Origin of magnetic frustration in Bi3Mn4O12(NO3)

Abstract

Bi3Mn4O12(NO3) (BMNO) is a honeycomb bilayers anti-ferromagnet, not showing any ordering down to very low temperatures despite having a relatively large Curie-Weiss temperature. Using ab initio density functional theory, we extract an effective spin Hamiltonian for this compound. The proposed spin Hamiltonian consists of anti-ferrimagnetic Heisenberg terms with coupling constants ranging up to third intra-layer and fourth inter-layer neighbors. Performing Monte Carlo simulation, we obtain the temperature dependence of magnetic susceptibility and so the Curie-Weiss temperature and find the coupling constants which best matches with the experimental value. We discover that depending on the strength of the interlayer exchange couplings, two collinear spin configurations compete with each other in this system. Both states have in plane Néel character, however, at small interlayer coupling spin directions in the two layers are antiparallel (N1 state) and discontinuously transform to parallel (N2 state) by enlarging the interlayer couplings at a first order transition point. Classical Monte Carlo simulation and density matrix renormalization group calculations confirm that exchange couplings obtained for BMNO are in such a way that put this material at the phase boundary of a first order phase transition, where the trading between these two collinear spin states prevents it from setting in a magnetically ordered state. Bi 3 Mn 4 O 12 (NO 3 ) (BMNO) is an experimental realization of frustrated honeycomb magnetic materials, synthesized by Smirnova et al. [1]. In this compound, the magnetic lattice can be effectively described by a weakly coupled honeycomb bilayers of Mn +4 ions (Fig. 1). The temperature dependence of magnetic susceptibility of BMNO does not indicate any ordering down to T = 0.4K, in spite of the Curie-Weiss temperature θ CW ≈ −257K [1, 2]. The absence of long-range ordering in BMNO is also confirmed by specific heat measurements [1, 2], neutron scattering [3] and high-field electron spin relaxation (ESR) experiments [4]. So far, the theoretical attempts to explain the magnetic properties of BMNO have been focusing on the frustration effect of second intra-layer coupling J 2 or the tendency toward dimerization by considering a large anti-ferromagnetic inter-layer nearest neighbor coupling J 1c [5][6][7][8][9][10][11][12]. In an attempt to calculate the exchange interactions by ab initio method, it is found that the dominant exchange interactions are nearest in-plane coupling (J 1 ) and also an effective inter-plane coupling (J c ) which exceeds J 1 [5]. However, in that work the experimental positions of the atoms in the structure are taken without geometry optimization and only 5 magnetic configurations are considered for the calculation of exchange interactions.In this paper, we obtain a Heisenberg spin Hamiltonian for BMNO, using an ab initio LDA+U calculation. In our calculations, we consider a detailed analysis of nonidentical Mn atoms which were assumed to be identical in the previous calculation [...

Frustrated magnetic interactions in an S=3/2 bilayer honeycomb lattice compound Bi3Mn4O12<

“…Instead, the frustrating intrabilayer interactions J 1c and J 2c probably give rise to the disordered ground state, as reported in Ref. [30].…”

“…Recently, Alaei et al reported a mechanism of the frustrating interactions in BMNO obtained using the ab initio density functional theory (DFT) calculations [30]. They calculated three intraplane interactions, J 1 , J 2 , and J 3 [ Fig.…”

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field

“…Concerning experimental realizations of the frustrated honeycomb-lattice bilayer spin system, the magnetic compound Bi 3 Mn 4 O 12 (NO 3 ) is a candidate, although, the exchange parameters of the spin Hamiltonian for Bi 3 Mn 4 O 12 (NO 3 ) are still under debate [7,8], and it might happen the J 2 does not have sufficient strength. The search for other honeycomb materials, where our findings would be observable, is desirable and is encouraged.…”

“…On one hand, the interest in this model stems from experiments on Bi 3 Mn 4 O 12 (NO 3 ), in which the ions Mn 4+ form a frustrated spin- 3 2 bilayer honeycomb lattice [4][5][6][7][8]. On the other hand, there are a few theoretical papers considering the ground-state and low-temperature properties of a Heisenberg antiferromagnet on a frustrated bilayer honeycomb lattice [9][10][11], in which classical spin [9] or quantum spin-1 2 [10,11] models in nonzero [9,11] or zero [10] magnetic field were discussed using various complementary approaches.…”

Optimizing configurations for determining the magnetic model based on ab initio calculations

“…where the configurations are labeled according to those presented in ref. 39 and sites are labeled as in Fig. 5.…”