Formation of Magnetic Microphases inCa3Co2O6

Abstract

We study a frustrated quantum Ising model relevant for Ca 3 Co 2 O 6 that consists of a triangular lattice of weakly-coupled ferromagnetic (FM) chains. According to our quantum Monte Carlo (QMC) simulations, the chains become FM and form a three-sublattice "up-up-down" structure for T ≤ T CI . In contrast, long-period spin-density-wave (SDW) microphases are stabilized along the chains for T CI < T < T c . Our mean field solutions reveal a quasi-continuous temperature dependence of the SDW wavelength, implying the existence of metastable states that explain the very slow dynamics observed in Ca 3 Co 2 O 6 . We also discuss implications of microphases for the related multiferroic compounds Ca 3 CoMnO 6 and Lu 2 MnCoO 6 . [3][4][5], the spin-driven "nematic" transition in pnictides [6][7][8][9], and dimensional reduction in BaCuSi 2 O 6 [10,11]. Ca 3 Co 2 O 6 is another example comprising a triangular lattice of FM Ising chains coupled by weak antiferromagnetic (AFM) exchanges. This compound exhibits field-induced magnetization steps whose heights depend on the field sweep history and rate [12][13][14][15][16]. We will show that this out-of-equilibrium behavior has its roots in exotic equilibrium properties that can be extended to the related multiferroic compound Ca 3 Co 2−x Mn x O 6 [17][18][19][20][21][22].The Co 3+ ions (Co II) on the trigonal prism sites of Ca 3 Co 2 O 6 contain 3d 6 localized electrons that generate an S = 2 spin with large Ising-like anisotropy [23][24][25][26]. These ions form a triangular lattice of FM Ising chains along the caxis (Fig. 1) and the structure comprises three sublattices of layers stacked along the c-axis in an ABCABC . . . configuration. Although the AFM inter-chain couplings J 2 and J 3 [27] [ Fig. 1(a)] are an order of magnitude smaller than the intrachain FM exchange, |J 1 | = 2 × 10 K [23, 27], we will show that they strongly affect the intra-chain spin correlations over a window of temperatures below T c .The initial interest in Ca 3 Co 2 O 6 was triggered by the observation of out-of-equilibrium magnetization steps measured below ∼ 8 K and ∼ 3.6 T that appear at regular field intervals. Previous works invoked a "rigid-chain model": every chain is replaced by a single Ising spin by assuming [28][29][30][31][32]. Each spin of the resulting triangular lattice Ising model (TLIM), represents the magnetization of the whole chain and it is flipped if gµ B H overcomes its molecular field. Within this simplified framework, the regular field intervals result from the equally-spaced discrete molecular field spectrum [28]. However, this 2D scenario was challenged by the recent discovery of long-wavelength intra-chain spindensity-wave (SDW) ordering below T c 25 K [16,33,34]. Motivated by this discovery, Chapon initiated the study of a more realistic 3D lattice model by using a random-phase approximation (RPA) which is only valid close to T = T c [35].By combining QMC simulations and mean field (MF) solu-

Magnetization dynamics and frustration in the multiferroic double perovskiteLu2MnCoO6

“…This model has also been proposed to describe the magnetic behavior of Ca 3 CoMnO 6 [11,[15][16][17][18]. ANNNI models postulate Ising spin chains where nearest and next-nearest neighbor interactions within chains compete while interchain interactions are ferromagnetic.…”

“…ANNNI models postulate Ising spin chains where nearest and next-nearest neighbor interactions within chains compete while interchain interactions are ferromagnetic. Moreover, some 3D antiferromagnetic spin chain structures can be mapped onto a 1D ANNNI scenario [18]. In ANNNI models, many different close-lying magnetic states are predicted to occur as a function of small changes in external tuning parameters, with different incommensurate orderings.…”

Kinetic arrest of field-temperature induced first order phase transition in quasi-one dimensional spin system Ca3Co2O6

“…This quasi 1-D compound undergo a paramagnetic to IP transformation around T I ∼ 26 K at H = 0 9-15 and below that in presence of small applied magnetic field it goes to FIM state at low-T. [7][8][9][10][11][12][13] Temperature dependent dc magnetization of the compound Ca 3 Co 2 O 6 in applied…”

“…[7][8][9][10][11][12][13][14][15][16][17] Presence of competing interactions in these geometrically frustrated systems gives rise to interesting magnetism. The compound Ca 3 Co 2 O 6 crystallizes in rhombohedral crystal system having spin chains made up of CoO 6 trigonal prisms (TP) and CoO 6 octahedra (OCT) sites along c-axis of the hexagonal crystal structure.…”

“…[13][14][15] (2) Below T I in small nonzero magnetic field, the possible magnetic state is ferrimagnetic (FIM) and with increase in field it progress towards the ferromagnetic state (FM).…”