1. Introduction

Tunable ferromagnetism is one of the most exotic properties in diluted magnetic materials of which local spins are meditated by carriers^[1-5]. Thus transport behaviors have been one of the prominent aspects in the studies of diluted magnetic materials. Particularly, magnetoresistance (MR) effect in diluted magnetic semiconductors (DMS) has been studied for decades for its diversified physical mechanisms and potential application on spintronic circuits^[6]. Diluted magnetic alloys, such as spin-glassy AuFe, AuMn usually exhibit negative MR ratios of only several percentages^[7]. For II–IV based DMSs with low carrier concentration (~10¹⁷ cm^–3), n-type (Cd,Mn)Se and p-type (Hg,Mn)Te show pronounced negative MR^[8]. On the other hand, classical III–V based ferromagnetic (FM) DMS (Ga,Mn)As has negative MR of about 10%–30%^[9].

Recently, a serious of new types of DMS with independent carrier and spin doping were discovered^[10-15]. Among these new materials, an exciting high Curie temperature of 230 K was reached in the so called “122” DMS (Ba,K)(Zn,Mn)₂As₂^[16]; large MR were found in polycrystalline (Sr,K)(Zn,Mn)₂As₂ and (Ba,K)(Cd,Mn)₂As₂^{[17, 18]}_. These features inspired further experimental and theoretical investigations on these new types of DMS^[19-21]. Interestingly, most of them are isostructural to corresponding Fe-based superconductors, which are composed of one FeAs layer sandwiched by two charge layers, offering intriguing possibilities to fabricate and study multilayer isostructure-hetrojuctions^{[13, 22-24]}.

The “111” DMS, Li(Zn,Mn)As and Li(Zn,Mn)P, crystalize into zinc-blende like structure^{[10, 25]}. The related compounds NaZnX (X = P, As and Sb) are found to crystallize in the tetragonal Cu₂Sb-type structure. Most of new types of DMS are based on arsenide compounds, while antimonide based materials are less investigated. Thus in the present work, we focus on the synthesis and characterization of the excess-Na and Mn doped Na(Zn,Mn)Sb. Although the parent phase NaZnSb is a gapless metal, its carrier concentration is only 10¹⁸ cm^–3[26]. Excess-Na doping increases the carrier concentration to 4 × 10¹⁹ cm^–3. Together with Mn-doping, spin-glass (SG) state is found in Na(Zn,Mn)Sb. Despite of short-range ordering, we still observe colossal negative MR in single crystal samples of Na(Zn,Mn)Sb.

2. Experiments

Polycrystalline specimens of Na_1+x(Zn_1–yMn_y)Sb were synthesized by solid state^{[10, 11]}. Single crystal samples were grown by self-flux method^[13]. The real atom ratio of the single crystals was determined by energy dispersive X-ray analysis (EDX).

The crystal structure of the polycrystalline and single-crystal specimens was characterized by X-ray diffraction (XRD) using a Philips X’pert diffractometer at room temperature. Rietveld refinements were performed with GSAS software packages to obtain lattice parameters^[27]. DC magnetic susceptibility was measured between 2 and 300 K with a superconducting quantum interference device (SQUID) magnetometer. A physical properties measurement system (PPMS) was used for AC magnetic susceptibility and electrical transport measurements. Resistivity measurements were conducted with the four-probe method, and Hall effect was measured with standard Hall bar contact.

3. Results and discussion

The XRD patterns and crystal structure of Na(Zn,Mn)Sb are shown in Fig. 1. In Fig. 1(a) all the peaks of the polycrystalline Na_1.1(Zn_1–yMn_y)Sb (0.05 ≤ y ≤ 0.40) can be indexed with a Cu₂Sb-type structure (space group P4/nmm). Fig. 1(b) shows the crystal structure of Na(Zn,Mn)Sb where (Zn,Mn)Sb₄ tetrahedra form square a-b planes and Na layers separate (Zn,Mn)Sb layers along c-axis. The volume of unit cell decreases with increasing Na, while Mn-doping increases the volume of unit cell (Fig. 1(c)). The changes of cell volume suggest successful chemical doping of Na and Mn. The real atom ratio of the single crystals with two nominalcompositions Na_1.1(Zn_0.9Mn_0.1)Sb and Na_1.1(Zn_0.4Mn_0.6)As are Na_1.09Zn_0.88Mn_0.12Sb and Na_1.12Zn_0.36Mn_0.64Sb respectively. The inset of Fig. 1(d) shows a typical piece of single crystal with dimensions of 3 × 2 × 0.25 mm³. The XRD patterns of Na_1.09Zn_0.88Mn_0.12Sb and Na_1.12Zn_0.36Mn_0.64Sb are shown in Fig. 1(d). Only peaks of (00l) appear, indicating the surfaces of the single crystals are perpendicular to the crystallographic c-axis.

For varying Na concentrations of Na_1+x(Zn_1–yMn_y)Sb, the samples with x = 0.1, i.e., Na_1.1(Zn_1–yMn_y)Sb, have most distinct magnetic transition. Thus we focus our discussion on the sample Na_1.1(Zn_1–yMn_y)Sb in the following text. Temperature-dependence of DC magnetization, (M(T)) for polycrystalline samples with 0.05 ≤ y ≤ 0.4 are plotted in Fig. 2(a), where samples with low Mn concentrations (y = 0.05 and 0.1) don’t show visible magnetic transition down to 2 K. For samples with more Mn, upturns appear on both ZFC and FC curves at about 12–15 K. On lowing temperature, “λ”-shape divergences between ZFC and FC can be found, which resemble spin-glass like transitions. For y ≤ 0.3, the irreversible temperatures (T_irr) and the maximum points on ZFC (T_s) increase from 8.6 to 12.9 K and 7.0 to 12.0 K with increasing Mn doping levels respectively. When y increases to 0.4, T_irr and T_s decrease to 9.7 and 10.0 K respectively. Fig. 2(b) shows field-dependence of magnetization (M(H)) where “S”-sharp curves also indicate spin-glass like states of magnetic moments. The open loops, which are sign of existence of FM component, are only visible in the sample with y > 0.1. Magnetic anisotropy of single crystal Na_1.12Zn_0.36Mn_0.64Sb is shown in Fig. 2(c) where out-of-plane (H//c) magnetization is larger than in-plane (H//ab) magnetization in both M(T) and M(H) curves. The open out-of-plane hysteresis loop demonstrates FM component along c-axis.

It is noteworthy that the magnetic signal indeed shows a non-monoclinic change with Mn doping levels (Figs. 2(a) and 2(b)). It firstly increases at lower Mn doping levels and then decreases at higher Mn concentrations. The magnetic signal is basically from spin glass ordering, which is generated by magnetic frustration. Generally, there are ferromagnetic and antiferromagnetic interactions in a diluted magnetic material. In Na(Zn,Mn)Sb, the former is carrier-mediated between two distanced Mn²⁺, and the latter is short range between neighbor Mn²⁺. When Mn concentration is low, neighbor Mn are relatively rare. Thus, ferromagnetic and antiferromagnetic interactions are comparable and spin glass ordering can be enhanced with increasing Mn. However, when Mn concentration is high, neighbor Mn dominate the lattice. Thus, antiferromagnetic interaction is predominating, and one can find that spin glass ordering is suppressed by further Mn-doping.

To confirm the spin-glass behaviors, AC susceptibility measurements were performed. As a typical example, Fig. 3(a) shows the results of AC susceptibility under zero field of different frequencies f with amplitude of H = 10 Oe for Na_1.1(Zn_0.75Mn_0.25)Sb. Both of the real part (χ′) and imaginary part (χ′') show frequencies-dependence, a hallmark of magnetic glassy state. The peaks on the real part χ′(T) (freezing temperature, T_f) and χ′'(T) shift to higher temperatures with increasing frequencies. This frequency dependence of T_f (Eq. (1)) is usually characterized by the term^[28],

$$K = \Delta T_{f}/[T_{f} (\Delta\log f)].$$

(1)

We obtained K = 0.033 which is in the range 0.004–0.08 for spin-glass systems. Another way to characterize spin-glass behavior is to fit T_f dependence of f with critical slowing down relation (Eq. (2))^[29],

$$\frac{\tau }{{\tau }_{0}}={\left(\frac{{T}_{f}-{T}_{0}}{{T}_{0}}\right)}^{-zv} ,$$

(2)

where τ₀ is the characteristic relaxation time of single spin flip, τ = 1/f, T₀ is underlying spin-glass transition temperature determined by the interactions in the system, z is the dynamic critical exponent, and ν is the critical exponent of the correlation length. The best fitting parameters obtained for polycrystalline Na_1.1(Zn_0.75Mn_0.25)Sb are T₀ = 11.52 K, τ₀ = 10^–10 s, and zν = 7.3. The values expected for canonical spin-glassed are τ₀ = 10^–10–10^–12 s and zν = 5–10. The obtained parameters are in the range of typical spin-glasses (Fig. 3(b)). For polycrystalline Na_1.1(Zn_0.6Mn_0.4)Sb the obtained parameters are K = 0.056, T₀ = 13.79 K, τ₀ = 10^–8, and zν = 4.9. The increasing K with the increasing Mn concentration indicates T_f becomes more frequencies-dependent. One can also notice that the parameter K is still within the range of typical spin-glasses but τ₀ doesn’t.

Fig. 4(a) shows resistivity dependence of temperature (ρ(T)) of the parent phase, polycrystalline NaZnSb. The metallic behavior is consistent with previous report^[26]. According to Hall effect measurements the majority carrier is hole with nearly constant concentration of 9 × 10¹⁸ cm⁻³ at 2 and 50 K (inset of Fig. 4(a)). Excess-Na doping induces extra holes into the material. Fig. 4(b) shows Hall resistivity of single crystal Na_1.09(Zn_0.88Mn_0.12)Sb at varying temperatures. At low temperature (10 and 15 K) where short-range ordering forms, it is surprising to find larger anomalous Hall effect (AHE) dominates low field range. Large AHE has also been found in SG-like Ge_1–x–ySn_xMn_yTe^[30]. The AHE indicates strong spin-orbit coupling and spin polarization^[31]. The hole concentrations of single crystal Na_1.09(Zn_0.88Mn_0.12)Sb is 3.0 × 10¹⁹ cm⁻³ at 100 K, which is over three times larger than that of parent phase. The hole concentration of Na(Zn,Mn)Sb is slightly smaller than that of Li(Zn,Mn)As and (Ba,K)(Zn,Mn)₂As₂^{[10, 11]}.

On the other hand, Mn-doping dramatically increases resistivity of the system, particularly at low temperature. Na_1.12(Zn_0.36Mn_0.64)Sb has ρ_5K = 6826.5 Ω∙mm and ρ_20K = 2455.2 Ω∙mm while Na_1.09(Zn_0.88Mn_0.12)Sb has ρ_5K = 9.1 Ω∙mm and ρ_20K =3.9 Ω∙mm. Nevertheless, Mn-doping actually decreases carrier concentration only by relatively small amplitude. The hole concentration of Na_1.12(Zn_0.36Mn_0.64)Sb is 1.7 × 10¹⁹ cm⁻³ at 100 K which is comparable to that of Na_1.09(Zn_0.88Mn_0.12)Sb (3.0 × 10¹⁹ cm⁻³ at 100 K). Thus, there must be other factor to increase resistivity in heavy Mn-doping level sample. In a material doped by magnetic element, both disorder-induced localization and magnetic scattering are feasible to reduce mean free path of carriers and in turn to increase resistivity. To clarify the puzzle, a sample with nonmagnetic-substitution, Na(Zn,Mg)Sb, was synthesized and characterized. Although only 5% Mg could be doped into Zn site without inducing a second phase, one can still find the distinctly difference between Na_1.1(Zn_0.95Mg_0.05)Sb and Na_1.1(Zn_0.95Mn_0.05)Sb. On lowering temperature, both of the samples show metallic behavior until 30–40 K and then monotonic increases of resistivity. However, amplitude of uprising on ρ(T) of Mn-doped-sample is 5 times larger than that of Mg-one, implying magnetic scattering is a main factor to influence conduction behavior in Na(Zn_,Mn)Sb compounds (Fig. 4(c)).

At low temperature, large MR has been observed in both polycrystalline and single crystal samples. For polycrystalline samples without spin glass (SG) transition, MR (MR ≡ [ρ(H) − ρ(0)]/ρ(0)) are significantly smaller, e.g. MR_2K = –5% and –13% in Na_1.1Zn_0.95Mn_0.05Sb and Na_1.1Zn_0.9Mn_0.1Sb. MR_2K dramatically increases to –90% in polycrystalline Na_1.1Zn_0.85Mn_0.15Sb where spin-glass transition occurs at about 5 K. Two single crystal samples also present colossal MR at low temperature. In Fig. 5(a), ρ(T) of single crystal Na_1.09(Zn_0.88Mn_0.12)Sb at various applied fields are plotted. The curves diverge at about 15 K where upturn on M(T) appears. The uprising on ρ(T) is completely suppressed by magnetic field at H = 7 T. In Fig. 5(b), MR_20K(H) doesn’t saturate at 7 T and the maximum value is –24%. On lowering temperature, MR(H) curves gradually saturate and reach larger value with MR_2K of –70%. The hysteresis on MR_2K(H) is about 1 T, close to the value obtained from M(H). Single crystal Na_1.12(Zn_0.36Mn_0.64)Sb shows similar behavior with larger MR_2K of –94% (Figs. 5(c)–5(d)).

Different from FM (Ba_0.9K_0.1)(Cd_2−xMn_x)₂As₂, (Sr_0.9K_0.1)(Zn_1.8Mn_0.2)₂As₂, and GaMnAsP, which also showed colossal negative MR in FM states, Na(Zn,Mn)Sb manifested colossal negative MR in SG states^{[17, 18, 32]}. On the other hand, the striking negative MR in SG (Cd,Mn)Se and (Hg,Mn)Te is associated with sp-d exchange effects or bound magnetic polarons^[8]. Note that their carrier concentrations are 2 orders lower than tile materials, thus the microscopic models for MR could be completely different. Taking into account the magnetic scattering from Mn, we propose that the negative MR is related with spin scatting declining under external fields. More importantly, in II–VI DMSs isovalent Mn²⁺ doping provides only spin but not carrier. As discussed above, carrier concentration of Na(Zn,Mn)Sb can be tuned by controlling extra Na-doping level. On the other hand, Na(Zn,Mn)Sb is not only isostructural to but also lattice-matched with some functional materials, such as high-temperature Fe-based superconductor NaFeAs and antiferromagnetic NaMnAs. This feature offers possibilities to fabricate and study isostructural heterojunctions composed by various combinations of these materials.

4. Conclusion

In summary, a new diluted magnetic compound Na(Zn,Mn)Sb with decoupled charge and spin doping has been synthesized. With co-doped Excess-Na and Mn to induce hole carrier and spin, Na(Zn,Mn)Sb can establish a spin-glass ordering at low temperature. The detailed studies indicate that colossal negative magnetoresistance is related with spin-glass ordering. The maximum value of magnetoresistance of –94% has been found in single crystal sample. The title material extends magnetic states to explore colossal magnetoresistance.

Acknowledgements

This work was financially supported by the Ministry of Science and Technology (MOST), NSF of China through the research projects (2018YFA03057001, 11820101003), and CAS Project for Young Scientists in Basic Research (YSBR-030). Z. Deng acknowledges support of Beijing Nova program (2020133) and the Youth Innovation Promotion Association of CAS (2020007).