Magnetic Frustration in a Quantum Spin Chain: The Case of LinaritePbCuSO4(OH)2

Abstract

We present a combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite PbCuSO4(OH)2, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector k=(0,0.186,1/2) was found below T(N)=2.8 K in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component (0.638μ(B)) is in the monoclinic ac plane forming an angle with the a axis of 27(2)°, while the other component (0.833μ(B)) points along the b axis. From a detailed thermodynamic study of bulk linarite in magnetic fields up to 12 T, applied along the chain direction, a very rich magnetic phase diagram is established, with multiple field-induced phases, and possibly short-range-order effects occurring in high fields. Our data establish linarite as a model compound of the frustrated one-dimensional spin chain, with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Long-range magnetic order is brought about by interchain coupling 1 order of magnitude smaller than the intrachain coupling.

Characterization of the spin-12linear-chain ferromagnet CuAs2O4

“…In such compounds it is frequently found that the spin exchange interactions between the Cu 2+ (S=1/2) ions are such that the next-nearest-neighbor (NNN) exchange is antiferromagnetic (AFM), the nearest-neighbor (NN) exchange is ferromagnetic (FM), and the NNN spin exchange is often considerably stronger than the NN spin exchange. Due to the inherent competition of the NN and NNN spin exchange interactions, the CuX 2 ribbon chains tend to develop unusual AFM incommensurate spiral spin structures [1][2][3][4][5][6][7][8][9] and sometimes concomitantly multiferroic behavior. [10][11][12][13] These CuX 2 ribbon chains are formed by linking CuX 4 basal-square-planes of axially elongated CuX 6 (X = O, Cl, Br,...) octahedra together via their trans-edges.…”

“…Some systems, such as Li 2 ZrCuO 4 and PbCuSO 4 (OH) 2 (linarite), prevent long-range FM ordering since they exhibit an AFM incommensurate spin-spiral structure along the ribbon chains. 8,9,19,20 Other systems, such as Ca 2 Y 2 Cu 5 O 10 and Li 2 CuO 2 , do contain FM ribbon chains, however, weak interchain interactions force the FM-ribbon chains to align antiparallel, resulting in long-range AFM ordering. [21][22][23][24][25][26] In the case of Li 2 CuO 2 , the absence of a spiral magnetic order in the ribbon chains is understood to be a consequence of order by disorder arising from interchain interactions.…”

Dynamics of linarite: Observations of magnetic excitations

“…Below T N = 2.8 K linarite shows magnetic long range order at zero field. Neutron scattering experiments 31 have confirmed the spin structure of the ground state to be an elliptical helix with the propagation vector k = (0, 0.186, 0.5). From bulk magnetic measurements, we have estimated the magnetic exchange interactions, with FM-NN J 1 ≈ −100 K, AFM-NNN J 2 ≈ 36 K and J ic ∼ 5 K 30 .…”

“…Unfortunately, for many of the candidates for exhibiting multipolar phases, the involved AFM magnetic couplings and thus the saturation field are quite large, making it difficult to probe the multipolar phases. In this respect, linarite, PbCuSO 4 (OH) 2 , is a promising spin-multipolar candidate as the Cu 2+ ions form a quasi-1D S = 1/2 spinchain along the crystallographic b-axis 17,[30][31][32][33] . The material crystallizes in a monoclinic space group P 2 1 /m with lattice parameters 31,32,34 (at 1.8 K) a = 9.682Å, b = 5.646Å, c = 4.683Å, and β = 102.65 • (Fig.…”

“…We have recently presented an extensive thermodynamic investigation of linarite, establishing a rich and detailed phase diagram along each of the principal directions 17,[31][32][33] . Below T N = 2.8 K linarite shows magnetic long range order at zero field.…”