Nanoscale degeneracy lifting in a geometrically frustrated antiferromagnet

Benjamin A. Frandsen, Emil S. Bozin, Eleni Aza, Antonio Fernández Martínez, Mikhail Feygenson, Katharine Page, and Alexandros Lappas

Phys. Rev. B 101, 024423 – Published 27 January 2020

Abstract

The local atomic and magnetic structures of the compounds $A {MnO}_{2}$ ( $A$ = Na, Cu), which realize a geometrically frustrated, spatially anisotropic triangular lattice of Mn spins, have been investigated by atomic and magnetic pair distribution function analysis of neutron total scattering data. Relief of frustration in ${CuMnO}_{2}$ is accompanied by a conventional cooperative symmetry-lowering lattice distortion driven by Néel order. In ${NaMnO}_{2}$ , however, the distortion has a short-range nature. A cooperative interaction between the locally broken symmetry and short-range magnetic correlations lifts the magnetic degeneracy on a nanometer length scale, enabling long-range magnetic order in the Na derivative. The degree of frustration, mediated by residual disorder, contributes to the rather differing pathways to a single, stable magnetic ground state in these two related compounds. This study demonstrates how nanoscale structural distortions that cause local-scale perturbations can lift the ground-state degeneracy and trigger macroscopic magnetic order.

Received 2 March 2019
Revised 29 November 2019
Corrected 20 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.024423

Physics Subject Headings (PhySH)

Antiferromagnetism Frustrated magnetism Magnetic phase transitions Magnetism

Antiferromagnets

Neutron diffraction Neutron pair-distribution function analysis

Condensed Matter, Materials & Applied Physics

Corrections

20 May 2020

Correction: Additional information for the Fulbright Foundation-Greece support statement has been inserted.

Authors & Affiliations

Benjamin A. Frandsen ^1,*, Emil S. Bozin ^2,†, Eleni Aza^3,4, Antonio Fernández Martínez³, Mikhail Feygenson^5,6, Katharine Page^5,7, and Alexandros Lappas ^3,‡

¹Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA
²Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973, USA
³Institute of Electronic Structure and Laser, Foundation for Research and Technology–Hellas, Vassilika Vouton, 71110 Heraklion, Greece
⁴Department of Materials Science and Engineering, University of Ioannina, 451 10 Ioannina, Greece
⁵Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁶Jülich Centre of Neutron Science, Forschungszentrum Jülich, 52428 Jülich Germany
⁷Materials Science and Engineering Department, University of Tennessee, Knoxville, Tennessee 37996, USA

^*benfrandsen@byu.edu
^†bozin@bnl.gov
^‡lappas@iesl.forth.gr

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Vol. 101, Iss. 2 — 1 January 2020

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Images

Figure 1
Structure of ${CuMnO}_{2}$ and $α − {NaMnO}_{2}$ . Atomic and magnetic structures of (a) ${CuMnO}_{2}$ and (b) $α − {NaMnO}_{2}$ . The distortion of the monoclinic unit cell (black) to triclinic cell (blue) is depicted. The arrows depict the three-dimensional antiferromagnetic spin configurations, corresponding to propagation vectors (in the triclinic setting) of $k = (0, 1 / 2, / 1 / 2)$ for CMO [11] and $k = (0, 1 / 2, 0)$ for NMO [12]. (c) Projection onto the basal plane of the triangular ${Mn}^{3 +}$ sublattice. Dashed and solid lines show the monoclinic and triclinic unit cells, respectively. (d) PDF patterns of ${NaMnO}_{2}$ (top) and ${CuMnO}_{2}$ (bottom) collected at room temperature. The blue curves represent the data, the red curves represent the atomic PDF fits using the monoclinic structural model, and the lower green curves represent the fit residuals, offset for clarity.
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Figure 2
Results of atomic PDF fits for ${CuMnO}_{2}$ and ${NaMnO}_{2}$ . (a) PDF refinements of the ${NaMnO}_{2}$ structure at 5 K using the monoclinic (left) and triclinic (right) models. The lower green curves are the fit residuals, multiplied by 2 for clarity. (b) Normalized difference in $χ^{2}$ between the monoclinic and triclinic models of ${NaMnO}_{2}$ as a function of temperature for short (blue circles) and long (green triangles) fitting ranges. (c) Color map of the triclinic splitting in ${NaMnO}_{2}$ as a function of temperature and fitting range. The horizontal dashed line marks $T_{N}$ . (d) Same as (c), but for ${CuMnO}_{2}$ .
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Figure 3
Magnetic scattering and magnetic PDF analysis of ${CuMnO}_{2}$ and ${NaMnO}_{2}$ . (a) Color map of the scattered intensity $S (Q)$ of ${NaMnO}_{2}$ with temperature on the vertical axis and $Q$ on the horizontal axis. (b) $S (Q)$ for ${NaMnO}_{2}$ at 5 K (blue curve), 50 K (orange curve), and 260 K (red curve), indicated by horizontal dashed lines in (a). (c) Corresponding mPDF data for ${NaMnO}_{2}$ at 5 and 50 K. The 50 K data are offset along the $y$ axis by $- 1.5 Å^{- 2}$ for clarity. The black curves and thick gray curves represent the Fourier filtered and unfiltered data, respectively. The blue and orange curves represent the mPDF fits for 5 and 50 K, respectively. (d)–(f) Equivalent results for ${CuMnO}_{2}$ . The intensity scale for (d) was chosen such that the strongest magnetic Bragg peaks for CMO and NMO have equal contrast. The magnetic model in Ref. [11] was used for the fits in (f).
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Figure 4
Temperature evolution of magnetic correlations in ${CuMnO}_{2}$ and ${NaMnO}_{2}$ . (a) Correlation length of the short-range antiferromagnetic order in ${NaMnO}_{2}$ determined from mPDF refinements using a three-dimensional model, displayed as a function of dimensionless temperature $T / T_{N}$ . Below the transition (indicated by the vertical dashed line), the correlation length is limited by the instrumental resolution. The horizontal dashed line indicates the nearest-neighbor Mn-Mn distance. Inset: Refined mPDF scale factor as a function of dimensionless temperature for a fitting range of 1.8 to 15 Å (blue circles) and 30 to 45 Å (orange squares). (b) Equivalent results for ${CuMnO}_{2}$ .
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