Diluted magnetic semiconductors (DMSs) have become a focus of research due to their potential application as spintronic devices^[1–8]. Scientists started to study the optical and electrical properties of Mn doped GaAs in the 1960s. To observe magnetic interactions in diluted magnetic systems, the atomic concentrations of magnetic elements must be at least a few percentage^[9]. However, the chemical solubility of magnetic elements in bulk III–V semiconductors is extremely low (~0.01%), and no ferromagnetic orders have been formed. With the development of low temperature molecular beam epitaxy (LT-MBE) technology, (Ga,Mn)As epitaxial films with Mn concentrations up to several percentage have been successfully fabricated on GaAs substrates^{[3, 4, 10–13]}. This breakthrough became a milestone in the research line of magnetic semiconductors. Through years of unremitting efforts, the Curie temperature T_C of (Ga,Mn)As film reached ~200 K when the doping concentration of Mn is ~12%^[14]. However, this temperature is still lower than the room temperature that is required by practical applications. Dielt et al. calculated that the Curie temperature of some semiconductors could be raised to above room temperature when Mn doping contents and hole concentrations reached a certain level^[15]. Therefore, mainstream research is still searching for DMS materials that can achieve higher T_C.

In the past decade, a series of bulk form DMSs have emerged that have similar crystal structure as that of iron-based superconductors^[16]. We therefore classify them as 111-type, 122-type, 1111-type DMSs, etc.^[17–22]. Among these newly discovered bulk form DMSs, the 122-type DMS system is one of the most important families^[23]. In general, the 122-type compounds can crystallize into two different structures. The first is the tetragonal ThCr₂Si₂ structure, such as the p-type (Ba,K)(Zn,Mn)₂As₂^{[17, 24]} and the n-type Ba(Zn,Co)₂As₂^[25]. (Ba,K)(Zn,Mn)₂As₂ exhibits high Curie temperature (T_C ~180 K). By further optimizing the preparation conditions of the polycrystalline samples, researchers finally succeeded in increasing the Curie temperature T_C to ~230 K, which exceeds the T_C record of (Ga,Mn)As. For the purpose of making p–n junctions, an n-type DMS Ba(Zn,Co)₂As₂ with the highest T_C ~ 45 K has also been successfully synthesized. Both (Ba,K)(Zn,Mn)₂As₂ and Ba(Zn,Co)₂As₂ provide valuable references for studying the origin of ferromagneticsim in DMS systems. The second is the hexagonal CaAl₂Si₂ structure, such as (Ca,Na)(Zn,Mn)₂Sb₂^[26], which has been reported as T_C ~ 10 K and H_C ~ 245 Oe recently. In these DMSs, spins and carriers are introduced by the substitutions of Mn²⁺ for Zn²⁺ and substitutions of atoms with lower valences for atoms with higher valences, respectively. This doping pattern makes it possible to control carriers and spins densities separately, and explore their individual effects on the formation of long-range ferromagnetic ordering.

In this paper, we report the successful synthesis of a new 122-type DMS (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ with hexagonal structure, which are further characterized by structural, magnetic and transport measurements. Hole carriers and local spins are introduced by (Ca²⁺,K⁺) and (Zn²⁺,Mn²⁺) substitutions in parent semiconductor CaZn₂As₂, respectively. After the optimization of carriers and spins densities, ferromagnetic ordering with maximum T_C ~ 7 K has been achieved. A clear hysteresis loop can be observed when the doping level is above ~2.5 % and the maximum coercive force H_c is ~ 60 Oe. When K and Mn are co-doped, the resistivity exhibits semiconducting behavior.

The polycrystalline samples of (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ were synthesized via the solid-state reaction of Ca, K, Zn, Mn, and As elements. All of the original elements (99.9 % or higher purity) are stored and handled in an argon filled glove box (the percentage of O₂ < 0.1 ppm and the percentage of H ₂O < 0.1 ppm). According to the nominal composition of (Ca _1−2xK_2x)(Zn_1−xMn_x)₂As₂, the ingredients were mixed and heated at 200 °C for 10 h in evacuated silica tubes, followed by 1000 min at 700 °C. After natural cooling, we grounded, pelletized, and sealed the products in evacuated silica tubes and heated them again at 700 °C for another 30 h. Excess amounts of Ca (1%) and K (10%) were added to compensate the thermal volatilization. In the powder X-ray diffraction (XRD) measurement, we use X-ray diffractometer (Model EMPRYREAN) with monochromatic Cu K_α1 radiation to characterize the crystal structure at room temperature. The DC magnetization measurements were performed on a Quantum Design Magnetic Property Measurement System (MPMS-3). We used the typical four-probe method to measure the electrical resistivity of all of the pellet samples.

In Fig. 1(a), we show the X-ray diffraction patterns for (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ (0 ≤ x ≤ 0.2). All of the detected peaks can be indexed by a hexagonal CaAl₂Si₂ structure, which infers that the specimens are isostructural to the parent semiconductor CaZn₂As₂ with the space group P3¯m1 (No. 164), whose crystal structure is shown in Fig. 1(b). Few impurities, KZn₄As₃^[27], can be observed and are marked by stars. These impurities are non-magnetic, and would have no influence on the discussion of the ferromagnetism in the following. We show the lattice parameters obtained from the Rietveld refinement in Fig. 1(c). We can see that the lattice parameters and the volume of the (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ unit cell (0 ≤ x ≤ 0.2) monotonically increase. Since the ionic radius of both K ion and Mn ion are larger than that of Ca ion and Zn ion, this clearly demonstrates the successful chemical doping of K and Mn. In Fig. 1(d), we plot the temperature dependent magnetization of Ca(Zn_0.9Mn_0.1)₂As₂ at 100 Oe. The paramagnetic behavior demonstrates that the ferromagnetic ordering does not appear when only Mn atoms are doped. This characteristic is consistent with other DMSs reported before, such as 1111-type and 122-type DMSs^{[17, 21]}. Moreover, the 1/(M − M₀) versus temperature curve is a straight line that intersects the −x axis. The Weiss temperature is negative, which suggests that antiferromagnetic interaction dominates for Ca(Zn_0.9Mn_0.1)₂As₂.

In Fig. 2(a), we show the temperature dependent DC magnetization for (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ (x = 0.025, 0.05, 0.1, 0.15, 0.2) measured in zero field cooling (ZFC) and field cooling (FC) condition under a 100 Oe external field. As we can see, the curve still exhibits the paramagnetic behaviour for x = 0.025, which indicates that ferromagnetic ordering does not exist for x = 0.025. The magnetization increases abruptly below T ~ 20 K when the concentration x is larger than 2.5 %. This implies that the ferromagnetic ordering has formed. Moreover, the higher concentrations x we dope, the higher T_C samples behave, reaching the maximum when x equals to 0.15. According to the first derivative of magnetization versus temperature plotted in Fig. 2(b), we define the minimum value of a curve as T_C (numerically, this minimum value is close to the true ferromagnetic transition temperature). The resulted maximum T_C ( ~ 7 K) is lower than that of (Ca,Na)(Zn,Mn)₂As₂^[28] (maximum T_C ~ 33 K), but comparable to the value of ~ 10 K in (Ca,Na)(Zn,Mn)₂Sb₂^[26]. That is probably because the lattice constants of (Ca,K)(Zn,Mn)₂As₂ is larger than those of (Ca,Na)(Zn,Mn)₂As₂ but close to the parameters in (Ca,Na)(Zn,Mn)₂Sb₂. Furthermore, the same behavior can also been observed in (Sr,Na)(Zn,Mn)₂As₂^[18] whose lattice constants are smaller but larger than those of (Ca,K)(Zn,Mn)₂As₂ and (Ca,Na)(Zn,Mn)₂As₂, respectively. Consequently, the maximum T_C of (Sr,Na)(Zn,Mn)₂As₂ ( ~24 K) is between that of (Ca,K)(Zn,Mn)₂As₂ ( ~7 K) and (Ca,Na)(Zn,Mn)₂As₂ ( ~33 K). However, we should mention that the relation phenomenal between the lattice constant and the Curie temperature is not strictly justified between different series of compounds. More experimental and theoretical work need to be done to clarify this. The formula of Curie - Weiss χ = C/(T − θ) + χ₀ can be used to fit the magnetization curves above T_C, where θ is the Weiss temperature, C is a constant used to calculate the effective magnetic moment, and χ₀ is a temperature independent term. The reverse of M − M₀ versus temperature is shown in Fig. 2(c). Based on the data at the high temperature range, the linear fitting lines intersecting the x axis give us the Weiss temperature θ. Similarly, θ values also reach maximum at x = 0.15.

We perform the iso-thermal magnetization measurement at 2 K, and show them in Fig. 2(d). Associated with the DC magnetization results, there are clear hysteresis loops when doping content x exceeds 2.5%. This implies the formation of the ferromagnetic ordering. In addition, the coercive force H_c has minimum of ~10 Oe for x = 0.05 and increases monotonically with increasing x, rising to the magnitude of ~60 Oe for x = 0.2. Zener’s model is effective to study the mechanism of ferromagnetism, and can explain such a change in T_C and H_c^[15]. In this model, RKKY-like interactions of Mn spins can be effectively mediated via hole carriers in the valence band, leading to the ferromagnetism. Using nuclear magnetic resonance and muon spin rotation experiments, researchers have investigated and reported similar trends in some DMS systems^{[29, 30]}. The saturation magnetic moment M_sat (the value read from M(H) curves) decreases from 0.47 µ_B/Mn for (Ca_0.9K_0.1)(Zn_0.95Mn_0.05)₂As₂ to 0.06 µ_B/Mn for (Ca_0.6K_0.4)(Zn_0.8Mn_0.2)₂As₂. In general, the M_sat of many ferromagnets is ~ 1 µ_B per magnetic atom or larger. Whereas, the value of M_sat is only on the order of 0.01 µ_B per magnetic atom or less for typical dilute alloy spin glasses^[31–33]. In this system, the minimum of M_sat (0.06 µ_B/Mn for x = 0.2) is still larger than that of typical dilute alloy spin glasses. Thus, we recognize the current system as ferromagnets. Simultaneously, we can also get the effective magnetic moment M_eff values by fitting to the Curie-Weiss formula, which declines with growing x. The obtained data are tabulated in Table 1. The diminishing behavior of both M_eff and M_sat probably happens because there is a competition between two interactions in this system: the first is the RKKY interaction mentioned above, and the second is the direct exchange antiferromagnetic coupling caused by Mn atoms at the nearest-neighbor (NN) sites. Similar to our previous work^[21], the probability of finding two Mn atoms at NN Zn sites is P(N; x) = CN4x^N(1 − x)^N, where N = 1 and x is the doping content. Theoretically, this probability will increase drastically with increasing x, which enhances the direct antiferromagnetic coupling interaction between Mn-Mn pairs. We notice that with this interaction, 100% Mn doped Ca(Zn_1−xMn_x)₂As₂, CaMn₂As₂, becomes an antiferromagnet with Neel temperature ~ 62 K^[34].

To verify the impact of carriers on the ferromagnetic ordering, we change the contents of K while fixing the concentration of Mn. In Fig. 3(a), we show the magnetic susceptibility of (Ca_1−2yK_2y)(Zn_0.95Mn_0.05)₂As₂ (0.05 ≤ y ≤ 0.2) measured under B_ext ~ 100 Oe. In the same way, we depict the first derivative of magnetization versus temperature in Fig. 3(b) and the 1/(M − M₀) versus temperature in Fig. 3(c). Resembling to the (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ mentioned above, T_C and θ monotonically increase with y. Both T_C and θ reach maximum value at y = 15%, indicating the enhancement of ferromagnetism. Furthermore, clear hysteresis loops can be observed at 2 K (in Fig. 3(d)), which presents a soft ferromagnetic behavior with H_c ~10 Oe. Our results indicate that carriers do play a vital role in the formation of ferromagnetic ordering. Nevertheless, for a fixed Mn concentration, the carrier density has to be an ideal level, no more and no less, to optimize the ferromagnetic exchange interaction and the Curie temperature T_C. The data are tabulated in Table 2.

In Fig. 4(a), we show the resistivity measurement results of CaZn₂As₂, Ca(Zn_0.9Mn_0.1)₂As₂ and (Ca_0.8K_0.2)Zn₂As₂, respectively. The results indicate that in terms of transport properties, both CaZn₂As₂ and Ca(Zn_0.9Mn_0.1)₂As₂ behave as semiconductors, while (Ca_0.8K_0.2)Zn₂As₂ behaves like a metal. As we have observed, when a small number of Mn atoms are doped at the Zn sites in Ca(Zn_0.9Mn_0.1)₂As₂ , the value of the resistivity ρ will increase by an order of magnitude (from ~10³ to ~10⁴ Ω·mm). Nevertheless, if an equal amount of small number of K atoms are doped at the Ca sites, such as in (Ca_0.8K_0.2)Zn₂As₂, ρ is drastically reduced by five orders of magnitude (from ~10³ to ~10⁻² Ω·mm). The enormous reduction in resistivity demonstrates that doping K atoms will introduce carriers. In Fig. 4(b), the resistivity of (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ (0.025 ≤ x ≤ 0.2) are plotted. At first, the magnitude of resistivity decreases as the concentrations x increases, achieving the minimum value ~0.003 Ω·mm at the doping level of ~5% at 4 K. Above 5% doping, the resistivity starts to increase with x up to 20%. This is presumedly because when more Mn atoms are doped into the Zn sites, the carriers are more likely to be scattered by magnetic fluctuations. Therefore, even though the carrier densities are increasing, the resistivity caused by more Mn atoms is growing. Nevertheless, the resistivity of these co-doped samples is still much lower than that of the parent compound CaZn₂As₂. This kind of behavior has also been observed in many DMSs such as (Sr,K)(Zn,Mn)₂As₂^[35], (Ca,Na)(Zn,Mn)₂Sb₂^[26], and so on.

In summary, we have successfully synthesized and characterized a novel DMS (Ca_1−2xK_2x)(Zn_1−xMn_x)₂As₂ via the structure, magnetic and electronic transport measurements. Doping Mn atoms provides the magnetic moments, and no ferromagnetic long range ordering formed in Ca(Zn_0.9Mn_0.1)₂As₂. Ferromagnetism occurs only when K and Mn are co-doped to a certain amount. The resultant maximum T_C and the coercive field H_c is ~ 7 K and ~ 60 Oe, respectively. Meanwhile, the samples with K and Mn co-doping demonstrate the semiconductor characteristic as seen from the electrical transport measurements. This work provides a new option in further research on DMS materials.

The work was supported by the Key R&D Program of Zhejiang Province, China (2021C01002) and NSF of China (No. 12074333).