Properties of spin-$\frac{1}{2}$ triangular-lattice antiferromagnets ${\mathrm{CuY}}_{2}{\mathrm{Ge}}_{2}{\mathrm{O}}_{8}$ and ${\mathrm{CuLa}}_{2}{\mathrm{Ge}}_{2}{\mathrm{O}}_{8}$

Properties of spin- $\frac{1}{2}$ triangular-lattice antiferromagnets ${CuY}_{2} {Ge}_{2} O_{8}$ and ${CuLa}_{2} {Ge}_{2} O_{8}$

Hwanbeom Cho, Marie Kratochvílová, Hasung Sim, Ki-Young Choi, Choong Hyun Kim, Carley Paulsen, Maxim Avdeev, Darren C. Peets, Younghun Jo, Sanghyun Lee, Yukio Noda, Michael J. Lawler, and Je-Geun Park

Phys. Rev. B 95, 144404 – Published 5 April 2017

Abstract

We found new two-dimensional (2D) quantum ( $S = 1 / 2$ ) antiferromagnetic systems: $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La). According to our analysis of high-resolution x-ray and neutron diffraction experiments, the Cu network of $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La) exhibits a 2D triangular lattice linked via weak bonds along the perpendicular $b$ axis. Our bulk characterizations from 0.08 to 400 K show that they undergo a long-range order at 0.51(1) and 1.09(4) K for the Y and La systems, respectively. Interestingly, they also exhibit field induced phase transitions. For theoretical understanding, we carried out the density functional theory (DFT) band calculations to find that they are typical charge-transfer-type insulators with a gap of $E_{g} ≅ 2 eV$ . Taken together, our observations make $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La) additional examples of low-dimensional quantum spin triangular antiferromagnets with the low-temperature magnetic ordering.

Received 14 October 2016
Revised 1 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.144404

Physics Subject Headings (PhySH)

Antiferromagnetism

Quantum spin models Single crystal materials

Magnetization measurements Neutron diffraction Specific heat measurements X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hwanbeom Cho^1,2, Marie Kratochvílová^1,2, Hasung Sim^1,2, Ki-Young Choi^1,2, Choong Hyun Kim^1,2, Carley Paulsen³, Maxim Avdeev⁴, Darren C. Peets^1,2, Younghun Jo⁵, Sanghyun Lee⁶, Yukio Noda⁷, Michael J. Lawler⁸, and Je-Geun Park^1,2,*

¹Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea
²Department of Physics & Astronomy, Seoul National University, Seoul 08826, Korea
³Institut Néel, C.N.R.S-Université Grenoble Alps, BP 166, 38042 Grenoble, France
⁴Australian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas Heights, New South Wales, 2234, Australia
⁵Quantum Materials Research Team, Korea Basic Science Institute, Daejeon 305-333, Korea
⁶Institute of Materials Structure Science, KEK, Tokai, Ibaraki, 319-1106, Japan
⁷Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan
⁸Department of Physics, Binghamton University, Vestal New York 13850, USA

^*Corresponding author: jgpark10@snu.ac.kr

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Vol. 95, Iss. 14 — 1 April 2017

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Figure 1
(a) The refinement results of the x-ray powder diffraction of $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La) and neutron powder diffraction data of $Cu Y_{2} G e_{2} O_{8}$ measured in Echidna, ANSTO. (b) The refinement results of the single-crystal XRD data of $CuL a_{2} G e_{2} O_{8}$ and a picture of single-crystal sample taken using an optical microscope (in the inset).
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Figure 2
Crystal structure of $CuL a_{2} G e_{2} O_{8}$ in the I 1 $m$ 1 unit cell setting. The blue, green, and grey balls indicate the copper, lanthanum, and germanium atoms, respectively. (a) There are four different exchange paths: $J_{1}$ , $J_{2}$ , $J_{3}$ , and $J_{4}$ . Ge1 and Ge2 atoms make $Ge O_{4}$ tetrahedrons that form a grid on the $a c$ plane and Ge3 atoms construct $Ge O_{5}$ trigonal bipyramids. (b) $Cu O_{4}$ plaquette forms a 2D triangular lattice within the $a c$ plane. (c) The Cu-O10 lengths are much longer than Cu-O6 ∼ O9 lengths on the distorted equatorial plane while La and Ge atoms are separating the nearest $Cu O_{4}$ plaquettes and so prohibiting the formation of the Cu-O-Cu bonding between the adjacent $Cu O_{4}$ plaquettes.
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Figure 3
(a) Temperature-dependent dc magnetic susceptibility $χ_{m}$ of $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La). The arrows indicate the inflection points originating from a long-range order. The inset shows the inverse susceptibility curves and the Curie-Weiss fitting results (dashed lines). (b) Temperature derivative of the magnetic susceptibility of $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La). (c) Field-dependent magnetization M(H) at various temperatures using polycrystalline $CuL a_{2} G e_{2} O_{8}$ . The first derivatives for both systems are shown in the inset. The position of the magnetic field-induced phase transition is indicated by an arrow. (d) Field-dependent magnetization M(H) for polycrystalline $Cu Y_{2} G e_{2} O_{8}$ and its first derivative are shown in the inset. The position of the magnetic field-induced phase transition is indicated by an arrow. (e) Magnetization M(H) in $H ∥ b$ for the $CuL a_{2} G e_{2} O_{8}$ single crystal at various temperatures and the first derivatives of M(H) are shown in the inset. (f) Comparison of dM/dH of the polycrystalline sample and single crystal in the crystallographic orientations $H ∥ b$ and $H ⊥ b$ , respectively.
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Figure 4
Heat capacity $C_{p} (T)$ of $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La). (a) There is a lambda-like sharp peak in both systems indicating a long-range order. The solid and dashed lines are fits for the $T^{3}$ law to remove the phonon contribution. The inset shows the temperature dependence of magnetic heat capacity $C_{m}$ divided by temperature. (b) The field-dependent heat capacity measured data on $Cu Y_{2} G e_{2} O_{8}$ (inset) and $CuL a_{2} G e_{2} O_{8}$ , which show the suppression of the long-ranged order with the external magnetic field. (c) and (d) The field-dependent transition points for the Y and La samples, respectively. The black crosses represent the Néel temperatures ( $T_{N}$ ) at each fields and the black diamond shows the saturation field $(H_{S})$ from the magnetization data. The solid line is the guide to eyes, indicating the existence of a critical field value, where the magnetic phase transition gets suppressed to the absolute zero temperature.
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Figure 5
(a) The total density of states calculated using the crystal structure of $CuL a_{2} G e_{2} O_{8}$ with the Coulomb interaction, $U = 5 eV$ . (b) The partial density of states projected on the copper $d$ orbitals.
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Figure 6
Diagrams of magnetic lattices of selected inorganic quantum 2D triangular systems. The solid arrows depict the strong exchange interactions and the dashed ones depict the weak exchange interactions. $CsCuC l_{3}$ has strong FM interlayer $(J_{⊥})$ interactions but weak AF triangular interactions (J, J´), whereas $C s_{2} CuB r_{4}$ and $C s_{2} CuC l_{4}$ have strong AF chain interactions (J) but weak AF inter-chain interactions ( $J^{'}$ ) and weak interlayer interactions $(J_{⊥})$ . $B a_{3} CoS b_{2} O_{9}$ shows a strong and regular AF triangular interaction (J, $J^{'}$ ) but weak AF interlayer interaction $(J_{⊥})$ . On the other hand, $Cu R E_{2} G e_{2} O_{8}$ ( $R E = Y$ and La) has a strong and regular AF triangular interaction $(J_{1} ≅ J_{2} ≅ J_{3})$ but weak interlayer interaction ( $J_{4}$ ) formed alternatively along the stacking axis.
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Physical Review B

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Properties of spin- $\frac{1}{2}$ triangular-lattice antiferromagnets ${CuY}_{2} {Ge}_{2} O_{8}$ and ${CuLa}_{2} {Ge}_{2} O_{8}$

Hwanbeom Cho, Marie Kratochvílová, Hasung Sim, Ki-Young Choi, Choong Hyun Kim, Carley Paulsen, Maxim Avdeev, Darren C. Peets, Younghun Jo, Sanghyun Lee, Yukio Noda, Michael J. Lawler, and Je-Geun Park

Phys. Rev. B 95, 144404 – Published 5 April 2017

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Properties of spin-12 triangular-lattice antiferromagnets CuY2Ge2O8 and CuLa2Ge2O8

Hwanbeom Cho, Marie Kratochvílová, Hasung Sim, Ki-Young Choi, Choong Hyun Kim, Carley Paulsen, Maxim Avdeev, Darren C. Peets, Younghun Jo, Sanghyun Lee, Yukio Noda, Michael J. Lawler, and Je-Geun Park

Phys. Rev. B 95, 144404 – Published 5 April 2017

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Properties of spin- $\frac{1}{2}$ triangular-lattice antiferromagnets ${CuY}_{2} {Ge}_{2} O_{8}$ and ${CuLa}_{2} {Ge}_{2} O_{8}$