Orbital fluctuations and orbital order below the Jahn-Teller transition in Sr${}_3$Cr${}_2$O${}_8$

We report on the magnetic and phononic excitation spectrum of Sr${}_3$Cr${}_2$O${}_8$ determined by THz and infrared (IR) spectroscopy, and electron spin resonance (ESR) measurements across the Jahn-Teller transition, which is detected by specific-heat measurements to occur at $T_{\text{JT}}=285$ K. We identify the singlet-triplet excitations in the dimerized ground state and estimate the exchange couplings in the system. ESR absorptions were observed up to $T^{*}=120$ K with a linewidth $\propto$$\exp (-\Delta /k_{B}T)$ and $\Delta /k_B=388$ K, indicating a phonon-mediated spin relaxation via the excited orbital state of the Cr $e$ doublet in the orbitally ordered state. Upon entering the low-symmetry Jahn-Teller distorted phase below $T_{\text{JT}}$, we find an extended regime $T^{*}<T<T_{\text{JT}}$, where the IR active phonons change only gradually with decreasing temperature. This regime is associated with strong fluctuations in the orbital and lattice degrees of freedom, in agreement with the loss of the ESR signal above $T^{*}$. Using the measured magnetic and phononic excitation spectrum we model the orbital contribution to the specific heat and find the persistence of strong fluctuations far below $T_{\text{JT}}$.

Figure 1

(a) Zeeman splitting of triplet states in a magnetic field. Modes 1, $1^{\text{'}}$, 2, and $3^{\text{'}}$ are described in the text. (b) Transmission spectra measured at different frequencies at 4 K. The spectrum obtained at 170 GHz and 7 K (dashed line) is shifted for clarity. (c) Bilayer structure of Cr${}^{5+}$ ions. (d) Magnetic field dependence of the observed absorption frequencies at 4 K for $\mathbf{H}\Vert c_h$ and $\mathbf{H}\Vert a_h$.

Figure 2

(a) $X$-band ESR spectrum measured at 30 K for $\mathbf{H}\perp a_h$ fitted by a Lorentzian line. Temperature dependence of (b) the ESR intensity $I_{\text{ESR}}$ together with the dc susceptibility ${\chi }_{\text{dc}}$ measured at 3.4 kOe and (c) of the ESR linewidth. The solid curve is a fit described in the text. Inset: Sketch of the spin relaxation via an Orbach process.

Figure 3

Reflectivity spectra of Sr${}_3$Cr${}_2$O${}_8$ with $\mathbf{E}\Vert c_h$ (a) at 295 and 250 K, and (b) at 150, 100, and 20 K. The spectra are shifted with respect to the ones at 150 and 295 K in order to clearly illustrate the evolution of phonon modes with temperature.

Figure 4

Specific heat divided by temperature $C/T$ vs $T$. The solid line is a superposition of the modeled magnetic (dashed line) and phonon contribution (dashed-dotted line) as described in the text. Upper and lower insets show the temperature dependence of orbital-related specific heat and entropy, respectively.