An official website of the United States government
Experimental and theoretical studies of magnetic anisotropy and relaxation behavior of six-coordinate tris(pivalato)-Co( ii ) and -Ni( ii ) complexes (NBu 4 )[M(piv) 3 ] (piv = pivalate, M = Co, 1 ; M = Ni, 2 ), with a coordination configuration at the intermediate between an octahedron and a trigonal prism, are reported. Direct current magnetic data and high-frequency and -field EPR spectra (HFEPR) of 1 have been modeled by a general Hamiltonian considering the first-order orbital angular momentum, while the spin Hamiltonian was used to interpret the data of 2 . Both 1 and 2 show easy-axis magnetic anisotropies, which are further supported by ab initio calculations. Alternating current (ac) magnetic susceptibilities reveal slow magnetic relaxation at an applied dc field of 0.1 T in 1 , which is characteristic of a field-induced single-ion magnet (SIM), but 2 does not exhibit single-ion magnetic properties at 1.8 K. Detailed analyses of relaxation times show a dominant contribution of a Raman process for spin relaxation in 1 .
more »
« less
An observable effect of spin inertia in slow magneto-dynamics: Increase of the switching error rates in nanoscale ferromagnets
The Landau-Lifshitz-Gilbert (LLG) equation, used to model magneto-dynamics in ferromagnets, tacitly assumes that the angular momentum associated with spin precession can relax instantaneously when the real or effective magnetic field causing the precession is turned off. This neglect of “spin inertia” is unphysical and would violate energy conservation. Recently, the LLG equation was modified to account for inertia effects. The consensus, however, seems to be that such effects would be unimportant in slow magneto-dynamics that take place over time scales much longer that the relaxation time of the angular momentum, which is typically few fs to perhaps ~100 ps in ferromagnets. Here, we show that there is at least one very serious and observable effect of spin inertia even in slow magneto-dynamics. It involves the switching error probability associated with flipping the magnetization of a nanoscale ferromagnet with an external agent, such as a magnetic field. The switching may take ~ns to complete when the field strength is close to the threshold value for switching, which is much longer than the angular momentum relaxation time, and yet the effect of spin inertia is felt in the switching error probability. This is because the ultimate fate of a switching trajectory, i.e. whether it results in success or failure, is influenced by what happens in the first few ps of the switching action when nutational dynamics due to spin inertia holds sway. Spin inertia increases the error probability, which makes the switching more error-prone. This has vital technological significance because it relates to the reliability of magnetic logic and memory.
more »
« less
- Award ID(s):
- 2001255
- PAR ID:
- 10251179
- Date Published:
- Journal Name:
- Journal of Physics: Condensed Matter
- ISSN:
- 0953-8984
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract A ferromagnetic gyroscope (FG) is a ferromagnet whose angular momentum is dominated by electron spin polarization and that will process under the action of an external torque, such as that due to a magnetic field. Here we model and analyze FG dynamics and sensitivity, focusing on practical schemes for experimental realization. In the case of a freely floating FG, we model the transition from dynamics dominated by libration in relatively high externally applied magnetic fields, to those dominated by precession at relatively low applied fields. Measurement of the libration frequency enablesin situdetermination of the magnetic field and a technique to reduce the field below the threshold for which precession dominates the FG dynamics. We note that evidence of gyroscopic behavior is present even at magnetic fields much larger than the threshold field below which precession dominates. We also model the dynamics of an FG levitated above a type-I superconductor via the Meissner effect, and find that for FGs with dimensions larger than about 100 nm the observed precession frequency is reduced compared to that of a freely floating FG. This is due to an effect akin to negative feedback that arises from the distortion of the field from the FG by the superconductor. Finally we assess the sensitivity of an FG levitated above a type-I superconductor to exotic spin-dependent interactions under practical experimental conditions, demonstrating the potential of FGs for tests of fundamental physics.more » « less
-
In this work, we theoretically study the switching and oscillation dynamics in strained non-collinear antiferromagnet (AFM) Mn3X (X = Sn, Ge, etc.). Using the perturbation theory, we identify three separable dynamic modes—one uniform and two optical modes, for which we analytically derive the oscillation frequencies and effective damping. We also establish a compact, vector equation for describing the dynamics of the uniform mode, which is in analogy to the conventional Landau–Lifshitz–Gilbert (LLG) equation for ferromagnet but captures the unique features of the cluster octuple moment. Extending our model to include spatial inhomogeneity, we are able to describe the excitations of dissipative spin wave and spin superfluidity state in the non-collinear AFM. Furthermore, we carry out numerical simulations based on coupled LLG equations to verify the analytical results, where good agreements are reached. Our treatment with the perturbative approach provides a systematic tool for studying the dynamics of non-collinear AFM and is generalizable to other magnetic systems in which the Hamiltonian can be expressed in a hierarchy of energy scales.more » « less
-
Abstract In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a2S state, with zero orbital andspin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”more » « less
-
ABSTRACT Type-C quasi-periodic oscillations (QPOs) are the low-frequency QPOs most commonly observed during the hard spectral state of X-ray binary systems. The leading model for these QPOs is the Lense-Thirring precession of a hot geometrically thick accretion flow that is misaligned with respect to the black hole spin axis. However, none of the work done to date has accounted for the effects of a surrounding geometrically thin disc on this precession, as would be the case in the truncated disc picture of the hard state. To address this, we perform a set of general relativistic magnetohydrodynamics simulations of truncated discs misaligned with the spin axes of their central black holes. Our results confirm that the inner-hot flow still undergoes precession, though at a rate that is only 5 per cent of what is predicted for an isolated precessing torus. We find that the exchange of angular momentum between the outer thin and the inner thick disc causes this slow-down in the precession rate and discuss its relevance to type-C QPOs.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-648X/ac0cb4
