Thermodynamic properties of Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: Validation of a quantum spin ice exchange Hamiltonian

The thermodynamic properties of the pyrochlore Yb2Ti2O7 material are calculated using the numerical linked-cluster calculation method for an effective anisotropic-exchange spin-12 Hamiltonian with parameters recently determined by fitting the neutron scattering spin-wave data obtained at high magnetic field. Magnetization M(T,h) as a function of temperature T and for different magnetic fields h applied along the three high-symmetry directions [100], [110], and [111] are compared with experimental measurements on the material for temperature T>1.8 K. The excellent agreement between experimentally measured and calculated M(T,h) over the entire temperature and magnetic field ranges considered provides strong quantitative validation of the effective Hamiltonian. It also confirms that fitting the high-field neutron spin-wave spectra in the polarized paramagnetic state is an excellent method for determining the microscopic exchange constants of rare-earth insulating magnets that are described by an effective spin-12 Hamiltonian. Finally, we present results which demonstrate that a recent analysis of the polarized neutron scattering intensity of Yb2Ti2O7 using a random phase approximation method [Chang , Nat. Commun. 3, 992 (2012)2041-172310.1038/ncomms1989] does not provide a good description of M(T,h) for T≲10 K, that is, in the entire temperature regime where magnetic correlations become non-negligible. With the compelling evidence that we now have at hand an accurate microscopic Hamiltonian for Yb2Ti2O7, our work exposes a paradox: why does this material fail to develop long-range ferromagnetic order?