUID magnetic measurements
By recording the magnetic hysteresis of the Fe 72 Cu 1 V 4 Si 15 B 8 ribbons with SQUID device at room temperature, two effects were detected: inverted hysteresis loops (IHL) and exchange bias (EB). Fig. 5 shows the dependence of magnetic moment m (emu) on the applied magnetic field. The inverted hysteresis loops were observed in all the studied 6 mmlong ribbon samples (as-prepared and annealed at 723 K, 773 K and 823 K for 1h), in line with the Faraday's balance results regarding the sample length. At high negative magnetic field (about H ≈ -2000 Oe), it was observed that magnetic moment changes from inverted into normal, i.e. orientation toward the field direction (inserts on the left side in the Fig. 5). Furthermore, magnetic properties of the Fe 72 Cu 1 V 4 Si 15 B 8 alloy exhibits changes after annealing caused by thermally induced structural transformations. Namely, the SQUID results show that the mass saturation magnetization M S (emu/g) increases with the increase in annealing temperature up to 773 К, while the annealing at higher temperature results in its decline ( Fig. 6 and Fig. 8a). The formation of magnetic nanocrystalline α-Fe (Si) particles in the amorphous matrix causes an increase in saturation magnetization at lower annealing temperatures. At annealing temperatures higher than 773 K, with further progress of crystallization, non-magnetic B atoms are accumulated along the α-Fe (Si) grain boundaries in larger amounts, reducing the ferromagnetic exchange interaction among the α-Fe (Si) crystals [43]. However, the structural characteristics at higher annealing temperatures, including a larger fraction of crystalline material in the alloy, hinder the movement of magnetic domain walls additionally diminishing the magnetization value. On the other hand, coercive field H c exhibits a constant increase with an increase of annealing temperature (Fig. 7 and Fig. 8c). This growing trend of H c can be explained by the progress of crystallization process with an increase in annealing temperature. As previously mentioned, during the crystallization, the α-Fe (Si) crystals, as well as the boride ones are formed. It is considered that the nanocrystal size, that is lower than the magnetic exchange length, significantly diminishes the contribution of magnetocrystalline anisotropy of the nanocrystals to the overall magnetic anisotropy of the material [2,44], which is directly related to coercivity. The ferromagnetic exchange length for Fe-based alloys is believed to be 20 nm -40 nm [45]. In the temperature interval up to 823 K, the average crystallite size of the dominant phase, α-Fe (Si), slightly increases with the progress of crystallization, from about 40 nm to 44 nm (see Fig. 3b). This increase can affect the average anisotropy, as the coercivity is proportional to the sixth power of the grain size [43]. The formation of small amounts of boride phase in this system additionally contributes to deterioration of the soft magnetic properties due to large magnetocrystalline anisotropy constant. Moreover, the structural changes induced by annealing lead to the change of the domain structure of material, which is reflected in the movement of the easy axis of magnetization, i.e. to the changes in magnetic anisotropy [45].
In most cases, exchange bias (EB) has been found below the Neil temperature, under which the antiferromagnetic exchange behavior occurs. At room temperature, ЕB effect was found in a two-layer film that consisted of a magnetically soft and a magnetically hard ferromagnetic layer, but with a pinning field applied [32]. Еxchange bias in the Fe 72 Cu 1 V 4 Si 15 B 8 alloy was found at room temperature for all investigated samples (as-cast and annealed at 723 K, 773 K and 823 K), but without the application of the cooling (pinning) field ( Fig. 7 and Fig. 8). The effect can be explained by the antiferromagnetic exchange of the surface layer and bulk of the material that is also the origin of IHL (equations (1) and (3)). field H c, measured at 300 K after annealing at temperature T an .
By analyzing the results of the magnetic measurements (Fig. 7) in the as-cast alloy H eb is negative -NEB (see Tab. II). Annealing at 723 K and 773 K was followed by the shift of the hysteresis loop to the right, i.e. to the positive EB effect (PEB).
Tab. II EB magnetic properties of the investigated samples. For the sample annealed at temperature of 723 K, the highest H eb value, as well as the largest hysteresis loop displacement to the right was recorded. This can be associated with an increase in saturation magnetization, M s , joint with a minimal increase of magnetic anisotropy; which was thereby, followed by a small increase in H c . This indicated a larger influence of the magnetic soft component (due to enhanced magnetic moment) on antiferromagnetic exchange. Further increase of annealing temperature up to 773 K, causes both a slight increase of M s , and an increase of H c , and due to the reduced influence of the magnetically soft component, the resulting hysteresis loop shifts to the left. EB remains positive due to still dominant influence of magnetically soft component in antiferromagnetic exchange. After annealing at 823 K, there was an evident decrease of М s , while H c still continues to grow, which significantly contributes to the hysteresis loop displacement to the left, i.e. EB became negative and |H eb823K | > |H eb300K |).
Also, the correlations of IHL and EB effect were detected. Namely, after annealing at 723 K, the highest value of positive H eb was observed, as well as the lowest value of the magnetic field where the hysteresis loop exhibits a transition from inverted into normal direction (about 250 Ое, see Fig. 6c).

Conclusion
In amorphous/nanocrystalline ribbon of Fe 72 Cu 1 V 4 Si 15 B 8 ("FINEMENT type" аlloy Fe-Cu-M-Si-B, M=V) obtained by melt spinning technique, both the IHL and the EB effects at room temperature were found. IHL trend was observed for the as-cast ribbons with length of 4 mm, 6 mm and 10 mm. In the as-cast ribbon H eb is negative as hysteresis loop was displaced to the left in relation to the H=0 axis.
Depending on annealing temperature, amorphous matrix with α-Fe (Si), Fe 23 B 6 and Fe 2 B nanocrystalline phases coexists. The structural changes induced by annealing up to 773 K have a positive influence on M s , which is linked to the stress relief and transformation of the residual amorphous matrix into nanocrystalline phase, where the α-Fe (Si) phase is more abundant and configuration of magnetic domains is more favorable (domain wall movement is higher). Further increase of Т аn results in the increase of the content of boride phases and deteriorates soft magnetic properties of the alloy. For Т аn > 773 K, transformation of Fe 23 B 6 into Fe 2 B and growth of crystallites, reduce M s as well as magnetic domain wall movement.
By annealing the 6 mm long ribbons, IHL effect is observed in all of the annealed samples due to antiferromagnetic exchange between the surface (magnetically harder component) and bulk (magnetically softer component). Positive H eb occurred and maximum shift to the right was recorded after annealing at 723 K. On the other hand, significant hysteresis loop displacement to the left was observed after annealing at 823 K, i.e. EB became negative and |H eb823K | > |H eb300K |).