Seminars

Consistent partial bosonization and spin dynamics of itinerant electrons
 

In some cases, when an accurate description of collective charge and spin excitations in solids is challenging, a realistic ab initio electronic problem can be replaced by a simplified bosonic model. This approach is widely used, for example, for description ofspin degrees of freedom via Heisenberg-like models, and of a charge ordering in alloys with the use of Ising model. The most straightforward way of deriving such models is to estimate all possible exchange interactions between spin and/or charge densities,and to write an effective classical Hamiltonian in terms of these interactions. A more physical approach consists in finding a possibility of mapping the introduced electronic model onto an effective bosonic problem, which is a highly nontrivial task.The most common way to perform this mapping is based on Schrieffer-Wolff transformation [Phys. Lett. A 64, 163 (1977); J. Phys. C: Solid State Phys. 10, L271 (1977); Phys. Rev. B 37, 9753 (1988)], which, strictly speaking,is justified only in the limiting case of a very large interaction between electrons. Moreover, spin degrees of freedom in the transformed problem (even when transformation is possible) are described in terms of composite fermionic variables and not in termsof physical bosonic fields. The latter requires to introduce constraints in order to conserve the length of the total spin, which is an artificial procedure. 

It should be emphasised that deriving an effective spin Hamiltonian following the mentioned routes does not answer one of the fundamental questions, namely how to introduce the correct equation of motion for spin degrees of freedom. Indeed, classical spin Hamiltoniansallow one to describe only a uniform precession of the local magnetic moment, because Gilbert damping can be taken into account only within a more complex model of classical spins coupled to electrons [New J. Phys. 17, 113058 (2015); Phys.Rev. Lett. 117, 127201 (2016)]. Secondly, Higgs fluctuations of the modulus of the local magnetic moment also cannot be addressed in the framework of the classical spin problems. Last but not least, one has to mention that all the above discussedapproaches rely on the assumption that the average local magnetization is nonzero. This fact does not allow one to use these state-of-the-art methods in the most challenging case, namely in the paramagnetic regime, which is characterised by a zero averagemagnetization.

In this talk, I will address these long-standing problems and provide a consistent description of spin dynamics of electronic systems. First, I will derive an effective quantum bosonic action written in terms of physical charge and spin variables startingfrom the initial interacting electronic problem. I will show that this derivation can be performed without assuming that the average magnetization is nonzero and without imposing any constraints such as artificial magnetic fields. I will show that the correspondingequation of motion for this action correctly describes the rotational dynamics of the local magnetic moment via the topological Berry phase, and also accounts for the Higgs fluctuations of the modulus of the magnetic moment. Finally, I will introduce a physicalcriterion for the formation of the local magnetic moment in the system and show that our approach is applicable even in the paramagnetic regime. 

Related works:
E. A. Stepanov et al.: Phys. Rev. Lett. 121, 037204 (2018); Phys. Rev. B 99, 115124 (2019); Phys. Rev. B 100, 205115 (2019); arXiv:2106.12462 (2021)