Thermodynamics of antiferromagnetic solids in magnetic fields

doi:10.1016/j.aop.2020.168168

Annals of Physics

Volume 418, July 2020, 168168

https://doi.org/10.1016/j.aop.2020.168168 Get rights and content

Highlights

•
Systematic thermodynamic analysis of antiferromagnetic solids in mutually perpendicular magnetic and staggered fields.
•
Analysis of the impact of the spin–wave interaction in thermodynamic quantities of antiferromagnetic solids.
•
Two-point function and partition function of antiferromagnetic solids.

Abstract

We analyze the thermodynamic properties of antiferromagnetic solids subjected to a combination of mutually orthogonal uniform magnetic and staggered fields. Low-temperature series for the pressure, order parameter and magnetization up to two-loop order in the effective expansion are established. We evaluate the self-energy and the dispersion relation of the dressed magnons in order to discuss the impact of spin–wave interactions on thermodynamic observables.

Section snippets

Motivation

The literature on the thermodynamic properties of antiferromagnets in three spatial dimensions is considerable. Low-temperature representations for the free energy density, staggered magnetization, and other observables describing quantum Heisenberg antiferromagnets have been derived, e.g., in Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Various authors have furthermore discussed how an external magnetic field influences the low-temperature physics of antiferromagnets (see Refs. [11]

Free energy density: Two-loop representation

The paradigmatic microscopic description of antiferromagnets is based on the Heisenberg model, whose Hamiltonian in the simplest situation, where only the nearest neighbor spin interactions are taken into account, takes the form $H = - J \sum_{n . n .} {\vec{S}}_{m} \cdot {\vec{S}}_{n} - \sum_{n} {\vec{S}}_{n} \cdot \vec{H} - \sum_{n} {(- 1)}^{n} {\vec{S}}_{n} \cdot {\vec{H}}_{s}, J = c o n s t .,$ where the summation in the first term extends over nearest neighbor spin pairs on a bipartite three-dimensional lattice. The exchange constant $J < 0$ defines the fundamental energy scale of the system. The first term is

Dressed magnons and interaction free energy density

Naively, one might expect that the first line of our result (2.8) for the free energy density, that is its one-loop part, corresponds to a gas of free magnons, while all the rest captures magnon–magnon interactions. That would, however, be premature: the magnons get dressed by self-energy corrections even at $T = 0$ . Part of the thermal two-loop free energy density can then be accounted for as the free energy density of such dressed, yet noninteracting, magnons. Whatever is left can be considered

Low-temperature series

The effective field theory expansion of the free energy density, Eq. (2.8), is valid at low temperatures and in weak external fields. More precisely, the quantities $T, H, H_{s}$ have to be small compared to a characteristic scale inherent in the underlying microscopic system. In the present case of the Heisenberg antiferromagnet, the thermal scale is given by the Néel temperature $T_{N}$ . The actual definition of low temperature and weak field is somewhat arbitrary. To be concrete, here we choose $T, H, M_{I I} (\propto$

Conclusions

Antiferromagnets subjected to magnetic and staggered fields can be addressed straightforwardly with the systematic effective Lagrangian method. Starting from the two-loop representation of the partition function, we have discussed the low-temperature behavior of $d = 3 + 1$ antiferromagnets in a configuration of mutually orthogonal external magnetic and staggered fields.

To have a clear picture of what “interaction” means in the free energy density – and any other thermodynamic quantity derived from

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Tomas Brauner acknowledges financial support from the ToppForsk-UiS program of the University of Stavanger and the University Fund, Grant No. PR-10614.

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Cited by (5)

Antiferromagnetic dispersion relations and nature of magnon pressure
2021, Physica B: Condensed Matter
Citation Excerpt :
It is the goal of the present investigation to help to close this gap. Our approach is based on magnon effective field theory that has been established in earlier work – see Refs. [38–44] – and has specifically been applied to two- and three-dimensional antiferromagnets in Refs. [45–58]. Here we first calculate the two-point functions for antiferromagnetic magnons residing in antiferromagnets exposed to mutually aligned magnetic and staggered fields.
We derive higher-order corrections in the magnon dispersion relations for two- and three-dimensional antiferromagnets exposed to magnetic and staggered fields that are mutually aligned. “Dressing” the magnons is the prerequisite to separate the low-temperature representation of the pressure into a piece due to noninteracting magnons and a piece that corresponds to the magnon–magnon interaction. Both in two and three spatial dimensions, the interaction in the pressure turns out to be attractive. While concrete figures refer to the spin- $\frac{1}{2}$ square-lattice and the spin- $\frac{1}{2}$ simple cubic lattice antiferromagnet, our results are valid for arbitrary bipartite geometry.
Spin order and entropy in antiferromagnetic ﬁlms subjected to magnetic ﬁelds
2021, Journal of Statistical Mechanics: Theory and Experiment
Order parameter and magnetization of aniferromagnets in mutually parallel staggered and magnetic fields
2020, Advances in Materials Science Research. Volume 44
Antiferromagnetic dispersion relations and nature of magnon pressure
2020, arXiv
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View full text

Thermodynamics of antiferromagnetic solids in magnetic fields

Highlights

Abstract

Section snippets

Motivation

Free energy density: Two-loop representation

Dressed magnons and interaction free energy density

Low-temperature series

Conclusions

Declaration of Competing Interest

Acknowledgments

Phys. Lett. A

Phys. Lett. A

J. Magn. Magn. Mater.

Ann. Phys., NY

Nuclear Phys. B

Nuclear Phys. B

Ann. Phys.

Nuclear Phys. B

Ann. Phys.

Phys. B

Phys. Rev.

J. Appl. Phys. (Suppl.)

J. Appl. Phys.

J. Appl. Phys.

Phys. Rev.

Phys. Rev.

J. Phys. C

Phys. Rev. B

Europhys. Lett.

Sov. Phys.—JETP

Sov. Phys. Usp.

Phys. Rev.