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# Highly dispersive magnons with spin-gap-like features in the frustrated ferromagnetic $S=\frac{1}{2}$ chain compound ${\mathrm{Ca}}_{2}{\mathrm{Y}}_{2}{\mathrm{Cu}}_{5}{\mathrm{O}}_{10}$ detected by inelastic neutron scattering

## Abstract

In this paper, we report inelastic neutron scattering experiments in Ca _{2}Y _{2}Cu _{5}O _{10} and map out the full one-magnon dispersion which extends up to a record value of 53 meV for frustrated ferromagnetic (FM) edge-sharing CuO _{2} chain (FFESC) cuprates. A homogeneous spin-1/2 chain model with a FM nearest-neighbor (NN), an antiferromagnetic (AFM) next-nearest-neighbor (NNN) inchain, and two diagonal AFM interchain couplings (ICs) analyzed within linear spin-wave theory (LSWT) reproduces well the observed strong dispersion along the chains and a weak one perpendicularly. The ratio α=| *J* _{a2}/ *J* _{a1}| of the FM NN and the AFM NNN couplings is found as ~0.23, close to the critical point α _{c}=1/4 which separates ferromagnetically and antiferromagnetically correlated spiral magnetic ground states in single chains, whereas α _{c}>0.25 for coupled chains is considerably upshifted even for relatively weak IC. Although the measured dispersion can be described by homogeneous LSWT, the scattering intensity appears to be considerably reduced at ~11.5 and ~28 meV. The gaplike feature at 11.5 meV is attributed to magnon-phonon coupling whereas based on density matrix renormalization group simulations of the dynamical structure factor the gap at 28 meV is considered to stem partly from quantum effects due to the AFM IC. Another contribution to that gap is ascribed to the intrinsic superstructure from the distorting incommensurate pattern of CaY cationic chains adjacent to the CuO _{2} ones. It gives rise to nonequivalent CuO _{4} units and Cu-O-Cu bond angles Φ and a resulting distribution of all exchange integrals. The *J*'s fitted by homogeneous LSWT are regarded as average values. The record value of the FM NN integral *J* _{1}=24 meV among FFESC cuprates can be explained by a *nonuniversal* Φ(≠90°) and Cu-O bond length dependent *anisotropic* mean direct FM Cu-O exchange $$\overline{K}_{pd}$$~120 meV, similar to a value of 105 meV for Li _{2}CuO _{2}, in accord with larger values for La _{2}CuO _{4} and CuGeO _{3} (~110 meV) reported by Braden *et al*. [Phys. Rev. B 54, 1105 (1996)] phenomenologically. Lastly, enhanced $$K_{pd}$$ values are also needed to compensate a significant AFM *J _{dd}* ≥ 6 meV from the

*dd*channel, generic for FFESC cuprates but ignored so far.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- National Inst. of Advanced Industrial Science and Technology (AIST), Tsukuba (Japan)
- Inst. of Theoretical Solid State Physics, IFW Dresden (Germany)
- Max-Planck Inst. of Chemical Physics, Dresden (Germany)
- Inst.of Theoretical Physics, TU Dresden (Germany)
- Inst. for Problems of Materials Science, NASU, Kiev (Ukraine); Donostia International Physics Center (DIPC), San Sebastian/Donostia (Spain)
- Inst. of Theoretical Solid State Physics, IFW Dresden (Germany); Inst.of Theoretical Physics, TU Dresden (Germany)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1561674

- Grant/Contract Number:
- AC05-00OR22725; FG02-13ER41967

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 10; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Matsuda, Masaaki, Ma, Jie, Garlea, Vasile O., Ito, T., Yamaguchi, H., Oka, K., Drechsler, S.-L., Yadav, R., Hozoi, L., Rosner, H., Schumann, R., Kuzian, R. O., and Nishimoto, S. Highly dispersive magnons with spin-gap-like features in the frustrated ferromagnetic S=12 chain compound Ca2Y2Cu5O10 detected by inelastic neutron scattering. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.100.104415.
```

```
Matsuda, Masaaki, Ma, Jie, Garlea, Vasile O., Ito, T., Yamaguchi, H., Oka, K., Drechsler, S.-L., Yadav, R., Hozoi, L., Rosner, H., Schumann, R., Kuzian, R. O., & Nishimoto, S. Highly dispersive magnons with spin-gap-like features in the frustrated ferromagnetic S=12 chain compound Ca2Y2Cu5O10 detected by inelastic neutron scattering. United States. doi:10.1103/PhysRevB.100.104415.
```

```
Matsuda, Masaaki, Ma, Jie, Garlea, Vasile O., Ito, T., Yamaguchi, H., Oka, K., Drechsler, S.-L., Yadav, R., Hozoi, L., Rosner, H., Schumann, R., Kuzian, R. O., and Nishimoto, S. Thu .
"Highly dispersive magnons with spin-gap-like features in the frustrated ferromagnetic S=12 chain compound Ca2Y2Cu5O10 detected by inelastic neutron scattering". United States. doi:10.1103/PhysRevB.100.104415.
```

```
@article{osti_1561674,
```

title = {Highly dispersive magnons with spin-gap-like features in the frustrated ferromagnetic S=12 chain compound Ca2Y2Cu5O10 detected by inelastic neutron scattering},

author = {Matsuda, Masaaki and Ma, Jie and Garlea, Vasile O. and Ito, T. and Yamaguchi, H. and Oka, K. and Drechsler, S.-L. and Yadav, R. and Hozoi, L. and Rosner, H. and Schumann, R. and Kuzian, R. O. and Nishimoto, S.},

abstractNote = {In this paper, we report inelastic neutron scattering experiments in Ca2Y2Cu5O10 and map out the full one-magnon dispersion which extends up to a record value of 53 meV for frustrated ferromagnetic (FM) edge-sharing CuO2 chain (FFESC) cuprates. A homogeneous spin-1/2 chain model with a FM nearest-neighbor (NN), an antiferromagnetic (AFM) next-nearest-neighbor (NNN) inchain, and two diagonal AFM interchain couplings (ICs) analyzed within linear spin-wave theory (LSWT) reproduces well the observed strong dispersion along the chains and a weak one perpendicularly. The ratio α=|Ja2/Ja1| of the FM NN and the AFM NNN couplings is found as ~0.23, close to the critical point αc=1/4 which separates ferromagnetically and antiferromagnetically correlated spiral magnetic ground states in single chains, whereas αc>0.25 for coupled chains is considerably upshifted even for relatively weak IC. Although the measured dispersion can be described by homogeneous LSWT, the scattering intensity appears to be considerably reduced at ~11.5 and ~28 meV. The gaplike feature at 11.5 meV is attributed to magnon-phonon coupling whereas based on density matrix renormalization group simulations of the dynamical structure factor the gap at 28 meV is considered to stem partly from quantum effects due to the AFM IC. Another contribution to that gap is ascribed to the intrinsic superstructure from the distorting incommensurate pattern of CaY cationic chains adjacent to the CuO2 ones. It gives rise to nonequivalent CuO4 units and Cu-O-Cu bond angles Φ and a resulting distribution of all exchange integrals. The J's fitted by homogeneous LSWT are regarded as average values. The record value of the FM NN integral J1=24 meV among FFESC cuprates can be explained by a nonuniversal Φ(≠90°) and Cu-O bond length dependent anisotropic mean direct FM Cu-O exchange $\overline{K}_{pd}$~120 meV, similar to a value of 105 meV for Li2CuO2, in accord with larger values for La2CuO4 and CuGeO3 (~110 meV) reported by Braden et al. [Phys. Rev. B 54, 1105 (1996)] phenomenologically. Lastly, enhanced $K_{pd}$ values are also needed to compensate a significant AFM Jdd ≥ 6 meV from the dd channel, generic for FFESC cuprates but ignored so far.},

doi = {10.1103/PhysRevB.100.104415},

journal = {Physical Review B},

number = 10,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}

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- Klyushina, E. S.; Islam, A. T. M. N.; Park, J. T.
- Physical Review B, Vol. 98, Issue 10

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Large quantum fluctuations in the strongly coupled spin- ${\scriptstyle \frac{1}{2}}$ chains of green dioptase ${\text{Cu}}_{6}{\text{Si}}_{6}{\text{O}}_{18}\cdot 6{\text{H}}_{2}\text{O}$

journal, July 2010

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- Physical Review B, Vol. 82, Issue 1

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NaCuMoO _{4} (OH) as a Candidate Frustrated *J* _{1} – *J* _{2} Chain Quantum Magnet

journal, October 2014

- Nawa, Kazuhiro; Okamoto, Yoshihiko; Matsuo, Akira
- Journal of the Physical Society of Japan, Vol. 83, Issue 10

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Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc–Zn

journal, August 2005

- Balabanov, Nikolai B.; Peterson, Kirk A.
- The Journal of Chemical Physics, Vol. 123, Issue 6

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Electronic and magnetic excitations in the half-stuffed Cu-O planes of ${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{4}{\mathrm{Cl}}_{2}$ measured by resonant inelastic x-ray scattering

journal, September 2017

- Fatale, S.; Fatuzzo, C. G.; Babkevich, P.
- Physical Review B, Vol. 96, Issue 11

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Possible quadrupolar nematic phase in the frustrated spin chain ${\mathrm{LiCuSbO}}_{4}$ : An NMR investigation

journal, December 2017

- Bosiočić, M.; Bert, F.; Dutton, S. E.
- Physical Review B, Vol. 96, Issue 22

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Femtosecond Dynamics of Momentum-Dependent Magnetic Excitations from Resonant Inelastic X-Ray Scattering in ${\mathrm{CaCu}}_{2}{\mathrm{O}}_{3}$

journal, April 2014

- Bisogni, Valentina; Kourtis, Stefanos; Monney, Claude
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Spin gap in malachite Cu ${}_{2}$ (OH) ${}_{2}$ CO ${}_{3}$ and its evolution under pressure

journal, December 2013

- Lebernegg, Stefan; Tsirlin, Alexander A.; Janson, Oleg
- Physical Review B, Vol. 88, Issue 22

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Spin structure of the dopable quasi-one-dimensional copper oxide ${\mathrm{Ca}}_{2}{\mathrm{Y}}_{2}{\mathrm{Cu}}_{5}{\mathrm{O}}_{10}$

journal, March 1999

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Role of Lattice Coupling in Establishing Electronic and Magnetic Properties in Quasi-One-Dimensional Cuprates

journal, June 2013

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Magnetic Excitations of Spin-Gap System Na _{3} Cu _{2} SbO _{6} with Distorted Honeycomb Structure

journal, October 2008

- Miura, Yoko; Yasui, Yukio; Moyoshi, Taketo
- Journal of the Physical Society of Japan, Vol. 77, Issue 10

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The precursor phase of the CMR metallic state probed by spin and lattice dynamics

journal, January 2005

- Hennion, M.; Moussa, F.
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Frustrated ferromagnetic spin- ${\scriptstyle \frac{1}{2}}$ chain in a magnetic field: The phase diagram and thermodynamic properties

journal, July 2006

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- Physical Review B, Vol. 74, Issue 2

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Direct determination of the effective electronic coupling in electron-transfer problems

journal, January 1993

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Unoccupied electronic structure of ${\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$

journal, November 1999

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- Physical Review B, Vol. 60, Issue 19

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Accurate *ab initio* determination of magnetic interactions and hopping integrals in La2−xSrxCuO4 systems

journal, March 2000

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- The Journal of Chemical Physics, Vol. 112, Issue 11

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Thermodynamics of multiferroic spin chains

journal, January 2010

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- Physical Review B, Vol. 81, Issue 1

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Numerical and approximate analytical results for the frustrated spin- 1/2 quantum spin chain

journal, November 1995

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Frustrating interactions and broadened magnetic excitations in the edge-sharing ${\mathrm{CuO}}_{2}$ chains in ${\mathrm{La}}_{5}{\mathrm{Ca}}_{9}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$

journal, August 2003

- Matsuda, M.; Kakurai, K.; Lorenzo, J. E.
- Physical Review B, Vol. 68, Issue 6

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${\mathrm{Ca}}_{2}{\mathrm{Y}}_{2}{\mathrm{Cu}}_{5}{\mathbf{O}}_{10}$ : The First Frustrated Quasi-1D Ferromagnet Close to Criticality

journal, September 2012

- Kuzian, R. O.; Nishimoto, S.; Drechsler, S. -L.
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High pressure induced coordination evolution in chain compound Li2CuO2

journal, November 2009

- You, Shujie; Li, Zhi; Yang, Liuxiang
- Journal of Solid State Chemistry, Vol. 182, Issue 11

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NMR and local-density-approximation evidence for spiral magnetic order in the chain cuprate ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$

journal, July 2004

- Gippius, A. A.; Morozova, E. N.; Moskvin, A. S.
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Absence of a spiral magnetic order in ${\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$ containing one-dimensional ${\mathrm{CuO}}_{2}$ ribbon chains

journal, December 2007

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- Physical Review B, Vol. 76, Issue 22

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Temperature-dependent optical conductivity of undoped cuprates with weak exchange

journal, August 2008

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Electronic states and magnetic properties of edge-sharing Cu-O chains

journal, March 1998

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Superconductivity, Spin Gaps and Luttinger Liquids in a Class of Cuprates

journal, August 1993

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Dynamical density-matrix renormalization-group method

journal, July 2002

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Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin- $s$ Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets

journal, January 2014

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- Physical Review B, Vol. 89, Issue 1

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Accurate and simple analytic representation of the electron-gas correlation energy

journal, June 1992

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Characterization of the spin- $\frac{1}{2}$ linear-chain ferromagnet CuAs ${}_{2}$ O ${}_{4}$

journal, January 2014

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- Physical Review B, Vol. 89, Issue 1

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Anisotropic superexchange of a 90° Cu-O-Cu bond

journal, July 1999

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Magnetic neutron diffraction in

journal, April 2005

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- Physica B: Condensed Matter, Vol. 359-361

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${\mathrm{Ca}}_{4}{\mathrm{Cu}}_{5}{\mathrm{O}}_{10}:$ Copper oxide chains highly occupied by Zhang-Rice singlets

journal, August 1998

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Magnetic excitations from the two-dimensional interpenetrating Cu framework in ${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{4}{\mathrm{Cl}}_{2}$

journal, July 2017

- Babkevich, P.; Shaik, N. E.; Lançon, D.
- Physical Review B, Vol. 96, Issue 1

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Dynamics of linarite: Observations of magnetic excitations

journal, January 2017

- Rule, K. C.; Willenberg, B.; Schäpers, M.
- Physical Review B, Vol. 95, Issue 2

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Recent progress on HYSPEC, and its polarization analysis capabilities

journal, January 2015

- Winn, Barry; Filges, Uwe; Garlea, V. Ovidiu
- EPJ Web of Conferences, Vol. 83

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Intersite Coulomb Interactions in Quasi-One-Dimensional Copper Oxides

journal, February 1997

- Okada, Kozo; Kotani, Akio
- Journal of the Physical Society of Japan, Vol. 66, Issue 2