Electron Spin Resonance on the Border Between Para- and Ferromagnetism: Quantum versus Classical
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Applied Magnetic Resonance
REVIEW
Electron Spin Resonance on the Border Between Para‑ and Ferromagnetism: Quantum versus Classical V. A. Atsarkin1 · N. Noginova2 Received: 28 April 2020 / Revised: 9 June 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The transition from para- to ferromagnetic behavior in magnetic systems can be considered to be a part of a general problem of the transition from quantum (oneparticle) to classical (multiple-particle) behavior. Here we present a brief review of recent studies in electron magnetic resonance (EMR) and spin relaxation in situations which are at the borderline between paramagnetic and ferromagnetic cases. Most attention is paid to EMR in magnetic nanoparticles. It is shown that the giant spin model based on the quantum spin Hamiltonian can be successively applied for interpretation of the specific features observed in the experiment, such as a narrow spectral component and “forbidden” half-field resonances. Another example is the transformation of the level anticrossing typical for anisotropic EPR spectra of paramagnetic ions into the magnetic pseudoresonance (which manifests itself as a giant peak of radio-frequency absorption) observed in ferromagnets with axial anisotropy. Finally, an emergence and an intensification of the Bloch relaxation gradually replacing the Landau–Lifshit–Gilbert mechanism near the Curie point is clearly demonstrated in colossal magnetoresistance materials.
1 Introduction A transition from paramagnetic to ferromagnetic behavior can be considered from general point of view as a transition from single-particle dynamics to many-particle thermodynamics, or, in the other words, from low-spin quantum mechanics to highspin classical master equations. This transition is illustrated in Fig. 1. Let us start from a single paramagnetic ion with effective spin S (for instance, S = 3/2) embedded in a diamagnetic solid matrix. This simple object is described by the spin-Hamiltonian quantum
* V. A. Atsarkin [email protected] 1
Kotel’nikov Institute of Radio Engineering and Electronics of RAS, 125009 Moscow, Russia
2
Norfolk State University, Norfolk, VA, USA
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V. A. Atsarkin, N. Noginova
Single spin (example: 3+ Cr , S=3/2)
Exchange cluster; 2-3 coupled spins
S
m
E
Molecular magnets; 5-20 coupled spins (example: Fe8)
1
±3/2
2
. . . . .
SpinHamiltonian H = γ(B·S)+DSz2 EPR fine structure; Curie (Brillouin) Law
1
Borderland
10
....... B
Bulk ferromagnet; 22 10 coupled spins
S 0
0 ±1/2
Magnec nanoparcles; 2 4 10 -10 coupled spins
B Complicated EPR spectrum; Brillouin Law at ground mulplet
B Complicated spectrum of lower mulplets
Landau-Lifshits Equaon; M=const; FMR: single Lorentzian
Tunneling
Fig. 1 The diagram illustrating the transition from para- to ferromagnetism upon increasing the number of interacting spins
formalism leading to the well-known energy level diagram in an external magnetic field B [1, 2]. The corresponding EPR spectrum has a simple fine structur
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