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Register a new userSpin dynamics and unconventional Coulomb phase in Nd$_2$Zr$_2$O$_7$
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We investigate the temperature dependence of the spin dynamics in the pyrochlore magnet Nd$_2$Zr$_2$O$_7$ by neutron scattering experiments. At low temperature, this material undergoes a transition towards an all in - all out antiferromagnetic phase and the spin dynamics encompass a dispersion-less mode, characterized by a dynamical spin ice structure factor. Unexpectedly, this mode is found to survive above $T_{rm N} approx 300$ mK. Concomitantly, elastic correlations of the spin ice type develop. These are the signatures of a peculiar correlated paramagnetic phase which can be considered as a new example of Coulomb phase. Our observations near $T_{rm N}$ do not reproduce the signatures expected for a Higgs transition, but show reminiscent features of the all in - all out order superimposed on a Coulomb phase.
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By combining neutron scattering and magnetization measurements down to 80 mK, we determine the $(H,T)$ phase diagram of the Nd$_2$(Zr$_{1-x}$Ti$_x$)$_2$O$_7$ pyrochlore magnet compounds. In those samples, Zr is partially substituted by Ti, hence tuning the exchange parameters and testing the robustness of the various phases. In all samples, the ground state remains all in / all out, while the field induces phase transitions towards new states characterized by 2 in - 2 out or 1 out - 3 in / 1 in - 3 out configurations. These transitions manifest as metamagnetic singularities in the magnetization vs field measurements. Strikingly, it is found that moderate substitution reinforces the stability of the all in / all out phase: the Neel temperature, the metamagnetic fields along with the ordered magnetic moment are higher in substituted samples with $x <$ 10%.
The search for quantum spin liquids (QSL) -- topological magnets with fractionalized excitations -- has been a central theme in condensed matter and materials physics. While theories are no longer in short supply, tracking down materials has turned out to be remarkably tricky, in large part because of the difficulty to diagnose experimentally a state with only topological, rather than conventional, forms of order. Pyrochlore systems have proven particularly promising, hosting a classical Coulomb phase in the spin ices Dy/Ho$_2$Ti$_2$O$_7$, with subsequent proposals of candidate QSLs in other pyrochlores. Connecting experiment with detailed theory exhibiting a robust QSL has remained a central challenge. Here, focusing on the strongly spin-orbit coupled effective $S=1/2$ pyrochlore Ce$_2$Zr$_2$O$_7$, we analyse recent thermodynamic and neutron scattering experiments, to identify a microscopic effective Hamiltonian through a combination of finite temperature Lanczos, Monte Carlo and analytical spin dynamics calculations. Its parameter values suggest a previously unobserved exotic phase, a $pi$-flux U(1) QSL. Intriguingly, the octupolar nature of the moments makes them less prone to be affected by crystal imperfections or magnetic impurities, while also hiding some otherwise characteristic signatures from neutrons, making this QSL arguably more stable than its more conventional counterparts.
Neutron scattering, specific heat and magnetisation measurements on both powders and single crystals reveal that Dy$_2$Ir$_2$O$_7$ realizes the fragmented monopole crystal state in which antiferromagnetic order and a Coulomb phase spin liquid co-inhabit. The measured residual entropy is that of a hard core dimer liquid, as predicted. Inclusion of Coulomb interactions allows for a quantitative description of both the thermodynamic data and the magnetisation dynamics, with the energy scale given by deconfined defects in the emergent ionic crystal. Our data reveal low energy excitations, as well as a large distribution of energy barriers down to low temperatures, while the magnetic response to an applied field suggests that domain wall pinning is important; results that call for further theoretical modelling.
Pr$_2$Zr$_2$O$_7$ is a pyrochlore quantum spin-ice candidate. Using Raman scattering spectroscopy we probe crystal electric field excitations of Pr$^{3+}$, and demonstrate the importance of their interactions with the lattice. We identify a vibronic interaction with a phonon that leads to a splitting of a doublet crystal field excitation at around 55~meV. We also probe a splitting of the non-Kramers ground state doublet of Pr$^{3+}$ by observing a double line of the excitations to the first excited singlet state $E^0_g rightarrow A_{1g}$. We show that the splitting has a strong temperature dependence, with the doublet structure most prominent between 50~K and 100~K, and the weight of one of the components strongly decreases on cooling. We suggest a static or dynamic deviation of Pr$^{3+}$ from the position in the ideal crystal structure can be the origin of the effect, with the deviation strongly decreasing at low temperatures.
We present thermodynamic and neutron scattering measurements on the quantum spin ice candidate Nd$_2$Zr$_2$O$_7$. The parameterization of the anisotropic exchange Hamiltonian is refined based on high-energy-resolution inelastic neutron scattering data together with thermodynamic data using linear spin wave theory and numerical linked cluster expansion. Magnetic phase diagrams are calculated using classical Monte Carlo simulations with fields along mbox{[100]}, mbox{[110]} and mbox{[111]} crystallographic directions which agree qualitatively with the experiment. Large hysteresis and irreversibility for mbox{[111]} is reproduced and the microscopic mechanism is revealed by mean field calculations to be the existence of metastable states and domain inversion. Our results shed light on the explanations of the recently observed dynamical kagome ice in Nd$_2$Zr$_2$O$_7$ in mbox{[111]} fields.
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