A comparative study of doping effects of V and Cr on a SrAlSi superconductor

Abstract

It is well known that the superconducting transition temperature (T_c) is very sensitive to the electronic density of states at the Fermi energy (N(E_F)) and the Debye frequency (Θ_D) for a BCS superconductor. However, which one plays a leading role in the ternary silicides AeMSi (Ae = Ca/Sr/Ba and M = Al/Ga) system is still unclear. Here, we report a comparative study of doping effects by V and Cr at Al sites in SrAlSi, which has a relatively high T_c among AeMSi systems. It is found that V and Cr atoms can be successfully introduced into SrAlSi with the actual solid solution limit up to 16 at% and 13 at%, respectively. In this case, the incorporation of V and Cr will have nearly identical effects in decreasing Θ_D. Hall effect measurements demonstrate that V and Cr have dramatically different effects on the carrier concentration upon doping. In SrAl_1−xV_xSi, the carrier concentration is decreased by about three orders of magnitude and V dopants lead to the quenching of superconductivity at the highest doping level. In contrast, Cr almost does not change the carrier concentration, leading to a minor change in T^onset_c of 0.6 K. Our results provide solid evidence that the N(E_F) should be responsible for the T_c in the transition metal doped AeMSi system.

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Introduction

Since the discovery of superconductivity in MgB₂ with a T_c of 39 K,¹ widespread interests have been aroused to explore its isostructural intermetallic compounds with novel physical properties.^1–9 MgB₂ crystallizes in the P6/mmm space group and belongs to the AlB₂ structural type, which is a common porotype for some transition metals and most lanthanide diborides. The AlB₂-type crystal structure consists of alternate stacking of Al layers with triangular lattices and B layers with hexagonal rings. Besides borides, some silicides also possess the AlB₂-type structure. For instance, CaSi₂ has the AlB₂-type structure under pressures over 16 GPa and becomes a superconductor with T_c = 14 K.³ Ternary silicides AeMSi with Ae = Ca/Sr/Ba and M = Al/Ga^1,10,11 are also isostructural to AlB₂, where M and Si commonly take the B sites while Ae occupies the Al sites. Among these ternary silicides, CaAlSi and SrAlSi show the relatively high T_c at 7.8 K⁴ and 4.2 K,⁵ respectively. Several interesting and important characteristics⁶ are revealed by close examination of these two superconductors. For example, opposite responses of T_c upon the application of pressures have been observed in these two compounds⁷ although their electronic structures^6b,8 are similar. Thermodynamic measurements suggest a strong-coupling limit in CaAlSi while the weak coupling strength in SrAlSi.^7,9 The Seebeck coefficient measurements¹⁰ of CaAlSi and SrAlSi indicate that the majority carriers in both are electron-like in contrast to the hole-like carriers in MgB₂.¹¹

For a BCS superconductor, chemical doping is an effective way to tune its superconducting properties. While the intrinsic characters of AeMSi materials are intensively investigated, the effects of transition metal dopants on their superconducting properties are far less understood. Lorenz et al. found the T_c reaches the maximum in CaAl_2−xSi_x (0.6 < x < 1.2) compounds when x = 1, and a possible doping-induced electronic transition at x = 0.75.¹⁰ Recently, Li et al. studied the doping effect by Cu at the Al sites in CaAlSi¹² with the maximum doping concentration of Cu reaching 6 at%. It was found that Cu doping slightly decreases T_c. However, it is unclear whether the N(E_F) or the Θ_D should play a decisive role without further quantitative results. To further explore the doping effects of the transition metal elements, we choose V and Cr to partially substitute Al in SrAlSi. The evolution of crystal structures, magnetic and transport properties of V-substituted and Cr-substituted SrAlSi compounds were carefully studied. We found that the actual solid solution limits of V and Cr in SrAlSi are 16 at% and 13 at%, respectively. V dopants ranging from 0 to 16 at% reduce the carrier concentration from 2.7 × 10²¹ electrons per cm³ to 5.5 × 10¹⁸ electrons per cm³. Correspondingly, T^onset_c decreases rapidly and superconductivity is quenched at the highest doping level. In comparison, Cr dopants ranging from 0 to 13 at% show almost no change in the carrier concentration and the maximum decrease in T^onset_c, 0.6 K, is attained at a Cr nominal dopant amount of ∼13 at%.

Experimental

Synthesis of SrAl_1−xV_xSi and SrAl_1−xCr_xSi compounds

SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15, 0.2 and 0.25) and SrAl_1−xCr_xSi (x = 0, 0.1, 0.2, 0.3 and 0.4) compounds were prepared by high temperature solid-state reactions. The reaction is detailed as follows: predetermined amounts of raw materials including strontium block (99%), aluminum powder (99.9%), vanadium powder (99.99%)/chromium powder (99.99%) and silicon powder (99.999%) were firstly mixed uniformly, then the mixture was pressed into a small thin disk with a diameter of about 1 cm. The disk was sealed into a silica tube under argon atmosphere ambient, and then it was put into a heater. The heater was raised to 950 °C and kept at this temperature for 2 days. The obtained samples were usually inhomogeneous after the first heating. So the samples were reground carefully in argon atmosphere ambient, pressed into pellets again and reheated at 950 °C for 7 days. The metal Sr is easy to volatilize at high temperatures, therefore extra 3% wt of Sr was added to complement the loss.

Powder X-ray crystallography

Room temperature powder X-ray diffraction (PXRD) data for samples SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15, 0.2 and 0.25) and SrAl_1−xCr_xSi (x = 0, 0.1, 0.2, 0.3 and 0.4) were collected on a PANalytical X'pert Pro diffractometer with Cu Kα radiation (40 kV, 40 mA) and a graphite monochromator. Rietveld refinements of data were performed with the FULLPROF package.

Characterization

Actual chemical compositions were determined by energy-dispersive X-ray analysis (EDX) and the morphologies were characterized by a scanning electron microscope (SEM).

Physical properties measurements

Electrical resistivity measurements were performed through the physical property measurement system (PPMS, Quantum Design) and magnetic susceptibilities were measured by a vibrating sample magnetometer (VSM, Quantum Design). The carrier concentration was measured by Hall effect measurement system at room temperature. Density of states (DOS) were calculated using CASTEP program code with plane-wave pseudopotential method¹³ and a generalized gradient approximation with Perdew–Burke–Ernzerhof formula (PBE) for the exchange–correlation potentials¹⁴ was adopted, where self-consistent field strength as 5 × 10⁻⁷ eV per atom was set.

Results and discussion

Fig. 1(a) displays PXRD patterns for a series of nominal SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15, 0.2 and 0.25) samples collected at room temperature. The analysis of PXRD patterns reveals that SrAlSi is the major phase in all samples, where most of diffraction peaks can be well indexed on AlB₂ structure (space group: P6/mmm). Extremely weak peaks (marked by (*)) due to the second phase SrAl₂O₄ are present, which is hard to be eliminated. The relative intensity ratio between the strongest peak of SrAl₂O₄ and SrAlSi is less than 3%. When x = 0.25, however, massive impurities SrSi (marked by (×)) and Al₄₅V₇ (marked by (#)) appear. Emergence of massive impurity phases indicates the solid solution limit of V in SrAl_1−xV_xSi compounds is about x = 0.2. The inset of Fig. 1(a) is the magnified (100) diffractions of the samples, we found that the peak shifts gradually to the higher angle with increasing x till x = 0.2, suggesting the solid solution limit indeed exists and the lattice constant a shrinks with doping. Fig. S1† shows the Rietveld refinements for PXRD data of nominal SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15 and 0.2). All the crystallographic data are summarized in Table S2.† In Fig. 1(b), we plotted the lattice constants a and c as a function of x, which are derived from structural refinements. It is observed that the lattice constant a decreases monotonically from 4.2415(4) Å to 4.2253(3) Å as x gradually varies from 0 to 0.2. We noted that the lattice constant c remains almost the same around 4.750 Å.

Fig. 1 (a) PXRD patterns of nominal SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15, 0.2 and 0.25) compounds. The reflection peaks marked by (*), (×) and (#) are assigned to impurities SrAl₂O₄, SrSi and Al₄₅V₇, respectively. The inset is the magnified (100) reflections of SrAl_1−xV_xSi compounds. (b) The lattice constants a and c as a function of x in SrAl_1−xV_xSi compounds.

Fig. 2(a) shows PXRD patterns for a series of nominal SrAl_1−xCr_xSi (x = 0, 0.1, 0.2, 0.3 and 0.4) samples collected at room temperature. All strong peaks can be indexed with the same hexagonal AlB₂ structure. The remaining weak peaks are attributed to side phases SrAl₂O₄ (marked by (*)) and SrCrO₃ (marked by (o)). It is also noticed that a mass of impurity phases CrAl_0.42Si_1.58 and Cr₅Si₃ arise with x = 0.4. To reveal the evolution of the crystal structure with the increasing content of Cr, we selected the (100) diffraction peak from SrAl_1−xCr_xSi crystals to analyze the peak shift, as shown in the inset of Fig. 2(a). Similar to the case of V-doped samples, the (100) peak shifts to higher diffraction angle with increasing x. Fig. S2† shows the Rietveld refinements for PXRD data of nominal SrAl_1−xCr_xSi (x = 0, 0.1, 0.2, 0.3 and 0.4). All the crystallographic data are summarized in Table S3.† The refined lattice parameters a and c of SrAl_1−xCr_xSi samples are shown in Fig. 2(b). The results showed that the lattice parameter a decreases from 4.2415(4) Å to 4.223(1) Å with increasing x till x = 0.3 and c keeps nearly a constant of 4.750 Å. We attributed the change in lattice parameters to the smaller radius of V and Cr atoms than Al atoms upon doping. The more Al atoms are replaced, the smaller the lattice constant a is. The interlayer spacing of SrAlSi is larger than the distance of intra layer atoms, indicating weaker interactions between interlayers. Accordingly the substitution for Al atoms by V/Cr atoms will bring negligible influence on the interlayer spacing. So the lattice constant c does not show prominent change. The SEM images of the SrAl_1−xV_xSi samples (Fig. S1†) and the SrAl_1−xCr_xSi samples (Fig. S2†) show that the morphology of the particles is the average size of the particles is around 3 μm. To further examine the exact contents of V and Cr in the samples, EDX (Table S1†) and Rietveld refinements (Tables S2 and S3†) were performed to evaluate the values of x in prepared SrAl_1−xV_xSi and SrAl_1−xCr_xSi compounds. As shown in Table S1,† the actual solid solution limits of V and Cr in SrAlSi reach 16 at% and 13 at%, respectively. In SrAl_1−xV_xSi, the results of EDX analysis agree with the nominal contents within the experimental error. The refinement results are also in good accordance with the EDX results (Tables 1 and 2). Meanwhile, larger discrepancy appeared between the measured compositions and the nominal compositions of SrAl_1−xCr_xSi, which could be raised from the appearance of extra impurity SrCrO₃ in the Cr doped system. The trend in variation of Cr measured contents is consistent with that in nominal contents.

Fig. 2 (a) PXRD patterns of nominal SrAl_1−xCr_xSi (x = 0, 0.1, 0.2 0.3 and 0.4) compounds. The diffraction peaks marked by (*), (o), (∀) and (Δ) are assigned to impurities SrAl₂O₄, SrCrO₃, CrAl_0.42Si_1.58 and Cr₅Si₃, respectively. The inset is the (100) reflections of SrAl_1−xCr_xSi compounds. (b) The lattice constants a and c as a function of x for SrAl_1−xV_xSi compounds.

Table 1 Comparison of nominal, refined and EDX characterized compositions for SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15 and 0.2) samples

V content (x)
Nominal	EDX results	Refined results
0	0	0
0.05	0.05	0.05(2)
0.10	0.11	0.11(2)
0.15	0.14	0.14(1)
0.20	0.16	0.16(1)

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Table 2 Comparison of nominal, refined and EDX characterized compositions for SrAl_1−xCr_xSi (x = 0, 0.1, 0.2 and 0.3) samples

V content (x)
Nominal	EDX results	Refined results
0	0	0
0.10	0.09	0.09(2)
0.20	0.11	0.11(1)
0.30	0.13	0.13(1)

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Fig. 3(a) shows the temperature dependence of susceptibility for zero-field-cooled (ZFC) V-doped samples at 40 Oe. In the high temperature range, the magnetic susceptibility is essentially flat and temperature independent, which is a Pauli paramagnet.⁵ Large diamagnetism due to superconductivity was observed and the temperature where the susceptibility starts to drop and deviate the temperature independent behaviour is defined as the T^onset_c. When x = 0, as is the case for SrAlSi, its T^onset_c is 3.8 K, which is close to the previously reported results.⁵ Furthermore, T^onset_c decreases monotonically as x increases. And when x reaches 0.2, the superconductivity almost disappears. In SrAl_1−xV_xSi, there only exists minor impurity SrAl₂O₄, which is a paramagnet¹⁵ and less than 3%. So we think that impurity SrAl₂O₄ will not affect the superconductivity. In addition, the measurements of magnetic susceptibility in SrAl_1−xV_xSi indicate a superconducting dome which is commonly observed in many superconductors. For example, BaAg_xSi_2−x^2e which is a derivant of the AeMSi (Ae = Ca/Sr/Ba and M = Al/Ga) superconductors manifests a superconducting dome. When x changes from 0.2 to 0.4, the onset of superconducting transition varys from 3.19 K to 2.78 K, variation is about 0.4 K. When x increases to 0.5, the onset of superconducting transition drops to 1.22 K. The temperature dependence of ZFC magnetization for samples of SrAl_1−xCr_xSi, measured under the identical conditions as for V-doped samples, as shown in Fig. 3(b), where a magnetic transition signal at about 25 K is attributed to impurity SrCrO₃.¹⁶ To see the variation of T^onset_c with Cr doping, a magnified magnetization curve around the T^onset_c is given in the inset of Fig. 3(b). It is noted that the T^onset_c just slightly decreases as x increases. When x increases to 0.3, T^onset_c reduces from 3.8 K to 3.2 K.

Fig. 3 Temperature dependence of susceptibilities for the samples measured at 40 Oe. (a) SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15, and 0.2), (b) SrAl_1−xCr_xSi (x = 0, 0.1, 0.2 and 0.3). The inset of (a) displays x-depended T^onset_c. Insets of (b) display the enlarged magnetization at a narrow temperature range and x-depended T^onset_c.

Fig. 4(a) displays the temperature dependence of electrical resistivity (ρ) for SrAl_1−xV_xSi compounds. At the same temperature, the electrical resistivity of SrAl_1−xV_xSi compounds with bigger x is larger than that with lower x. The increasing electrical resistivity might be attributed to the decreased carrier concentration which will be mentioned in the latter and the incensement of crystal defects induced by the more substitutions of V for Al sites. In the high temperature range, the resistivity of SrAl_1−xV_xSi varies smoothly. Sharp drops of resistivity due to superconductivity were observed with lowered temperature and the temperature where the resistivity start to drop and deviate the normal state behaviours is defined as the T^onset_c. T^onset_c decreases rapidly with the increasing content of V, which is consistent with the results in Fig. 3(a). When x = 0.2, superconductivity almost disappears although a weak superconducting phase remains which probably results from the inhomogeneous compositions in the sample. Fig. 4(b) displays the temperature dependence of electrical resistivity for SrAl_1−xCr_xSi samples with various Cr concentrations. The increasing electrical resistivity with higher Cr content might be attributed to the impurities and the incensement of crystal defects. It was observed that the transition temperature shifts to lower temperature with the increasing content of Cr. When x = 0.3, the transition temperature reaches 3.4 K, which is in good agreement with the results of the magnetism measurements.

Fig. 4 Temperature-dependent resistivity (ρ) of samples. (a) SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15 and 0.2) compounds, (b) SrAl_1−xCr_xSi (x = 0, 0.1, 0.2 and 0.3) compounds. Insets display the normalized resistivity (ρ/ρ_5K). The inset of (a) displays x-depended T^onset_c.

In order to get insight into the doping effects, we investigate the carrier concentration of V-doped and Cr-doped samples by Hall effect measurements at room temperature, as shown in Table 3. For SrAl_1−xV_xSi, the carrier concentration is 2.7 × 10²¹ electrons per cm³ when x = 0, which is close to the concentration of CaAlSi.¹⁷ It decreases to 3.1 × 10²⁰ electrons per cm³ when x = 0.1 and continuously drops to 5.5 × 10¹⁸ electrons per cm³ when x = 0.2. In contrast, Cr dopant almost maintains the carrier concentration at the order of 10²¹ electrons per cm³ when x changes from 0 to 0.3 (shown in Table 4). These results are well explained by that the V atom has one less valence electron than the Cr atom.

Table 3 Carrier concentration at room temperature for a series of SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15 and 0.2) compounds

SrAl1−xVxSi
Nominal V content (x)	Measured V content (x)	Carrier concentration (electrons per cm^3)
0	0	2.7 × 10^21
0.05	0.05	5.6 × 10^20
0.10	0.11	3.1 × 10^20
0.15	0.14	8.8 × 10^18
0.20	0.16	5.5 × 10^18

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Table 4 Carrier concentration at room temperature for a series of SrAl_1−xCr_xSi (x = 0, 0.1, 0.2 and 0.3) compounds

SrAl1−xCrxSi
Nominal Cr content (x)	Measured Cr content (x)	Carrier concentration (electrons per cm^3)
0	0	2.7 × 10^21
0.1	0.09	5.5 × 10^20
0.2	0.11	6.1 × 10^20
0.3	0.13	3.7 × 10^21

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In order to further explore the doping effects, the total and partial density of states of SrAlSi are calculated and plotted in Fig. 5. Prior to DOS calculation, we first made geometric relaxation by calculation based on density function theory. The lattice constants of SrAlSi are extracted to be a = b = 4.250 Å, c = 4.778 Å, which are slightly larger than the experimental data (a^exp = b^exp = 4.2415(4) Å, c^exp = 4.750 Å). The errors are less than 1%, confirming the validity of our calculation. Partial density of states of SrAlSi indicates that all states included are strongly hybridized. Our calculated results for SrAlSi agree well with the previous ones.^8a N(E_F) would be affected by the doping of V/Cr inducing the shift of the Fermi energy of SrAlSi. We found a small peak in DOS above the Fermi level in SrAlSi, and the DOS at the Fermi level, N(E_F), is 3.66 st. per eV per cell in SrAlSi. The decreasing carrier concentration through doping with V means that the Fermi surface is pushed to lower energy and results in the lower N(E_F). Meanwhile, the N(E_F) of SrAl_1−xCr_xSi is approximately the same to SrAlSi since the carrier concentration is almost unchanged through doping with Cr.

Fig. 5 Total and partial density of states of SrAlSi.

SrAlSi, which has a relatively high T_c among AeMSi (Ae = Ca/Sr/Ba and M = Al/Ga) system, is a typical BCS superconductor. To explain the effects of V and Cr doping on SrAlSi, the BCS theory is applied to show the variation trend of T_c. According to the BCS theory, T_c = 1.13 Θ_D exp (−1/N(E_F)V), where Θ_D is the Debye frequency, N(E_F) is the electronic density of states at the Fermi level and V is the electron–phonon coupling potential. For SrAl_1−xTm_xSi (Tm = V/Cr), V are assumed to be constant since the actual doping content of Tm is less than 16%. In the case of SrAl_1−xTm_xSi (Tm = V/Cr), the incorporation of V and Cr will have nearly identical effect in decreasing Θ_D, because the Θ_D is proportional to M^−1/2 (M is the atomic mass) and the atomic mass of V and Cr are nearly equal. In SrAl_1−xCr_xSi system, both the N(E_F) and the T^onset_c are almost unchanged along with increased Cr dopants, indicating the Θ_D has little influence on T^onset_c. Meanwhile, the carrier concentration in SrAl_1−xV_xSi is decreased about three orders of magnitude with doping and V dopants lead to the quenching of superconductivity. In contrast, Cr almost does not change the carrier concentration, leading to a minor change in T^onset_c of 0.6 K. With the comparison of SrAl_1−xV_xSi and SrAl_1−xCr_xSi, we can conclude that the N(E_F) is the leading role of changing T_c in the AeMSi (Ae = Ca/Sr/Ba and M = Al/Ga) system. This result is consistent with the case of MgB₂ superconductor. Slusky et al.¹⁸ found that introducing electrons into MgB₂ through partial substitution of Al for Mg can rapidly destroyed superconductivity in MgB₂. Our results provide solid evidences that the N(E_F) should be responsible for the T_c in the transition metal doped AeMSi system.

Conclusions

In summary, SrAl_1−xV_xSi (x = 0, 0.05, 0.1, 0.15, 0.2 and 0.25) and SrAl_1−xCr_xSi (x = 0, 0.1, 0.2, 0.3 and 0.4) compounds were successfully synthesized by high temperature solid-state reactions to investigate the doping effects of V and Cr at Al sites on SrAlSi. The actual solid solution limits of V and Cr in SrAlSi are 16 at% and 13 at%, respectively. Particular attention was paid to the carrier concentration and the trend of T_c variation of SrAl_1−xM_xSi. In SrAl_1−xV_xSi, V decreases the carrier concentration by about three orders of magnitude and leads to the quenching of superconductivity at a V dopant level of x = 0.2. The lower N(E_F) is responsible for the decreasing T^onset_c and the quenching superconductivity in SrAl_1−xV_xSi. In contrast, Cr does not significantly change the carrier concentration with increasing x till x = 0.3, which results in almost the same value of N(E_F) of SrAlSi and makes the T^onset_c decrease only by 0.6 K. With the comparison of SrAl_1−xV_xSi and SrAl_1−xCr_xSi, we can conclude that the N(E_F) is the leading role of changing T_c in the AeMSi (Ae = Ca/Sr/Ba and M = Al/Ga) system. These results reported here indicate the valence electrons of transition metal dopants have a profound effect on superconductivity and will offer clues to better understand the doping effect on superconductors and other related functional materials.

Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (Grant No. 91422303, 51532010 and 51472266), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB07020100).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra17081a

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