Tuning the $S=1/2$ square-lattice antiferromagnet $\mathrm{S}{\mathrm{r}}_{2}\mathrm{Cu}(\mathrm{T}{\mathrm{e}}_{1\text{\ensuremath{-}}x}{\mathrm{W}}_{x}){\mathrm{O}}_{6}$ from N\'eel order to quantum disorder to columnar order

Tuning the $S = 1 / 2$ square-lattice antiferromagnet $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ from Néel order to quantum disorder to columnar order

O. Mustonen, S. Vasala, K. P. Schmidt, E. Sadrollahi, H. C. Walker, I. Terasaki, F. J. Litterst, E. Baggio-Saitovitch, and M. Karppinen

Phys. Rev. B 98, 064411 – Published 13 August 2018

Abstract

The spin-1/2 square-lattice Heisenberg model is predicted to have a quantum disordered ground state when magnetic frustration is maximized by competing nearest-neighbor $J_{1}$ and next-nearest-neighbor $J_{2}$ interactions $(J_{2} / J_{1} \approx 0.5)$ . The double perovskites $S r_{2} CuTe O_{6}$ and $S r_{2} CuW O_{6}$ are isostructural spin-1/2 square-lattice antiferromagnets with Néel $(J_{1}$ dominates) and columnar $(J_{2}$ dominates) magnetic order, respectively. Here we characterize the full isostructural solid-solution series $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6} (0 \leq x \leq 1)$ tunable from Néel order to quantum disorder to columnar order. A spin-liquid-like ground state was previously observed for the $x = 0.5$ phase, but we show that the magnetic order is suppressed below 1.5 K in a much wider region of $x \approx 0.1 - 0.6$ . This coincides with significant $T$ -linear terms in the low-temperature specific heat. However, density-functional theory calculations predict most of the materials are not in the highly frustrated $J_{2} / J_{1} \approx 0.5$ region square-lattice Heisenberg model. Thus, a combination of both magnetic frustration and quenched disorder is the likely origin of the spin-liquid-like state in $x = 0.5$ .

Received 17 April 2018
Revised 24 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.064411

Physics Subject Headings (PhySH)

Magnetic order

Antiferromagnets Crystal structures Strongly correlated systems

Density functional theory Muon spin relaxation & rotation Specific heat measurements Susceptibility measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

O. Mustonen¹, S. Vasala², K. P. Schmidt³, E. Sadrollahi³, H. C. Walker⁴, I. Terasaki⁵, F. J. Litterst^2,3, E. Baggio-Saitovitch², and M. Karppinen^1,*

¹Department of Chemistry and Materials Science, Aalto University, FI-00076 Espoo, Finland
²Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr Xavier Sigaud 150, Urca, Rio de Janeiro, 22290-180, Brazil
³Institut für Physik der Kondensierten Materie, Technische Universität Braunschweig, 38110 Braunschweig, Germany
⁴ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, United Kingdom
⁵Department of Physics, Nagoya University, Nagoya 464-8602, Japan

^*Corresponding author: maarit.karppinen@aalto.fi

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Vol. 98, Iss. 6 — 1 August 2018

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Figure 1
(a) Phase diagram of the spin-1/2 square-lattice Heisenberg model as a function of $J_{2} / J_{1}$ , where $J_{1}$ is the nearest neighbor and $J_{2}$ is the next-nearest-neighbor interaction [13, 18, 51]. Known compounds realizing the model are placed at their respective positions. The classical ground states of the model are ferromagnetic order, Néel antiferromagnetic (NAF) order, and columnar antiferromagnetic (CAF) order. A quantum spin-liquid state has been predicted for $J_{2} / J_{1} \approx 0.4 - 0.6$ at the NAF-CAF boundary. Isostructural double perovskites $S r_{2} CuTe O_{6}$ and $S r_{2} CuW O_{6}$ are in the NAF and CAF regions, respectively. (b) The $B$ -site ordered double-perovskite structure of $S r_{2} CuTe O_{6}$ and $S r_{2} CuW O_{6}$ [24, 25]. (c) The square of $S = 1 / 2 C u^{2 +}$ cations in the $a b$ plane of $S r_{2} CuTe O_{6}$ and $S r_{2} CuW O_{6}$ with the view down the $c$ axis. The Te/W cation in the center of the $C u^{2 +}$ square determines whether $J_{1}$ or $J_{2}$ interaction dominates.
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Figure 2
(a) Magnetic susceptibility of selected samples as a function of temperature. Zero-field cooled and field-cooled data overlap and only the former is shown. (b) The position $T_{\max}$ and height $χ_{\max}$ of the broad maximum in magnetic susceptibility as a function of $x$ in $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ .
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Figure 3
(a) Reduced specific heat of selected samples as a function of temperature. (b) Low-temperature $C_{p} / T − T^{2}$ plot showing the $T$ -linear relationship of most samples as indicated by a non-zero $y$ -intercept. (c) $T$ -linear term γ of specific heat as a function of $x$ in $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ .
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Figure 4
Zero-field spectra of $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ with (a) $x = 0.9$ and (b) $x = 0.8$ showing spontaneous rotation signals in the magnetically ordered state. (c) Zero-field spectra of $x = 0.7$ at 5.5 and 1.5 K revealing only weak rotation signals and considerable dynamic damping. (d) Comparison of the temperature-dependent local fields $B_{i}$ for $x = 0.9$ and $x = 1$ (data from Ref. [21]). Drawn lines are interpolations using a standard approximation as described in the main text. (e) Temperature dependence of ratio between paramagnetic and total asymmetries measured in a weak transverse field of 5 mT for $x = 0.7$ , 0.8, 0.9. (f) Zero-field spectra for $x = 0.1$ , 0.2, 0.3, 0.4, 0.5, 0.6 at 1.5–1.8 K showing no indication of magnetic ordering or static magnetism.
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Figure 5
Energy difference between Néel and columnar antiferromagnetic order as a function of composition in $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ calculated using GGA+ $U$ .
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Figure 6
Schematic phase diagram of $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ . The black squares represent measured Néel temperatures and the blue circles represent the lowest temperature measured for samples that remain entirely dynamic and do not order.
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Tuning the $S = 1 / 2$ square-lattice antiferromagnet $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ from Néel order to quantum disorder to columnar order

O. Mustonen, S. Vasala, K. P. Schmidt, E. Sadrollahi, H. C. Walker, I. Terasaki, F. J. Litterst, E. Baggio-Saitovitch, and M. Karppinen

Phys. Rev. B 98, 064411 – Published 13 August 2018

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Tuning the S=1/2 square-lattice antiferromagnet Sr2Cu(Te1−xWx)O6 from Néel order to quantum disorder to columnar order

O. Mustonen, S. Vasala, K. P. Schmidt, E. Sadrollahi, H. C. Walker, I. Terasaki, F. J. Litterst, E. Baggio-Saitovitch, and M. Karppinen

Phys. Rev. B 98, 064411 – Published 13 August 2018

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Tuning the $S = 1 / 2$ square-lattice antiferromagnet $S r_{2} Cu (T e_{1 − x} W_{x}) O_{6}$ from Néel order to quantum disorder to columnar order