Thermodynamics of multiferroic spin chains

Abstract

The minimal model to describe many spin chain materials with ferroelectric properties is the Heisenberg model with ferromagnetic nearest neighbor coupling J1 and antiferromagnetic nextnearest neighbor coupling J2. Here we study the thermodynamics of this model using a densitymatrix algorithm applied to transfer matrices. We find that the incommensurate spin-spin correlations -crucial for the ferroelectric properties and the analogue of the classical spiral pitch angledepend not only on the ratio J2/|J1| but also strongly on temperature. We study small easy-plane anisotropies which can stabilize a vector chiral order as well as the finite-temperature signatures of multipolar phases, stable at finite magnetic field. Furthermore, we fit the susceptibilities of LiCuVO4, LiCu2O2, and Li2ZrCuO4. Contrary to the literature, we find that for LiCuVO4 the best fit is obtained with J2 ∼ 90 K and J2/|J1| ∼ 0.5 and show that these values are consistent with the observed spin incommensurability. Finally, we discuss our findings concerning the incommensurate spin-spin correlations and multipolar orders in relation to future experiments on these compounds.

On the Nature of the Spin Frustration in the CuO2 Ribbon Chains of LiCuVO4: Crystal Structure Determination at 1.6 K, Magnetic Susceptibility Analysis, and Density Functional Evaluation of the Spin Exchange Constants

“…It should be noted that Enderle et al 9,11 extracted the spin exchange constants for the crystal structure at 1.42 K, 9,11 but Drechsler et al 13 employed the room-temperature crystal structure 10 for their calculations. In addition, the thermodynamic property study by Sirker 12 covered a wide range of temperature well above 1.42 K. Therefore, in resolving the controversy concerning the relative magnitudes of J 1 and J 2 , it is necessary to check if the crystal structure of LiCuVO 4 undergoes any significant change when the temperature is lowered from room temperature. Therefore, in the following, we first determine the crystal structure of LiCuVO 4 at 1.6 K by single-crystal neutron diffraction to ensure that the crystal structure of LiCuVO 4 does not undergo any significant change when the temperature is lowered.…”

“…They reproduced this observation by performing DFT calculations for LiCuVO 4 on the basis of its X-ray crystal structure (i.e., A recent inelastic neutron scattering investigation showing the two-spinon and four-spinon continuum 11 is also consistent with this observation. However, Sirker 12 re-analyzed the magnetic susceptibility and arrived at a strikingly different set of the spin exchanges (i.e., J 1  7.8 meV with J 2 /J 1   0.5). A similar conclusion was reported by Drechsler et al,13 who employed the same Hamiltonian to fit the magnetic susceptibility and magnetization data of Enderle et al 9 Furthermore, their DFT calculations led to two sets of spin exchange constants for LiCuVO 4 , which are drastically different from those they reported in ref.…”

Thermodynamic properties of LiCu2O2 multiferroic compound

“…∆ ≤ 1 is the exchange anisotropy, usually presenting in low-dimensional system with multiple magnetic transitions [25]. Theoretically, an XXZ-type anisotropy (∆ 1) is expected to stabilize a vector chiral order [22]. And recent experiment also shows that substantial exchange anisotropies exist in the edge-sharing spin-chain compounds [26].…”

“…Although many experiments and theoretical studies on LiCu 2 O 2 have been performed [20][21][22][23][24], the nature of the ground state and the origin of the ferroelectricity remain under debate.…”

Spin-flop and antiferromagnetic phases of the ferromagnetic half-twist ladder compounds Ba3Cu3In4O12and Ba3Cu3Sc4O12

“…Spin-1/2 chains of Cu 2+ with FM exchange J 1 < 0 have recently been identified in oxides [6][7][8][9][10][11][12][13] on either side of the quantum critical point [14], α c = −1/ 4, that is the exact boundary between a FM and a singlet ground state (GS) for isotropic exchange. Theory indicates the possibility of exotic ground states (GS) in FM/AFM chains with isotropic or anisotropic exchange [15][16][17][18][19][20]. Such chains include [21].…”