Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions

Abstract

We investigate the ground state and critical temperature phase diagrams of the classical and quantum $S=1/2$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered $XY$ phase, known as ${\Gamma }_5$, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the ${\psi }_3$ state in most parts of the ${\Gamma }_5$ regime. Likewise, thermal fluctuations treated classically, select the ${\psi }_3$ state at $T=0^{+}$. In contrast, classical Monte Carlo finds that the system orders at $T_c$ in the ${\psi }_2$ state of ${\Gamma }_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from ${\psi }_2$ to ${\psi }_3$ at a temperature $T_{{\Gamma }_5}<T_c$. The same method finds that the system orders via a single transition at $T_c$ directly into the ${\psi }_3$ state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at $T_c$ for the $S=1/2$ quantum model is corroborated by high-temperature series expansion. To investigate the $T=0$ quantum ground states, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic $S=1/2$ Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. We find that near the boundary of ferromagnetism and ${\Gamma }_5$ antiferromagnetism the system may potentially realize a quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same ordered phases as in the classical model.

arXiv comment26 pages, 14 figures

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