Tuning the exchange bias effect via thermal treatment temperature in bulk Ni₅₀Mn₄₂In₃Sb₅ Heusler alloys

As a key physical phenomenon in spin electronic device, the exchange bias (EB) effect has been widely studied in Fe-Mn-Ga, La-Sr-Co-Mn-O, and Ni-Mn-X (X = In, Sb, and Sn) systems not only for fundamental scientific interest but also for the different potential applications, such as ultrahigh density magnetic recording, giant magnetoresistance, and spin valve devices. ^1–4) Owing to the presence or copresence of various magnetic states [e.g. antiferromagnetism (AFM), ferromagnetism (FM), spin glass (SG), superspin glass (SSG) and reentrant spin glass (RSG)]. ^5–9) NiMn-based Heusler alloys are an important class of materials exhibiting various EB effects. ¹⁰⁾ For example, Pan et al. reported a giant conventional exchange bias (CEB) field of 5.3 kOe in the SSG Mn₅₀Ni₃₈Al₁₂ bulk Heusler alloy after field cooling (FC) under 3 T at 2 K, which is contributed to the enhanced AFM and the corresponding pinning effect. ¹¹⁾ Wang et al. obtained a large spontaneous exchange bias (SEB) in bulk Ni-Mn-In Heusler alloys, due to the formation of super ferromagnetic unidirectional anisotropy during the initial magnetization process. ¹²⁾ Apparently, the type and behavior of spin glass state at low temperatures is one of the important factors generating and affecting the EB effect. On the other hand, the nature of SG is strongly influenced by the composition, and in the case of Heusler alloys, it is the Mn-Mn exchange interaction. ¹³⁾ In particular, a stoichiometric excess of Mn will reduce the Mn-Mn distance compared with its austenite counterpart and combine with the Ni-Mn hybridization, leading to an enhanced fluctuation between AFM and FM. ¹⁴⁾ The metastable state with long-range disordered frozen FM clusters and AFM matrix is defined as spin glass. ¹⁵⁾ Thus, in the past, the most common strategy to tuning the EB effect was to control the nature of spin glass by adjusting the composition. ¹⁶⁾ For example, we had previously constructed an interesting transition from cluster spin glass (CSG) to SSG at low temperature tuned by Sb-doping in Ni₅₀Mn₃₈Ga_12-xSb_x Heusler alloys and obtained a large SEB of 2930 Oe in SSG Ni₅₀Mn₃₈Ga₁₀Sb₂ at 2 K. ¹⁷⁾ In addition to the strategy of tuning composition, Czaja et al. recently observed a significant change of both the martensite transformation starting temperature (M_S) and the exchange bias field (H_EB) upon increasing the thermal treatment temperature. ¹⁸⁾ They attributed this phenomenon to the combined influence of grain size enlargement and composition change resulting from the metastability of the phase at elevated temperatures. However, there are few reports focusing on the effect of thermal treatment temperature on tuning the EB effect by changing the SG behavior.

Herein we have prepared bulk Ni₅₀Mn₄₂In₃Sb₅ Heusler alloy, since an interesting magnetic phase transition was demonstrated in Ni₅₀Mn₃₆Sb_14-xIn_x in our previous work, first from paramagentic (PM) austenite to AFM martensite, and then into SG. ¹⁹⁾ On the other hand, Cong et al. reported a transition from superparamagnetic (SPM) to SSG states in Ni_50-xCo_xMn₃₉Sn₁₁. ²⁰⁾ As analyzed, these two magnetic states were proved to have a decisive influence on the magnetic properties. In addition, due to the increase of the M_S with the increase of Mn content, the Ni₅₀Mn₄₂In₃Sb₅ alloys were quenched at different temperatures 1173 and 473 K, which were respectively higher and lower than the M_S (about 550 K). The structure and magnetic properties of the samples were studied, and it was found that two samples with different magnetic states were obtained through different thermal treatment temperatures. They were frozen into SG and SSG at low temperatures after field cooling and zero-field cooling, resulting in two totally different EB effects.

Ni₅₀Mn₄₂In₃Sb₅ alloys were prepared via the arc melting method using Ni, Mn, In, and Sb elements (99.99% purity) in a high-purity Ar atmosphere. The samples were then sealed in a quartz tube filled with Ar and annealed at 1173 K for 12 h. Some of the alloys were then quenched directly at 1173 K by water, while others were slowly cooled to 473 K followed by quenching, named as AWQ1173 and AWQ473, respectively. The crystal structures at room temperature were determined using powder X-ray diffraction (XRD) using a Bruker D8 advanced X-ray diffractometer (Bruker, D8 ADVANCE, Germany) with Cu Kα1 radiation (λ = 1.54056 Å). The magnetic properties, including the magnetization–temperature (M-T) curve in the ZFC and field heating (FH) modes, the AC susceptibility, and the magnetic hysteresis (M–H) loops after the ZFC and FC processes, were measured via a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, MPMS-XL-5).

From the XRD patterns in Fig. 1(a), we had refined the XRD results at 300 K through Le Bail fitting, and found that the crystals were both in line with the seven-layer modulated (14 M) martensite structures. ²¹⁾ The calculated lattice parameters are a = 4.3655 Å, b = 5.7280 Å, c = 29.1283 Å, β = 92.871° and a = 4.3392 Å, b = 5.7761 Å, c = 29.2020 Å, β = 93.273° for AWQ1173 and AWQ473, respectively, which is almost same. The space groups are both P2₁/m. In this case, the (2 1 0) peak of 14 M martensite modulation structure basically overlapped with the (2 2 0) peak of L2₁ austenite structure. ²²⁾ On the other hand, it is well known that the process of quenching could partially retained the high-temperature phase. Thus, the difference in peak intensity for two samples was mainly caused by the residual austenite. Compared with the sample of AWQ1173, the martensite transformation of AWQ473 was more complete, resulting in a weak peak intensity at the position of 14 M (2 1 0). Therefore, the thermal treatment temperatures did not have a great impact on the sample structures in this case. As the M-T curves drawn in Figs. 1(b1) and 1(b2), the two species exhibited a similar magnetic phase transition. Upon decreasing the temperature, the typical feature of SG, a splitting between the ZFC and FH, can be clearly observed, which may be due to the interaction between the FM and AFM orders. It has been reported that spin freezing occurs collectively in the magnetic clusters of some Heusler alloys, leading to a frustrated magnetic state at low temperatures. ²³⁾ Although the splitting behavior are both found in the two samples, the peak temperatures of the ZFC are different, 93.9 K for AWQ1173 and 108.2 K for AWQ473, respectively. At the same time, the temperature at which the splitting of the ZFC and FH curves starts also changes greatly, and the magnetization of the AWQ473 is about ten times that of the AWQ1173. Thus, it is believed that the two samples are in different magnetic states after quenching: the spin freezing is easier to occur at higher temperature in the AWQ473 as the temperature decreases, resulting in a difference in the spin freezing temperature. Normally, the homogeneous and inhomogeneous freezing will create two different SG-like states, SSG and SG cluster, respectively. ²⁴⁾ It is noted that the size of SSG clusters is smaller and the interactions among the magnetic clusters are stronger than that of SG. And as a result, the two states will cause two different EB effects.

Zoom In Zoom Out Reset image size

To further investigate the nature of the two species at low temperature, the real part of AC susceptibility (χ') was performed ranging from 13 to 633.3 Hz in the presence of an AC field of 2 Oe. From the real part of AC susceptibility χ', the characters of magnetic phase transitions of the alloys varying temperature could be observed, such as the appearance of peaks and the frequency relaxation. As seen in Figs. 2(a) and 2(b), a prominent peak was observed in both χ'(T) curves, which was defined as the spin freezing temperature T_f . In addition, another typical nature of SG-like behavior, shifting of the characteristic peak T_f towards higher temperatures with increasing of measured frequencies is observed in AC susceptibility as well. Herein, the frequency dependence of T_f in the χ'(T) curves can be quantified using the following expression: ²⁴⁾

$$\begin{eqnarray}&&{\rm{\Phi }}=\displaystyle \frac{{\rm{\Delta }}{T}_{f}}{{T}_{f}{\rm{\Delta }}\left({\mathrm{log}}_{10}f\right)}\end{eqnarray} \tag{ 1 }$$

where Φ is the empirical parameter, and ∆T_f is the total change in the frequency interval. Normally, the value of Φ can be used to describe the magnetic order of the system: 0.03 < Φ < 0.06 for SG, and 0.005 < Φ < 0.02 for SSG. ²⁵⁾ As calculated, two vastly different Φ (0.06 for for AWQ1173 and 0.013 for AWQ473) were obtained, indicating the presence of two different glass behaviors SG and SSG for AWQ1173 and AWQ473, respectively.

Zoom In Zoom Out Reset image size

Since the SSG state is a medium to strong interaction regime (homogeneous freezing), the possibility of obtaining the SSG behavior in AWQ473 was further investigated using the conventional critical slowing down model based on the AC magnetic susceptibility. ²⁶⁾ In this model the characteristic relaxation time, τ₀, diverges at the transition temperature according to:

$$\begin{eqnarray}&&{\tau }_{}\,=\,{\tau }_{0}{\left(\displaystyle \frac{{T}_{f}}{{T}_{g}}-1\right)}^{-zv}.\end{eqnarray} \tag{ 2 }$$

For weak interacting magnetic regimes (inhomogeneous freezing) such as SG state, the frequency dependence of T_f is given by the Vogel–Fulcher law: ²⁶⁾

$$\begin{eqnarray}&&{\tau }_{}\,=\,{\tau }_{0}\exp \left(\displaystyle \frac{{E}_{a}}{{k}_{B}\left({T}_{f}-{T}_{g}\right)}\right)\end{eqnarray} \tag{ 3 }$$

where T_g is the value of T_f in the zero-frequency limit, τ₀ is the relaxation time of the individual particle magnetic moment, zv is the critical exponent of the correlation length, E_a is the activation energy, and k_B is the Boltzmann constant. The divergence of the correlation length or, equally, the relaxation time near T_g , indicates the presence of a true equilibrium thermodynamic phase transition. Our fitting with Eqs. (2) and (3) shows a good agreement with the experimental data and the obtained values of τ₀, T_g , E_a /k_B , and zv are listed in Table I. The values of τ₀ and zv for AWQ473 obtained using the conventional critical slowing down model are 2.744 × 10⁻¹¹ s and 4.867, respectively, fitted to reported range for SSG (10⁻¹² s < τ₀ < 10⁻⁹ s, 4 < zv < 12). ²⁷⁾ The plot of ln(τ) versus ln[(T_f -T_g )/T_g ] and the plot of ln(ω) versus 1/(T_f -T_g ) for the AWQ1173 and AWQ473 samples are drawn in Figs. 2(c) and 2(d), respectively. As seen, they both exhibit an obvious linear dependence and are both evidenced in two curves, which is further proved to be the existence of SG and SSG behavior at low temperatures as reported in the literature. For weak interacting regime of SG, the fitted values of E_a /k_B , τ₀, and T_g for AWQ1173 derived using the Vogel-Fulcher law are approximately 45 K, 3.328 × 10⁻⁶ s, and 42.004 K, respectively, well fitted to SG systems as reported before. ²⁸⁾ It could be seen that two completely different spin glasses were formed at low temperatures by two quenching temperatures, namely SG and SSG.

Table I. Fitting parameters used in different models for the AWQ1173 and AWQ473 Ni₅₀Mn₄₂In₃Sb₅ alloys.

Models	Parameter	AWQ1173	AWQ473
Model-independent	${\rm{\Phi }}$	0.06	0.013
	Tg (K)	42.004	156.090
Critical slowing down	${\tau }_{0}$ (s)	2.226 × 10−7	2.744 × 10−11
	zν	5.058	4.867
Vogel–Fulcher	${\tau }_{0}$ (s)	3.328 × 10−6	3.745 × 10−6
	Ea/kB (K)	45.277	24.348

As previous reported, the EB effect in some Heusler alloys can be attributed to the exchange coupling between the SG and the AFM matrix, since the short-range ordered FM clusters are assumed to be formed in the SG state during application of an external field in the cooling process. ²⁹⁾ Recently, it was found that H_EB depends strongly on the size of the FM clusters in the AFM matrix. ³⁰⁾ The size of the FM clusters in the SG and SSG systems are different at varying temperatures under ZFC and FC processes, resulting in a huge difference in the EB effect. In the present study, due to the significantly larger magnetization of the AWQ473 sample and the existence of large difference in the Φ parameter between these two alloys with different thermal temperature, it is speculated that the SG and SSG states may result in different EB effects at temperatures below T_g .

To figure it out such ideas, the M-H curves at 2, 50, and 150 K under different external cooling magnetic fields of two samples were measured in Fig. 3, and as expected, totally two different evolution of EB effects were identified. The H_EB reached a maximum of 9063 Oe at 2 K after FC under 2 T (2TFC) for the AWQ473 sample, which is the maximum value reported for NiMn-based Heusler alloys so far and is of great significance for improving the giant magnetoresistance effect. The H_EB under ZFC is 143 Oe at 2 K, which is almost negligible compared with the EB after FC. As can be seen from Table II, as the temperature increases, the relatively large clusters in the pinning phase transition toward a new pinned phase because of the increase in the thermal activation energy; leading to a decrease of H_EB. In contrast, the AWQ473 exhibited a prominent SEB of 581 Oe at 2 K after ZFC, which is four times that of AWQ1173. Such SEB obviously comes from exchange occurring between the SSG and the AFM matrix. With temperature increasing, the H_EB remained 166 Oe up to 150 K, which is equivalent to that of AWQ1173 at 2 K. Meanwhile, AWQ473 only has an H_EB of 29 Oe at 150 K, almost zero. Although the H_EB about 166 Oe is not large, the relatively high temperature (about 150 K) that produces this EB effect is of great significance to practical applications. This result has a great guiding significance for the preparation of high-performance SEB materials through the thermal treatment.

Zoom In Zoom Out Reset image size

From Fig. 3, AWQ1173 exhibited an obvious AFM state at 150 K without the SG exchange. However, the M-H curve for AWQ473 at 150 K could be more likely attributed to a SPM state because the corresponding hysteresis loop has a sigmoidal shape and shows no coercivity or remanence. ³¹⁾ In order to study the magnetic properties of AWQ473 above T_g ≈ 150 K, the M-H curves were measured between 150 and 300 K, and the magnetization data were fitted using two different Langevin equations. In Fig. 4(b), the M-H curves were fitted with a general Langevin equation [Eq. (4)], and as compared, a modified Langevin equation was used to fit the data in Fig. 4(a) [Eq. (5)]. ³²⁾ These equations are as follows:

$$\begin{eqnarray}&&{\rm{M}}\left(H\right)=N\mu \left[\coth \left(\xi \right)+\displaystyle \frac{1}{\xi }\right]\end{eqnarray} \tag{ 4 }$$

and

$$\begin{eqnarray}&&{\rm{M}}\left(H\right)=N\mu \left[\coth \left(\xi \right)+\displaystyle \frac{1}{\xi }\right]+{\chi }_{0}H\end{eqnarray} \tag{ 5 }$$

where N is the density of particles with average cluster magnetic moment μ, and ξ = μ₀ μH/k_B T, with k_B being the Boltzmann constant. It was found that all the M-H curves of AWQ473 from 150 to 300 K can be well fitted using a modified Langevin equation. Based on the fitting analysis, Eq. (5) with the extra χ₀ H term results in a better fit to the magnetization data. The susceptibility (χ₀) in the magnetic context indicates the magnetizable degree of an object. In this case, it is highly affected by the AFM matrix, the hysteresis loop of which is almost equivalent to M(H) = χ₀ H. The resultant values of N, μ, and χ₀ obtained from the fittings vary with temperature. As an example, fitting the curve at 200 K, which is well below the martensite transition temperature and above T_g , yields the following refined parameters: N = (4.64 ± 0.15) × 10²⁵ m⁻³, μ = (1.17 ± 0.03) × 10³ μ_B , and χ₀ = (6.24 ± 0.02) × 10⁻⁷ m³ kg⁻¹, indicating that the intermediate (T_g  ≤ T ≤ M_s) martensite phase has a SPM nature. ²⁰⁾ The obtained value of μ is a little larger compared with that of previous reports, ⁸⁾ implying the large size of SPM clusters. From the fitting results, as the temperature decreases, the SPM effect of the AWQ473 becomes more significant, and the size of the SPM clusters also increases accordingly. As the AFM exchange is reflected in the hysteresis loop, the well fitted modified Langevin equation of Eq. (5) shows that the SPM clusters are embedded in the AFM matrix, which generates a non-negligible SEB at 150 K.

Zoom In Zoom Out Reset image size

Herein, it is believed that the difference in EB effect is contributed to the thermal temperature. After the Ms, the AWQ1173 and AWQ473 samples are in an AFM and SPM state, respectively. At lower temperatures, the magnetization of the martensite progressively increases as it undergoes FM ordering at T_g . Below that temperature, the cusp in the ZFC curve marks the value of T_f , highlighting the point at which the systems enter a non-homogeneous magnetic state, manifested by the typical splitting between the ZFC and FC curves. Given the SG and SSG appearance for the AWQ1173 and AWQ473, respectively, it is inferred that at least one of the components of this low-temperature state should be an FM cluster. Therefore, during the 2TFC process, the AFM state of the AWQ1173 is frozen into a SG state and produces pinning, resulting in a large EB value. However, in the ZFC process, the AFM freezing cannot be driven by the external magnetic field; therefore, no large SG clusters are produced, and the EB effect is almost zero. However, the SPM AWQ473 sample is cooled to about 150 K in zero field, and the large SPM cluster is frozen to SSG clusters. This behavior is similar to the phenomenon in the magnetic nanoparticles, that the interactions among the magnetic clusters are negligible compared to the thermal energy at higher temperatures and the system shows SPM behavior. As cooling below blocking temperature, the interactions become much stronger than the thermal energy, and the clusters then would collectively freeze into the SSG state. A pinning effect is produced by the exchange between the FM cluster and the AFM matrix in the SSG state, resulting in a SEB. Therefore, the magnetization intensity in this case is significantly higher than that of the AWQ1173 sample in the AFM matrix under an external magnetic field.

In this work, we had synthesized the Ni₅₀Mn₄₂In₃Sb₅ Heusler alloys at two different quenching temperatures, and demonstrated that the fluctuations at low temperature and the corresponding EB effects could be successfully controlled accordingly. As analyzed by empirical parameter Φ, Critical slowing down law, and Vogel-Fulcher law, we contribute such huge difference in the EB effect to the presence of SG and SSG, which is frozen from AFM and SPM, respectively. Through the Langevin equation and the modified Langevin equation, the SPM embedded in the AFM matrix of AWQ473 is confirmed and studied. This investigation was the first time to find the effect of heat treatment temperature on the behavior of spin glass, which is of great significance to seeking Heusler alloys with suitable characteristics for the next-generation devices.

Acknowledgments