First-principles study of magnetism in spinel MnO2

Abstract:

First-principles electronic structure methods have been used to calculate the ground state, transition temperature, and thermodynamic properties of magnetic excitations in spinel MnO2 . The magnetic interactions are mapped onto a Heisenberg model whose exchange interactions are fitted to results of first-principles calculations of different spin configurations. The thermodynamics are calculated using Monte Carlo methods. The Heisenberg model gives an extremely accurate representation of the true first-principles magnetic energies. We find a critical temperature and Weiss constant significantly larger than experimental results and believe the error to come from the local spin density approximation. We predict a new magnetic ground state different from that proposed previously, but consistent with experimental data.

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I. INTRODUCTION 

Spinel MnO2 ~often referred to as l-MnO2) has very interesting and complex magnetic behavior. The nearestneighbor interaction between Mn41 ions has both ferromagnetic and antiferromagnetic contributions, which depend differently on the Mn41-Mn41 distances.1–3 Pure MnO2 has been shown experimentally to be at least weakly antiferromagnetic.1,3,4 However, other Mn41 oxides, such as Li4Mn5O12 , have been found to be ferromagnetic due to slightly different distances between the Mn41-Mn41 neighbors.3 In this work we focus on the magnetic ordering in the pure MnO2 .

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II. THEORETICAL BACKGROUND 

A. Heisenberg model 

The most common approach to studying magnetism in solids with first-principles methods is to use density functional theory in the local spin density approximation ~LSDA!. Unfortunately, most calculations are limited to only collinear spins, which by itself is clearly inadequate for studying the spin thermodynamics, where many noncollinear spin configurations are relevant. There are well-developed techniques for the study of noncollinear magnetism with first-principles methods ~for a fairly recent review see Ref. 6!; however, directly calculating all the spin configurations needed for thermodynamic simulation ~using, for example, Monte Carlo methods! would be extremely computationally intensive. Recently, techniques for first-principles spin dynamics have been developed,7–10 but they have not yet obtained widespread usage in standard electronic structure codes and their effectiveness is still under investigation. A straightforward and more established approach to studying magnetic thermodynamics is to parametrize the firstprinciples magnetic energies with a Heisenberg model Hamiltonian simple enough to allow very rapid calculation of the energies of different spin configurations.11–16 We have therefore chosen to represent the magnetic energies using a classical Heisenberg model17

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B. Fitting the exchange-coupling parameters 

There is a very extensive literature on different methods used to obtain the values of the exchange-coupling interactions ~see Ref. 6 and references therein!. In the present work we perform a least-squares fit of the unknown exchange interactions to a set of first-principles energies calculated for different collinear spin arrangements. This fitting approach has been used previously with good success to study a number of different systems.

There are a number of weaknesses of this approach that should be mentioned. First, the Heisenberg model is only appropriate for localized electrons, and great care must be taken when applying it to itinerant magnets. However, MnO2 is expected to have very well localized moments on the Mn atoms so the Heisenberg model is appropriate for this system.

Another problem is that the Heisenberg model is most accurate as a quantum-mechanical Hamiltonian, where the Si are quantum-mechanical spin operators. However, there are difficulties using the fitting outlined above in the quantummechanical case because there is a complex correspondence between the Heisenberg Hamiltonian eigenstates and the first-principles collinear spin energies.19 In addition, an accurate thermodynamic calculation with a three-dimensional quantum Heisenberg Hamiltonian is a very formidable problem. Therefore, although it is an uncontrolled approximation, we are forced to model the system with a classical Heisenberg model. It should be noted that in the limit of large spin values the quantum-mechanical Heisenberg model will behave classically. It is of some consolation that in MnO2 the Mn have a fairly large magnetic moment and that we are therefore closer to the domain of applicability of the classical Heisenberg model than we would be for a simple spin- 1 2 system.

Finally, a further approximation is made by fixing the spin magnitude on every Mn. This approximation could be lifted by expanding our Heisenberg model to allow for differentsize spin vectors, but for MnO2 the moments are unlikely to change dramatically between different Mn atoms and the errors associated with fixing the moments are not likely to be significant. As will be seen in Sec. III, the model and fitting used here yield a nearly perfect representation of the firstprinciples magnetic energies.