1 Introduction

High interstitial steels are materials alloyed with C + N, where their combination improves the mechanical properties and stability of the austenitic matrix, compared with single carbon or nitrogen alloying.[1] From a metallurgical point of view, interstitial elements such as C, N, and B determine the type and number of stable phases and therefore the microstructure and properties of the steels.[2,3] According to experimental evidence presented by Gavriljuk et al.,[1] a combination of strength and ductility is connected with an increase in free electron concentration, leading to the stabilization of the austenite and increasing of the solubility of interstitials.[4]

Mechanical properties of a high interstitial steels have been widely reported,[1,5,6] exhibiting yield strengths between 650 and 1000 MPa in a temperature range between room temperature and 173 K, maintaining relatively constant ductility. Unlike FeCrNi austenitic stainless steels, FeCr18.2Mn18.9–0.96C + N and other C + N steels display an inflexion in the impact toughness absorbed energy curve below 223 K, reporting a ductile-to-brittle transition temperature (DBTT) of 182.15 K (longitudinal test) and 224.15 K (transverse test).[7]

Regarding magnetic properties, the paramagnetic-to-antiferromagnetic transition undergone by the Fe–Mn alloys has been studied and used as a parameter to develop functional alloys, such as precision resistance alloy, Covar alloy among others.[8,9] The effect of different alloy elements as Al, Si, and Ge on magnetic susceptibility and TN has been addressed, finding that doping with these elements has a weakening effect of the itinerant electron characteristics of antiferromagnetism.[10,11,12] Additionally, for some other systems like Fe–Cr–Ni it has been determined a Type-1 antiferromagnetic (AFM) ordering below the Neel temperature and a systematical influence on TN by the lattice parameter.[13]

Furthermore, there is a strong relationship between deformation mechanisms, stacking fault energy (SFE), austenite stability, Gibbs free energy, and magnetic transitions. The stacking fault energy is one of the parameters governing both twinning- and strain-induced γ → ε transformation in austenitic alloy. In particular, many studies on the evaluation of SFE of high Mn austenitic steels through thermodynamic calculations[14,15,16] and experimental measurements[17] have been carried out due to the strong connection between SFE structure, composition, and deformation mechanisms.

Different thermodynamic models have been developed for SFE prediction, generally based on the Olson and Cohen equilibrium thermodynamic formalism,[18] which includes the contribution of the Gibbs free energy, the molar surface density, and the interface energy. Some other terms associated with the prediction of stacking fault energy such as strain energy,[18,19,20] the magnetic contribution to the Gibbs free energy,[21,22] and a grain size-dependent excess free energy[23,24] have been added to establish a more accurate model. The stacking fault energy reported for the alloy FeCr18.2Mn18.9–0.96C + N is 40 mJ/m2,[6] a value obtained through experimental methods which suggests dislocation slip and TWIP (twinning-induced plasticity) as deformation mechanisms.

New thermodynamic models have been proposed to determine the SFE as a function of magnetic ordering and chemical composition,[25,26,27] considering the magnetic contribution on the SFE, especially the magnetic transition temperature between antiferromagnetism (AFM) and paramagnetism (PM) known as Néel temperature (TN).[28] Thermodynamic evaluations of the binary system Fe–Mn and ternary Fe–Mn–C have revealed an important contribution to SFE of the transition temperature between antiferromagnetic (> 15 pct Mn) and paramagnetic (< 15 pct Mn) state. For paramagnetic alloys, the SFE was shown to be more sensitive to temperature, but for antiferromagnetic alloys, it is dependent of the Mn concentration.[29] Furthermore, the magnetic order–disorder phenomena affect the Gibbs energy of the phases. Hillert and Jarl[22] proposed a model that represents the magnetic contribution to the Gibbs energy, based on the work of Inden.[21] Curtze and Kuokkala[28] discovered that the magnetic contribution to the SFE is substantial at low temperatures but stabilizes as temperature increases. Magnetic properties of high interstitial steels reported by Warnes and King[30] found that the effect of the alloying elements in the reduction of TN increases in the order Cr, Ni, Mo, and Si, and the only element increasing TN is Mn. Jin et al.[31] adjusted the Warnes and King equation, proposing an improved TN equation for medium and low Mn-high C, as well as high Mn-low C, to adjust the accuracy of the new equation for high C TWIP steels. Additionally, Foldeaki et al.[32] found that the atomic magnetic moment and the molecular-field coefficients have a strong dependence on the metallurgy processes, as the production route, deformation, and heat treatment. Mn and Fe are the elements having the most appreciable contribution, it has been shown that chromium affects the ferromagnetic interactions and manganese has an effect on the antiferromagnetic ones.

Nevertheless, the influence of a plastic deformation on the paramagnetic-to-antiferromagnetic transition has not been considered in the literature yet. Thus, the ambition of this work is to study the effect of deformation on magnetic properties of the high interstitial stainless steel Fe61.2Cr18.2Mn18.9–0.96C + N in a range of temperature from 50 K to 370 K with an experimental approach and to determine the magnetic behavior of the material at 0 K through ab initio calculations.

This study provides a contribution to the understanding of the influence of magnetism on the SFE of high interstitial steel from an ab initio approach. The use of stainless steels in structural components under cryogenic conditions requires an alloy where the face-centered cubic (FCC) austenitic phase remains stable in relation to a transformation into the ferromagnetic body-centered cubic (bcc) martensitic phase and a low magnetic susceptibility,[30] in this way comprehending the effect of deformation on magnetic behavior at low temperatures represents an important contribution for the use of these materials at this specific conditions.

2 Materials and Methods

A FeCr18.2Mn18.9–0.96C + N steel was melted in an induction furnace, followed by electroslag remelting at atmospheric pressure. After hot working to 120 mm diameter rods, the samples were cut by spark EDM, heat treated at 1373 K (1100 °C), and water quenched, machined to final size. Tensile tests were carried out at T = 298 K in a Z100 Zwick universal test machine following the DIN EN ISO 6892 standard. Deformation was interrupted at 10, 20, and 30 pct elongation. Material with no deformation was kept as a reference. The composition of the alloy, measured by OES (optical emission spectrometry), is shown in Table I. X-ray diffraction (XRD) was carried out at room temperature, to identify the crystal structure of the alloys, using a Panalytical X’pert PRO-MPD diffractometer with Ultra-fast X’Celerator detector using a CuKα radiation source (l = 1.54 Å). Data were recorded at 2θ between 15 and 90 deg with steps of 0.0263 deg every 100 seconds. The morphology and microstructure of the alloys were characterized using a ZEISS EVO MA10 scanning electron microscope (SEM).

Table I Composition of the Alloy Measured by OES
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The measurement of the magnetization as a function of the applied field (M vs. H) was performed using a vibrating sample magnetometer (VSM) of Quantum Design, with field values between − 30 and 30 kOe, at different temperatures (50 K, 100 K, 200 K, 250 K, and 300 K) for each specimen (0, 10, 20, and 30 pct deformation). For magnetization as a function of temperature (M vs. T), the same equipment is used, following the Zero Field Cooled (ZFC)–Field Cooled (FC) mode between 50 K and 370 K. The ZFC test consists of cooling the sample to 50 K in the absence of an applied field, then bringing it to 370 K with an applied magnetic field (100, 500, 2000, 5000, 100000, 25000, and 30000 Oe), measuring the magnetic moment as a function of the temperature. The FC test consists of cooling the sample from 370 K to 50 K with an applied magnetic field, taking measurements of the magnetic moment as a function of temperature.

From data obtained through VSM technique, magnetization as a function of temperature and external field curves were built. Magnetic susceptibility was calculated using Eq. [1]

$$\chi =\frac{M}{H},$$
(1)

where M corresponds to magnetization and H is the magnetic field strength. Additionally, inverse of magnetic susceptibility \({\chi }^{-1}(T)\) was plotted.

Regarding computational methods, solid solution modeling was carried out using the special quasi-random structures (SQS)[33,34] methodology implemented in the alloy theoretic automated toolkit (ATAT) program.[35] An objective function is minimized considering the XRD lattice parameters experimental reported (i) a supercell size of 60 atoms, (ii) a chemical composition of Fe60Cr20Mn20, and (iii) a third-nearest-neighbor distance for FCC and HCP structures to range between 3.0 and 6.0 Å. Consequently, a random structure with the best chemical disorder arrangement for the alloy was obtained. Afterward, the carbon and nitrogen addition as interstitial atoms at 1 at. pct were modeled in octahedral sites into Fe60Cr20Mn20 giving origin Fe60Cr20Mn20–C + N.[36,37,38]

DFT periodic calculations were carried out using the Vienna Ab initio Simulation Package (VASP, version 6.3.2).[39,40,41,42,43] This software has been designed for metallic systems using plane waves that describe the delocalized electrons evenly over the cell. The PBE GGA exchange-correlation functional was chosen due to the cost-efficiency ratio reported for extended systems.[44,45,46,47,48] For each metal, the valence electrons are expanded in plane waves basis set, and the core electrons are described through the projector-augmented wave (PAW) pseudopotential.[41,49,50] The Monkhorst–Pack sampling of the Brillouin zone was used for the (5 5 5) K-point mesh. All FCC and HCP supercells were fully optimized regarding positions, cell shape, and cell volume using ISIF = 3. The energy cut-off of the plane waves was set to 500 eV, the self-consistent field (SCF) tolerance was 1 × 10−6 eV, and the relaxation of geometry was considered converged when the energy difference to the previous optimization step was less than 1 × 10−5 eV. The collinear spin correction energy (ISPIN = 2) was included in the optimized geometry to account the magnetic properties of the studied alloys.[38,51,52] We also specified the initial magnetic moment for each atom: Fe (S = 1), Mn (S = 1.5), and Cr (S = 2) for ferromagnetic state (FM) and Fe (S =  1), Mn (S =  − 0.5), and Cr (S =  − 1) for antiferromagnetic state (AFM). Moreover, a spin state (AFM–FM = PM) was evaluated, considering half of the moments up and the other moments down. These magnetic states correspond to the highest and most stable total spin state. The magnetic critical temperature Tc was computed based on the mean-field approximation[53] as follows:

$${k}_{\mathrm{B}} {T}_{\mathrm{c}}=\frac{2}{3} \left({E}_{\mathrm{AFM}}-{E}_{\mathrm{FM}}\right),$$
(2)

where \({k}_{\mathrm{B}}\) is the Boltzmann constant, \({E}_{\mathrm{AFM}}\) and \({E}_{\mathrm{FM}}\) are the energies of antiferromagnetic and ferromagnetic phases, respectively.

To study phase stability and solubility of carbon and nitrogen in the alloys, the formation enthalpy from the total energy of the optimized supercell of the alloys was determined, and the weighted energies of each element in their most stable magnetic state. Thus, the formation enthalpy for Fe60Cr20Mn20–C + N is defined as[54] follows:

$${\Delta H}_{\mathrm{f}}={E}_{{\mathrm{Fe}}_{60}{\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}-\mathrm{C}+\mathrm{N}}-\frac{1}{103}\left(60{E}_{\mathrm{Fe}}+20{E}_{\mathrm{Mn}}+20{E}_{\mathrm{Cr}}+ 1{E}_{\mathrm{C}}+2{E}_{\mathrm{N}}\right),$$
(3)

where \({E}_{\mathrm{Fe}}\), \({E}_{\mathrm{Mn}}\) , and \({E}_{\mathrm{Cr}}\) are energies per atom in the unit cell for Fe bcc in FM state, Cr bcc in AFM state, and Mn bcc* in AFM state. Further, \({E}_{\mathrm{C}}\) is obtained as the energy of graphite per atom, and \({E}_{\mathrm{N}}\) is the energy of N2 per atom.

Additionally, the SFE was calculated using the axial interaction model,[55,56] which has been recently reported by Stocks et al.[57] Based on this approach, the SFE can be evaluated considering the interactions of the (111) layer up to the nearest neighbor (ANNI model) defined in terms of the total energy of FCC, and HCP structures. Thus, the SFE can be expressed as follows:

$${\mathrm{SFE}}_{\mathrm{ANNI}} =\frac{{E}_{\mathrm{HCP}}-{E}_{\mathrm{FCC}}}{A},$$
(4)

where \({{E}_{\mathrm{FCC}},\mathrm{and }\,E}_{\mathrm{HCP}}\) are the total energies per atom of the FCC and HCP phases, respectively, and A is the area of the (111) plane. This equation estimates the SFE using solely ab initio calculations, enabling the rationalization of strain-hardening behavior based on the structural and physicochemical features of alloys. Finally, the electronic properties of these materials are discussed in terms of Bader charge analysis.[58,59] Based on these calculations, we intend to understand how C and N in solid solution affect the stability and magnetic behavior of the alloys. Finally, it is important to mention that the deformation effect was not simulated in this work, however, future works could be realized using molecular dynamic, Monte Carlo, and uniaxial tensile simulation to analyze the stress–strain curves which will allow to understand the deformation mechanisms as dislocation glide, TRIP, and TWIP from an atomistic approach, as was carried out recently for the high entropy alloy CoCrFeMnNi.[60,61]

3 Results

3.1 Microstructure and XRD Analysis

Figure 1(a) shows the microstructure of the Fe61.2Cr18.2Mn18.9–0.96C + N alloy, which is a fully annealed structure with coarse austenitic grains, no martensitic phase formation is observed. The alloy exhibits equiaxed grains with an average size of 100 \(\mu \) m and numerous annealed twins. Grains lose their equiaxed characteristics for the sample with a deformation percentage of 10 pct, color contrast in some grains (Figures 1(b) through (d)) has a wavy appearance that is related to changes in crystal orientation. For samples with greater deformation, features inside grains are observed and could be attributed to dislocation cells and mechanical twins produced as deformation mechanisms during the tensile test, which is in agreement with those reported by Gavriljuk et al.[6] Regarding EDS analysis, a uniform distribution of the constituent elements is observed.

Fig. 1
figure 1

SEM micrographs for the FeCr18.2Mn18.9–0.96C + N alloy with strains of (a) 0 pct, (b) 10 pct, (c) 20 pct, and (d) 30 pct

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XRD analyses at room temperature are shown in Figure 2. They indicate the presence of an FCC single-phase solid solution crystal structure. The formation of ε-martensite or α-martensite is not observed in samples with 0, 10, 20, and 30 pct of plastic deformation. As a reference, the crystallographic file with code COD 1524833 was simulated, through which the crystalline structure of the alloy corresponding to the space group Fm−3m with FCC structure was confirmed. The diffraction pattern of the material shows the austenite planes (111)γ, (200)γ, and (220)γ. With increasing deformation, the reflections (111), (200) are slightly shifted toward smaller angles (Figures 2(b) and (c)), indicating an increase of the lattice parameter due to the deformation (Table II), also a broadening of the reflections as deformation increase is observed.

Fig. 2
figure 2

(a) XRD pattern at different deformations, (b) magnification of (111) reflection, and (c) magnification of (200) reflection

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Table II Lattice Parameters Obtained for Each Stage of Deformation
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3.2 Magnetic Response

Magnetization as a function of external field (M vs. H) and magnetization as a function of temperature (M vs. T) was measured, magnetic susceptibility and its inverse are plotted in Figure 3.

Fig. 3
figure 3

Magnetization as a function of the external field at different values of deformation (a) 0 pct, (b) 10 pct, (c) 20 pct, and (d) 30 pct

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In the curves shown in Figure 3, there are no indications of spontaneous magnetization in the observed range, and the material exhibits a linear dependence of magnetization on the applied external field. Magnetization increases with increasing temperature. For deformed samples there is a decrease in the magnetization of the alloy (Figures 3(b) through (d)). The greatest change is observed for a 10 pct deformation, however, the magnetization values corresponding to the samples with 20 and 30 pct deformation do not have an appreciable change with respect to the sample deformed by 10 pct.

It is noteworthy that some works have been addressed concerning the magnetization as a function of the external field for similar materials exhibiting Langevin superparamagnetism characterized by a curvature or deviation from linearity near zero magnetic field.[62,63,64] Nevertheless, for the case of the material tested in the scope of this work, the Langevin superparamagnetism was not detected.

In the curves M(T)|H (Figure 4), a decrease in magnetization is observed with respect to the increase in the deformation. Additionally, a clear transition of the material from the paramagnetic state to the antiferromagnetic state at the so-called Néel temperature is observed (TN) below which neighboring spins are locked in antiparallel alignment. The outcome is a sample with a low magnetic moment and susceptibility that actually tends to zero as the accumulation of individual magnetic moments cancels out.

Fig. 4
figure 4

Magnetization as a function of the temperature at different values of deformation (a) 0 pct, (b) 10 pct, (c) 20 pct, and (d) 30 pct

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All four samples revealed an inflection in the susceptibility graph as a function of temperature (Figure 5(a)), indicating a transition between the paramagnetic and antiferromagnetic state, with maximum susceptibility values of 0.017, 0.0093, 0.0079, and 0.0092 emu/Oe mol for the samples with a 0, 10, 20, and 30 pct deformation, respectively, given at the Néel temperature of each one of them. A plot of the reciprocal of magnetic susceptibility (χ−1) vs. temperature is shown in Figure 5(b).

Fig. 5
figure 5

(a) Magnetic susceptibility as a function of temperature, and (b) inverse of the magnetic susceptibility

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As expected, the extrapolated values for Curie temperature θ (Table III) are negative, indicating the presence of an antiferromagnetic coupling in the alloy. Additionally, the values of θ/TN fall within the expected range for FCC alloys.[32] Néel temperature was calculated using empirical equations proposed by Jae–Eun–Jin[31] Eq. [5] and Warnes y King equation[30] (Eq. [6]).

Table III Néel Temperature Obtained Through Different Methods, Calculated Curie Temperature, and Effective Magnetic Moment Above the Neel Temperature
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$${T}_{\mathrm{N}} (\mathrm{K})=0.000013{(\mathrm{Mn})}^{3}-0.08984{\left(\mathrm{Mn}\right)}^{2}+11.76\left(\mathrm{Mn}\right)-19.92\left(\mathrm{C}\right)-12.72\left(\mathrm{Si}\right)-6.61\left(\mathrm{Al}\right)-1.70\left(\mathrm{Cr}\right)+152.4 \left(\mathrm{at}\, \mathrm{pct}\right),$$
(5)
$${T}_{\mathrm{N}} \left(\mathrm{K}\right)=90-1.25\mathrm{Cr}-2.75\mathrm{Ni}-5.5\mathrm{Mo}-14.0\mathrm{Si}-7.75\mathrm{Mn} \left(\mathrm{wt}\, \mathrm{pct}\right).$$
(6)

The Curie–Weiss law of 1/χ = (T + θ)/C[65] provides a good description of the magnetic susceptibility above TN. Here, T is the absolute temperature, θ is the paramagnetic Curie temperature, and C is the Curie constant. The values of θ of the alloys with different degrees of deformation were found to be negative (Table III), confirming the presence of strong antiferromagnetic interactions of moments in the alloy.[66]

Values of paramagnetic effective moment (meff) in Bohr magnetron were calculated using the experimental data of \({\chi }^{-1 }\) as a function of temperature through Eq. [7] and are indicated in Table III. A decrease in meff with increasing deformation suggests that magnetization of steels with high interstitial content weakens with increasing deformation in the material up to 20 pct.

$${m}_{\mathrm{eff}}({\mu }_{\mathrm{B}}/ \mathrm{f}.\mathrm{u}.) ={\left(3{k}_{\mathrm{B}}*C*\frac{\mathrm{mol}}{\rho }*{\mu }_{\mathrm{B}}*{N}_{\mathrm{A}}\right)}^{1/2},$$
(7)

where kB is the Boltzmann constant, NA corresponds to Avogadro number, and the term \(\rho \) is the density of the alloy.

3.3 Electronic and Magnetic Analysis Through Ab Initio DFT Solid Solution Modeling (T = 0 K)

Magnetic behavior at T = 0 K of the free interstitial Fe60Cr20Mn20 system and the alloy Fe60Cr20Mn20–C + N containing carbon and nitrogen was analyzed through ab initio methods. 60 Atoms-supercells were built and optimized considering different octahedral environments. The octahedral hole was chosen according to the heat of mixing reported for the metal–carbon and metal–nitrogen binary systems.[67] The most stable FCC structure is described in Figure 6. Nitrogen atoms prefer Cr–N bonds, which are longer (1.930 Å) than Fe–C bonds (1.868 Å), which can be attributed to differences in electronegativity.

Fig. 6
figure 6

Structural parameters for the alloy Fe60Cr20Mn20–C + N obtained by SQS + DFT

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The energetic results with and without magnetic corrections show that carbon and nitrogen additions stabilize the FCC structure by 28 eV. The magnetic corrections to the energy using spin-polarized calculations with initial specified magnetic moment for each atom were evaluated (Table IV). For Fe60Cr20Mn20, a ferromagnetic state is found at T = 0 K, while an antiferromagnetic/ferromagnetic state was determined for Fe60Cr20Mn20C + N. Thus, the Fe-based tertiary alloy holds up the ferromagnetic state of the iron atom, while opposite behavior occurs when carbon and nitrogen are added, as the new Mn–C, Cr–N, Mn–N bonds maximize the antiferromagnetic state of these atoms reaching in the tertiary alloy an antiferromagnetic/ferromagnetic state. This corresponds to a “paramagnetic state” which has been also reported for the CrMnFeCoNi Cantor alloy at room temperature.[68] These results show that the C + N addition promotes a higher stabilization of the FCC phase than the C and N addition separately. Therefore, the C, N addition favors a magnetic transformation from ferromagnetic to paramagnetic state at T = 0 K. Based on the above-mentioned, using Eq. [2] a magnetic critical temperature Tc was estimated obtaining 207 K and 248 K for Fe60Cr20Mn20 and Fe60Cr20Mn20–C + N, respectively.

Table IV Total Energy with Spin-Polarized Corrections Using Non- and Specific Initial Magnetic Moments
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The local magnetic moments of individual atoms in the tertiary alloys were obtained and are described in Table V. The net total magnetic moment of the whole cell for Fe60Cr20Mn20 is 24.87 μB, only 0.4 μB per atom. For Fe60Cr20Mn20–C + N it is 19.41 μB, being 0.31 per atom. Similar results were reported by Schneeweiss et al.[53] The highest magnetic moment corresponds to the Fe atom, which remain strong in both alloys. The local moments of Mn and Cr atoms also changed suggesting that the magnetic state of these atoms begin to gain strength.

Table V Local Magnetic Moments of Individual Atoms in the Studied Alloys
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On the other hand, the enthalpy of formation and stacking fault energy of the alloys using the most stable magnetic state in Eqs. [2] and [3], respectively, were calculated (Table VI). The values found are in the range of the enthalpy of formation of other alloys, as the Cantor Alloy (− 8.43 kJ/mol). These results show that C and N content decreases the enthalpy of formation thus stabilizing the system. Values of the SFE with and without magnetic corrections were predicted for Fe60Cr20Mn20 and Fe60Cr20Mn20–C + N, respectively. As shown in Table VI values of SFE increased when magnetic contributions were added. In this case, the magnetic contribution diminishes the SFE of the alloy by 5 mJ/m2 approximately. This amount could be enough to influence the deformation mechanisms of an alloy. For the specific case of the alloy of this work, the values of SFE fall in the range of TWIP and dislocation glide, with and without magnetic contribution.

Table VI Calculated Enthalpy of Formation and SFE for the Alloys
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Finally, an analysis of the structure and the electronic behavior through a charge analysis for Fe60Cr20Mn20 and Fe60Cr20Mn20–C + N was made. Table VII shows that Fe acts as electron acceptor, while Mn and Cr as electron donors, which agrees with the electronegativity of the atoms. When carbon and nitrogen are added, it acts as an electron donor bringing a negative charge.

Table VII Bader Charge Analysis for the Alloys Modeled (e)
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4 Discussion

Figure 7 shows the Néel temperature as a function of the external field at different deformations. A jump of approximately 5 K is observed in the value of Neel temperature of the sample with no deformation compared to the deformed by a 10 pct. However, there is no a significative difference between the Néel temperatures obtained at a 10, 20, and 30 pct of deformation. These three last conditions of deformation are in a close range and are affected by the intensity of the external field.

Fig. 7
figure 7

Néel temperature as a function of the external field at different deformations

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The calculated Néel temperature values using Eqs. [5] and [6] are indicated in Table III. Taking as reference the experimental value for the undeformed sample (227.89 K), the equation proposed by Warnes and King has a better agreement. Critical temperature (Tc) estimated through ab initio method corresponds to 248 K for Fe60Cr20Mn20–C + N, which differs by 20 grades with respect to experimentally observed Néel temperature.

The system FeMnCr has complex magnetic interactions, Fe has an antiparallel alignment with respect to Mn magnetic moments lowering the magnetization.[69,70] Regarding to Fe/Cr interactions, many magnetic states, ranging from magnetic frustration at high Cr concentrations to antiferromagnetic ordering at low Cr concentrations, have been observed.[71,72,73] Manganese magnetic moments align antiferromagnetically with respect to chromium.[68] Moreover, alloys are expected to be ferromagnetic at low temperatures if γ-phase stability is established by adding Cr, Ni, Mo, or Si, whereas alloys should be antiferromagnetic or superparamagnetic if structural stability is achieved by C, N, or Mn.

As shown in the computational results described in Section III–C, the Gibbs free energy is affected by magnetic order–disorder. This behavior was explained by Inden[21] using a thermodynamic model that takes into account the influence of magnetism on heat capacity and the maximum magnetic entropy of an element moving through the FM to disordered state, described as a function of mean magnetic moment. Applying this concept to the material of the present work, the magnetic transition can affect the mechanical properties, the SFE, and the deformation mechanisms of the material. It has been shown that there is an important magnetic contribution on the SFE. According to Pepperhoff et al.,[74] magnetic orientations influence the atomic structure and the interactions between the atoms, also Néel transition contributes to the change in the Gibbs energy.[22] According to ab initio calculations shown in Section III–C, the SFE value for Fe60Cr20Mn20–C + N system with magnetic contributions is 35.32 mJ/m2, whereas 42.93 mJ/m2 is the value predicted without magnetic contributions, which supports the importance of magnetism and, consequently, the activation of the different deformation mechanisms. Gavrilyuk et al.[1] have reported a SFE of 40 mJ/m2 for the FeCrMn–C + N alloy, suggesting TWIP and dislocation glide as deformation mechanisms. As reported by DeCooman[75] some empirically ranges have been proposed by various authors[27,76,77,78] at which deformation mechanisms are activated depending on the SFE, the variation in the ranges could be attributed to the composition of the studied alloys, for instance, the amount of Mn has an important effect in the SFE of antiferromagnetic alloys.[29]

The development of new texture is one of the significant changes that a material might go on during a deformation process, describing the preferential orientation of the grains in certain directions. The maximum Néel temperature measured (TN) corresponds to 233.08 K and it is observed in the material with a 20 pct deformation, which has a greater texturing than the samples with 0 and 10 pct of deformation, suggesting that texturing of the material could have an effect on the magnetic transition temperature of the alloy.

Interestingly, the Néel temperature is close to the reported DBTT (224.15 K) of the investigated material,[1] and possibly the magnetic transition could influence excess free energy according to the Inden model, affecting the stability of the austenite and the impact toughness.

5 Conclusions

Following conclusions can be addressed from the previous work:

  • Alloys under study have a fully austenitic structure with an average grain size of 100 \(\mu \)m, the presence of ε or α martensite is not observed in any of the samples. With increasing deformation lattice parameter increases causing reflections to shift slightly toward smaller angles. Main deformation mechanisms are identified as slip dislocation and TWIP.

  • Ab initio calculations showed that C and N as alloying elements enhance the stability of the FCC phase, and that magnetic ordered state modifies the phase stability. For the system Fe60Cr20Mn20, a ferromagnetic state is found at T = 0 K, while an antiferromagnetic/ferromagnetic state was determined for Fe60Cr20Mn20–C + N.

  • VSM test showed that the alloy has a linear dependence of magnetization on the applied external field. Magnetization increases with increasing temperature. For deformed samples there is a decrease in the magnetization of the alloy.

  • All samples undergo a paramagnetic-to-antiferromagnetic transition at the Néel temperature. A considerable change in the experimental magnetic response of the material was noticed when it has been deformed to 10 pct, but its magnetic properties were not very sensitive to variations in the deformation of 20 and 30 pct having similar values of Néel temperature, magnetization, and magnetic susceptibility as it was expected.

  • Néel temperature estimated through the three different methodologies (VSM, Warnes, and King equation and ab initio) are in concordance having values of 227.89 K 212.24 K and 248 K, respectively. The Curie–Weiss law indicates that at 0 K, the material is antiferromagnetic.

  • The information provided support to the assertion that the defect density must also be taken into account when describing the magnetic properties of this class of materials, in addition to the structural phase.

  • These type of materials are suitable for applications at low temperatures as structural components.