Softening of breathing elastic mode and trigonal elastic mode in disordered pyrochlore magnet NaCaCo$_2$F$_7$

Abstract

Cobalt pyrochlore fluoride NaCaCo2F7 is a disordered frustrated magnet composed of Co 2+ ions with an effective spin-1 2 magnetic moment and exhibits spin freezing below T f ∼2.4 K. We perform ultrasound velocity measurements on a single crystal of the cubic NaCaCo2F7. The temperature dependence of the bulk modulus (the breathing elastic mode) exhibits Curie-type softening upon cooling below ∼20 K down to T f , which is suppressed by the magnetic field. This Curie-type softening should be a precursor to the enhancement of the strength of exchange disorder via the spin-lattice coupling, which causes the spin freezing. In contrast to the magnetic-field-suppressed Curie-type softening in the bulk modulus, the trigonal shear modulus exhibits softening with a characteristic minimum upon cooling, which is enhanced by the magnetic field at temperatures below ∼20 K. This magnetic-field-enhanced elastic anomaly in the trigonal shear modulus suggests a coupling of the lattice to the dynamical spin-cluster state. For NaCaCo2F7, the observed elastic anomalies reveal an occurrence of magnetic-field-induced crossover from an isostructural lattice instability toward the spin freezing to a trigonal lattice instability arising from the emergent dynamical spin-cluster state.