Antiferromagnetic and Orbital Ordering on a Diamond Lattice Near Quantum Criticality

Abstract

We present neutron scattering measurements on powder samples of the spinel FeSc2S4 that reveal a previously unobserved magnetic ordering transition occurring at 11.8(2) K. Magnetic ordering occurs subsequent to a subtle cubic-to-tetragonal structural transition that distorts Fe coordinating sulfur tetrahedra and lifts the orbital degeneracy. The orbital ordering is not truly long ranged, but occurs over finite-sized domains that limit magnetic correlation lengths. The application of 1 GPa hydrostatic pressure appears to destabilize this Néel state, reducing the transition temperature to 8.6(8) K and redistributing magnetic spectral weight to higher energies. The relative magnitudes of ordered ⟨m⟩2=3.1(2) μB2 and fluctuating moments ⟨δm⟩=13(1) μB2 show that the magnetically ordered state of FeSc2S4 is drastically renormalized and close to criticality.

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Plain Language Summary

In magnetic materials, electrons select which orbitals to occupy and how to orient their spins to minimize their energy. In general, a separation in energy scales results in orbital occupation occurring at high temperature, followed by collective spin ordering at a much lower temperature. In the intermediate temperature regime, the collective physics is governed by the spin-to-spin interactions that have been established at high temperatures by orbital ordering. There is great interest in studying materials in which the spin and orbital energy scales are comparable such that there exists a temperature regime with collective spin-orbital physics. In such materials, it may be possible to form a spin-orbital quantum liquid where electrons fail to select an orbital or a spin direction but instead remain in a quantum fluctuating state to absolute zero temperature. Here, we provide evidence for a peculiar coexistence of spin and orbital order with strong quantum fluctuations in the spinel FeSc2S4 .

The spin and orbital energy scales are similar in FeSc2S4 , a material in which the iron ions have both spin and orbital degrees of freedom. Previous work indicated a spin-orbital liquid ground state in this material. We consider the elastic neutron scattering cross section of an 0.8-g sample of FeSc2S4 and find that a magnetic ordering transition occurs at roughly 12 K. Applying 1 GPa hydrostatic pressure reduces the transition temperature by roughly 3 K. The detailed nature of the spin-orbital order that we report provides unique atomic scale insights into FeSc2S4 , and the observation of strong quantum fluctuations positions FeSc2S4 near a so-called quantum critical point where spin and possibly even orbital ordering collapse.

We expect that our findings will motivate future studies of FeSc2S4 with the goal of driving this material through the quantum phase transition.