Single-ion anisotropy and magnetic field response in spin ice materials Ho${}_2$Ti${}_2$O${}_7$ and Dy${}_2$Ti${}_2$O${}_7$

Abstract

Motivated by its role as a central pillar of current theories of dynamics of spin ice in and out of equilibrium, we study the single-ion dynamics of the magnetic rare earth ions in their local environments, subject to the effective fields set up by the magnetic moments they interact with. This effective field has a transverse component with respect to the local easy-axis of the crystal electric field, which can induce quantum tunnelling. We go beyond the projective spin-1/2 picture and use instead the full crystal-field Hamiltonian. We find that the Kramers vs non-Kramers nature, as well as the symmetries of the crystal-field Hamiltonian, result in different perturbative behaviour at small fields ($\lesssim 1$ T), with transverse field effects being more pronounced in Ho${}_2$Ti${}_2$O${}_7$ than in Dy${}_2$Ti${}_2$O${}_7$. Remarkably, the energy splitting range we find is consistent with time scales extracted from experiments. We also present a study of the static magnetic response which highlights the anisotropy of the system in the form of an off-diagonal $g$ tensor and we investigate the effects of thermal fluctuations in the temperature regime of relevance to experiments. We show that there is a narrow yet accessible window of experimental parameters where the anisotropic response can be observed.

17 pages, 8 figures

References in corpus (6)

• Why spin ice obeys the ice rules
• Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
• Spin Dynamics at Very Low Temperature in Spin Ice Dy${}_2$Ti${}_2$O${}_7$
• Brownian Motion and Quantum Dynamics of Magnetic Monopoles in Spin Ice
• Ultrasonic investigations of spin-ices Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$ in and out of equilibrium
• Hydrogenic states of monopoles in diluted quantum spin ice

Cited by in corpus (18)

• Crystal field parameters of the rare earth pyrochlores $R_2$Ti${}_2$O${}_7$ ($R$ = Tb, Dy, Ho)
• First principles calculation and experimental investigation of lattice dynamics in the rare earth pyrochlores R2Ti2O7 (R=Tb, Dy, Ho)
• Correlated Quantum Tunnelling of Monopoles in Spin Ice
• Quantum versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14
• Magneto-elastic induced vibronic bound state in the spin ice pyrochlore Ho${}_2$Ti${}_2$O${}_7$
• Proposal for the Detection of Magnetic Monopoles in Spin Ice via Nanoscale Magnetometry
• Anomalous magnetic noise in imperfect flat bands in the topological magnet Dy2Ti2O7
• Phonon-mediated spin-flipping mechanism in the spin ices Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$
• Common Glass-Forming Spin-Liquid State in the Pyrochlore Magnets Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$
• Monopolar and dipolar relaxation in spin ice Ho${}_2$Ti${}_2$O${}_7$
• Dipolar spin ice states with fast monopole hopping rate in CdEr${}_2$X${}_4$ (X = Se, S)
• Deviation from the dipole-ice model in the new spinel spin-ice candidate, MgEr${}_2$Se${}_4$
• Nuclear spin assisted quantum tunnelling of magnetic monopoles in spin ice
• Modification of Spin Ice Physics in Ho${}_2$Ti${}_2$O${}_7$ Thin Films
• Magnetic field tuning of crystal field levels and vibronic states in Spin-ice Ho${}_2$Ti${}_2$O${}_7$ observed in far-infrared reflectometry
• Room temperature spin-ice physics in cadmium cyanide
• Probing ice-rule-breaking transition in $\mathrm{D}{\mathrm{y}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ thin film by proximitized transport and magnetic torque
• Experimental measurement of the isolated magnetic susceptibility