Anomalous critical point behavior in dilute magnetic semiconductor $(\mathrm{C}{\mathrm{a}}_{,}\mathrm{Na}){(\mathrm{Z}{\mathrm{n}}_{,}\mathrm{Mn})}_{2}\mathrm{S}{\mathrm{b}}_{2}$

Anomalous critical point behavior in dilute magnetic semiconductor $(C a_{,} Na) {(Z n_{,} Mn)}_{2} S b_{2}$

Shuang Yu, Xinyu Liu, Guoqiang Zhao, Yi Peng, Xiancheng Wang, Jianfa Zhao, Wenmin Li, Zheng Deng, Jacek K. Furdyna, Y. J. Uemura, and Changqing Jin

Phys. Rev. Materials 4, 024411 – Published 18 February 2020

Abstract

In this paper we report successful synthesis and magnetic properties of $(Ca, Na) {(Zn, Mn)}_{2} S b_{2}$ as a ferromagnetic dilute magnetic semiconductor (DMS). In this DMS material the concentration of magnetic moments can be controlled independently from the concentration of electric charge carriers that are required for mediating magnetic interactions between these moments. This feature allows us to separately investigate the effect of carriers and of spins on the ferromagnetic properties of this DMS alloy, and particularly of its critical ferromagnetic behavior. We use a modified Arrott plot analysis to establish critical exponents β, γ, and δ for this alloy. We find that at low Mn concentrations $(< 10$ at. %), it is governed by short-range three-dimensional (3D)-Ising-like behavior, with experimental values of β, γ, and δ very close to theoretical 3D-Ising values of 0.325, 1.24, and 4.815. However, as the Mn concentration increases, this DMS material exhibits a mixed-phase behavior, with γ retaining its 3D-Ising characteristics, but β crossing over to longer-range mean-field behavior.

Received 10 November 2019
Revised 12 January 2020
Accepted 28 January 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.024411

Physics Subject Headings (PhySH)

Exchange interaction Ferromagnetism

Magnetic semiconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shuang Yu^1,2, Xinyu Liu³, Guoqiang Zhao ^1,2, Yi Peng¹, Xiancheng Wang^1,2, Jianfa Zhao^1,2, Wenmin Li^1,2, Zheng Deng^1,2,*, Jacek K. Furdyna³, Y. J. Uemura⁴, and Changqing Jin^1,2,5,†

¹Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physics, University of Chinese Academy of Sciences, Beijing 100190, China
³Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
⁴Department of Physics, Columbia University, New York, New York, 10027, USA
⁵Materials Research Lab at Songshan Lake, 523808 Dongguan, China

^*dengzheng@iphy.ac.cn
^†Jin@iphy.ac.cn

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Vol. 4, Iss. 2 — February 2020

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Figure 1
(a) Schematic diagram of $(Ca, Na) {(Zn, Mn)}_{2} S b_{2}$ structure; (b) Unit cell volume change as a function of Mn and Na doping levels. Note that the Zn/Mn layers are the sites of magnetic spins, and that carriers originate in the Ca/Na layers.
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Figure 2
(a) $M (T)$ for $(C a_{1 - x} N a_{x}) {(Z n_{1 - y} M n_{y})}_{2} S b_{2} (x, y = 0.05$ , 0.1 0.15) at $H = 500 Oe$ , and (b) $M (H)$ curves measured at 2 K. Inset in (a): a typical example of Curie-Weiss fitting for the $(C a_{0.9} N a_{0.1}) {(Z n_{0.9} M n_{0.1})}_{2} S b_{2}$ data. (c) $d M (T) / d T$ for $(C a_{0.9} N a_{0.1}) {(Z n_{1 - y} M n_{y})}_{2} S b_{2}$ , with $y = 0.05$ , 0.1 and 0.15. $T_{C}$ are marked in the figure. Temperature dependence of resistivity $ρ (T)$ at zero field for (d) $(C a_{1 - x} N a_{x}) Z n_{2} S b_{2} (x = 0$ , 0.05, 0.1), (e) $(C a_{1 - x} N a_{x}) {(Z n_{0.9} M n_{0.1})}_{2} S b_{2} (x = 0.05$ , 0.1, 0.15), (f) $Ca {(Z n_{1 - y} M n_{y})}_{2} S b_{2} (y = 0$ , 0.05, 0.1, 0.15), (g) $(C a_{0.9} N a_{0.1}) {(Z n_{1 - y} M n_{y})}_{2} S b_{2} (y = 0.05$ , 0.1, 0.15). (h) Hall measurement results for $(C a_{0.9} N a_{0.1}) {(Z n_{0.9} M n_{0.1})}_{2} S b_{2}$ below and above the Curie temperature.
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Figure 3
(a) $M (H)$ curves for $(C a_{0.9} N a_{0.1}) {(Z n_{0.9} M n_{0.1})}_{2} S b_{2}$ at various temperatures ranging from 5.8 to 12.1 K with a step 0.2 or 0.3 K. The plots of $H / M^{1 / γ}$ versus $M^{1 / β}$ for the $(C a_{0.9} N a_{0.1}) {(Z n_{0.9} M n_{0.1})}_{2} S b_{2}$ specimen for (b) Standard mean-field model, (c) 3D-Heisenberg model, (d) 3D-Ising model, and (e) Tricritical mean-field model. (f) Temperature dependence of the normalized slopes, obtained from Figs. 3–3.
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Figure 4
(a) Temperature variations of $M_{s}$ and ${χ_{0}}^{- 1}$ along with the fits (solid lines) following Eqs. (2) and (3), which give the values of the critical exponents and $T_{C}$ as mentioned in the plot. (b) Fitting results of $M (H)$ at 8.8 K obtained with Eq. (4). (c) Reconstructed modified Arrott-plot using obtained critical exponents, as discussed in the text.
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Figure 5
(a) $M (H)$ curves for $(C a_{0.9} N a_{0.1}) {(Z n_{0.85} M n_{0.15})}_{2} S b_{2}$ at various temperatures ranging from 5.5 to 9.8 K, in steps of 0.3 K. (b)–(e): Plots of $H / M^{1 / γ}$ versus $M^{1 / β}$ for this specimen for (b) standard mean-field model, (c) 3D-Heisenberg model, (d) 3D-Ising model, and (e) tricritical mean-field model, respectively. (f) Temperature dependence of the normalized slopes, obtained from Figs. 5–5.
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Figure 6
(a) Temperature variation of $M_{s}$ and ${χ_{0}}^{- 1}$ , along with fits (solid lines) following Eqs. (2) and (3), which give the values of critical exponents and $T_{C}$ shown in the plot. (b) Fitting results of $M (H)$ at 7.5 K obtained with Eq. (4). (c) Reconstructed modified Arrott-plot using critical exponents shown in (a), as discussed in the text.
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Physical Review Materials

Anomalous critical point behavior in dilute magnetic semiconductor (Ca,Na)(Zn,Mn)2Sb2

Shuang Yu, Xinyu Liu, Guoqiang Zhao, Yi Peng, Xiancheng Wang, Jianfa Zhao, Wenmin Li, Zheng Deng, Jacek K. Furdyna, Y. J. Uemura, and Changqing Jin

Phys. Rev. Materials 4, 024411 – Published 18 February 2020

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Anomalous critical point behavior in dilute magnetic semiconductor $(C a_{,} Na) {(Z n_{,} Mn)}_{2} S b_{2}$