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Magnetized liquid $^{3} He$ $^{3} He$ at finite temperature: A variational calculation approach

Gholam Hossein Bordbar

Department of Physics, School of Sciences, Shiraz University, Shiraz 71454, Iran

E-mail Address: ghbordbar@shirazu.ac.ir

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and

Mohammad Taghi Mohammadi Sabet

Department of Physics, School of Sciences, Shiraz University, Shiraz 71454, Iran

Corresponding author.

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https://doi.org/10.1142/S0217979216501290Cited by:4 (Source: Crossref)

Abstract

Using the spin-dependent (SD) and spin-independent (SI) correlation functions, we have investigated the properties of liquid $^{3} He$ $^{3} He$ in the presence of magnetic field at finite temperature. Our calculations have been done using the variational method based on cluster expansion of the energy functional. Our results show that the low field magnetic susceptibility obeys Curie law at high temperatures. This behavior is in a good agreement with the experimental data as well as the molecular field theory results in which the spin dependency has been introduced in correlation function. Reduced susceptibility as a function of temperature as well as reduced temperature has been also investigated, and again we have seen that the spin-dependent correlation function leads to a good agreement with the experimental data. The Landau parameter, $F_{0}^{a}$ $F_{0}^{a}$ , has been calculated, and for this parameter, a value about $- 0.75$ $- 0.75$ has been found in the case of spin–spin correlation. In the case of spin-independent correlation function, this value is about $- 0.7$ $- 0.7$ . Therefore, inclusion of spin dependency in the correlation function leads to a more compatible value of $F_{0}^{a}$ $F_{0}^{a}$ with experimental data. The magnetization and susceptibility of liquid $^{3} He$ $^{3} He$ have also been investigated as a function of magnetic field. Our results show a downward curvature in magnetization of system with spin-dependent correlation for all densities and relevant temperatures. A metamagnetic behavior has been observed as a maximum in susceptibility versus magnetic field, when the spin–spin correlation has been considered. This maximum occurs at $45 T \leq B \leq 100 T$ $45 T \leq B \leq 100 T$ for all densities and temperatures. This behavior has not been observed in the case of spin-independent correlation function.

Keywords:

PACS: 67.30.−n, 67.30.ep

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Vol. 30, No. 22

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Received 11 October 2015

Accepted 21 March 2016

Published: 5 August 2016

Keywords

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Magnetized liquid $^{3} He$ $^{3} He$ at finite temperature: A variational calculation approach

Abstract

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System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

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Abstract

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