Magnetic Resonance in XY-Antiferromagnet on a Pyrochlore Lattice Er2Ti2O7

In certain magnetic systems, the arrangement of magnetic ions within the crystal lattice is such that all pairwise interactions cannot be simultaneously satisfied. This phenomenon, known as geometric frustration, often leads to the degeneracy of the ground state. In the Heisenberg model on a pyrochlore lattice with antiferromagnetic exchange interaction, the ground state of the system remains infinitely degenerate at zero temperature (the degree of degeneracy is proportional to the number of magnetic ions, N. This degeneracy can be partially lifted by strong XY anisotropy, leaving a one-parameter degeneracy with a degree of N^{1/3}. This remaining degeneracy can be lifted by fluctuations, a phenomenon known as "Order by Disorder”. In case of quantum fluctuations the effect is called “Order by Quantum Disorder” (ObQD). The pyrochlore antiferromagnet with XY anisotropy, Er_2Ti_2O_7, demonstrates this effect. Theoretical calculations have shown that zero-point fluctuations generate anisotropy of the form A*cos(6 \alpha), leading to a gap of approximately 0.02 meV below the ordering temperature. Inelastic neutron scattering experiments confirm the presence of an energy gap in the spin wave spectrum of approximately \Delta = 0.053 \pm 0.006 meV. It is also known that the magnetic field exerts a significantly anisotropic influence on this gap. Preliminary studies of antiferromagnetic resonance spectra at frequencies from 20 GHz have shown the presence of a uniform spin oscillation mode \nu = \gamma*H, although deviations from this behavior may become noticeable at lower frequencies (~10 GHz). Thus, studying the quantum gap in the excitation spectrum of erbium titanate and its behavior in a magnetic field remains a significant research challenge. To address this challenge, it is necessary to investigate the uniform spin oscillation mode using electron spin resonance at frequencies around the gap (~10 GHz), where its dependence on the magnetic field is most pronounced. The influence of the magnetic field orientation on the gapped mode is significantly anisotropic and largely unexplored, thus requiring sample rotation during the experiment. A low-temperature stepper motor based on a rotor with crossed windings was developed, utilising the magnetic field of the existing superconducting solenoid in the cryostat for rotation. The prototype motor was installed on a transmission type microwave spectrometer with a rectangular resonator. Tests successfully reproduced the angular dependences of the magnetic resonance spectrum in the well-studied antiferromagnet MnCO_3 at temperatures of 0.5 – 7.5 K within an angular range of ±100° from the initial position. The overheating of the cell and cryostat was studied, and the heat dissipation of the mechanism was evaluated during operation. Subsequent measurements of the AFMR spectra of the XY antiferromagnet on the pyrochlore lattice Er_2Ti_2O_7 at low frequencies revealed that the uniform oscillation mode, previously considered isotropic \gamma H, actually exhibits a strong dependence on the magnetic field at frequencies around 10 GHz. The observed shift in the resonance line position, nearly twice as large, cannot be explained by changes in the g-factor in a crystal with cubic symmetry. This is interpreted as the presence of a gap in the spin wave excitation spectrum, strongly dependent on the direction of the magnetic field. The temperature behavior of the gapped mode aligns with results obtained by neutron scattering. The shifting of the absorption line to higher fields upon heating is a fingerprint of a gapped mode, with the gap decreasing with increasing temperature and vanishing at T_N, although complete agreement is not achieved due to the system's complex behavior near the ordering temperature. This study has identified significant features in the AFMR spectra of the XY antiferromagnet on the pyrochlore lattice Er_2Ti_2O_7. These results open prospects for further research in this direction.