Unified Description of Spin-Lattice Coupling and Thermodynamics in the Pyrochlore Heisenberg Antiferromagnet

Abstract

We study an extended model to describe the spin-lattice coupling, incorporating individual vibrations of bonds and atomic sites alongside distance-dependent exchange interactions. The proposed spin Hamiltonian can be effectively considered as an interpolation between two well-established minimum models, the bond-phonon model and the site-phonon model. The extended model, which treats bond phonons and site phonons on comparable footing, well reproduces successive field-induced phase transitions as well as the thermodynamic properties of a three-up-one-down state in the pyrochlore-lattice Heisenberg antiferromagnet, including negative thermal expansion, an enhanced magnetocaloric effect, and a sharp specific-heat peak. The present approach is broadly applicable to various spin models, providing a framework for identifying the primary phonon modes responsible for spin-lattice coupling and for understanding complex magnetic phase diagrams.

Figures (4)

• Figure 1: Two minimal models describing the SLC: (a) the bond-phonon model assuming independent bond-length change $\rho_{ij}$, and (b) the site-phonon model assuming independent site displacement ${\mathbf u}_{i}$. The BP model does not effectively produce any further-neighbor interactions, while the SP model does not take into account magnetostriction.
• Figure 2: (a),(b) Experimental (a) magnetization and (b) magnetostriction curves of polycrystalline CdCr$_{2}$O$_{4}$ at $T_{\rm ini} = 4.2$ K obtained using the single-turn-coil technique, where the sample temperature is expected to be under (quasi)adiabatic conditions. In panel (a), $dM/dH$ is displayed by thin colors in the right axis. In panel (b), the data up to 50 T (black) are obtained in a nondestructive pulsed magnet. (c),(d) Calculated (c) magnetization and (d) magnetostriction curves for the extended SLC model [Eq. (\ref{['Eq5']})] with $b = 0.2$ and various values of $\eta$ at $T/J = 0.01$. In (a) and (c), the field derivative of the magnetization (for $\eta = 0.6$) is plotted in the right axis. (e) Theoretical phase diagram of Eq. (\ref{['Eq5']}) with $b = 0.2$ as a function of magnetic field $h$ and the SP contribution $\eta$ at $T/J = 0.01$.
• Figure 3: [(a)--(c)] Temperature dependence of (a) magnetization, (b) thermal expansion, and (c) specific heat for the extended SLC model [Eq. (\ref{['Eq5']})] with $b = 0.2$ and various $\eta$ values in the low-field side of the 1/2-magnetization plateau at $h/J = 3.7$. (d) Theoretical phase diagram of Eq. (\ref{['Eq5']}) with $b = 0.2$ as a function of temperature $T$ and the site-phonon contribution $\eta$ at $h/J = 3.7$. A phase transition to a three-up--one-down LRO state (crossover to a spin-liquid plateau state) is characterized by a sharp (broad) specific-heat peak, which is indicated by red circles (open blue diamonds).
• Figure 4: (a) Temperature dependence of specific heat at 24 T and 34 T for $H \parallel [111]$ in CdCr$_{2}$O$_{4}$, obtained using a flat-top nondestructive long pulsed magnet 2015_Koh2021_Mat2021_Ima2022_Koh. (b) Temperature dependence of specific heat at several $h$ values for the extended SLC model [Eq. (\ref{['Eq5']})] with $b = 0.2$ and $\eta = 0.6$. (c) Magnetocaloric effect (MCE) for $H \parallel [111]$ in CdCr$_{2}$O$_{4}$, measured under adiabatic conditions in a nondestructive pulsed magnet. The inset shows a magnified view of the $T(H)$ curve around $H_{\rm c2}$ measured using a different setup. All the data correspond to the field-increasing process. The thick gray lines indicate the phase boundaries separating the canted 2:2, three-up--one-down, and paramagnetic phases.