https://doi.org/10.1140/epjb/s10051-022-00330-z
Regular Article - Solid State and Materials
Dissipation and friction of a quantum spin system
1
School of Physics and Microelectronics, Zhengzhou University, 450001, Zhengzhou, China
2
International Laboratory for Quantum Functional Materials of Henan, School of Physics and Microelectronics, Zhengzhou University, 450001, Zhengzhou, China
3
Key Laboratory for Special Functional Materials of Ministry of Education, School of Materials and Engineering, Henan University, 475001, Kaifeng, China
Received:
28
June
2021
Accepted:
8
April
2022
Published online:
26
April
2022
We investigated the dissipation dynamics of a magnetic tip scanning the surface of a 3D ferromagnetic substrate at a velocity 
via a functional integral approach based on the Holstein–Primakoff boson representation of spin operators. The magnetic surface was parameterized by the XXZ model. And the degrees of freedom in the tip were taken as a single spin operator (M). The magnetic surface was coupled to the tip via a local exchange potential 
. Moreover, the tip induced a surface potential 
acting on the magnetic surface spin operators. After tracing over total internal degrees of freedom, we obtained the in–out quantum action. We calculated the imaginary part of the in–out quantum action and the frictional force as functions of speed 
. We found that the imaginary part of the in–out quantum action is suppressed as 
. The imaginary part of the in–out quantum action is proportional to the probability of ground state decay. Therefore, it implies dissipation of the system. The frictional force linearly depends on the velocity as 
. While 
the dependence of the frictional force on v becomes nonlinear.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022
