*3.3. VSM Analysis*

Figures 3 and 4 illustrate the ZFC ± 90 kOe *M(H)* curves of the YFexCr1−xO3 series taken at 5 K (top) and 300 K (bottom), respectively. At RT, the samples with x = 0.25 and 0.50 behaved as ordinary paramagnets (see Figure 3d,f), while the samples with x = 0.60, 0.75, and 0.90 suggested an onset of a weak ferromagnetism (see Figure 4b,d,f). For the x = 1.0 sample (YFeO3 compound, RS7), shown in Figure 5a, *M(H)*, curves recorded at different temperatures show the magnetic features of a weak ferromagnet with high magnetic anisotropy, i.e., with characteristics similar to that found in the pure YFeO3 compound (set-like *M(H)* curve). Therefore, this sample (RS7) revealed an interesting and complex magnetic behavior that is mainly attributed in the literature to an exchange spring effect. In particular, the magnetic spring effect can be often observed by an exchange magnetic coupling between coexisting and interacting soft and hard magnets in a sample, as reported by Popkov et al. [5].

**Figure 3.** *M(H)* curves recorded for a maximum field of 90 kOe at 5 K (top) and 300 K (bottom) for the RSX samples. RS1 in (**a**,**b**), RS2 in (**c**,**d**), and RS3 in (**e**,**f**), respectively.

Thus, since the NDP, Rietveld, and SEM data of the SR7 sample suggested the presence of a single-phase structure, and the presence of two magnetic phases of two crystalline structures (as occurs in bilayer films) cannot be inferred as a reason for the observed phenomenon. However, the atomic disordering in the orthorhombic structure and the change in cell volume could lead to local different magnetic phases, which will be magnetically interacting and producing the observed *M(H)* behavior discussed above.

Looking at the 5 K *M(H)* loop for the x = 0 sample (see Figure 3a), we can observe the characteristic *M(H)* curve reported for the YCrO3 compound [15]. Below *TN,* the non-saturation regime of the *M(H)* curve occurred till values of +90 kOe, indicating a remarkable antiferromagnetic state, while above *TN,* a paramagnetic-like behavior was regarded; see Figure 3b. On the other hand, the loss of hysteresis in the RS2 and RS6 samples (Figure 3c,e and Figure 4a,c,e) indicated the substitution of Cr by Fe atoms in the orthorhombic crystal configuration, as confirmed by our XRD data. Table 2 contains the remanence (*Mr*), coercivity (*HC*), and saturation magnetization (*σsat*) values of the hysteresis ferromagnetic part. Using the slope of the *M(H)* curves, it was possible to subtract the antiferromagnetic contribution of the *M(H)* curves, thus leaving the purely ferromagnetic component, as shown in Figure 5b. Thus, these *M(H)* curves recorded at different temperatures really showed large *HC* fields, but their value decreased when the temperature decreased, concomitantly with the increase of the saturation magnetization (the area inside the *M(H)* loop remained nearly constant). In addition, all *M(H)* curves show more clearly the step-like behavior near the zero-applied field region of the *M(H)* curve, a feature discussed above and attributed to a magnetic spring-like effect.

**Figure 4.** *M(H)* curves recorded for a maximum field of 90 kOe at 5 (top) and 300 K (bottom) for the RSX samples. RS4 in (**a**,**b**), RS5 in (**c**,**d**), and RS6 in (**e**,**f**), respectively.

**Figure 5.** *M(H)* loops for the RS7 sample recorded at different temperatures (**a**). *M(H)* loops after the subtraction of the paramagnetic contribution of the AFM phase (**b**).

The magnetic parameters in Table 2 were plotted as a function of Fe concentration (x), as seen in Figure 6a,b,d. At 300 K, the *HC* field dependence with x had two marked regions (I and II): (i) region-I can be interpreted as the magnetic domain reorientations (magnetization reversal) due to the increasing concentration of Fe atoms that are replacing Cr, forming the pure YFeO3 crystalline phase; (ii) region-II has relatively high values of the *HC* fields and that occur above x = 0.75, reaching a maximum value of 46.7 kOe forx=1 (RS7 sample).


**Table 2.** Remanence (*Mr*), coercive field (*HC*), and magnetic saturation (*σSat*) of the ferromagnetic component, and susceptibility of the antiferromagnetic component to the RSx samples with x = 1, 0.9, 0.75, and 0.60. For the samples with x = 0, 0.25, and 0.50, the values correspond to the 'paramagnetic' state.

The remanence (*Mr*) is calculated from *Mr* = (*MR*<sup>+</sup> + *MR*−)/2, where *MR+* and *MR*<sup>−</sup> are the values of the upper and lower magnetization, respectively, when the magnetic field is zero. The coercive field (*HC*) is calculated from *HC* = (*HC*<sup>+</sup> − *HC*−)/2, where *HC+* and *HC*<sup>−</sup> are the values of the right and left fields when magnetization is zero.

**Figure 6.** (**a**) Dependence of the *HC* (kOe) vs. x (Fe concentration) at 300 K. (**b**) Dependence of the *Mr* and *σsat* vs. x (Fe concentration) at 300 K. (**c**) *Mr* vs. *σsat* graph at 300 K. (**d**) *HC*, *Mr*, and *σsat* vs. (Fe concentration) at 5 K.

These values were larger than those reported by Popkov et al. [5] for four YFeO3 crystalline samples synthesized by different routes. On the other hand, the *Mr* and *σsat* values had a similar dependence with Fe concentration at 300 K and 5 K, as can be seen in Figure 6b,d. The behavior of *Mr* vs. *σsat* is shown in Figure 6c. The *Mr* and *σsat* quantities could reach maximum values of 0.75 and 0.79 emu/g, respectively. This *σsat* value of 0.79 emu/g was consistent with others found in the literature for either powder or single crystals [3,4,16–19], as summarized in Figure 7. In particular, the value of 0.79 emu/g, obtained for a field of 3.5 kOe, was almost two times higher than the values reported by Zhang et al. [4] and four times higher than that obtained by Shen et al. [20] for a similar system. Therefore, the RS7 sample behaved as an ordinary single crystal of the YFO phase with a multidomain magnetic structure [4,20]. In addition, it is worth mentioning that the RS7 sample exhibited weak ferromagnetism enhanced at 90 kOe.

**Figure 7.** *Mr* vs. *σsat* relation built from data recorded at RT and reported in the literature for similar compounds. Comparison between powder and single crystal YFexCr1−xO3 [3,5,16–19].

The WFC and ZFC *M(T)* measurements for all RSx samples were collected under two probe fields, namely, 50 Oe and 1000 Oe, and the results are shown in Figures 8–10. For the lowest applied field, the ZFC and WFC *M(T)* curves, displayed in Figure 8a, clearly show the magnetization transition from the AFM to PM state of the YCrO3 compound at 159 K, assigned to *TN*. No other magnetic transition was observed in *M(T)* curves, indicating that no secondary phase was formed during the auto combustion synthesis, in agreement with the XRD data. For the YFe0.25Cr0.75O3 compound, the *TN* value increased to 174 K (see Figure 8b), but a further increase of Fe content, for example, x = 0.50, led to a cancelation of total magnetization and a compensation temperature between the antiferromagnetic sub-lattices of 245 K. The zero-net magnetization was observed as an enhancement of the

diamagnetism contribution, as shown in Figure 8c. At x = 0.60 and 0.75, see Figure 8d,e, a slight increase in the magnetization was observed, in agreement with the onset of WFM, as also seen in the *M(H)* curves. At x = 0.90 and 1.0 (Figures 8f and 9), a significant increase in the magnetization was observed with significant overlap between ZFC and WFC *M(T)* curves above 250 K.

**Figure 8.** ZFC and WFC *M(T)* curves at a probe field of 50 Oe for the (**a**) RS1, (**b**) RS2, (**c**) RS3, (**d**) RS4, (**e**) RS5, and (**f**) RS6 samples.

**Figure 9.** ZFC and WFC *M(T)* curves recorded for a probe field of 50 Oe for the RS7 sample. Black line indicates WFC and red line ZFC, respectively.

**Figure 10.** ZFC and WFC *M(T)* curves recorded at a probe field of 1000 Oe for the (**a**) RS1, (**b**) RS2, (**c**) RS3, (**d**) RS4, (**e**) RS5, and (**f**) RS6 samples.

The determination of the *TN* of the Fe-substituted YCO compounds was done recording the ZFC and WFC *M(T)* curves at a higher field (1000 Oe). At this probe field, the magnetization of the samples with x = 0.75 and x = 0.90 showed a strong interaction with the external field, confirming the enhancement of the WFM. From ca. 5 K to higher temperatures, both ZFC and WFC *M(T)* curves coincided for the sample with x = 0.9.

Based on the above experimental results, it can be inferred that the anisotropic exchange-spring in crystalline compounds cause a significant increase in the coercive field of 46.7 kOe at 300 K. This interesting magnetic response has also been observed by Popkov et al. [5]. In our case, the hard and soft magnetic phases are intrinsically correlated to the same structure, but they are due to chemical disorders in the sites of the orthorhombic crystal nanostructure. Moreover, the hysteresis loop shape depends on the finite-size effects under an applied DC magnetic field (in our case, we use the highest value reported in the literature of 90 kOe). Hence, the observed ascending/descending hysteresis loops at several temperatures is explained due to spin reorientation of the antiferromagnetic vector in the *x–z* plane, reaching the *z*-axis at a critical magnetic field, as reported by Jacobs et al. [21], where a value of 74 kOe at 4.2 K was obtained for the YFeO3 single crystal. According to Popkov et al. [5], in nanocrystalline materials, the typical WFM hysteresis cycle is observed only for the YFO phase when their grain sizes are equal and larger than 41 nm, i.e., the YFO material may exhibit WFM, and the exchange spring-like effect may occur due to its high magnetocrystalline anisotropy energy. Consequently, considering our experimental results that showed a grain size of 84 (8) nm, we can also expect the observed ascending/descending branch behaviors of the *M(H)* loops of the YFO sample. More precisely, the combined magnetic effects of the enhanced WFM and the presence of AFM interactions among the Fe ions of the different sites of the orthorhombic crystal structure gave rise to different local anisotropy contributions, producing high magnetocrystalline anisotropy due to the size effect and the enhancement of DM (Dzyaloshinskii–Moriya) interactions in the samples.

The two effects cannot be separated, and the improvement of WFM features can be explained assuming a canting angle of 13◦, as demonstrated by previous neutron diffraction analysis [11]. The presence of AFM interactions in the Fe-substituted YCO compounds is also confirmed by the changes of *TN* values as a function of Fe content, as displayed in Figure 11. Indeed, the *TN* values increase nonlinearly with increasing Fe content, reaching the reference value for YFO [8]. Of course, the Fe substitution phenomenon is randomly changing locally the anisotropy by changing the lattice parameters, as shown by the XRD results. These modifications favor the spin reorientation and magnetization reversal phenomena.

**Figure 11.** Néel temperature *TN* dependence on x (Fe concentration) estimated from 1000 Oe *M(T)* curves. The solid line passing by experimental points is only a guide for viewing.
