Magnetic Evolution of Carrier Doping and Spin Dynamics in Diluted Magnetic Semiconductors (Ba,Na)(Zn,Mn)₂As₂

Abstract

The investigation of novel diluted magnetic semiconductors (DMSs) provides a promising platform for studying magnetism and transport characteristics, with significant implications for spintronics. DMSs based on BaZn₂As₂ are particularly noteworthy due to their high Curie temperature (T_C) of 260 K, diverse magnetic states, and potential for multilayer heterojunctions. This study investigates the magnetic evolution of carrier doping and spin dynamics in the asperomagnet (Ba,Na)(Zn,Mn)₂As₂, utilizing a combination of magnetization measurements, ac susceptibility, and muon spin rotation (µSR). Key findings include the following: (1) lower transition temperatures and coercive forces in (Ba,Na)(Zn,Mn)₂As₂ compared to the ferromagnet (Ba,K)(Zn,Mn)₂As₂; (2) a dynamic fluctuation peak around the transition temperature observed in both the ac susceptibility and longitudinal field (LF) µSR; and (3) the coexistence of static and dynamic states at low temperatures, exhibiting spin-glass-like characteristics. This study, to the best of our knowledge, may represent the first investigation of asperomagnetic order utilizing µSR techniques. It enhances the understanding of magnetic interactions in BaZn₂As₂-based systems and provides valuable insights into the exploration of high T_C DMSs.

1. Introduction

Diluted magnetic semiconductors (DMSs) [1,2,3,4] are of great research interest for their exceptional properties and potential in spintronic devices [5,6]. Studying new DMSs with high Curie temperature (T_C) and versatile magnetic states offers valuable insights into the interactions between magnetism and transport properties [7]. Manganese (Mn)-doped II-VI [2] and III-V DMSs [3,6,8], such as (Ga,Mn)As, have been extensively researched since their discovery [9,10]. However, T_C is still far from room temperature, and the underlying mechanisms of magnetic exchange interactions continue to be a matter of ongoing debate [8,11]. In 2007, Masek, Jungwirth, and their colleagues introduced a new generation of DMSs featuring independent spin and charge doping mechanisms, such as Li(Zn,Mn)As [12], which was synthesized shortly thereafter [13]. Unlike (Ga,Mn)As, where Ga³⁺/Mn²⁺ substitutions provide both charge carriers and spin simultaneously, the Li(Zn, Mn)As allows for independent control of charge (e.g., excess Li¹⁺) and spin (e.g., Zn²⁺/Mn²⁺). Li(Zn,Mn)As is isostructural to (Ga,Mn)As, and its study may offer valuable insights into magnetic interactions and magnetic orderings in DMSs. Consequently, a novel wave of experimental research has emerged since 2011 [4], concentrating on the development of a series of Mn-based DMS systems characterized by independent spin and charge doping [1,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67]. Among them, DMSs based on BaZn₂As₂ have emerged as a prominent material system due to their high T_C of 260 K [65], diverse magnetic states [1,21,44], and potential for multilayer heterojunctions [68]. Despite the advantages mentioned above, the understanding of the nature of magnetic interactions in DMSs based on BaZn₂As₂ is still far from perfect. (Ba,K)(Zn,Mn)₂As₂ (BKZMA) shows ferromagnetic (FM) properties, whereas (Ba,Na)(Zn,Mn)₂As₂ (BNZMA) exhibits an asperomagnetic order [1], an intermediate regime between an FM and a canonical spin glass (SG). Asperomagnets can be considered variants of SG. Their essential feature is that some random frustration of the exchange interactions leads to many nearly degenerate ground states. Furthermore, the reduced FM order observed in BKZMA can be ascribed to the influence of chemical pressure [40,41,42]. In contrast, the diminished FM order in BNZMA is attributed to an increased concentration of hole carriers [1], which can enhance the antiferromagnetic portion of the oscillatory Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions [69,70]. To enhance the understanding of magnetic interactions in BNZMA, this study focuses on the study of the magnetic evolution of carrier doping and spin dynamics by utilizing a combination of magnetization measurements, ac susceptibility, and muon spin rotation (µSR). Following this introductory chapter, we will present the magnetic evolution of carrier doping and spin dynamics, along with a comparison to previously reported findings in BKZMA [21,65], all in the results section. The main results and potential directions for further research will be elucidated in the discussion and concluding section, which follows a brief explanation of the materials and methods employed.

2. Results

2.1. Structural Characterization

The parent compound β-BaZn₂As₂ crystallizes in the ThCr₂Si₂-type structure, characterized by the space group I4/mmm [21]. Similar to BKZMA, BNZMA also displays the same structural characteristics, as shown in Figure 1b. The X-ray diffraction (XRD) patterns, presented in Figure 1a, along with the refined data obtained from the powder specimen of (Ba_0.9Na_0.1)(Zn_0.85Mn_0.15)₂As₂, were analyzed using Rietveld refinement and can be accurately indexed to a single phase. The resultant weighted reliability factor (R_wp) is approximately 3.40%. As the doping levels of sodium (Na) increase, a monotonic decrease is observed in the a-axis, c-axis, and volume, as illustrated in Figure 2b. This observation indicates successful doping, as the ionic radius of Na¹⁺ (1.02 Å) is smaller than that of Ba²⁺ (1.35 Å), both with coordination numbers of six.

2.2. Magnetization and Magnetic Critical Behaviors

Under an external magnetic field of 500 Gauss (G), the magnetic susceptibility χ_ZFC (T) (measured in zero field cooling (ZFC) mode) and χ_FC(T) (measured in field cooling (FC) mode) of all these (Ba_1−xNa_x)(Zn_0.85Mn_0.15)₂As₂ samples (where x = 0.10, 0.15, 0.20, 0.25, and 0.30) are shown in Figure 3a and Figure 3b, respectively. Three key findings can be clearly seen. (1) As illustrated in Figure 4, prior research indicates that BKZMA is a ferromagnet [21], whereas BNZMA exhibits an asperomagnetic order at 12 K (8 K) in the fields parallel (perpendicular) to the c-axis [1]. To enable a direct comparative analysis, we adopted the Curie–Weiss law to investigate the magnetic interactions within the compound (Ba_1−xX_x)(Zn_0.85Mn_0.15)₂As₂, where X denotes Na and potassium (K). With a nominal hole carrier doping level (via Ba/K or Ba/Na substitution) ranging from 10% to 30%, the transition temperature in BKZMA varies from 40 K to 190 K [21]; whereas in BNZMA, it only ranges from 38.5 K to 72.7 K. This disparity suggests that the crystal structure distortion plays a significant role in influencing magnetic interactions, particularly given that both compounds exhibit similar hole carrier doping levels with equivalent Ba/K or Ba/Na substitutions. This observation was also in accordance with the physical pressure study conducted on BKZMA [40,41,42]. (2) The susceptibility values in BNZMA are approximately one order of magnitude smaller than those in BKZMA [21], which is consistent with previous studies on the single crystal (Ba_0.907Na_0.093)(Zn_0.819Mn_0.181)₂As₂ [1]. Furthermore, as illustrated in Figure 3b, the coercive fields for BNZMA are only in the range of several hundred Gauss (G), indicating that it exhibits soft magnetic properties, in contrast to the hard magnetic characteristics of BKZMA [21,27,65]. (3) In both the polycrystalline and single-crystalline samples, the zero-field-cooled (ZFC) magnetization demonstrated a notable divergence from the field-cooled (FC) magnetization below a particular temperature for both BKZMA [21,27,65] and BNZMA [1]. This phenomenon cannot be ascribed to magnetic anisotropy because a variety of material systems with polycrystalline states demonstrate this characteristic, including Li(Zn,Cu,Mn)As [39], Na(Zn,Mn)Sb [64], Ba(Zn,Cu,Mn)₂As₂ [29], (Ba,K)(Cu,Mn)₂Se₂ [37], (Ba,Na)F(Zn,Mn)Sb [63], SrF(Zn,Mn,Cu)Sb [48], and (La,X)(Zn,Mn)AsO [15,17,23,35,62], where X denotes Ca, Sr, or Ba. The bifurcation point is referred to as the spin freezing temperature, T_f. ac susceptibility measurements of the single crystal (Ba_0.907Na_0.093)(Zn_0.819Mn_0.181)₂As₂ have indicated a spin-glass-like characteristic [1]. Nevertheless, the material does not display the characteristic behavior of a canonical SG, as evidenced by the continuous increase in χ_FC with decreasing temperature. To explore this further, we investigated the dynamic magnetic properties near T_f of BNZMA at a different doping level and employed both ac susceptibility and longitudinal field (LF) μSR techniques, as detailed in the following sections.

The ac susceptibility can serve as a valuable probe for investigating magnetic dynamics within the low-frequency regime, characterized by correlation times that span from approximately 1 s to 10⁻⁵ s [71]. As a complementary technique, magnetic resonance is utilized in conjunction with µSR over time scales ranging from approximately 10⁻⁶ s to 10⁻¹² s [72,73]. By integrating these two methods, it is possible to ascertain the correlation time or fluctuation rate over an extensive range [74]. As illustrated in Figure 5, a distinct peak is evident around T_f in both the real and imaginary components of the (Ba_0.75Mn_0.25)(Zn_0.85Mn_0.15)₂As₂ polycrystalline samples, while the position of the peak varies with frequency. Figure 6a shows the LF µSR time spectra at various selected temperatures. The analysis was conducted using the following function over a time range of one to eight microseconds, with a packing number of ten:

$$Asymmetry\left(t\right)={Asy}_{temp.}exp\left[-{\left({{\displaystyle \frac{t}{T}}}_1\right)}^{\beta }\right]\left(0.5\le \beta \le 1\right)$$

In physics, stretched exponential functions are typically linked to relaxation phenomena observed in disordered or inhomogeneous systems. They are interpreted as arising from a combination of exponential decays, characterized by variable relaxation rates. The shape of the probability density function of the relaxation rates is influenced by the parameter β; specifically, lower values of $\le 1$ correspond to a broader distribution. The stretched exponential function with β = $0.5$ is justified for the case of the dilute magnetic system in the limit of fast dynamics [75] Asymmetry(t) is the temperature dependent of the asymmetry, while the Asy_temp. is the initial asymmetry at t = 0. 1/T₁, indicating the spin dynamics. As shown in Figure 6b, a clear peak of 1/T₁ appears around the T_f. In summary, a typical spin-glass-like behavior was observed in both ac susceptibility and µSR techniques. This feature is also noted in the SG CuMn alloy [75].

2.3. Magnetic Ground State

The magnetic ground state and spin dynamics can be investigated through longitudinal LF µSR measurements at a base temperature [72,73]. The presence of static magnetism suggests that when an external magnetic field is applied parallel to the initial direction of the muon spin, it decouples the spectral line shape (Asymmetry(t)) from the internal magnetic fields. When the external fields are approximately ten times greater than the internal fields, Asymmetry(t) stabilizes and becomes constant over time. However, in a dynamic magnetic system (Figure 3 in reference [76]), this decoupling is not achievable for small fields, resulting in Asymmetry(t) remaining largely unaffected by the external field. As shown in Figure 7, when the field reaches 1 kG, which is about ten times larger than the coercive force in (Ba_0.75Na_0.25)(Zn_0.85Mn_0.15)₂As₂ polycrystalline specimen, there exists a coexistence of the static and dynamic magnetism. This feature is also noted in the SG CuMn alloy (Figure 9 in reference [75]).

3. Materials and Methods

Polycrystalline specimens of (Ba_1−xNa_x)(Zn_0.85Mn_0.15)₂As₂ (where x = 0.10, 0.15, 0.20, 0.25, and 0.30) were synthesized using a solid-state reaction method with high-purity reagents [13]. The precursor materials, BaAs and Na₃As, were sintered at 500 °C and 200 °C for 40 h in a sealed titanium tube with high-purity Ba, Na, and As. These precursors, along with Zn, Mn, and As powders, were loaded into a titanium tube with the nominal composition of (Ba,Na)(Zn,Mn)₂As₂ under an argon atmosphere at 1 atm pressure then placed in a quartz tube. The mixtures were heated to 750 °C for 30 h and cooled to room temperature at 2 °C/min. Specimens were analyzed using X-ray powder diffraction with a Philips X’pert diffractometer and CuKα-radiation. Direct current (dc) magnetic susceptibility was measured with a superconducting quantum interference device (SQUID) magnetometer, while alternating current (ac) magnetic susceptibility measurements were conducted on a physical property measurement system (PPMS). Positive muon spin relaxation (μSR) measurements were performed on polycrystalline specimens of (Ba_0.75Na_0.25)(Zn_0.85Mn_0.15)₂As₂ at the Center for Molecular and Materials Sciences at TRIUMF in Vancouver, Canada.

4. Discussion and Conclusions

Asperomagnets and speromagnets are differentiated by the length scale at which spin correlations average to zero. In the case of speromagnets, this occurs over, at most, a few interatomic spacings, characterized by antiferromagnetic nearest-neighbor correlations. Conversely, in asperomagnets, the length scale is significantly greater, resulting in integrated correlations that exhibit ferromagnetic behavior on a mesoscopic scale [77]. Compared to ferromagnets, asperomagnets exhibit ferromagnetic hysteresis with notable remanence (M_r) at low temperatures. The ratio of remanence to saturation moment (M_r / M_s) ranges from 0.1 to 0.5 [78]. In the representative material DyCu, this value is 0.26 [79]. When roughly comparing the value between the asperomagnet (Ba_0.8Na_0.2)(Zn_0.85Mn_0.15)₂As₂ (Figure 3b; M_r = 0.34) and ferromagnet (Ba_0.8K_0.2)(Zn_0.90Mn_0.10)₂As₂ (Figure 2b in reference [21]; M_s = 1.10), this value is approximately 0.31.

In addition to the impact of the higher hole concentrations [1], several factors may contribute to the asperomagnetic behavior observed in BNZMA, including complex magnetic coupling and disorder. This is because the ionic radius of Na¹⁺ (1.02 Å) is much smaller than that of Ba²⁺ (1.35 Å), which may cause the possibility of structural defects, such as interstitial Na¹⁺ ions, disorder, or compositional inhomogeneities. Previous studies have demonstrated the relationship between structure and magnetism by confirming the superstructures in the Li(Zn,Mn)As system [53]. Moreover, the replacement of Ba/Na could be viewed as a chemical pressure, which also tunes the magnetic coupling. This could be further supported by the physical pressure experiments on BKZMA [40,41,42]. Consequently, further exploration through more comprehensive studies, particularly on single crystals with fewer defects, is still needed. Such studies should integrate various techniques, including, but not limited to, scanning transmission electron microscopy (STEM), scanning tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES), alongside theoretical calculations.

In summary, a systematic investigation of magnetic evolution, carrier doping, and spin dynamics has been conducted on the asperomagnet BNZMA. This compound exhibits significant differences when compared to its counterpart BKZMA and canonical SG. These observations yield two interesting insights: first, the presence of complex magnetic interactions within this system; and second, the magnetic evolution in response to temperature, chemical pressure, and doping levels. This information will be invaluable for materials scientists aiming to discover higher T_C or even room-temperature DMSs beyond the BaZn₂As₂ system in the future.