Essential role of magnetic frustration in the phase diagrams of doped cobaltites

Letter

Essential role of magnetic frustration in the phase diagrams of doped cobaltites

Peter P. Orth, D. Phelan, J. Zhao, H. Zheng, J. F. Mitchell, C. Leighton, and Rafael M. Fernandes

Phys. Rev. Materials 6, L071402 – Published 5 July 2022

Abstract

Doped perovskite cobaltites (e.g., ${La}_{1 - x} {Sr}_{x} {CoO}_{3}$ ) have been extensively studied for their spin-state physics, electronic inhomogeneity, and insulator-metal transitions. Ferromagnetically interacting spin-state polarons emerge at low $x$ in the phase diagram of these compounds, eventually yielding long-range ferromagnetism. The onset of long-range ferromagnetism ( $x \approx 0.18$ ) is substantially delayed relative to polaron percolation ( $x \approx 0.05$ ), however, generating a troubling inconsistency. Here, Monte Carlo simulations of a disordered classical spin model are used to establish that previously ignored magnetic frustration is responsible for this effect, enabling faithful reproduction of the magnetic phase diagram.

Received 18 May 2021
Revised 25 October 2021
Accepted 14 June 2022

DOI:https://doi.org/10.1103/PhysRevMaterials.6.L071402

Physics Subject Headings (PhySH)

Magnetic interactions Magnetic phase transitions Magnetism Percolation

Complex oxides

Monte Carlo methods Percolation theory Specific heat measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Peter P. Orth ^1,2,*, D. Phelan^3,4, J. Zhao³, H. Zheng³, J. F. Mitchell ³, C. Leighton ⁴, and Rafael M. Fernandes⁵

¹Ames Laboratory, Ames, Iowa 50011, USA
²Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
³Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁴Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁵School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

^*porth@iastate.edu

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Issue

Vol. 6, Iss. 7 — July 2022

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Images

Figure 1
Magnetic/electronic phase diagram of single-crystal ${La}_{1 - x} {Sr}_{x} {CoO}_{3}$ (LSCO). Shown are the Curie temperature ( $T_{C}$ ), spin/cluster glass freezing temperature ( $T_{G}$ ), onset temperature for ferromagnetic (F) fluctuations/clusters ( $T^{*}$ ), and non-F matrix spin-state crossover temperature ( $T_{SST}$ ). Superimposed is the magnitude of the Curie-Weiss temperature $θ_{CW}$ , which inverts from antiferromagnetic (AF) to F at $x \approx 0.04$ . $FM = ferromagnetic$ metal, $PM = paramagnetic$ metal, $PI = paramagnetic$ insulator, and $GI = glassy$ magnetic insulator; U designates uniform states, and PS magnetically/electronically phase separated states. $T_{C}, T_{G}, T^{*}$ , and $θ_{CW}$ are from this Letter, supplemented with Refs. [10, 22, 23, 24]; $T_{SST}$ data are taken from Ref. [25]. The vertical line at $x_{c} = 0.18$ marks the cluster percolation threshold, and the vertical line at $x = 0.22$ the transition from PS to U states at low temperature (and from negative to positive temperature coefficient of resistance at high temperature). For $x > 0.30$ , where single-crystal data are not available, $T_{C}$ and $T^{*}$ values from polycrystalline samples have been used [26].
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Figure 2
Doping ( $x$ ) dependence of the 7-K heat capacity ( $C_{p}$ , red, left axis), magnetization per hole (blue, right axis, normalized to the $x = 0$ value), and F volume fraction (black, right axis). The latter is estimated by extrapolating the high-field magnetization-field behavior to zero field. Dashed lines are guides to the eye. Inset: Schematic of seven-site spin-state polaron with F exchange coupling $J_{34}$ between sites.
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Figure 3
(a) Schematic of two nearby seven-site polarons with exchange interactions $J_{34}, J_{44} < 0$ (F) and $J_{33} > 0$ (AF). ${Co}^{4 +}$ ( ${Co}^{3 +}$ ) sites are shown in red (blue). In this F configuration, the AF $J_{33}$ bonds (green dashed) are frustrated. (b) Fraction of spinful sites $s$ (either ${Co}^{4 +}$ or ${Co}^{3 +}$ ) as a function of ${Co}^{4 +}$ doping $x$ . The horizontal green dashed line denotes the site percolation threshold on the cubic lattice, $s_{c} = 0.31$ , which is reached at $x = 0.05$ . The inset shows the fraction of spins in isolated seven-site polarons, which peaks at $x = 0.03$ . Data was obtained for system size $N = L^{3}$ with $L = 32$ and averaged over $N_{dis} = 50$ disorder realizations. Inset data was obtained for system size $N = 10^{3}$ and is averaged over $10^{3}$ disorder realizations. (c), (d) Fraction of filled bonds $b$ as a function of ${Co}^{4 +}$ doping $x$ . Different bonds are described in the legend; “All” refers to counting $J_{33}, J_{34}$ , and $J_{44}$ bonds. The horizontal gray line denotes the bond percolation threshold on the cubic lattice $b_{c} = 0.25$ . The system exhibits only finite-size clusters for $x < 0.08$ ( $b_{All} < b_{c}$ ). If AF bonds were absent, the $T = 0$ paramagnetic-to-ferromagnetic transition would occur at $x = 0.13$ ( $b_{(34) + (44)} = b_{c}$ ), when a macroscopic percolating cluster that only contains F $J_{34}$ and $J_{44}$ bonds emerges. However, the presence of AF $J_{33}$ bonds decouples the percolation of F bonds from the onset of F order. Fraction of filled bonds was obtained for same parameters as filled sites in panel (b).
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Figure 4
(a) Numerical finite-temperature phase diagram of the frustrated $J_{33} - J_{34} - J_{44}$ model as a function of ${Co}^{4 +}$ doping, obtained from percolation analysis and MC simulations. The different phases are paramagnetic (P), ferromagnetic (F), and glassy, which is characterized by short-range AF and F correlations. Couplings are set to $J_{34} = J_{44} = - 1$ (F) and $J_{33} = 0.2$ (AF). Transition temperatures $T_{F}$ (red dots) are obtained from MC simulations via crossing of F Binder cumulants (see Supplemental Material Sec. S3). Such crossings are notably absent for $x \leq 0.225$ . The gray dashed line at $x = 0.08$ denotes the bond percolation threshold [ $b_{All} = b_{c}$ , see Fig. 3]. The brown line denotes the $T = 0$ P-F quantum critical point (QCP) in the unfrustrated model ( $J_{33} = 0$ ), obtained from $b_{(34) + (44)} = b_{c}$ in Fig. 3. The transition temperature to the glassy phase (solid gray line) is schematic and smoothly connects the various numerically obtained points. (b)–(d) MC simulation results of observables $m_{F}^{2}, m_{AF}^{2}, χ_{F}, χ_{AF}$ for $x = 0.2$ and $x = 0.5$ and different system sizes, $L = 8, 12$ . Long-range F order develops for $x = 0.5$ , while only short-range F and AF correlations coexist at $x = 0.2$ , which is characteristic of a glassy phase.
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