Competing antiferromagnetic and spin-glass phases in a hollandite structure

Abstract

We introduce a simple lattice model with Ising spins to explain recent experimental results on spin freezing in a hollandite-type structure. We argue that geometrical frustration of the lattice in combination with nearest-neighbour antiferromagnetic (AFM) interactions is responsible for the appearance of a spin-glass phase in presence of disorder. We investigate this system numerically using parallel tempering. The model reproduces the magnetic behaviour of oxides with hollandite structure, such as α − MnO2 and presents a rich phenomenology: in absence of disorder three types of ground states are possible, depending on the relative strength of the interactions, namely AFM ordered and two different disordered, macroscopically degenerate families of ground states. Remarkably, for sets of AFM couplings having an AFM ground state in the clean system, there exists a critical value of the disorder for which the ground state is replaced by a spin-glass phase while maintaining all couplings AFM. To the best of our knowledge this is the only existing model that presents this kind of transition with short-range AFM interactions. We argue that this model could be useful to understand the relation between AFM coupling, disorder and the appearance of a spin-glass phase.

Incommensurate helical spin ground states on the hollandite lattice

“…Such phase diagram is similar to that of the Ising spins. 27 Our results are summarized in Fig.4 which shows the case J 1 > 0. For large values of the ratios J 2 /J 1 and J 3 /J 1 we find the same AFM ground states as in the Ising case 27 .…”

“…27 Our results are summarized in Fig.4 which shows the case J 1 > 0. For large values of the ratios J 2 /J 1 and J 3 /J 1 we find the same AFM ground states as in the Ising case 27 . For smaller values of the ratios we find coplanar helical phases, that are, in general, incommensurate with the lattice.…”

“…We therefore consider a model similar to the one of Ref. 27 where three couplings strengths -J 1 , J 2 , J 3 -were used for the spin-spin interactions, one for each of the three types of nearest neighbors. Assignment of J 1 , J 2 and J 3 is shown in Fig.2.…”

“…27 cannot reproduce realistic low temperature magnetic configurations of manganites, like non-collinear AFM or helical magnetic ground states, that have been suggested in some compounds. 24,25 In this paper we extend the previous work 27 and study the classical Heisenberg model on the Hollandite lattice in order to investigate the ground state magnetic phase diagram as a function of the model parameters. By exploring all possible magnetic interactions between the spins we probe different uniform compositions of the Hollandite structure and therefore give an explanation to some of the magnetic ground states that have been experimentally suggested.…”

“…[12][13][14][15] One example of such lattice with geometrical frustration is the Hollandite lattice, 16,17 which is the crystal structure of some transition metal oxides as in the case of α-MnO 2 . 16,18,19 This manganese oxide has recently attracted considerable attention from both experimental and theoretical condensed matter research communities [20][21][22][23][24][25][26][27][28][29] because of its large number of applications as a catalyst for oxygen reduction reaction 30 , microbial fuel cells 31 , electrode materials for Li-ion batteries 32 , lithium-air batteries 29,[33][34][35][36] and in supercapacitors 37 , etc.. Hollandite-type compounds display pores with a diameter of ∼4.6 Å, (see Fig.1(a)). These large channels can accommodate cations such as K + , Na + , and Ba 2+ , leading to non-stoichiometric compounds such as K 1.5 19 The presence of these impurities makes it hard to determine their composition, in particular the water content.…”