{'fraction_non_alphanumeric': 0.019726858877086494, 'fraction_numerical': 0.0, 'mean_word_length': 5.534653465346534, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Longitudinal Spin Dynamics in Ferromagnets Including Dipolar Forces

The influence of dipolar forces on longitudinal spin fluctuations in a ferromagnet is explored within the framework of spin-wave theory for a Heisenberg magnet. Explicit results are provided for long-wavelength fluctuations. The dipolar-induced contribution to the dynamic response function, observed in neutron scattering experiments, is peaked near a low-frequency band edge, controlled by the size of the external field, and the intensity is insensitive to variations in the wave vector. These findings are compared with the corresponding prediction for a purely exchange-coupled magnet.