A Near Room Temperature Curie Temperature in a New Type of Diluted Magnetic Semiconductor (Ba,K)(Zn,Mn)2As2

Abstract

Achieving room‐temperature ferromagnetism is one of the major challenges for diluted magnetic semiconductors (DMS). (Ba,K)(Zn,Mn)₂As₂ (BZA) belongs to a new type of DMS materials that feature independent spin and carrier doping. In previous studies, BZA shows a reliable Curie temperature (T_C) of 230 K, a record among these types of materials. In this work, progress in further experimentally enhancing T_C of BZA to 260 K is reported by increasing Mn concentration with parallel K doping, as supported by complementary first‐principles calculations. A sufficient carrier concentration can suppress the short‐range antiferromagnetic interaction of the nearest Mn─Mn pair, which suppresses ferromagnetism in DMS materials. Consequently, a higher T_C has been obtained in BZA with improved Mn‐ and K‐doping levels by using high‐pressure synthesis that effectively eliminates structural distortion and overcomes the limitation of chemical solution in BZA. The work demonstrates an effective strategy to enhance T_C in DMS systems.

Introduction

Combining the features of carrier control in semiconductors and spin control in ferromagnets, diluted magnetic semiconductors (DMS) have significant advantages in spintronics and have thus been extensively studied in recent decades.^[1–3] For example, spin-orbit torque, which was first discovered in DMS, is now an important mechanism for the new generation of magnetic memories and sensors.^[4] In the 1990s, the typical DMS, (Ga,Mn)As, was successfully conducted spin and carrier doping via the substitution of Mn²⁺ into Ga³⁺ sites.^[3,5] However, a single-element substitution such as this can lead to a lack of independent tuning for conducting or magnetic properties.^[6,7] Furthermore, the dual roles of Mn complicate the underlying theoretical understanding, including whether double exchange is a relevant mechanism in these systems.^[8] To overcome the aforementioned difficulties, a series of new type DMS materials with independent spin and carrier doping have been discovered, that is, Li(Zn,Mn)As and (Ba,K)(Zn,Mn)₂As₂ (BZA).^[9–13] Among these new DMS materials, the reliable Curie temperature (T_C = 230 K) of BZA was the highest.^[3,14,15]

Owing to the application potential of high-T_C BZA, it has been proposed to develop isostructural heterojunctions between BZA, superconducting (Ba,K)Fe₂As₂, and high Néel temperature semiconductor BaMn₂As₂ to explore their emerging phenomena and functionalities.^[3,14,16] Particularly, their matching ThCr₂Si₂-type crystal structure and the small mismatch (less than 5%) within the a-b plane between them represent the unique features of BZA and analogs and could lead to unprecedented fabrications of potential heterojunctions for DMS materials, as shown in Figure 1. Taking the Andreev reflection junction as a typical example, the first theoretical consideration of the spin-flip Andreev reflection was studied with DMS, and recently it led to spin-triplet superconductivity at the interface of ferromagnet/superconductor.^[17,18] Furthermore, the versatile design of materials properties, for example, superconductivity with ferromagnetism, topological magnetism, and enhanced spin–orbit couplings, could be accomplished via proximity effects.^[19] These prospects have inspired further trials to improve T_C of BZA.^[20–23] The intuitive way of improving T_C is to increase the doping level of magnetic cations in DMS materials.^[16] For example, T_C of (Ga,Mn)As has been enhanced to 200 K via heavy Mn doping.^[24,25] It is worth noting that further Mn doping is a long-term challenge for (Ga,Mn)As, due to heterovalent (Ga³⁺, Mn²⁺) substitution. The latter results in not only limited chemical solubility but also interstitial Mn defects, which act as electron donors to balance hole carriers from substitutional Mn.^[9,26] Such a disadvantage is overcome by isovalent (Zn²⁺, Mn²⁺) substitution in BZA. The Mn concentration over 15% is theoretically tolerable owing to the existence of isostructural BaMn₂As₂ with fully occupied Mn.^[27]

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It is well known that the magnetic exchange interaction between nearest Mn ions is antiferromagnetic superexchange, and it tends to dominate the interactions among all Mn ions and results in antiferromagnetism in DMS materials with increasing Mn-doping. Taking the advantage of independent spin and carrier doping, it is possible to study the individual doping effect on ferromagnetism. Our calculations indicate that carrier-doping, namely K-doping, can suppress the antiferromagnetic superexchange in BZA. Moreover, the sufficient carrier-doping can overcome the dominating antiferromagnetic interaction and further enhance T_C in heavy Mn-doped BZA. However, extra Mn doping has not been successful with conventional synthesis conditions. Generally, the doping levels in most of the DMS materials are limited due to either structural distortion or valence disequilibrium which can be induced by the impurity doping. High-pressure synthesis or annealing has shown the capability to recover structural distortions and maintain unstable valences in many materials.^[28] With high-pressure and high-temperature annealing, the Mn concentration of BZA was increased to 28%, ≈2 times that of conventional synthesized samples. The high-pressure stabilized high doping levels in polycrystalline BZA finally led to the highest T_C of 260 K.

Results and Discussion

Crystal Structure

K and/or Mn-doped BZA samples crystalize into ThCr₂Si₂-type structure as shown in Figure 1a. In previous reports, Mn-related impurities formed when Mn doping level was over 15%.^[8] Taking advantage of the high-pressure technique, higher concentrations of Mn can be stabilized in bulk BZA. The purity of all the samples ((Ba_0.7K_0.3)(Zn_1-xMn_x)₂As₂ with x = 0.18, 0.2, 0.22, 0.24, 0.26, 0.28) was confirmed with powder X-ray diffraction (XRD) measurements. Figure 2a shows the XRD patterns and corresponding Rietveld refinement of (Ba_0.7K_0.3)(Zn_0.76Mn_0.24)₂As₂ as a typical example. All the Bragg peaks are indexed under the space group of I4/mmm, indicating the high purity of the samples. Rietveld refinements were used to calculate the lattice parameters of samples. The dopant dependences of the lattice parameters, a and c, are shown in Figure 2b. We can see that the lattice parameters change monotonically with increasing Mn concentrations, suggesting successful chemical substitution.

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Magnetic Properties

Temperature-dependent magnetization (M(T)) measurements were performed to determine T_C of the aforementioned samples. For the sake of simplification, M(T) under the field cooling (FC) process for three selected samples are shown in Figure 3a. Similar to the previous report of BZA with lower doping levels, the upturns on the M(T) curves, which indicate the forming of ferromagnetic ordering, are defined as T_C.^[18] Figure 3b shows a clearly dome-shaped x dependence on T_C and coercive force (H_C). T_C increases with increasing Mn concentrations in the first place, and the highest T_C = 260 K is obtained in the sample with (Ba_0.7K_0.3)(Zn_0.76Mn_0.24)₂As₂. The overdoped Mn damages ferromagnetism due to the increased antiferromagnetic interaction between the nearest neighboring Mn²⁺.

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Field-dependent magnetizations (M(H)) at 5 K and in the vicinity of T_C are shown in Figure 3c,d, respectively. At low temperatures, one can find robust magnetic loops with H_C of ≈0.5 T. The doping-level dependence of H_C also shows a dome-shaped relationship similar to the x dependence of T_C. The sample (Ba_0.7K_0.3)(Zn_0.76Mn_0.24)₂As₂ with the highest T_C exhibits the largest H_C of 0.8 T. The saturate magnetizations (M_S) are ≈1 μ_B/Mn consistent with lower Mn-doped samples.^[9,22] In the vicinity of T_C, magnetic loops are measured to confirm the ferromagnetic ordering. At 257 K, (Ba_0.7K_0.3)(Zn_0.76Mn_0.24)₂As₂ still shows an open loop indicating the forming of ferromagnetic ordering, while the rest of the samples exhibit nearly linear loops indicating paramagnetic states.

Magnetoresistance and Hall Effect

Negative magnetoresistance (MR) is also strong evidence of ferromagnetism in DMS materials, due to the reduction in spin scattering with increasing external magnetic fields.^[5,29–31] The temperature dependence of resistivity shows semiconducting behavior within the measuring temperature range (5 to 300 K). Below T_C, MR can be found for all the samples. At 5 K, butterfly-like MR(H) curves are observed, as shown in Figure 4a. The peaks at around 0.5 T are consistent with H_C from M(H) curves. It is worth noting that the MR is far from reaching saturation at 7 T, where the magnetic moment is nearly saturated. In such conditions, the MR is presumably from the weak localization effects.^[32,33] At high temperatures, negative MR is also clearly present in the vicinity of T_C, as shown in Figure 4b, evidencing the forming of ferromagnetic ordering. For the sample (Ba_0.7K_0.3)(Zn_0.76Mn_0.24)₂As₂ with T_C of 260 K, the maximum MR are −7.5% and −1.7% at 5 and 300 K, respectively. The MR with similar magnitudes have been reported in BZA with lower doping levels.^[27]

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To determine the carrier concentrations, Hall effect measurements were conducted. Figure 4c shows the anomalous Hall effect of (Ba_0.7K_0.3)(Zn_0.76Mn_0.24)₂As₂ at 5 K. For a ferromagnetic DMS material, the carrier scattering by the magnetic ions causes the carriers to accumulate asymmetrically in the transverse direction of the current. This scattering results in an additional contribution to the normal Hall effect, namely, the anomalous Hall effect. This is an important feature of long-range ferromagnetic ordering in a DMS material. The Hall resistance (R_Hall) can be phenomenologically described by Equation (1) 1 $$$\begin{equation}{{R}_{Hall}} = {{R}_0}H + {{R}_s}M\end{equation}$$$where R₀ is the ordinary Hall coefficient, R_s for the anomalous one, and M for the magnetization moment.^[34] At high magnetic fields, the magnetization saturates and then the anomalous Hall component R_sM becomes independent of the magnetic field. Thus, one can deduce the ordinary Hall coefficient R₀ from the high-field slope of R_Hall. The calculated carrier concentration n_p = +3.9 × 10²⁰ cm⁻³ at 5 K, and the positive sign indicates p-type carriers. The value of carrier concentration is comparable to previous studies on lower Mn-doped BZA and classical (Ga,Mn)As.^[9,22,35]

First-Principles Simulations

To study the magnetic interactions between Mn impurities in BZA, a Heisenberg Hamiltonian with the nearest coupling J₁, the next-nearest coupling J_2, the third-nearest neighbor couplings J₃, and the interlayer couplings J_⊥ of the Mn─Mn pairs is employed, as described by Equation (2), 2 $$$\begin{equation}H = \sum\limits_{\left\langle {i,j} \right\rangle } {{{J}_1}{{S}_i} \cdot {{S}_j}} + \sum\limits_{\left\langle {i,j} \right\rangle } {{{J}_2}{{S}_i} \cdot {{S}_j}} + \sum\limits_{\left\langle {\left\langle {\left\langle {i,j} \right\rangle } \right\rangle } \right\rangle } {{{J}_3}{{S}_i} \cdot {{S}_j}} + \sum\limits_{\left\langle {i,i^{\prime}} \right\rangle } {{{J}_ \bot }{{S}_i} \cdot {{S}_{i^{\prime}}}} \end{equation}$$$

Using the density functional theory calculations, the exchange couplings J₁, J₂, J₃ and J_⊥ for the different supercells of Ba(Zn_0.75Mn_0.25)₂As₂, (Ba_0.875K_0.125)(Zn_0.75Mn_0.25)₂As₂, (Ba_0.75K_0.25)(Zn_0.75Mn_0.25)₂As₂ and (Ba_0.5K_0.5)(Zn_0.75Mn_0.25)₂As₂ are calculated. Further details can be found in the Supporting Information. The results are listed in Table 1, with ferromagnetic for J > 0, and antiferromagnetic for J < 0.

Table 1 First-principles magnetic exchange couplings of Mn─Mn pairs in Ba(Zn_0.75Mn_0.25)₂As₂, Ba(Zn_0.75Mn_0.25)₂As₂, (Ba_0.875K_0.125)(Zn_0.75Mn_0.25)₂As₂, (Ba_0.75K_0.25)(Zn_0.75Mn_0.25)₂As₂ and (Ga_0.91Mn_0.09)As. J₁, J₂, J_3, and J_⊥ are intralayer couplings of the nearest, the next-nearest, the third-nearest neighbors and interlayer couplings respectively. Two Mn impurities are coupled ferromagnetically for conditions with J > 0 and antiferromagnetically for conditions with J < 0.

First-principles calculations
	J1 [meV]	J2 [meV]	J3 [meV]	J⊥[meV]
Ba(Zn0.75Mn0.25)2As2 (Ba0.875K0.125)(Zn0.75Mn0.25)2As2	−8.76 −5.46	−2.47 −0.71	0.17 0.58	−1.47 1.15
(Ba0.75K0.25)(Zn0.75Mn0.25)2As2	−1.49	1.73	1.11	2.62
(Ba0.5K0.5)(Zn0.75Mn0.25)2As2 (Ga0.91Mn0.09)As	0.31 8.31	2.95 −0.63	2.95 0.81	2.32 ∖

To estimate the Néel temperature (T_N) for the antiferromagnetic cases and the T_C for the ferromagnetic cases, the following mean-field formula is used, as described by Equation (3), 3 $$$\begin{equation}{{T}_{N/C}} = \frac{2}{{3{{k}_{\mathrm{B}}}}}S(S + 1)\sum\limits_i {\sum\limits_\alpha {Z_i^\alpha {{P}_\alpha }{{J}_i}} } \end{equation}$$$where J_i (i = 1, 2, 3, ⊥) represents the above exchange couplings, Z_i^α is the coordination number of Mn impurities in one inequivalent doping configuration α for a given doping concentration, and P_α is the probability of this doping configuration. Further details can be found in the Supplemental Materials. S = 5/2 is used for the spin of the Mn impurities with five local d orbits. A rescaled method is adopted to counteract the overestimation of the mean-field result, where the calculated mean-field T_C of (Ba_0.75K_0.25)(Zn_0.85Mn_0.15)₂As₂ is approximated to correspond to T_C of 230 K of (Ba_0.7K_0.3)(Zn_0.85Mn_0.15)₂As₂ in the experiment. All mean-field T_C and T_N for Ba(Zn_0.75Mn_0.25)₂As₂ and (Ba_1-yK_y)(Zn_1-xMn_x)₂As₂ are divided by the mean-field T_C of (Ba_0.75K_0.25)(Zn_0.75Mn_0.15)₂As₂ to obtain the ratios, which are used to multiply 230 K and estimate more reliable T_C or T_N as depicted in Figure 5.

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For comparison, the magnetic exchange couplings J₁, J_2, and J₃ and T_C of (Ga_1-xMn_x)As are also calculated in a similar way. The rescaled method is also adopted to counteract the overestimation of the mean-field result, where the calculated mean-field T_C of (Ga_0.figur84Mn_0.16)As is approximated to correspond to the T_C of 200 K of (Ga_0.84Mn_0.16)As in experiments.^[24,36] As shown in Figure 5a, the T_C increases with increased Mn concentration for (Ga_1-xMn_x)As and (Ba_0.75K_0.25)(Zn_1-xMn_x)₂As₂ with x in the range of 5% to 30%. This behavior is consistent with the experimental result of (Ba_0.7K_0.3)(Zn_1-xMn_x)₂As₂. As shown in Figure 5b, (Ba_1-yK_y)(Zn_0.75Mn_0.15)₂As₂ shows antiferromagnetic behavior without hole doping (namely, K doping). With the increased carrier concentration y, the antiferromagnetic coupling is suppressed and becomes ferromagnetic for y reaching 25%. For K-underdoped samples (Ba_0.875K_0.125)(Zn_1-xMn_x)₂As₂, it is antiferromagnetic coupling, and the T_N increases with increased x as depicted in Figure 5c.

Conclusion

The new type of diluted magnetic semiconductors (Ba_0.7K_0.3)(Zn_1-xMn_x)₂As₂ with a record high T_C are synthesized via the proper high-pressure annealing. With Mn content of 24%, we obtain the highest reliable T_C of 260 K among diluted magnetic semiconductors with independent spin and carrier doping, showing promising application potential. Moreover, first-principles calculations of magnetic interactions between nearest-neighbor Mn ions show that the antiferromagnetism can be suppressed by increasing K doping in the DMS (Ba,K)(Zn,Mn)₂As₂. Thus our results suggest a promising method to achieve room temperature or even higher Tc ferromagnetism for (Ba,K)(Zn,Mn)₂As₂ and analogs. It is noted that further K doping over 30% could not be accomplished at current synthesis conditions. Although Ba²⁺ and K⁺ have similar ionic sizes, Ba(Zn,Mn)₂As₂ and K(Zn,Mn)As crystalize into a tetragonal and a hexagonal structure, respectively.^[37] Much higher synthesis pressures would be required to break the limitation of the (Ba,K) solution in (Ba,K)(Zn,Mn)₂As₂.

On the other hand, the DMS (Ba,K)(Zn,Mn)₂As₂, antiferromagnetic BaMn₂As₂, and superconducting (Ba,K)Fe₂As₂ have the identical crystal structure. In addition, there is quite good lattice matching within the a-b plane (mismatch <5%). This unique feature provides distinct advantages in fabricating new functional devices based on the heterojunctions of various combinations of aforementioned diluted magnetic semiconductors, superconductors, and magnetic states.^[3,17,19] The near room-temperature ferromagnetism means that (Ba,K)(Zn,Mn)₂As₂ shows promise for the development of new spintronic devices.

Experimental Section

Synthesis

High-purity raw materials, including Ba, K, Zn, Mn, and As, were mixed and ground in a glove box according to the nominal molar ratio. The mixture loaded in a crucible was sealed in a Nb tube and then a quartz tube, and calcined at 950 K for 12 h. The products were then reground, and annealed under 800 K and 5.5 GPa for 1 h with a high-pressure press. Such high-pressure annealing treatment can increase the chemical solution of Zn-Mn and retain volatile elements simultaneously. It is noted that the high-pressure annealing in this work is different from the high-pressure used in the previous report.^[15] For the former, the samples are fabricated via high-pressure annealing at 800 K to overcome the limitation of chemical solution in the lattice of BZA. For the latter, the samples were synthesized under ambient pressure, and then loaded into high-pressure generators, diamond anvil cells, to study the pressure effect on ferromagnetic interaction and T_C of BZA within temperature range of 2–300 K.

General Properties Characterization

Powder X-ray diffraction (XRD) was carried out for the component analysis of resulting products, using Cu-K_α radiation with a Philips X'pert diffractometer at room temperature. Energy dispersive X-ray analysis (EDX) of a commercial scanning electron microscope (SEM) was used for the confirmation of chemical compositions of polycrystal specimens. The real doping ratio is consistent with nominal composition. For the sake of simplification, the nominal formulas are used in the following text. Characterization of dc magnetic susceptibility for all the samples was accomplished by superconducting quantum interference device (SQUID). Electricity transport measurements were conducted via a physical property measurement system (PPMS).

First-Principles Calculations

First-principles simulations were performed with the projector augmented wave (PAW) method using the Vienna ab Initio simulation package (VASP).^[38,39] The choice of the electron exchange-correlation functional was generalized gradient approximation (GGA) with the form of Perdew-Burke-Ernzerhof (PBE) realization.^[40] The GGA plus on-site Coulomb repulsion U (GGA + U) approach by Dudarev et al. was used to describe strongly localized Mn 3d orbitals.^[41] The effective on-site Coulomb interaction parameter (U = 4 eV) was applied to Mn 3d orbitals. Lattice constants and atomic positions were fully relaxed until the maximum force acting on all atoms was less than 1 × 10⁻³ eV and the total energy was converged to 1 × 10⁻⁷ eV with the Gaussian smearing method. The kinetic energy cutoff of 450 eV was employed. The Brillouin zone was sampled with a 4 × 4 × 8 Monkhorst–Pack grid for calculations of magnetic exchange couplings with 2 × 2 × 1 supercells of (Ba_1-yK_y)(Zn_1-xMn_x)₂As₂.^[42] All doping configurations with corresponding doping probabilities are generated by disorder code.^[43,44]

Acknowledgements

The work was supported by the National Key R&D Program of China (No. 2022YFA1403900), and the CAS Project for Young Scientists in Basic Research (No. YSBR-030). Z.D. acknowledges support of the Youth Innovation Promotion Association of CAS (No. 2020007). B.G. is supported by the National Natural Science Foundation of China (No. 12074378), Chinese Academy of Sciences (No. JZHKYPT-2021-08 and No. XDB33000000). Y.P. and X.L. contributed equally to this work.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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