Doping Effects on Magnetic and Electronic Transport Properties in (Ba_1−xRb_x)(Zn_1−yMn_y)₂As₂ (0.1 ≤ x, y ≤ 0.25)

Abstract

Diluted magnetic semiconductors (DMSs) represent a significant area of interest for research and applications in spintronics. Recently, DMSs derived from BaZn₂As₂ have garnered significant interest due to the record Curie temperature (T_C) of 260 K. However, the influence of doping on their magnetic evolution and transport characteristics has not been thoroughly investigated. This study aims to fill this gap through susceptibility and magnetization measurements, electric transport analysis, and muon spin relaxation and rotation (µSR) measurements on (Ba_1−xRb_x)(Zn_1−yMn_y)₂As₂ (0.1 ≤ x, y ≤ 0.25, BRZMA). Key findings include the following: (1) BRZMA showed a maximum T_C of 138 K, much lower than (Ba,K)(Zn,Mn)₂As, because of a reduced carrier concentration. (2) A substantial electromagnetic coupling is evidenced by a negative magnetoresistance of up to 34% observed in optimally doped BRZMA. (3) A 100% static magnetic ordered volume fraction is achieved in the low-temperature region, indicating a homogeneous magnet. (4) Furthermore, a systematic and innovative methodology has been initially proposed, characterized by clear step-by-step instructions aimed at enhancing T_C, grounded in robust experimental findings. The findings presented provide valuable insights into the spin–charge interplay concerning magnetic and electronic transport properties. Furthermore, they offer clear direction for the investigation of higher T_C DMSs.

1. Introduction

Diluted magnetic semiconductors (DMSs) [1,2,3,4] are crucial for studying the complex interactions between magnetism and transport properties, with significant potential for spintronic applications [5,6,7]. Among them [3], diluted ferromagnetic semiconductors (DFSs), such as (Ga,Mn)As and its related III–V compounds, have been extensively researched [2,7,8,9] since their initial discovery [10] and subsequent advancements [11]. However, their fabrication into thin films is limited to low-temperature molecular beam epitaxy (LT-MBE) [2], restricting access to key physical measurements, such as neutron scattering for magnetic structure detection [6]. Furthermore, controlling charge and spin concentration doping separately in manganese (Mn)-doped III-V DFSs is difficult due to the partial substitution of trivalent gallium (Ga³⁺) with divalent Mn²⁺. This limitation hinders comprehensive investigations into individual carriers and spin doping effects, intensifying the debate over microscopic description of magnetic interactions [8,12].

Since 2011, a new class of DFSs with independent spin and charge doping mechanisms has emerged [13], confirming theoretical predictions [14], and driving substantial experimental research growth [4]. Among these new material systems, BaZn₂As₂ (BZA)-based DFSs have garnered significant attention due to their exceptionally high Curie temperature (T_C) of 260 K [15], and their exotic properties [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. Previous research shows that the parent compound BaZn₂As₂ crystallizes in the ThCr₂Si₂-type structure at high temperatures exceeding 900 °C, which is characterized by the space group I4/mmm [16]. This compound is a non-magnetic semiconductor with a bandgap of approximately 0.2 eV, in which carrier and spin co-doping could indue ferromagnetism [16,32,33,34,35,36]. The valence states of barium (Ba), zinc (Zn), and arsenic (As) are +2, +2, and −3, respectively, to attain electrochemical equilibrium. Although manganese (Mn) is a multi-valent ion, its valence in BZA DFSs is 2+, as confirmed by the Mn L₂,₃-edge X-ray absorption spectroscopy (XAS) (see figure 2 in Ref. [19]). Consequently, carriers can only be introduced through the replacement of Ba²⁺ with K⁺ or Rb⁺. Despite the passage of over a decade since the demonstration of carrier doping effects through Ba²⁺/K¹⁺ substitution in (Ba,K)(Zn,Mn)₂As₂ (BKZMA) DFSs using magnetization techniques [16], a comprehensive investigation that separately examines the effects of both carrier and spin doping within this material system has yet to be conducted. This study seeks to address this gap for the first time by investigating the newly fabricated polycrystalline specimens (Ba,Rb)(Zn,Mn)₂As₂ (BRZMA) DFSs using magnetization, electrical transport, and muon spin rotation/relaxation/resonance (µSR) measurements. More importantly, we also propose a systematic and innovative methodology, characterized by clear step-by-step instructions aimed at enhancing T_C, grounded in robust experimental findings.

2. Materials and Methods

Polycrystalline specimens of (Ba_1−xRb_x)(Zn_1−yMn_y)₂As₂ (where x = 0.10, 0.15, 0.20, and 0.25; y = 0.10, 0.15, 0.20, and 0.25) were synthesized using a solid-state reaction method [13,16,37] with high-purity reagents produced by Alpha Company. The precursor materials, BaAs and RbAs, were initially sintered at 500 °C and 200 °C for 40 h, respectively, in a sealed titanium tube containing high-purity Ba, rubidium (Rb), and As. These precursors, along with Zn, Mn, and As powders, were loaded into a titanium tube according to the nominal composition of (Ba,Rb)(Zn,Mn)₂As₂, under an argon atmosphere at 1 atm pressure, before being placed in a quartz tube. The mixtures were gradually heated to 750 °C at a rate of 3 °C/min and maintained at that temperature for 20 h before cooling to room temperature at a rate of 2 °C/min at the Institute of Physics, Chinese Academy of Siences (IoPCAS) in Beijing, China. The specimens were analyzed using X-ray powder diffraction with a Philips X’pert diffractometer employing Cu Kα radiation at room temperature at the IoPCAS in Beijing China. Direct current (DC) magnetic susceptibility was characterized by using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design), while electrical transport measurements were conducted using a four-probe technique on a physical property measurement system (PPMS, Quantum Design) at the IoPCAS in Beijing China. Positive muon spin relaxation (μSR) measurements were performed on polycrystalline specimens (Ba_0.8Rb_0.2)(Zn_0.85Mn_0.15)₂As_2, which measure approximately 5 mm in diameter and 6 mm in thickness, at TRIUMF in Vancouver, Canada.

3. Results and Discussions

3.1. Crystal Structure Characterization

Like the parent compounds, β-BaZn₂As₂ and BKZMA [16], (Ba_1−xRb_x)(Zn_1−yMn_y)₂As₂ (where x = 0.10, 0.15, 0.20, and 0.25; y = 0.10, 0.15, 0.20, and 0.25) also crystallizes in the ThCr₂Si₂-type structure, as illustrated in Figure 1. This compound features alternating layers of Ba or Rb, and (Zn,Mn)As, formed from edge-sharing ZnAs₄ tetrahedra, resulting in a quasi-two-dimensional (2D) architecture (Figure 1a). The X-ray diffraction (XRD) patterns (Figure 1b) and the refined data obtained from the powder specimen of (Ba_0.8Rb_0.2)(Zn_0.85Mn_0.15)₂As₂, analyzed through Rietveld refinement (Figure 2), can be accurately indexed to a single phase. The resultant weighted reliability factor (R_wp) is approximately 6.84%, which shows a reliable analysis.

The larger ionic radius of Rb⁺ (1.52 Å) compared to Ba²⁺ (1.35 Å) results in a monotonic variation in lattice parameters with Ba²⁺/Rb⁺ replacement (Figure 3a), with the coordination numbers of six, consistent with Vegard’s law [38] and confirming successful chemical doping. Vegard’s law for alloyed materials is a linear function: E_alloy = xE_A +(1 − x)E_B, where E_A, E_B, and E_alloy are the respective properties of pure A, Pure B, and the alloy A_xB_1−x, and x is the fraction of one ingredient in a materials point. The replacement of Zn²⁺/Mn²⁺ magnetic ions shows distinct behaviors, as illustrated in Figure 3b. The unit cell volume increases due to the smaller ionic radius of Zn²⁺ (0.60 Å) compared to Mn²⁺ (0.66 Å), with the coordination numbers of four. However, there was an increase in the a-axis and a decrease in the c-axis. It is important to note that the length of the c-axis is approximately three times greater than that of the a-axis. We infer that this discrepancy is due to the distortion of the (Zn,Mn)As₄ tetrahedra, which results from the combined effects of differing ionic radii and magnetic coupling. A similar trend was noted in the BZA-based DFSs (see figure 1b in Ref. [17]).

3.2. Magnetic and Electronic Transport Properties

Under an external magnetic field of 500 Gauss (Oe), the magnetic susceptibility measured during zero-field-cooled (ZFC, represented by empty symbols) and field-cooled (FC, represented by solid symbols) for (Ba_1−xRb_x)(Zn_0.85Mn_0.15)₂As₂ (where x = 0.10, 0.15, 0.20, and 0.25) is illustrated in Figure 4. It is widely acknowledged that the ferromagnetic ordering temperature, commonly referred to as the T_C, is associated with the transition of spontaneous magnetization from a value of zero to a non-zero state. This transition reflects the magnitude of the exchange integral from a microscopic perspective.

The Curie–Weiss law represents one of the most straightforward methodologies for determining the value of T_C [39], as evidenced in various similar DMS materials with the independent spin and charge doping mechanism [13,16,17,26,30,37,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58]. Following the same idea, we also employed a modified Curie–Weiss law [39] to ascertain the T_C, as detailed below.

$$\chi ={\displaystyle \frac{C}{T-{\theta }_{cw}}}+{\chi }_0$$

where C is the Curie constant, and $\theta$_cw refers to the Curie–Weiss temperature or T_C. Compared to the typical Curie–Weiss law, a temperature-independent small positive susceptibility (${\chi }_0$) was added. This may be attributed to Pauli paramagnetism [39], originating from the non-localized conduction electrons via Ba²⁺/Rb¹⁺. The sample (Ba_0.8Rb_0.2)(Zn_0.85Mn_0.15)₂As₂, illustrated in Figure 5, serves as a representative example. In DMSs, the transition from paramagnetic to ferromagnetic states generally occurs over a relatively wide range of temperature regions [1,6,7]. A comparable phenomenon is clearly observable in the first-order analysis of magnetic susceptibility for BRZMA, particularly in the derivative d(M/H)/dT, as illustrated in Figure 5 (red line). Significant changes are observed starting at approximately 150 K, reaching a maximum around 99 K, which strongly indicates that the transition center, T_C, is unequivocally situated within this region. It can be stated that we are able to ascertain relatively accurate values by employing optimized analysis temperature regions in conjunction with the modified Curie–Weiss law [39]. As shown in Figure 5, a maximum value of approximately 149 K and a minimum value of 124 K were obtained across different temperature analysis regions. We chose the fitting temperature region from 200 K to 300 K to determine the T_C with the value of approximately 138 K. This value is further substantiated by the subsequent results from muon spin rotation (µSR; see Figure 11a presented in the section on static and dynamic magnetism). Briefly speaking, the static ordered volume fraction, f_M, generally begins to increase near the transition temperatures of magnetic materials and ultimately attains 100% in homogeneous magnets at a sufficiently low temperature [59]. In the BRZMA system, with a Rb value of 20% and a Mn value of 15%, f_M demonstrates a variation from 6% at 136 K to 17% at 118 K, which corresponds precisely with the estimated critical temperature (T_C) of 138 K. In this respect, more insight will be given in the following sections.

For a comparable analysis, we utilized the same fitting regions ranging from 200 K to 300 K to ascertain all values of T_C in (Ba_1−xRb_x)(Zn_1−yMn_y)₂As₂ (0.1 ≤ x, y ≤ 0.25), as illustrated in Figure 4a and Figure 6a. The values presented are subsequently summarized in

Table 1. Summary of magnetic and electric transport results for (Ba,Rb)(Zn,Mn)As systems. H_C is the coercivity, while M_r is the magnetic remanence after the subtraction of a small T-linear contribution for a comparable analysis, though some doped materials seem not totally saturated. MR is the negative magnetoresistance measured at 2 K, with an external magnetic field of up to 7 T.

(Ba1−xRbx)(Zn1−yMny)2As2		TC (K)	HC (Oe)	Mr (μB per Mn)	MR (7 T, 2 K)
x	y
0.10	0.15	15.2 ± 1.7	1400	0.40	24%
0.15	0.15	138.3 ± 0.9	9900	0.91	33%
0.20	0.15	138.3 ± 0.7	12,900	1.07	34%
0.25	0.15	105.8 ± 0.7	11,600	0.83	31%
0.20	0.10	80.8 ± 1.0	8400	0.70	12%
0.20	0.20	131.1 ± 0.9	7400	0.54	31%
0.20	0.25	125.3 ± 1.4	5300	0.43	33%

. An initial increase in the doping levels of Rb or Mn results in a corresponding increase in T_C, which is followed by a decrease, suggesting the existence of an optimal doping concentration. Furthermore, the optimal doping levels of Rb at 20% and Mn at 15% can also be characterized by the maximum values of both the coercive force (H_C = 1.29 T) and the magnetic remanence (M_r = 1.07 µB), as illustrated in Figure 4b and Figure 6b, which are also summarized in Table 1.

Figure 7 presents the magnetoresistance (MR) in BRZMA, where MR is defined as MR = [ρ(μ₀H) − ρ(0)]/ρ(0). Though various DMSs exhibit this characteristic behavior [8,60,61], the underlying physics of MR becomes increasingly intricate due to the interplay of multiple degrees of freedom [62,63], which include spin, charge, orbital, and lattice dynamics, in addition to factors such as disorder and strong electron correlation. Nonetheless, it is evident that doping effects can effectively tune the MR in BRZMA, as illustrated in Figure 7a,b. As the levels of Rb doping increase, the MR value initially exhibits an increase, followed by a subsequent decrease. A comparable trend in MR values was noted with escalating levels of Mn doping. In conclusion, the MR value reaches its maximum of approximately 34% at the optimal doping levels of Rb and Mn, as summarized in Table 1. Recent investigations into Na(Zn,Mn)Sb [64,65] have clarified the MR effects through modifications in the band structure, both experimentally and theoretically. We infer that a similar explanation may also occur in BRZMA. The introduction of hole carriers by Ba²⁺/Rb¹⁺ modulates the Fermi level, while Zn²⁺/Mn²⁺ involvement gradually adjusts the spin structures. As temperature decreases, spins align to minimize energy, forming a metastable phase at the T_C. External magnetic fields can realign spins and magnetic domains step by step as strength increases from 0 to 7 T. Scattering effects minimize when all spins align and magnetic domains are in one direction, resembling a uniform FM state, resulting in observable MR effects.

The temperature dependence of resistivity, denoted as ρ(T), demonstrates semiconducting characteristics across all specimens of (Ba_1−xRb_x)(Zn_0.85Mn_0.15)₂As₂, where x takes values of 0.10, 0.15, 0.20, and 0.25, as illustrated in Figure 8a. An increase in the Rb doping level correlates with a continuous reduction in the magnitude of ρ(T), indicating the effective introduction of hole carriers. It is important to note that the energy gap is approximately 27 meV, as estimated by the thermal activation model for the sample containing 20% Rb and 15% Mn. Semiconducting behavior was observed in all specimens of (Ba_0.8Rb_0.2)(Zn_1−yMn_y)₂As₂ (where y = 0.10, 0.15, 0.20, and 0.25), as shown in Figure 8b. As the Mn doping levels increase, there is a consistent rise in the magnitude of ρ(T), indicating enhanced scattering effects due to the presence of Mn. Additionally, the specific doping level (x = 0.2, y = 0.15) also yields the highest values for MR, as shown in Figure 7.

3.3. Origin of a Lower T_C

In Table 1, the sample with Rb at 20% and Mn at 15% exhibited a maximum T_C of 138 K, which is significantly lower than that of BKZMA. Previous research on BKZMA [15] has revealed that a sufficient carrier concentration can suppress the short-range antiferromagnetic interactions between the nearest Mn-Mn pairs, thereby inducing a higher T_C. We infer that the lower carrier concentration in BRMZA results in a lower T_C. Consequently, we have measured the Hall effect in the sample with Rb at 20% and Mn at 15% using a homemade Hall bar structure, as shown in Figure 9. The raw data are shown in Figure 9a, which contains a significant longitudinal resistance signal resulting from electrode asymmetry. To extract the genuine Hall signal, we performed an antisymmetric process as follows:

$$R_{xy}^{+}\left(B\right)={\displaystyle \frac{R^{+}\left(B\right)-R^{-}\left(-B\right)}{2}}$$

$$R_{xy}^{-}\left(B\right)={\displaystyle \frac{R^{-}\left(B\right)-R^{+}\left(-B\right)}{2}}$$

where $R^{+}\left(B\right)$ and $R^{-}\left(B\right)$ represent the magnetoresistance measured under forward and reverse magnetic field orientations, respectively. Owing to magnetic hysteresis, $R^{+}\left(B\right)$ and $R^{-}\left(B\right)$ exhibit non-overlapping behavior, as illustrated in Figure 9a. The Hall coefficients (R_H), derived from linear fitting of $R_{xy}^{+}\left(B\right)$ and $R_{xy}^{-}\left(B\right)$, are consistent, from which we can get the electron carrier density, $n={\displaystyle \frac{1}{R_{H}et}}=7.14\times {10}^{18} {\mathrm{c}\mathrm{m}}^{-3}$, where t = 0.44 mm is the sample thickness. It should be noted that, in the calculations, we assume a uniform sample thickness and homogeneous current distribution. However, these assumptions are highly idealized for polycrystalline samples, and, thus, the carrier densities can only be estimated to be within an order of magnitude of 10¹⁹ cm⁻³. The summarized results for BRZMA and BKZMA are presented in

Table 2. Summary of the T_C and carrier concentrations for (Ba,Rb)(Zn,Mn)₂As₂ and (Ba,K)(Zn,Mn)₂As₂. Please note that we use the same carrier concentration, 4.30 × 10²⁰ cm⁻³, for all three 10% (Ba,K) substitution samples referenced in [16], based on the fact that Zn²⁺/Mn²⁺ does not introduce additional carriers.

(Ba1−xAx)(Zn1−yMny)2As2			Carrier Concentration (cm−3)		TC (K)	Reference
A	x	Mny
Rb	0.20	0.15	7.14 × 1018	Measured at 2 K	138	Current work
K	0.10	0.05	4.30 × 1020	Measured at 2 K	30	[16]
K	0.10	0.10	4.30 × 1020	Measured at 2 K	40	[16]
K	0.10	0.15	4.30 × 1020	Measured at 2 K	40	[16]
K	0.30	0.15	8.00 × 1020	Measured at 250 K	230	[66]
K	0.30	0.24	3.90 × 1020	Measured at 5 K	260	[15]

, which confirms our hypothesis that lower carrier concentrations lead to a decrease in T_C. The ionic radii of K⁺ (1.38 Å) and Ba²⁺ (1.35 Å) are quite similar; consequently, the carrier can be successfully introduced via K⁺/Ba²⁺ replacement with minimal disruption to the crystal structure. However, the radius of Rb⁺ (1.52 Å) is significantly larger than that of Ba²⁺, making carrier doping considerably more challenging from a crystallographic perspective. In addition, the nominal doping ratio is also different. This may account for the low carrier concentration in the BRZMA system, compared to BKZMA system, despite having the same nominal doping levels.

3.4. Solution for a Higher T_C

According to the results of BRZMA, we know that there exist optimal doping levels for carrier and spin concentrations. Consequently, we can tune the magnetism to achieve a higher T_C through the following methods in both the exploration of new materials and the modification of the properties of existing materials. Let us consider BKZMA as a case study, as it holds a record T_C of 260 K [15].

Step 1: Estimation of the approximate optimal spin doping level, denoted as Mn_y. Fixing the Ba²⁺/K¹⁺ carrier doping level at a specific sufficient value, such as 35%, enables significant variation in Zn²⁺/Mn²⁺ replacement, which aids in estimating an optimal spin doping level. This is due to a competition between the Mn-Mn antiferromagnetic interaction and the carrier-induced ferromagnetic interactions [32,33,34,35,36]. Increased Mn doping enhances antiferromagnetic interactions; consequently, the maximum T_C occurs with an increase in the Mn doping level.

Step 2: Estimation of the approximate optimal carrier doping level, denoted as K_x. Fixing the spin concentration with the value of Mn_y then enables significant variation in Ba²⁺/K¹ replacement. In addition to the current studied BRZMA case, it is worth noting that the phenomenon of the optimal level of carrier occurs in various DMSs, such as Li(Zn,Mn)P [40,41] and (Sr,Na)(Zn,Mn)₂As₂ [67].

Step 3: Ascertain the optimal carrier doping level, K_max and Mn_max. It is crucial that there exists a close interplay between the carrier concentration and spin. Consequently, K_x and Mn_y are both independent and interconnected, and they do not correspond to the K_max and Mn_max. Therefore, further fine-tuning of doping levels for K and Mn is necessary to achieve the maximum T_C.

Step 4: Involving chemical pressure. The T_C decreases in BZA-based DMSs when physical pressure is applied [21,22,28]. This decrease is attributed to modifications in the magnetic interactions that result from the changes in the configuration of the (Zn,Mn)As₄ tetrahedra and the strength of interlayer As-As bonding [28]. To be specific, the interlayer As-As distance decreases, while the two As-Zn/Mn-As bond angles change monotonically before the transition of the crystal structure [68]. Furthermore, attempts were also conducted at the As site utilizing chemical pressure [30]; however, no results were obtained at the Ba site. Chemical pressure through equivalent substitution [30] is somehow akin to the physical pressure. In (Sr,Na)(Cd,Mn)₂As₂ DFSs [56], the numerical equivalence relationship between the physical pressure and chemical pressure can even be estimated. Consequently, we could use a small amount of Rb¹⁺ to replace the K¹⁺ in the optimal BKZMA system. Since the radius of Rb¹⁺ (1.52 Å) is bigger than that for K¹⁺ (1.38 Å) and Ba²⁺ (1.35 Å), this replacement could be viewed as an anti-physical pressure effect and, consequently, can increase T_C further. We also suggest that Na¹⁺ (1.02 Å) and Rb¹⁺ could be used together to finely tune the doping effects to achieve optimal results.

Step 5: Just like the (Ga,Mn)As system, post-annealing treatment [6,8,9,11] may also be needed to further enhance the T_C.

In summary, to achieve a higher T_C, we should first determine the optimal carrier doping levels and then apply chemical pressure through equivalent substitution, together with the post-annealing treatment. However, this strategy may be more effective in single crystals with few defects than in polycrystalline samples when solely considering magnetic interactions. It is worth mentioning that the record 260 K [15] in BKZMA is not the ultimate goal.

3.5. Static and Dynamic Magnetism

μSR is a sensitive technique utilized to detect both static and dynamic magnetism in various magnetic and superconducting systems [59,69]. Pioneering μSR research on DFSs focused on thin films subjected to appropriate heat treatment, which demonstrated a sharp transition at the T_C with a complete magnetic volume fraction [70]. Inspired by this, the μSR technique was applied to a new class of DFSs featuring independent spin and charge doping mechanisms to investigate their static and dynamic magnetism [13,16,29,41,47,48,52,67,71,72]. To eliminate the possibility of magnetic impurity clusters in (Ba_0.8Rb_0.2)(Zn_0.85Mn_0.10)₂As₂, we employed the most direct weak transverse field (wTF)-μSR measurements. Figure 10 exhibits the time spectrum, which was analyzed using the following function [59].

Asymmetry (t) = Asy_temp. [cos (γ_μH_extt + θ)] exp(−λ_dt)

The muon gyromagnetic ratio, γ_μ, and the external transverse field, H_ext, are fixed values, while the temperature-dependent asymmetry, Asy_temp., and relaxation rate, λ_d, serve as free parameters. θ represents a phase offset with a fixed value, determined by the initial measured conditions. In the paramagnetic state, the Asy_temp. reaches its maximum value (Asy_max) at 157.8 K and 203.5 K, as depicted in Figure 10a. As the temperature decreases, the Asy_max decreases significantly, as shown in Figure 10b, serving as an indicator of the static ordered volume fraction, f_M. Notably, (1 − Asy_temp./Asy_max) represents f_M and is plotted in Figure 11a. f_M begins to build up when crossing T_C and reaches 100% at sufficiently low temperatures (below 75 K). This indicates that intrinsic homogeneous magnetism has been achieved [59]. Additionally, the relaxation rate, λ_d, is completely suppressed at the base temperature (~2 K). Furthermore, longitudinal field (LF)–μSR measurements were also conducted, verifying the magnetic ground state, as shown in Figure 11b. With the increase in the longitudinal fields to ~2 kOe, the majority part of the sepctra was decoupled; this means that at least the static magnetism dominates the magnetic ground state [59]. With the increase in the longitudinal fields to approximately 2 kOe, the majority of the spectra was decoupled. This indicates that static magnetism predominantly determines the magnetic ground state. Considering the big coercive force (~1.29 T), 100% f_M, and zero λ_d, we can infer that there exists no dynamic magnetism at the base, just similar to the homogeneous magnet Li(Zn,Mn)As [65], in contrast to the SG CuMn [69] and Na(Zn,Mn)Sb [65], or the asperomagnet (Ba,Na)(Zn,Mn)₂As₂ [73], in which static and dynamic magnets co-exist. This hypothesis could be tested in the future by increasing the longitudinal field to a higher value, such as 4 kOe.

Figure 11. (a) Analyzed results of (Ba_0.8Rb_0.2)(Zn_1−yMn_y)₂As₂, obtained from the wTF spectrum. Static ordered volume fraction, f_M, and the relaxation rate, λ_d, as functions of temperature. The blue rows indicate the T_C, which is derived from the Curie–Weiss law and the d(M/H)/dT, respectively. (b) Longitudinal field (LF)–μSR spectra of (Ba_0.8Rb_0.2)(Zn_1−yMn_y)₂As₂ were measured at a base temperature of T = 2 K.

Figure 11. (a) Analyzed results of (Ba_0.8Rb_0.2)(Zn_1−yMn_y)₂As₂, obtained from the wTF spectrum. Static ordered volume fraction, f_M, and the relaxation rate, λ_d, as functions of temperature. The blue rows indicate the T_C, which is derived from the Curie–Weiss law and the d(M/H)/dT, respectively. (b) Longitudinal field (LF)–μSR spectra of (Ba_0.8Rb_0.2)(Zn_1−yMn_y)₂As₂ were measured at a base temperature of T = 2 K.

4. Conclusions and Outlook

In summary, a new homogeneous magnet, DFSs BRZMA, in a polycrystalline state was fabricated, achieving a maximum T_C of 138 K and demonstrating negative magnetoresistance of up to 34%. In comparison to BKZMA, the lower carrier concentration in BRZMA is a key factor contributing to these properties. Consequently, we propose a systematic and novel method for achieving a higher T_C, which encompasses both the exploration of new materials and the modification of the properties of existing materials. These findings provide a clear pathway toward achieving a higher T_C in DFSs and offer critical insights into the ferromagnetic coupling mechanisms in this field.

Furthermore, there exist numerous intriguing topics for further exploration, although these topics fall outside the scope of the current experimental research study. (1) According to the relaxation rate, λ_d, derived from the wTF-μSR, a possible peak is observed in the position where static ordered volume fractions, f_M, changes between 0 and 100%. It is noteworthy that this peak is situated very close to the minimum of the d(M/H)/dT. Consequently, it is imperative to undertake two actions. First, 1/T₁ measurements, derived from the temperature dependence of LF-μSR under a fixed field, are necessary for verification. Second, comprehensive theoretical explanations are required to elucidate the critical behaviors observed. (2) A verification of the proposed method is essential, particularly within the BKZMA system, as it contains records of T_C with a value of 260 K [15]. (3) In addition to these experimental efforts, theoretical simulations, especially advanced high-throughput simulations and machine learning tools, are crucial for enhancing our understanding of the data and accelerating the pace of research.