Local atomic and magnetic structure of dilute magnetic semiconductor $(\mathrm{Ba},\mathrm{K}){(\mathrm{Zn},\mathrm{Mn})}_{2}{\mathrm{As}}_{2}$

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Local atomic and magnetic structure of dilute magnetic semiconductor $(Ba, K) {(Zn, Mn)}_{2} {As}_{2}$

Benjamin A. Frandsen, Zizhou Gong, Maxwell W. Terban, Soham Banerjee, Bijuan Chen, Changqing Jin, Mikhail Feygenson, Yasutomo J. Uemura, and Simon J. L. Billinge

Phys. Rev. B 94, 094102 – Published 6 September 2016

Abstract

We have studied the atomic and magnetic structure of the dilute ferromagnetic semiconductor system $(Ba, K) (Zn, Mn)_{2} {As}_{2}$ through atomic and magnetic pair distribution function analysis of temperature-dependent x-ray and neutron total scattering data. We detected a change in curvature of the temperature-dependent unit cell volume of the average tetragonal crystallographic structure at a temperature coinciding with the onset of ferromagnetic order. We also observed the existence of a well-defined local orthorhombic structure on a short length scale of $≲ 5 Å$ , resulting in a rather asymmetrical local environment of the Mn and As ions. Finally, the magnetic PDF revealed ferromagnetic alignment of Mn spins along the crystallographic $c$ axis, with robust nearest-neighbor ferromagnetic correlations that exist even above the ferromagnetic ordering temperature. We discuss these results in the context of other experiments and theoretical studies on this system.

Received 8 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.094102

Physics Subject Headings (PhySH)

Magnetic semiconductors

Neutron pair-distribution function analysis X-ray pair-distribution function analysis

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Benjamin A. Frandsen¹, Zizhou Gong¹, Maxwell W. Terban², Soham Banerjee², Bijuan Chen³, Changqing Jin³, Mikhail Feygenson⁴, Yasutomo J. Uemura¹, and Simon J. L. Billinge^2,5,*

¹Department of Physics, Columbia University, New York, New York 10027, USA
²Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
³Institute of Physics, Chinese Academy of Sciences, Beijing, China
⁴Jülich Center for Neutron Science, Forschungszentrum Jülich GmbH, D-52425, Jülich, Germany
⁵Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA

^*sb2896@columbia.edu

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Vol. 94, Iss. 9 — 1 September 2016

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Figure 1
Crystal structure of ${Ba}_{1 - x} K_{x} ({Zn}_{1 - y} {Mn}_{y})_{2} {As}_{2}$ . (a) Average crystallographic unit cell determined by x-ray and neutron diffraction experiments. (b) View of the Zn(Mn)/As layer from above. The dashed lines represent the square planar network of nearest neighbor Mn atoms. The $+$ and $-$ signs indicate whether the As atom is located above or below the Mn plane, respectively. The numerical labels assigned to the atoms are explained in the text, and are to be understood in reference to the Zn(Mn)/As plane in the lower half of the unit cell.
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Figure 2
DC magnetic susceptibility of ${Ba}_{1 - x} K_{x} ({Zn}_{1 - y} {Mn}_{y})_{2} {As}_{2}$ . Solid (dashed) curves represent field-cooled (zero-field-cooled) measurements. A clear ferromagnetic response is seen for the samples with $(x, y) = (0.2, 0.15)$ , (0.3, 0.15), and (0.4, 0.15) around 180 K, 220 K, and 200 K, respectively.
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Figure 3
Atomic PDF fits for the $(x, y) = (0.3, 0.15)$ sample at 300 K obtained from x-ray total scattering data. The blue curves represent experimental data, the red curves the calculated fit, and the green curves the residual, offset for clarity. The top set of curves comes from a fit from 1.5 Å to 20 Å using the tetragonal structure, and the lower set comes from a fit from 1.5 Å to 6.0 Å using the lower-symmetry orthorhombic model described in the main text. Inset: Close-up view of the ${MnAs}_{4}$ tetrahedral unit. The arrows indicate the displacements of the atoms in the distorted structure. The numerical labels are to be understood in reference to a ${MnAs}_{4}$ unit in the lower half of the unit cell displayed in Fig. 1.
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Figure 4
Results of structural refinements of ${Ba}_{0.7} K_{0.3} ({Zn}_{0.85} {Mn}_{0.15})_{2} {As}_{2}$ . (a) Temperature dependence of the unit cell volume from the tetragonal model. (b) Orthorhombicity (defined in main text) determined from refinements using the orthorhombic model. (c) Separation distance of the four distinct Mn-As bonds in the local orthorhombic structure. Based on the labels in Fig. 1, these bonds are Mn1-As1 (blue triangles), Mn2-As1 (blue circles), Mn1-As2 (red circles), and Mn2-As2 (red triangles). The open gray squares show the Mn-As distance in the tetragonal model. (d) Angle formed by the Mn1-As2-Mn2 chain of atoms in the orthorhombic model. The error bars represent the estimated standard deviation of the parameters obtained from the least-squares refinements.
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Figure 5
Neutron PDF fits to ${Ba}_{1 - x} K_{x} ({Zn}_{1 - y} {Mn}_{y})_{2} {As}_{2}$ . (a) Refinement of the tetragonal model (red curve) against the 2 K data for the sample with $(x, y) = (0.2, 0.15)$ (blue circles), with the fit residual shown below in green. (b) Nuclear PDF fit residuals for the (0, 0.15) (left, red), (0.2, 0.15) (middle, blue), and (0.4, 0.15) (right, green) samples. The latter two are shifted horizontally for clarity. The vertical dashed lines represent the Mn-Mn NN distance. The solid colored curves for the $x = 0.2$ sample represent mPDF calculations described in the main text.
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Figure 6
(a) Experimental mPDF patterns (blue curves) obtained as fit residuals from the nuclear PDF for 2 K (top) and 300 K (bottom), with calculated mPDFs from various models described in the text shown as red and orange curves. Mn-Mn bond lengths are shown as gray vertical lines. (b) mPDF scale factors from refinements of two models described in the text, with $T_{C} = 180$ K indicated by the dashed vertical line. The error bars represent the estimated standard deviation of the parameters obtained from the least-squares refinements.
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Physical Review B

covering condensed matter and materials physics

Local atomic and magnetic structure of dilute magnetic semiconductor $(Ba, K) {(Zn, Mn)}_{2} {As}_{2}$

Benjamin A. Frandsen, Zizhou Gong, Maxwell W. Terban, Soham Banerjee, Bijuan Chen, Changqing Jin, Mikhail Feygenson, Yasutomo J. Uemura, and Simon J. L. Billinge

Phys. Rev. B 94, 094102 – Published 6 September 2016

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Physical Review B

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Local atomic and magnetic structure of dilute magnetic semiconductor (Ba,K)(Zn,Mn)2As2

Benjamin A. Frandsen, Zizhou Gong, Maxwell W. Terban, Soham Banerjee, Bijuan Chen, Changqing Jin, Mikhail Feygenson, Yasutomo J. Uemura, and Simon J. L. Billinge

Phys. Rev. B 94, 094102 – Published 6 September 2016

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Local atomic and magnetic structure of dilute magnetic semiconductor $(Ba, K) {(Zn, Mn)}_{2} {As}_{2}$