A substantial increase of Curie temperature in a new type of diluted magnetic semiconductors via effects of chemical pressure

The diluted magnetic semiconductors (DMSs) have been investigated extensively as they offer an opportunity to control the ferromagnetic properties by changing carrier density. The advantage leads to potential applications in spintronic devices.^1–31. I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004). https://doi.org/10.1103/revmodphys.76.3232. T. Jungwirth, J. Wunderlich, V. Novak, K. Olejnik, B. L. Gallagher, R. P. Campion, K. W. Edmonds, A. W. Rushforth, A. J. Ferguson, and P. Nemec, Rev. Mod. Phys. 86, 855 (2014). https://doi.org/10.1103/revmodphys.86.8553. H. Ohno, Science 281, 951 (1998). https://doi.org/10.1126/science.281.5379.951 Specifically, recently couples of Fe-doped III–V DMS reached relatively high Curie temperature,^4–64. N. T. Tu, P. N. Hai, L. D. Anh, and M. Tanaka, Appl. Phys. Lett. 108, 192401 (2016). https://doi.org/10.1063/1.49486925. N. T. Tu, P. N. Hai, L. D. Anh, and M. Tanaka, Appl. Phys. Express 11, 063005 (2018). https://doi.org/10.7567/apex.11.0630056. N. T. Tu, P. N. Hai, L. D. Anh, and M. Tanaka, Appl. Phys. Lett. 112, 122409 (2018). https://doi.org/10.1063/1.5022828 which challenges existing concepts and motivates further understanding of ferromagnetism in DMS. The spin and charge doping are induced by one element doping such as Mn doping into (Ga,Mn)As leading to difficulty in tuning either conducting or magnetic properties.⁷7. A. Hirohata, H. Sukegawa, H. Yanagihara, I. Zutic, T. Seki, S. Mizukami, and R. Swaminathan, IEEE Trans. Magn. 51, 0800511 (2015). https://doi.org/10.1109/tmag.2015.2457393 Consequently, a series of a new type of DMS materials with independent carrier and spin doping have been discovered to overcome aforementioned difficulty, e.g., Li_1+x(Zn,Mn)As termed “111” type or (Ba,K)(Zn,Mn)₂As₂ (BZA) termed “122” type. BZA holds the record of Curie temperature among the “111” and “122”-type DMSs.^7–117. A. Hirohata, H. Sukegawa, H. Yanagihara, I. Zutic, T. Seki, S. Mizukami, and R. Swaminathan, IEEE Trans. Magn. 51, 0800511 (2015). https://doi.org/10.1109/tmag.2015.24573938. I. Zutic and T. Zhou, Sci. China: Phys., Mech. Astron. 61, 067031 (2018). https://doi.org/10.1007/s11433-018-9191-09. J. K. Glasbrenner, I. Zutic, and I. I. Mazin, Phys. Rev. B 90, 140403 (2014). https://doi.org/10.1103/physrevb.90.14040310. K. Zhao, Z. Deng, X. C. Wang, W. Han, J. L. Zhu, X. Li, Q. Q. Liu, R. C. Yu, T. Goko, B. Frandsen, L. Liu, F. Ning, Y. J. Uemura, H. Dabkowska, G. M. Luke, H. Luetkens, E. Morenzoni, S. R. Dunsiger, A. Senyshyn, P. Böni, and C. Q. Jin, Nat. Commun. 4, 1442 (2013). https://doi.org/10.1038/ncomms244711. K. Zhao, B. J. Chen, G. Q. Zhao, Z. Yuan, Q. Q. Liu, Z. Deng, J. L. Zhu, and C. Q. Jin, Chin. Sci. Bull. 59, 2524 (2014). https://doi.org/10.1007/s11434-014-0398-z

Given a DMS material, effective ways to modify T_C can be achieved by increasing the carrier density using an applied electric field, photoexcitations, or pressure.^7,127. A. Hirohata, H. Sukegawa, H. Yanagihara, I. Zutic, T. Seki, S. Mizukami, and R. Swaminathan, IEEE Trans. Magn. 51, 0800511 (2015). https://doi.org/10.1109/tmag.2015.245739312. H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T. Dietl, Y. Ohno, and K. Ohtani, Nature 408, 944 (2000). https://doi.org/10.1038/35050040 Particularly, pressure is expected to increase both carrier concentration and Mn–As hybridization which result in an enhancement of ferromagnetic interactions in DMS materials.¹³13. M. Csontos, G. Mihaly, B. Janko, T. Wojtowicz, X. Liu, and J. K. Furdyna, Nat. Mater. 4, 447 (2005). https://doi.org/10.1038/nmat1388 On the other hand, internal chemical pressure, which plays a comparable role as external physical pressure, is widely used to modify physical properties in many functional materials. For instance, an equivalent increase in superconducting critical temperature in cuprate superconductors has been reported via relatively low pressures (4–6 GPa) induced by chemical pressure.^14,1514. M. Almamouri, P. P. Edwards, C. Greaves, and M. Slaski, Nature 369, 382 (1994). https://doi.org/10.1038/369382a015. W. B. Gao, Q. Q. Liu, L. X. Yang, Y. Yu, F. Y. Li, C. Q. Jin, and S. Uchida, Phys. Rev. B 80, 094523 (2009). https://doi.org/10.1103/physrevb.80.094523 Superconductivity in the iron-based compound BaFe₂As₂ can be induced by moderate pressure (<6 GPa) and isovalent chemical doping (BaFe₂As_2−xP_x), respectively.^16,1716. S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Phys. Rev. B 81, 184519 (2010). https://doi.org/10.1103/physrevb.81.18451917. S. A. J. Kimber, A. Kreyssig, Y. Z. Zhang, H. O. Jeschke, R. Valenti, F. Yokaichiya, E. Colombier, J. Yan, T. C. Hansen, T. Chatterji, R. J. McQueeney, P. C. Canfield, A. I. Goldman, and D. N. Argyriou, Nat. Mater. 8, 471 (2009). https://doi.org/10.1038/nmat2443 Comparing to external physical pressure, internal chemical pressure, which can be applied by isovalent substitutions, does not require any specific devices (e.g., diamond anvil cell or piston cylinder cell). Nevertheless, chemical pressure-effects in DMS materials are rarely reported.

Previous studies of physical pressure-effects on “122” BZA only presented negative pressure-effect on T_C. The proposed reason is that physical pressure distorts [MnAs₄] tetrahedra and then reduces effective Mn–As hybridization which in turn damages ferromagnetic ordering.^18–2018. F. Sun, G. Q. Zhao, C. A. Escanhoela, B. J. Chen, R. H. Kou, Y. G. Wang, Y. M. Xiao, P. Chow, H. K. Mao, D. Haskel, W. G. Yang, and C. Q. Jin, Phys. Rev. B 95, 094412 (2017). https://doi.org/10.1103/physrevb.95.09441219. G. Q. Zhao, Z. Li, F. Sun, Z. Yuan, B. J. Chen, S. Yu, Y. Peng, Z. Deng, X. C. Wang, and C. Q. Jin, J. Phys.: Condens. Matter 30, 254001 (2018). https://doi.org/10.1088/1361-648x/aac36720. F. Sun, N. N. Li, B. J. Chen, Y. T. Jia, L. J. Zhang, W. M. Li, G. Q. Zhao, L. Y. Xing, G. Fabbris, Y. G. Wang, Z. Deng, Y. J. Uemura, H. K. Mao, D. Haskel, W. G. Yang, and C. Q. Jin, Phys. Rev. B 93, 224403 (2016). https://doi.org/10.1103/physrevb.93.224403 In this work, we generated chemical pressure by changing atom size on another group of DMS (Sr,Na)(Cd,Mn)₂As₂.²¹21. B. J. Chen, Z. Deng, W. M. Li, M. R. Gao, Z. Li, G. Q. Zhao, S. Yu, X. C. Wang, Q. Q. Liu, and C. Q. Jin, J. Appl. Phys. 120, 083902 (2016). https://doi.org/10.1063/1.4961565 Replacing Sr by Ca, (Ca,Na)(Cd,Mn)₂As₂ was synthesized as a new DMS material. From Sr- to Ca-compound, the unit cell volume decreases by 6.2% suggesting positive chemical pressure effect. It is found that local geometry of [MnAs₄] tetrahedron in (Ca,Na)(Cd,Mn)₂As₂ is optimized by chemical pressure. Consequently, a successful improvement of ferromagnetic ordering by chemical pressure has been observed: comparing to (Sr,Na)(Cd,Mn)₂As₂, both maximum Curie temperature and saturation moment in (Ca,Na)(Cd,Mn)₂As₂ are significantly enhanced.

Polycrystalline samples of (Ca,Na)(Cd,Mn)₂As₂ were synthesized by solid state reaction with high purity elements. The stoichiometric ratios of starting materials were well mixed and pressed into pellets. All the processes were conducted under the protection of high-purity argon due to the air-sensitive starting materials. The pellets were sealed in tantalum-tubes with 1 bar of argon, and then the Ta-tubes were enclosed into evacuated quartz tubes. The samples were first heated at 600 °C for 12 h. Then, the products were reground, pelleted, and sintered at 650 °C for another 12 h. The recovered samples were characterized by powder X-ray diffraction (PXRD) with a Rigaku diffractometer using Cu-Kα radiation at room-temperature. A Scanning Electron Microscope (SEM) was used to investigate the morphology and particle size. Real compositions of all the elements were measured with energy dispersive X-ray (EDX) analysis on the SEM. The real atom ratios of our samples are consistent with their normal stoichiometry. For example, the real composition of nominal (Ca_0.95Na_0.05)(Cd_0.95Mn_0.05)₂As₂ is determined as (Ca_0.9546Na_0.0454)(Cd_0.9396Mn_0.0604)₂As₂. Consequently, we use normal composition of each sample in this manuscript, for the sake of simplification. The dc magnetic properties were measured with a Superconductivity Quantum Interference Device (SQUID, Quantum Design), and transport properties were examined by Physical Property Measurement System (PPMS, Quantum Design). We calculated the equation of state (EoS) by first-principles calculations with a plane augmented-wave (PW) pseudopotential and generalized gradient approximation implemented in the VASP code with 16 × 16 × 8 k-point grid and 500 eV energy cutoff to build up relationship between cell volume and pressure [P(V)] of SrCd₂As₂.

Both CaCd₂As₂ and SrCd₂As₂ crystallize into a hexagonal structure with P-3m1 space group (No. 164) as shown in Fig. 1(a). Powder X-ray diffraction patterns for samples show that all of the peaks can be well indexed into P-3m1 space group (Fig. S1). For all the samples, crystal grains have sharp boundaries indicating good crystallization, as shown in Fig. 1(b). The lattice constants were calculated by Rietveld refinement. Both of a-axis and c-axis shrink linearly with increasing Mn doping level as shown in Fig. 1(c) because Mn²⁺ (0.66 Å) is smaller than Cd²⁺ (0.78 Å), well following the Vegard law, an evidence of successful (Cd,Mn) substitution. CaCd₂As₂ and SrCd₂As₂ are quasi-2D-materials where Ca/Sr ions layers and honeycomblike Cd₂As₂ layers stack alternately along the c axis.²²22. P. Klufers and A. Mewis, Z. Naturforsch., B 32, 753 (1977). https://doi.org/10.1515/znb-1977-0706 Given lattice constants for SrCd₂As₂ (a ∼ 4.4516 Å, c ∼ 7.4221 Å, V ∼ 127.4 ų) and CaCd₂As₂ (a ∼ 4.3909 Å, c ∼ 7.1870 Å, V ∼ 120.0 ų), chemical compression effect is visible in the latter, particularly along the c-axis. Besides, two more principal deviations between CaCd₂As₂ and SrCd₂As₂ are the Cd/Mn–As bond lengths and As–Cd/Mn–As bond angles in Cd₂As₂ layers which will be discussed in more details.

Figure 2(a) shows temperature dependent of magnetization [M(T)] curves for (Ca_1−xNa_x)(Cd_1−yMn_y)₂As₂ (x = 0.025, 0.05, 0.1, 0.15; y = 0.05, 0.15, 0.2) under field H = 500 Oe. There is no obvious difference between zero field cooling (ZFC) and field cooling (FC), but clear ferromagnetic signatures are observed for all samples, i.e., sharp upturns with decreasing temperature. T_C were determined from valleys of dM/dT curves. Above T_C, susceptibility is fitted with the Curie-Weiss law [inset of Fig. 2(a)], (χ − χ₀)⁻¹ = (T − θ)/C, where χ₀ stands for a temperature-independent term and θ stands for paramagnetic temperature. Neither T_C nor θ monotonically increases with increasing Mn or Na doping level [Fig. 2(c)]. Maximum T_C ∼ 19 K and θ ∼ 22 K are obtained for x = 0.05 and y = 0.15. The maximum T_C of (Ca,Na)(Cd,Mn)₂As₂ is about 50% higher than that of (Sr,Na)(Cd,Mn)₂As₂ (the maximum T_C ∼ 13 K).²¹21. B. J. Chen, Z. Deng, W. M. Li, M. R. Gao, Z. Li, G. Q. Zhao, S. Yu, X. C. Wang, Q. Q. Liu, and C. Q. Jin, J. Appl. Phys. 120, 083902 (2016). https://doi.org/10.1063/1.4961565 In Fig. 2(c), Tc decreases slightly with a higher Na-doping level when x > 0.05, presumable due to more defects induced by Na doping in specimens. After reaching maximum T_C, ferromagnetic ordering is also weakened by overdoped Mn, similar to analogs (Sr,Na)(Zn,Mn)₂As₂ and (Sr,Na)(Cd,Mn)₂As₂.^21,2321. B. J. Chen, Z. Deng, W. M. Li, M. R. Gao, Z. Li, G. Q. Zhao, S. Yu, X. C. Wang, Q. Q. Liu, and C. Q. Jin, J. Appl. Phys. 120, 083902 (2016). https://doi.org/10.1063/1.496156523. X. Yang, Y. Li, P. Zhang, H. Jiang, Y. Luo, Q. Chen, C. Feng, C. Cao, J. Dai, T. Qian, G. Cao, and Z.-A. Xu, J. Appl. Phys. 114, 223905 (2013). https://doi.org/10.1063/1.4842875 A presumably reason is that increasing chemical substitution tends to enhance antiferromagnetic coupling between either substitutional Mn and interstitial Mn or substitutional Mn in the nearest neighbor Cd sites due to high Mn concentration. Effective paramagnetic moments (M_eff) are calculated from the Curie constant C. For example, M_eff of (Ca_0.95Na_0.05)(Cd_0.95Mn_0.05)₂As₂ is 5.3μ_B/Mn which is close to an expected value of s = 5/2 configuration of Mn²⁺ [$g\sqrt{s\left(s+1\right)}$ = 5.9μ_B with g = 2]. Ferromagnetic characteristics, which are spontaneous magnetization under very low fields and narrow but clear hysteresis loops, are also found in M(H) curves as plotted in Fig. 2(b). Coercive fields are smaller than 100 Oe. Saturation moments (M_sat) decrease with increasing Mn [Fig. 2(d)] due to increased antiferromagnetic interactions as proposed to explain the decrease in T_C. Nevertheless, maximum M_sat of (Ca,Na)(Cd,Mn)₂As₂ is significant larger than that of (Sr,Na)(Cd,Mn)₂As₂ (maximum M_sat < 1μ_B/Mn). The larger M_sat indicates that more local spins on Mn are ferromagnetic ordered, consistent with higher T_C in (Ca,Na)(Cd,Mn)₂As₂.²¹21. B. J. Chen, Z. Deng, W. M. Li, M. R. Gao, Z. Li, G. Q. Zhao, S. Yu, X. C. Wang, Q. Q. Liu, and C. Q. Jin, J. Appl. Phys. 120, 083902 (2016). https://doi.org/10.1063/1.4961565

Electrical transport measurements are shown in Fig. 3. The temperature dependent resistivity [ρ(T)] for parent compound CaCd₂As₂ shows semiconducting behavior within a temperature range of 2–300 K [Fig. 3(a)]. It is worth noting that the resistivity of CaCd₂As₂ is much smaller than SrCd₂As₂ (ρ_300K ∼ 1 * 10⁴ Ω mm and ρ_120K ∼ 1 * 10⁷ Ω mm).²¹21. B. J. Chen, Z. Deng, W. M. Li, M. R. Gao, Z. Li, G. Q. Zhao, S. Yu, X. C. Wang, Q. Q. Liu, and C. Q. Jin, J. Appl. Phys. 120, 083902 (2016). https://doi.org/10.1063/1.4961565 It is consistent with the aforementioned scenario that shortened Cd/Mn–As bond lengths and optimized As–Zn/Mn–As bond angle within sublayers enhance intrasublayer Cd/Mn–As hybridization and in turn benefit conduction. On the other hand, ρ_2K of CaCd₂As₂ is 3 orders magnitude larger than all the Na-doped (Ca,Na)(Cd,Mn)₂As₂, indicating significantly increased carrier concentrations via Na doping. The scheme is further supported as shown in Fig. 3(a) by the decrease in resistivity of (Ca_1−xNa_x)(Cd_0.85Mn_0.15)₂As₂ with an increasing Na-doping level. In contrast, as shown in Fig. 3(b), resistivity of (Ca_0.95Na_0.05)(Cd_1−yMn_y)₂As₂ gradually increases with increasing Mn concentrations.

Figure 4(a) shows ρ(T) curves for (Ca_0.95Na_0.05)(Cd_0.85Mn_0.15)₂As₂ under various fields. Negative magnetroresistance [MR = Δρ/ρ₀ = (ρ_H − ρ₀)/ρ₀] is found below ∼18 K consistent with T_C from magnetization data. Above 18 K, positive MR emerges. The consistency indicates that the negative MR is related to ferromagnetic ordering. In Fig. 4(b), MR does not saturate at H = 7 T and T = 2 K, where the spins are almost fully aligned according to the M(H) curve. In (Ga,Mn)As and analog (Sr,Na)(Cd,Mn)₂As₂, the unsaturated MR is explained with giant splitting of the valence band. In order to understand such behavior, the negative magnetroresistance dates at 2 K are fitted with following equation:^24–2624. A. Kawabata, Solid State Commun. 34, 431 (1980). https://doi.org/10.1016/0038-1098(80)90644-425. T. Omiya, F. Matsukura, T. Dietl, Y. Ohno, T. Sakon, M. Motokawa, and H. Ohno, Physica E 7, 976 (2000). https://doi.org/10.1016/s1386-9477(00)00099-026. F. Matsukura, M. Sawicki, T. Dietl, D. Chiba, and H. Ohno, Physica E 21, 1032 (2004). https://doi.org/10.1016/j.physe.2003.11.165

$$\mathrm{\Delta }\rho /{\rho }_H=\mathrm{\Delta }\sigma /\sigma =k{B}^{1/2}=-n_v{e}^2{C}_0\rho {\left(eB\hslash \right)}^{1/2}/\left(2{\pi }^2\hslash \right),$$

(1)

where C₀ ≈ 0.605, e is the elemental charge, $\hslash$ is the reduced Planck constant, and 1/2 ≤ n_v ≤ 2 depending on the number of hole sub-bands contributing to the charge transport. The best fitting to Eq. (1) gives n_v = 0.62, close to that of (Sr,Na)(Cd,Mn)₂As₂. The maximum MR is ∼15% at T = 2 K and H = 7 T. It is larger than analogs (Sr,Na)(Zn,Mn)₂As₂ and (Ca,Na)(Zn,Mn)₂As₂ as well as (Ba,K)(Zn,Mn)₂As₂ which has a much higher T_C.^10,27,2810. K. Zhao, Z. Deng, X. C. Wang, W. Han, J. L. Zhu, X. Li, Q. Q. Liu, R. C. Yu, T. Goko, B. Frandsen, L. Liu, F. Ning, Y. J. Uemura, H. Dabkowska, G. M. Luke, H. Luetkens, E. Morenzoni, S. R. Dunsiger, A. Senyshyn, P. Böni, and C. Q. Jin, Nat. Commun. 4, 1442 (2013). https://doi.org/10.1038/ncomms244727. B. J. Chen, K. Zhao, Z. Deng, W. Han, J. L. Zhu, X. C. Wang, Q. Q. Liu, B. Frandsen, L. Liu, S. Cheung, F. L. Ning, T. J. S. Munsie, T. Medina, G. M. Luke, J. P. Carlo, J. Munevar, Y. J. Uemura, and C. Q. Jin, Phys. Rev. B 90, 155202 (2014). https://doi.org/10.1103/physrevb.90.15520228. K. Zhao, B. J. Chen, Z. Deng, W. Han, G. Q. Zhao, J. L. Zhu, Q. Q. Liu, X. C. Wang, B. Frandsen, L. Liu, S. Cheung, F. L. Ning, T. J. S. Munsie, T. Medina, G. M. Luke, J. P. Carlo, J. Munevar, G. M. Zhang, Y. J. Uemura, and C. Q. Jin, J. Appl. Phys. 116, 163906 (2014). https://doi.org/10.1063/1.4899190

The carrier type of the parent phase CaCd₂As₂ and doped phase (Ca,Na)(Cd,Mn)₂As₂ is p-type. The hole concentration of these samples is about 10¹⁹–10²⁰ cm⁻³. Figure 4(c) shows Hall resistivity [ρ_xy(H)] below and above T_C for (Ca_0.9Na_0.1)(Cd_0.85Mn_0.15)₂As₂ as a typical example. At T = 2 K, the clear anomalous Hall effect (AHE) is a strong evidence for intrinsic ferromagnetism in a DMS material. Carrier concentration calculated with linear ρ_xy(H) at a high-field range is n_p = 2.98 × 10¹⁹ cm⁻³. At 300 K, ρ_xy is proportional to field and we obtain n_p = 5.38 × 10¹⁹ cm⁻³.

Considering key roles of local geometry of [Zn/MnAs]₄ tetrahedra to ferromagnetic interaction in BZA, we compare Cd/Mn–As bond lengths and As–Cd/Mn–As bond angles of CaCd₂As₂ and SrCd₂As₂ to seek microscopic insight into the origin of improved ferromagnetic ordering in CaCd₂As₂. For carrier-mediated ferromagnetism in DMS, itinerant carriers play an important role in ferromagnetic interaction.^29–3829. Z. Deng, C. Q. Jin, Q. Q. Liu, X. C. Wang, J. L. Zhu, S. M. Feng, L. C. Chen, R. C. Yu, C. Arguello, T. Goko, F. L. Ning, J. S. Zhang, Y. Y. Wang, A. A. Aczel, T. Munsie, T. J. Williams, G. M. Luke, T. Kakeshita, S. Uchida, W. Higemoto, T. U. Ito, B. Gu, S. Maekawa, G. D. Morris, and Y. J. Uemura, Nat. Commun. 2, 422 (2011). https://doi.org/10.1038/ncomms142530. Z. Deng, K. Zhao, B. Gu, W. Han, J. L. Zhu, X. C. Wang, X. Li, Q. Q. Liu, R. C. Yu, T. Goko, B. Frandsen, L. Liu, J. S. Zhang, Y. Y. Wang, F. L. Ning, S. Maekawa, Y. J. Uemura, and C. Q. Jin, Phys. Rev. B 88, 081203 (2013). https://doi.org/10.1103/physrevb.88.08120331. R. Wang, Z. X. Huang, G. Q. Zhao, S. Yu, Z. Deng, C. Q. Jin, Q. J. Jia, Y. Chen, T. Y. Yang, X. M. Jiang, and L. X. Cao, AIP Adv. 7, 045017 (2017). https://doi.org/10.1063/1.498271332. G. Q. Zhao, C. J. Lin, Z. Deng, G. X. Gu, S. Yu, X. C. Wang, Z. Z. Gong, Y. J. Uemera, Y. Q. Li, and C. Q. Jin, Sci. Rep. 7, 14473 (2017). https://doi.org/10.1038/s41598-017-08394-z33. C. Ding, H. Y. Man, C. Qin, J. C. Lu, Y. L. Sun, Q. Wang, B. Q. Yu, C. M. Feng, T. Goko, C. J. Arguello, L. Liu, B. A. Frandsen, Y. J. Uemura, H. D. Wang, H. Luetkens, E. Morenzoni, W. Han, C. Q. Jin, T. Munsie, T. J. Williams, R. M. D’Ortenzio, T. Medina, G. M. Luke, T. Imai, and F. L. Ning, Phys. Rev. B 88, 041102 (2013). https://doi.org/10.1103/physrevb.88.04110234. W. Han, K. Zhao, X. C. Wang, Q. Q. Liu, F. L. Ning, Z. Deng, Y. Liu, J. L. Zhu, C. Ding, H. Y. Man, and C. Q. Jin, Sci. China: Phys., Mech. Astron. 56, 2026 (2013). https://doi.org/10.1007/s11433-013-5320-135. H. Y. Man, S. L. Guo, Y. Sui, Y. Guo, B. Chen, H. D. Wang, C. Ding, and F. L. Ning, Sci. Rep. 5, 15507 (2015). https://doi.org/10.1038/srep1550736. F. Sun, C. Xu, S. Yu, B. J. Chen, G. Q. Zhao, Z. Deng, W. G. Yang, and C. Q. Jin, Chin. Phys. Lett. 34, 067501 (2017). https://doi.org/10.1088/0256-307x/34/6/06750137. B. A. Frandsen, Z. Z. Gong, M. W. Terban, S. Banerjee, B. J. Chen, C. Q. Jin, M. Feygenson, Y. J. Uemura, and S. J. L. Billinge, Phys. Rev. B 94, 094102 (2016). https://doi.org/10.1103/physrevb.94.09410238. S. C. Erwin and I. Zutic, Nat. Mater. 3, 410 (2004). https://doi.org/10.1038/nmat1127 Given the quasi-2D structure of CaCd₂As₂ and SrCd₂As₂, one can expect that carriers are more itinerant along the ab-plane than the c-axis. If one takes a close look at Cd₂As₂ planes, it is easy to find two sublayers within one CdAs plane [Fig. 1(a)]. It is reasonable to assume that intrasublayer component is more important than the intersublayer one to modify carrier mobility within the Cd₂As₂ plane. With the same doping levels, the sublayer of CaCd₂As₂ has shorter Cd/Mn–As bond length and more optimal As–Cd/Mn–As bond angles than that of SrCd₂As₂. As shown in Fig. 1(d), the (Ca_0.95Na_0.05)(Cd_0.95Mn_0.05)As₂ has the average Cd/Mn–As bond length of 2.700 Å and the average As–Cd/Mn–As bond angle within sublayers of 108.9° that is close to the ∼109.47° for a nondistorted ideal tetrahedron.¹⁸18. F. Sun, G. Q. Zhao, C. A. Escanhoela, B. J. Chen, R. H. Kou, Y. G. Wang, Y. M. Xiao, P. Chow, H. K. Mao, D. Haskel, W. G. Yang, and C. Q. Jin, Phys. Rev. B 95, 094412 (2017). https://doi.org/10.1103/physrevb.95.094412 On the other hand, in (Sr_0.95Na_0.05)(Cd_0.95Mn_0.05)As₂, the average Cd/Mn–As bond length is 2.712 Å and the average As–Cd/Mn–As bond angle is 113.6° that is apparently deviated from ∼109.47°. The shortened Cd/Mn–As bond length will definitely increase Mn–As hybridization. Additionally, the ideal As–Cd/Mn–As bond angle will increase the overlap of Mn–As planar orbitals and guarantee the maximum strength of Mn–As hybridization, hence increasing the ferromagnetic interactions. Previous studies of physical pressure-effects on “122” BZA indicated that shortened Zn/Mn–As bond length and optimized As–Zn/Mn–As bond angle (∼109.47° for a regular tetrahedron) will enhance Cd/Mn–As hybridization.¹⁸18. F. Sun, G. Q. Zhao, C. A. Escanhoela, B. J. Chen, R. H. Kou, Y. G. Wang, Y. M. Xiao, P. Chow, H. K. Mao, D. Haskel, W. G. Yang, and C. Q. Jin, Phys. Rev. B 95, 094412 (2017). https://doi.org/10.1103/physrevb.95.094412 In short, (Ca,Na)(Cd,Mn)₂As₂ has stronger intrasublayer Cd/Mn–As hybridization than that for (Sr,Na)(Cd,Mn)₂As₂. As a result, we found improved ferromagnetic ordering in (Ca,Na)(Cd,Mn)₂As₂. Consequently, it is reasonable to assume that more chemical pressure could further improve T_C within this system, e.g., replacing Ca with Mg.

We calculated the equation of state (EoS) equation with first-principles calculations with the plane augmented-wave (PW) pseudopotential method implemented in the VASP code³⁹39. G. Kresse and D. Joubert, Phys. Rev. B 59(3), 1758 (1999). https://doi.org/10.1103/physrevb.59.1758 to build up relationship between cell volume and pressure [P(V)] of SrCd₂As₂ (Fig. S2). Based on the P(V) curve, we estimate that an external pressure of 3.6 GPa can reduce cell volume of SrCd₂As₂ to 120.0 ų (volume of CaCd₂As₂ at ambient pressure).

In summary, we successfully synthesized a new type of DMS, (Ca,Na)(Cd,Mn)₂As₂. The carriers and spins are introduced via (Ca,Na) and (Cd,Mn) substitutions independently. The Curie temperature of (Ca,Na)(Cd,Mn)₂As₂ is 50% higher than that of (Sr,Na)(Cd,Mn)₂As₂ due to the effects of chemical pressure, and the saturation moment is also enhanced dramatically. The significant improvement of ferromagnetism in (Ca,Na)(Cd,Mn)₂As₂ indicates the prospect to search for high temperature diluted magnetic semiconductors via proper chemical pressure.