Orbital- and spin-driven lattice instabilities in quasi-one-dimensional ${\mathrm{CaV}}_{2}{\mathrm{O}}_{4}$

Orbital- and spin-driven lattice instabilities in quasi-one-dimensional ${CaV}_{2} O_{4}$

T. Watanabe, S. Kobayashi, Y. Hara, J. Xu, B. Lake, J.-Q. Yan, A. Niazi, and D. C. Johnston

Phys. Rev. B 98, 094427 – Published 26 September 2018

Abstract

Calcium vanadate ${CaV}_{2} O_{4}$ has a crystal structure of quasi-one-dimensional zigzag chains composed of orbital-active $V^{3 +}$ ions and undergoes successive structural and antiferromagnetic phase transitions at $T_{s} \sim 140$ K and $T_{N} \sim 70$ K, respectively. We perform ultrasound velocity measurements on a single crystal of ${CaV}_{2} O_{4}$ . The temperature dependence of its shear elastic moduli exhibits huge Curie-type softening upon cooling that emerges above and below $T_{s}$ depending on the elastic mode. The softening above $T_{s}$ suggests the presence of either onsite Jahn-Teller-type or intersite ferrotype orbital fluctuations in the two inequivalent $V^{3 +}$ zigzag chains. The softening below $T_{s}$ suggests the occurrence of a dimensional spin-state crossover, from quasi-one to three, that is driven by the spin-lattice coupling along the inter-zigzag-chain orthogonal direction. The successive emergence of the orbital- and spin-driven lattice instabilities above and below $T_{s}$ , respectively, is unique to the orbital-spin zigzag chain system of ${CaV}_{2} O_{4}$ .

Received 30 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.094427

Physics Subject Headings (PhySH)

Frustrated magnetism

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Watanabe^1,*, S. Kobayashi¹, Y. Hara², J. Xu³, B. Lake³, J.-Q. Yan^4,†, A. Niazi^4,‡, and D. C. Johnston^4,5

¹Department of Physics, College of Science and Technology (CST), Nihon University, Chiyoda, Tokyo 101-8308, Japan
²National Institute of Technology, Ibaraki College, Hitachinaka 312-8508, Japan
³Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
⁴Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
⁵Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

^*tadataka@phys.cst.nihon-u.ac.jp.
^†Present address: Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
^‡Present address: Department of Physics, Jamia Millia Islamia, New Delhi 110025, India.

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Vol. 98, Iss. 9 — 1 September 2018

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Figure 1
Bonding network in the crystal structure of ${CaV}_{2} O_{4}$ : (a) V atoms and (b) ${VO}_{6}$ octahedra. In (a) and (b), V1 and V2 denote the inequivalent V sites. The angle $α$ displayed in the crystal axes corresponds to the monoclinic angle in the monoclinic crystal phase below $T_{s}$ [6]. In (a), the propagation vector k and polarization vector u of the longitudinal sound waves for $C_{11}$ , $C_{22}$ , and $C_{33}$ are indicated. In (b), the propagation vector k and polarization vector u of the transverse sound waves for $C_{44}$ , $C_{55}$ , and $C_{66}$ are indicated.
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Figure 2
(a) Schematic $t_{2 g}$ energy levels of $V^{3 +} 3 d^{2}$ electrons in the orthorhombic (left) and monoclinic (right) crystal phases of ${CaV}_{2} O_{4}$ . (b) Schematic of the V $t_{2 g}$ orbitals in the zigzag chain of ${CaV}_{2} O_{4}$ . In (b), two competing AF interactions of the nearest-neighbor $J_{z z}$ along the zigzags and the next-nearest-neighbor $J_{leg}$ along the leg are indicated. Additionally, the propagation vector k and polarization vector u of the transverse sound wave corresponding to the $ε_{x x} - ε_{y y}$ elastic mode ( $d_{y z} / d_{z x}$ -active mode) for the $t_{2 g}$ orbitals are indicated. For the V1 and V2 zigzag chains of ${CaV}_{2} O_{4}$ , $C_{55}$ , and $C_{44}$ , respectively, correspond to this elastic mode.
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Figure 3
Compressive elastic moduli of ${CaV}_{2} O_{4}$ as functions of temperature. (a) $C_{11} (T)$ , (b) $C_{22} (T)$ , and (c) $C_{33} (T)$ . The labeled arrows indicate $T_{s}$ and $T_{N}$ .
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Figure 4
Shear elastic moduli of ${CaV}_{2} O_{4}$ as functions of temperature. (a) $C_{44} (T)$ , (b) $C_{55} (T)$ , and (c) $C_{66} (T)$ . The labeled arrows indicate $T_{s}$ and $T_{N}$ . The experimental data in the temperature ranges indicated by double-headed arrows are displayed rescaled in Fig. 5.
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Figure 5
Expanded view of the shear elastic moduli for ${CaV}_{2} O_{4}$ given in from Fig. 4: (a) $C_{44} (T)$ in the orthorhombic PM phase ( $T > T_{s}$ ), (b) $C_{55} (T)$ in the orthorhombic PM phase ( $T > T_{s}$ ), and (c) $C_{66} (T)$ in the monoclinic PM phase ( $T_{N} < T < T_{s}$ ). The solid black curves in all three plots are fits using Eq. (1) of the experimental data; values for the fitting parameters are also listed. The ${VO}_{6}$ octahedra of the V1 and V2 zigzag chains are illustrated along with the sound propagation vector k and polarization vector u. In (a), the angle $α$ displayed in the crystal axes corresponds to the monoclinic angle in the monoclinic crystal phase ( $T < T_{s}$ ) [6].
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Figure 6
(a) Ferro-type orbital configuration of ${CaV}_{2} O_{4}$ projected onto the $b c$ plane, which displays ${VO}_{6}$ octahedra of the V1 and V2 zigzag chains. (b) V1 and V2 bonding networks indicating the inter-zigzag-chain neighboring exchange interactions $J_{a}^{\pm}$ and $J_{b}^{\pm}$ . In (a) and (b), angle $α$ shown with the crystal axes corresponds to that in the monoclinic crystal phase ( $T < T_{s}$ ) [6]. In (b), the sound propagation vector k and polarization vector u for $C_{66}$ tilts the angle between the $a$ and $b$ axes.
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Physical Review B

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Orbital- and spin-driven lattice instabilities in quasi-one-dimensional ${CaV}_{2} O_{4}$

T. Watanabe, S. Kobayashi, Y. Hara, J. Xu, B. Lake, J.-Q. Yan, A. Niazi, and D. C. Johnston

Phys. Rev. B 98, 094427 – Published 26 September 2018

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Physical Review B

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Orbital- and spin-driven lattice instabilities in quasi-one-dimensional CaV2O4

T. Watanabe, S. Kobayashi, Y. Hara, J. Xu, B. Lake, J.-Q. Yan, A. Niazi, and D. C. Johnston

Phys. Rev. B 98, 094427 – Published 26 September 2018

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Orbital- and spin-driven lattice instabilities in quasi-one-dimensional ${CaV}_{2} O_{4}$