# External magnetic field

### This page gives hints on how to take into account an external magnetic field with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (EB)

Mentioned in help_features#2.5.

### Table of content:

- 1. Introduction.
- 2. Related input variables.
- 3. Selected input files.
- 4. References.

### 1. Introduction.

An applied external magnetic field has been implemented in ABINIT by considering the Zeeman spin response only (i.e., neglecting the orbital contribution).

Following the procedure of Bousquet et al.,[Bousquet2011] the applied B field is introduced by adding the "Zeeman term" term in the non-collinear Kohn-Sham potential:

This contribution is trivial to implement, and also dominant in amplitude, but has historically been neglected with respect to the orbital responses, which are rich in more complex physics.

Unlike an applied electric field, such a Zeeman term in the potential is compatible with periodic boundary conditions. It is also compatible with collinear calculations by reducing its application on ``up'' and ``down'' spin channels with B=Bez.

In ABINIT, the finite Zeeman field is controlled by the keyword zeemanfield which allows to control the amplitude of the applied B-field (in Tesla) along the three cartesian directions.

Such an applied Zeeman field allows one to calculate the spin contribution of the magnetic and magnetoelectric susceptibilities, and to observe phase transitions under finite magnetic field, if present.
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### 2. Related input variables.

Basic input variables:

... zeemanfield [ZEEMAN FIELD]

Input variables for experts:

... bfield [finite B FIELD calculation]
... nucdipmom [NUClear DIPole MOMents]
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### 3. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v6/Input: t17.in

tests/v7/Input: t32.in
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### 4. References.

[Bousquet2011] E. Bousquet, N. A. Spaldin and K. T. Delaney, "Unexpectedly Large Electronic Contribution to Linear Magnetoelectricity", Phys. Rev. Lett. 106, 107202 (2011).
DOI: 10.1103/PhysRevLett.106.107202.

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