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ABSTRACT Recently a new diluted magnetic semiconductor, (Ba,K)(Zn,Mn)2As2 (BZA), with high Curie temperature was discovered, showing an independent spin and charge-doping mechanism. This

makes BZA a promising material for spintronics devices. We report the successful growth of a BZA single crystal for the first time in this study. An Andreev reflection junction, which can be

used to evaluate spin polarization, was fabricated based on the BZA single crystal. A 66% spin polarization of the BZA single crystal was obtained by Andreev reflection spectroscopy

analysis. SIMILAR CONTENT BEING VIEWED BY OTHERS CRYSTAL-SYMMETRY-PAIRED SPIN–VALLEY LOCKING IN A LAYERED ROOM-TEMPERATURE METALLIC ALTERMAGNET CANDIDATE Article 31 March 2025 ANTISKYRMIONS

AND THEIR ELECTRICAL FOOTPRINT IN CRYSTALLINE MESOSCALE STRUCTURES OF MN1.4PTSN Article Open access 20 December 2022 LARGE SPIN–ORBIT TORQUE IN BISMUTHATE-BASED HETEROSTRUCTURES Article 05

December 2023 INTRODUCTION Diluted magnetic semiconductors (DMSs) have attracted research attention because of their physical properties and applications for spintronics devices since the

discovery of (Ga,Mn)As film by H. Ohno in the 1990s1,2,3,4,5,6,7. In these III–V DMSs, such as (Ga,Mn)As and (In,Mn)As, divalent Mn substitution into trivalent Ga (or In) sites leads to

severely limited chemical solubility, resulting in metastable specimens that only exist as epitaxial thin films2. The heterovalent substitution, which simultaneously dopes hole carriers and

spins, makes the flexible tuning of quantum freedom i.e., the individual control of charge and spin concentrations, difficult in DMS. To solve these problems, several new types of DMSs with

independent spin or charge doping were synthesized. Examples include “111” type Li(Zn,Mn)As, “122” type (Ba,K)(Zn,Mn)2As2 (BZA), and “1111” type (La,Ca)(Zn,Mn)SbO, which are named by the

chemical ratio of their parent phases8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28. Among the new DMSs, the ThCr2Si2-type BZA has a Curie temperature (_T_c) of up to 230 K,

which marks the current reliable record _T_c for DMSs where ferromagnetism is mediated by carriers12,13. BZA is one of the milestones in DMS research28. A robust nearest-neighbor

ferromagnetic correlation that exists above the ferromagnetic ordering temperature suggested the potentialof discovering a higher _T_c in further study25. Angle-resolved photoemission

spectroscopy showed a clear impurity band of Mn-doping well below the Fermi energy26,27. Besides, the excellent match of lattice parameters (within 5% mismatch) among “122” type DMS BZA,

“122” iron-based superconductor (Ba,K)Fe2As2, and antiferromagnetic BaMn2As2 is promising for fabricating heterojunctions with different types of ordering13. Thus, BZA provides a unique

opportunity to elucidate the intrinsic physics of DMSs, and their physically transparent description may also be general and applicable to other DMS materials24,28,29. For both fundamental

understanding and potential applications on spintronicss devices, direct measurement of spin polarization (_P_) in BZA is an important parameter. The Andreev reflection (AR) technique has

been applied to measure the spin polarization rate of prototypical III-V based DMS, such as 85% for (Ga,Mn)As30, 57% ± 5% for (Ga,Mn)Sb31 and 72% for (In,Mn)As32. Single crystals with

various K- and Mn-doping levels have been grown, and the _T_c of crystals are controlled with K and Mn concentrations, that is, carrier and spin density, respectively. As an initial attempt,

selecting a (Ba0.904K0.096)(Zn0.805Mn0.195)2As2 crystal that shows good shape and size allows the fabrication of Andreev reflection junction. In this study, we report the basic properties

of (Ba0.904K0.096)(Zn0.805Mn0.195)2As2 single crystal and the degree of spin polarization obtained from the crystal-based Andreev reflection spectroscopy. RESULTS AND DISCUSSION CHEMICAL

COMPOSITION AND CRYSTAL STRUCTURE Chemical compositions and morphology of the single crystal were investigated through energy dispersive X-ray analysis (EDX) and inductively coupled plasma

(ICP) mass spectrometry. The real atom ratio, (Ba0.904K0.096)(Zn0.805Mn0.195)2As2, was determined by ICP. We also used EDX to analyze the real atom ratio and the doping homogeneity, and its

results were consistent with the ICP results. Figure 1 shows the obtained BZA crystals with a typical size of 3 × 3 mm2. The X-ray diffraction patterns of the obtained crystals only show the

(002n) peaks of the BZA structure as illustrated in Fig. 1. The unit cell constants are calculated as c = 13.4658(6) Å, which is consistent with previous reports13. To further confirm the

phase, single crystals were ground to conduct powder X-ray diffraction. The obtained pattern fits well with the structure of ThCr2Si2. MAGNETIC PROPERTIES The DC magnetic susceptibility of

the BZA single crystal was characterized using a superconducting quantum interference device magnetometer (Quantum Design) in both zero-field-cooling (ZFC) and field-cooling (FC) modes. Both

in-plane magnetization _M_ versus _T_ data (Mab(T)) and the _H_ // _c_ axis Mc(T) at _H = _500 Oe, shown in Fig. 2(a), exhibit clear ferromagnetic enhancements at around 50 K. A precise

determination of _T_c can be done via critical exponent analysis, which requires a fine measurement of M-H data in a sufficiently small temperature interval over a large temperature region.

Ferromagnetism is also evident from the _M_(_H_) plots shown in Fig. 2(b) inset with a saturation moment _M__sat_ of about 0.5 and 0.3 (±0.03) μB/Mn in Mc(H) and Mab(H), respectively. The

_M__sat_ is defined as high-field _M_(_H_) data at 2 K after subtracting the small T-linear component6. As discussed in our previous paper on polycrystalline samples, the antiferromagnetic

coupling of Mn to the nearest neighboring Zn sites can reduce the saturation moment and also cause a linear component on the M(H) curves simultaneously18. The small T-linear component of a

current single crystal is calculated at 0.059 and 0.057 μB/T along the c-axis and the ab-plane, respectively. The coercive forces, _H__c__c_ in Mc(H) and _H__c__ab_ in Mab(H), are about 5300

and 1200 Oe. The values of _H__c__c_ and the _H__c__ab_ become smaller when temperature rises while _M__sat_ values along the c-axis are always larger than those in the ab-plane at any

temperature from 10 to 105 K, as shown in Fig. 2(c) and (d), respectively. The crystals show clear anisotropic behavior with easy axis along c from the measurements of M(T) and M(H).

ELECTRICAL TRANSPORT PROPERTIES Figure 3(a) shows the temperature dependence of resistivity with electrical current in the ab-plane (ρab(T)). Resistivity grows as temperature falls by virtue

of the semiconductor behavior and localization effect33. Magnetoresistance (MR) and Hall effect measurements were performed with the electrical current in the ab-plane ranging from 2 to 130

 K and with the magnetic field parallel to the c-axis of up to 14 T. Figure 3(b) shows the change of (MR-Rxx) at several selected temperatures from 2 to 130 K, and Fig. 3(d) shows the

corresponding Hall resistance, Rxy. The negative slope in Hall resistance at high magnetic field indicates a p-type carrier, which is consistent with the substitution of monovalent K into

divalent Ba. The salient features of Rxx and Rxy are the gradual emergence of hysteresis at temperatures below 10 K, from which a coercive field _H__c__c_ around 5300 Oe can be clearly

identified at 2 K, which agrees well with the magnetization measurement shown in Fig. 2(b). Based on the transport measurements, we observed non-linear Hall resistance at low magnetic field

of up to 70 K. The Hall resistance above 70 K becomes linear, which suggests spin correlation effect does not occur. However, this temperature was not necessarily similar to the

ferromagnetic transition (long-range order) temperature if a region with short-range spin correlation exists, such as in GaMnAs1 and in BZA25. Therefore, 50 and 70 K represent two emergence

points with different types of spin correlation for long-range ordering and short-range fluctuations, respectively. In addition, we also noticed an MR-Rxx “overlap” between 50 and 60 K,

which is near _T_c as shown in Fig. 3(b). The “overlap” results from the sudden reduction of MR above _T_c of 60 K, which is easily identifiable in Fig. 3(c). This phenomenon was also

observed in (Ga,Mn)As1,34. To determine the carrier density for BZA, we made a more quantitative analysis of hall resistance. Generally, the scattering from the magnetic ions in the

ferromagnetic statue of a DMS material causes the carriers to accumulate asymmetrically in the transverse direction relative to the electric current, giving an additional contribution to the

normal Hall effect, which is called anomalous Hall effect33. The Hall resistance, therefore, can be phenomenologically expressed as

$${\rm{R}}{\rm{x}}{\rm{y}}{={\rm{R}}}_{{\rm{0}}}{{\rm{B}}+{\rm{R}}}_{{\rm{s}}}{\rm{M}}({\rm{B}}),$$ (1) where R0 is the ordinary Hall coefficient; Rs is the anomalous Hall coefficient; and M

is the magnetization moment. As mentioned, a small paramagnetic background occurs during field-dependent magnetization measurements at low temperatures in this material, and the

magnetization saturates only until the magnetic field reaches ~11–14 T. In Fig. 3(c), the Rxy at these high-field regions are almost straight lines, implying the dominance of a single-type

carrier near the Fermi surface responding to the magnetic field. Therefore, a single band model of Eq. 1 justifies the Hall effect analysis in BZA. As the magnetization saturates at a high

magnetic field, the anomalous Hall resistance RsM(B) becomes independent of the magnetic field, and we can deduce the ordinary Hall coefficient R0, which is simply equivalent to the

high-field slope of Rxy in Fig. 3(c). Then, the hole carrier density np for every temperature can be deduced from the relation np = 1/e|R0|. Figure 3(d) shows the plot of np versus T, where

the carrier density increases monotonically from 2.82 × 1020 cm−3 at 2 K to 4.80 × 1020 cm−3 at 130 K. Highly similar to a semiconducting behavior, the observed increase of carrier density

under elevated temperatures may arise from the enhanced thermal excitation of carriers from the impurity band to the conduction band. SPIN POLARIZATION The spin polarization rate is one of

the key parameters of DMS for direct fundamental and applied relevance. _P_ values of various traditional DMS materials have been determined by analysis of Andreev reflection spectroscopy.

Similarly, we use Andreev reflection spectroscopy to directly probe the electron spin polarization in the BZA single crystal. This method is successfully applicable in measuring the spin

polarization in (Ga,Mn)As30, (Ga,Mn)Sb31, and (In,Mn)As32 along with other ferromagnetic materials, such as (La,Sr)MnO335, CrO236, EuS37, and HgCr2Se438. The inset of Fig. 4 shows a

schematic view of the BZA/Pb junction. The typical junction area is around 100 × 100 μm2. The differential conductance, defined as G(_V_) = dI(_V_)/d_V_, was measured as a function of

dc-bias voltage (_V_) crossing the junction by using phase-sensitive lock-in techniques. The amplitude of the ac modulation output from the lock-in amplifier was kept around 20 nA, which is

sufficiently small to avoid spurious artificial effects. Normalization of the differential conductance G to G0 was conducted with G0 at a magnetic field of 0.25 T. In Fig. 4, we present the

temperature dependence of G/G0 from 1.7 to 35 K, where a dramatic drop appears at T = 7.2 K. This temperature corresponds exactly to the superconducting phase transition of Pb, and the

dropping of G/G0 confirms that the Andreev reflection process occurs at the interface between BZA single crystal and the superconducting Pb film. From the plot of G/G0 versus dc-bias _V_ in

Fig. 5 with several temperatures from 1.7 to 7 K, we also observed a suppression of the Andreev reflection spectra inside the superconducting gap, which can be attributed to the

ferromagnetism originating from spin-imbalanced density of states around the Fermi level in BZA. The imbalance of spin density partially inhibits the formation of Cooper pairs and their

tunneling into the superconductor. We used the modified Blonder–Tinkham–Klapwijk (BTK) theory39 to quantitatively describe the electron tunneling process at interface between ferromagnetic

material and s-wave superconductor. Taking account two basic processes: Andreev reflection and normal reflection, current density _I_tot across the interface can be described by Eq. 2,

$${I}_{{\rm{tot}}}=(1-|P|){I}_{{\rm{u}}}+|P|{I}_{{\rm{p}}}$$ (2) where the spin unpolarized current _I_u and spin polarized current _I_p are separately taken into account with a weight of

the spin polarization _P_, which is defined as _P_ = (N↑ − N↓)/(N↑ + N↓) where N↑/N↓ is the density of state for spin up/down band. For each current _I_u and _I_p, it takes

$$I=2{\rm{e}}AN{{\rm{\nu }}}_{F}{\int }^{}(f(E-V))-f(E)(1+{A}_{u}(E)-{B}_{u}(E)){\rm{d}}E$$ (3) $$I=2{\rm{e}}AN{{\rm{\nu }}}_{F}{\int }^{}(f(E-V))-f(E)(1+{A}_{p}(E)-{B}_{p}(E)){\rm{d}}E$$

(4) where _e_ is the electron charge; _A_ is the junction area; _N_ is the density of state around Fermi level _E_F; _ν_F is the Fermi velocity; _f_(_E_) is the Fermi-Dirac distribution at

temperature of _T_; _V_ is the biase voltage across the junction; _A__u_ and _B__u_ are respectively the Andreev reflection and normal reflection probability for spin unpolarized current

while _A__p_ and _B__p_ are corresponding polarized current respectively. Table 1 lists the expressions of _A__p_, _B__p_, _A__u_, and _B__u_. The deviative of _I_tot with biase voltage _V_

to attain the conductivity _G_(_V_) (_G_(_V_) = d_I_tot/d_V_) with a final normalization to _G_0 from |_E|_ >> Δ limit, results _G_(_V_)/G0:

$$\frac{G(V)}{{G}_{0}}=\frac{1}{{G}_{0}}\frac{d{I}_{tot}}{dV}=\frac{1}{{G}_{0}}[(1-|P|)\frac{d{I}_{u}}{dV}+|P|\frac{d{I}_{p}}{dV}],\,{G}_{0}\equiv \mathop{\mathrm{lim}}\limits_{|E| > >

\Delta }\frac{d{I}_{tot}}{dV}$$ (5) Figure 5 presents the fitting curves along with the experimental data for comparison with all data that fit well in the entire temperature range and the

extracted fitting parameters. We only found the superconducting gap, Δ, as a decreasing behavior in elevated temperatures from the fitting result with different temperatures, strongly

suggesting the determination of parameters, _P_ and _Z_, in the fitting process and the temperature dependence of Δ, _Z_, and _P_ are all behaved as expected behavior from the BTK theory.

The curve fittings have also resulted in a small _Z_ value (Z = 0.38 << 1), which implies the manifestation of a clean and transparent interface between BZA crystal and Pb film in our

junctions. A small _Z_ value is a crucial requirement in spectral analysis because it directly warrants the reliability and accuracy for extracting the spin polarization in the fitting

process, our result on _Z_ further confirms the determination of spin polarization _P_ in our Andreev reflection spectra analysis, which is 66% ± 1% for the BZA single crystal. CONCLUSIONS

We have successfully grown the (Ba,K)(Zn,Mn)2As2 single crystal for the first time. The crystal shows a ferromagnetic transition with easy magnetization axis along the c-axis. The carrier

density is determined from the anomalous Hall effect from 2.82 × 1020 to 4.80 × 1020 cm−3 as the temperature increases from 2 to 130 K. More significantly, the Andreev reflection junction

from the selected large single crystal was fabricated to testify spin polarization degree of BZA, and 66% spin polarization was reached. The success on Andreev reflection junction paves a

solid route for fabricating multilayer junctions based on BZA DMS. METHOD Single (Ba0.904K0.096)(Zn0.805Mn0.195)2As2 crystal was grown via the flux technique. Precursor materials of

(Zn,Mn)As mixture were first prepared with high-purity Zn, Mn, and As in a sealed tube. The samples were heated at 750 °C and held for several hours before cooling down to room temperature.

Mixtures of precursors with high-purity Ba and K in appropriate molar ratio were loaded into the niobium tube with argon under 1 atm pressure before sealing into a quartz tube. The process

was handled in a glove box with high-purity argon to protect the materials from reacting with air or water. The quartz tube was heated at 1200 °C and held for several hours before cooling

down to room temperature at a rate of 3 °C/h. The recovered samples were characterized by X-ray powder diffraction with a Philips X’pert diffractometer using Cu-_Kα_ radiation. Real

compositions were determined by using EDX on a commercial scanning electron microscope and ICP mass spectrometry. The DC magnetic properties were examined by using a Superconductivity

Quantum Interference Device (Quantum design), and transport properties and Andreev reflection junction were observed by a Physical Property Measurement System (Quantum design) with lock-in

techniques. During the transport experiments, the single crystals were cleaved to obtain a clean fresh surface for good ohmic contact. A standard four-point method was employed to eliminate

contact resistance with a center electrode pad of 0.5 mm × 0.5 mm2 by using sliver paint as an electric contact and gold wire as electric leads. A current of 50 μA was used during all

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_Phys. Rev. B._ 25, 7 (1982). Article  Google Scholar  Download references ACKNOWLEDGEMENTS This study was supported by the Natural Science Foundation (NSF) and Ministry of Science and

Technology(MOST) of China through research projects, as well as by CAS External Cooperation Program of BIC (112111KYS820150017). This work was also supported by NSF of China 61425015. The

work at Columbia was supported by NSF DMR-1436095, DMR-1610633, and the REIMEI project of the Japan Atomic Energy Agency. AUTHOR INFORMATION Author notes * G. Q. Zhao and C. J. Lin

contributed equally to this work AUTHORS AND AFFILIATIONS * Institute of Physics, Chinese Academy of Sciences; Collaborative Innovation Center of Quantum Matter, Beijing, 100190, China G. Q.

Zhao, C. J. Lin, Z. Deng, G. X. Gu, S. Yu, X. C. Wang, Y. Q. Li & C. Q. Jin * University of Chinese Academy of Sciences, Beijing, 100190, China G. Q. Zhao, Y. Q. Li & C. Q. Jin *

Department of Physics, Columbia University, New York, NY, 10027, USA Z. Z. Gong & Yasutomo J. Uemura Authors * G. Q. Zhao View author publications You can also search for this author

inPubMed Google Scholar * C. J. Lin View author publications You can also search for this author inPubMed Google Scholar * Z. Deng View author publications You can also search for this

author inPubMed Google Scholar * G. X. Gu View author publications You can also search for this author inPubMed Google Scholar * S. Yu View author publications You can also search for this

author inPubMed Google Scholar * X. C. Wang View author publications You can also search for this author inPubMed Google Scholar * Z. Z. Gong View author publications You can also search for

this author inPubMed Google Scholar * Yasutomo J. Uemura View author publications You can also search for this author inPubMed Google Scholar * Y. Q. Li View author publications You can

also search for this author inPubMed Google Scholar * C. Q. Jin View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS C.Q.J. conceived the

project. G.Q.Z. grows the single crystals. G.Q.Z. and C.J.L. conducted the measurements. G.Q.Z., C.J.L., G.X.G., Z.D., Y.Q.L. & C.Q.J. performed the data analysis. The obtained results

are discussed with X.C.W., S.Y., Z.Z.G., Y.J.U., G.Q.Z., Y.Q.L. & C.Q.J. wrote the manuscript. All authors reviewed the manuscript. CORRESPONDING AUTHORS Correspondence to Y. Q. Li or

C. Q. Jin. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare that they have no competing interests. ADDITIONAL INFORMATION PUBLISHER'S NOTE: Springer Nature remains neutral

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http://creativecommons.org/licenses/by/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Zhao, G.Q., Lin, C.J., Deng, Z. _et al._ Single Crystal Growth and Spin

Polarization Measurements of Diluted Magnetic Semiconductor (BaK)(ZnMn)2As2. _Sci Rep_ 7, 14473 (2017). https://doi.org/10.1038/s41598-017-08394-z Download citation * Received: 30 January

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