Spin-orbiton and quantum criticality in ${\mathrm{FeSc}}_{2}{\mathrm{S}}_{4}$

Spin-orbiton and quantum criticality in ${FeSc}_{2} S_{4}$

L. Mittelstädt, M. Schmidt, Zhe Wang, F. Mayr, V. Tsurkan, P. Lunkenheimer, D. Ish, L. Balents, J. Deisenhofer, and A. Loidl

Phys. Rev. B 91, 125112 – Published 5 March 2015

Abstract

In ${FeSc}_{2} S_{4}$ spin-orbital exchange competes with strong spin-orbit coupling, suppressing long-range spin and orbital order and, hence, this material represents one of the rare examples of a spin-orbital liquid ground state. Moreover, it is close to a quantum-critical point separating the ordered and disordered regimes. Using terahertz and far-infrared spectroscopy we study low-lying excitations in ${FeSc}_{2} S_{4}$ and provide clear evidence for a spin-orbiton, an excitation of strongly entangled spins and orbitals. It becomes particularly well pronounced upon cooling, when advancing deep into the quantum-critical regime. Moreover, indications of an underlying structureless excitation continuum are found, a possible signature of quantum criticality.

Received 10 November 2014
Revised 21 January 2015

DOI:https://doi.org/10.1103/PhysRevB.91.125112

Authors & Affiliations

L. Mittelstädt¹, M. Schmidt¹, Zhe Wang¹, F. Mayr¹, V. Tsurkan^1,2, P. Lunkenheimer^1,*, D. Ish³, L. Balents⁴, J. Deisenhofer¹, and A. Loidl¹

¹Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
²Institute of Applied Physics, Academy of Sciences of Moldova, MD-2028 Chisinau, Republic of Moldova
³Physics Department, University of California, Santa Barbara, California 93106-4030, USA
⁴Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA

^*Corresponding author: peter.lunkenheimer@physik.uni-augsburg.de

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Vol. 91, Iss. 12 — 15 March 2015

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Figure 1
Schematic $x, T$ phase diagram based on theoretical considerations [1, 11] (see text for details). The control parameter $x$ measures the ratio of the magnetic exchange to the effective spin-orbit coupling. SOS, QC, AFM, and OO denote spin-orbital singlet, quantum-critical, antiferromagnetic, and orbitally ordered states, respectively. The vertical dashed line indicates the position of ${FeSc}_{2} S_{4}$ .
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Figure 2
Three-dimensional plot of the dielectric loss of ${FeSc}_{2} S_{4}$ vs wave number and temperature. The loss is color coded to indicate equal-loss contours above the temperature wave-number plane.
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Figure 3
(a) Dielectric loss of ${FeSc}_{2} S_{4}$ at low wave numbers for selected temperatures between 4 and 70 K. The solid lines represent fits using Lorentzian line shapes including a temperature-dependent background (see text). Right column: Temperature dependence of eigenfrequency (b), of the dielectric strength (c), and of the damping constant (d) of the spin-orbiton. The solid lines in (b)–(d) serve as guides to the eye. The dashed vertical line indicates a temperature $T^{*} \approx 17 K$ , below which a change of the characteristics of the excitation is observed.
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Figure 4
(a) FIR measurements between 80 and $600 {cm}^{- 1}$ are compared with a fit utilizing four Lorentz oscillators. The four phonon modes are indexed from 1 to 4. The right frames show the temperature dependence of eigenfrequency $ω_{0}$ (b), dielectric strength Δε (c), damping γ (d), and the Fano factor $ω_{q}$ (e) of phonon 1 close to $115 {cm}^{- 1}$ . In (b)–(e), typical error bars are indicated. The solid lines are drawn to guide the eyes.
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Figure 5
Temperature dependence of the reflectivity in ${FeSc}_{2} S_{4}$ in the frequency regime of the lowest phonon mode. For clarity reasons, the reflectivity curves for 80, 100, and 275 K are shifted upwards. The reflectivity of phonon mode 1 of ${FeSc}_{2} S_{4}$ was fitted with a pure Lorentz oscillator model (dashed red lines) or with a Fano resonance model, Eq. (1) (solid blue lines).
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Figure 6
Low-frequency dielectric loss of ${FeSc}_{2} S_{4}$ . Combined THz and FIR results of the dielectric loss are shown for wave numbers between 10 and $135 {cm}^{- 1}$ , covering spin-orbital excitations and the lowest phonon mode. The results at 5 K are compared to measurements at 80 K. The high-temperature spectrum is composed of a linear excitation continuum (yellow) and a Fano-type phonon mode (blue). As revealed by the inset, showing a magnified view of the low-frequency results, a heavily damped spin-orbital mode is superimposed to the continuum. At 5 K, excess intensity is observed, consistent with a spin-orbiton emerging from a superlinear background. The dashed lines are guides for the eyes.
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Physical Review B

covering condensed matter and materials physics

Spin-orbiton and quantum criticality in ${FeSc}_{2} S_{4}$

L. Mittelstädt, M. Schmidt, Zhe Wang, F. Mayr, V. Tsurkan, P. Lunkenheimer, D. Ish, L. Balents, J. Deisenhofer, and A. Loidl

Phys. Rev. B 91, 125112 – Published 5 March 2015

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Physical Review B

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Spin-orbiton and quantum criticality in FeSc2S4

L. Mittelstädt, M. Schmidt, Zhe Wang, F. Mayr, V. Tsurkan, P. Lunkenheimer, D. Ish, L. Balents, J. Deisenhofer, and A. Loidl

Phys. Rev. B 91, 125112 – Published 5 March 2015

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Spin-orbiton and quantum criticality in ${FeSc}_{2} S_{4}$