Broadband Spectroscopy of Thermodynamic Magnetization Fluctuations through a Ferromagnetic Spin-Reorientation Transition

Abstract

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or “magnetization noise”, in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar+ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, S(ν), exhibits a remarkably robust ν−3/2 power law over frequencies ν from 1 kHz to 1 MHz. As the SRT region is traversed, however, S(ν) spectra develop a steadily-increasing critical frequency, ν0, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.

Higher-order moments, cumulants, and spectra of continuous quantum noise measurements

“…Figure 7 shows for comparison the corresponding power spectra S q (ω). The imaginary part of S (3) z is zero for all angles which is consistent with time-reversal symmetry of z(t) for a system in thermal equilibrium 46 . Interestingly, also the real part of S (3) z is zero for ϕ = 0 while S (4) z exhibits strong correlations for all angles.…”

Field-Induced Magnetic Monopole Plasma in Artificial Spin Ice

“…The ASI samples were mounted face-up in the x − y plane, on a positioning stage that could be temperaturecontrolled from -10 • C to +30 • C. The horizontal and vertical islands were oriented along x and ŷ, respectively. The magneto-optical noise spectrometer is adapted from an instrument previously developed to measure out-ofplane magnetization fluctuations [32]. A weak probe laser (<1 mW), incident in the x − z plane, was linearly polarized and focused to a small ( 4 µm diameter) spot on the ASI at 45 • incidence; ∼300 islands were therefore probed.…”

Phase Diagram of the Dynamics of a Precessing Qubit under Quantum Measurement

“…For weak quantum measurement, it is particularly useful for monitoring quantum evolution [15][16][17][18][19] and maneuvering quantum state [20][21][22]. More recently, great efforts have been devoted to the development of different experimental techniques to detect the single qubit dynamics [23][24][25][26][27][28][29], and to characterize the decoherence induced by environments [30][31][32].…”