Exchange anisotropy as mechanism for spin-stripe formation in frustrated spin chains

Abstract

We investigate the spin-stripe mechanism responsible for the peculiar nanometer modulation of the incommensurate magnetic order that emerges between the vector-chiral and the spin-density-wave phase in the frustrated zigzag spin-1/2 chain compound β-TeVO4. A combination of magnetictorque, neutron-diffraction and spherical-neutron-polarimetry measurements is employed to determine the complex magnetic structures of all three ordered phases. Based on these results, we develop a simple phenomenological model, which exposes the exchange anisotropy as the key ingredient for the spin-stripe formation in frustrated spin systems.Textured phases, frequently found in nature, typically develop as a result of conflicting interactions that favor rival ground states. In biological systems, alternating patterns have been explained by couplings between competing order parameters [1][2][3], whereas in strongly correlated electron systems stripe phases have been related to the competition between short-(e.g., exchange) and long-range (e.g., dipolar) interactions, leading, for instance, to stripe domains in feromagnetic films [4][5][6][7] or charge patterns in superconductors [8][9][10][11][12]. Moreover, a theoretical study by Edlund et al. [13] showed that a degeneracy of eigenstates in discretized-spin models allows for stripe formation that does not depend on the details of the microscopic interactions. Despite the ubiquity of inhomogeneous phases, the recent discovery of a peculiar antiferromagnetic stripe phase -a nanometer-scale modulation of the underlying incommensurate magnetic order in β-TeVO 4 [14] -exceeds the reach of any known model and thus calls for a new, general explanation.In the monoclinic structure of β-TeVO 4 (space group P 2 1 /c) distorted corner-sharing VO 5 pyramids with magnetic V 4+ ions form zigzag spin-1/2 chains that run along the crystalographic c axis [15,16]. Geometrical frustration stems from the competition between the ferromagnetic nearest-neighbor superexchange interaction J 1 ∼ −38 K and the antiferromagnetic nextnearest-neighboring interaction J 2 ∼ −0.8 J 1 , while the chains are coupled by more than an order of magnitude weaker, also frustrated, interactions. As a result, an incommensurate amplitude-modulated, i.e., a spin-density-wave (SDW), state defined by the magnetic wave vector k = (−0.195, 0, 0.413) is established at T N 1 = 4.65 K, while a vector chiral (VC) spin order develops below T N 3 = 2.28 K. Between these two phases, in the temperature range from T N 2 = 3.28 K to T N 3 , an intriguing spin-stripe phase emerges that is characterized by additional super-satellite reflections appearing in neutron-diffraction profiles at k ± ∆k [∆k(2.5 K) = (−0.030, 0, 0.021)], which have weak inten-. The resulting stripe order exhibits a remarkable long-scale modulation that alters the main SDW ordering in contrast to other known stripe patterns in magnetic systems. The negligible long-range dipolar interactions and the realization of an incommensurate, "nondiscrete", magnetic order lead to t...

Elementary excitation in the spin-stripe phase in quantum chains

“…To further investigate the relation between the spinstripe order witnessed previously by neutron diffraction [19,22] and the stripe dynamics observed by µSR, we performed additional neutron diffraction measurements (see Methods). We measured the temperature dependence of the strongest magnetic reflection and its satellites (Fig.…”

“…For frustrated spin-1/2 chains with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions, which in β-TeVO 4 amount to J 1 ≈ −38 K and J 2 ≈ −0.8 J 1 , respectively [19], the SDW and VC phases are predicted theoretically [24,25], while the intermediate spin-stripe phase is not. The formation of the latter has been associated with exchange anisotropies and interchain interactions [19,22], but still awaits a comprehensive explanation.…”

Magnetic ground state of the frustrated spin- 12 chain compound β–TeVO4 at high magnetic fields

“…The response for B||a and B||c is rather similar, i.e., the anomalies for B||a (B||c) are found at 2.8 (2.5), 18.7 (18.1) and 21.5 (21.0) T. On the other hand, for B||b the low-field anomaly is shifted to significantly higher field, i.e., it occurs at 9.7 T, whereas the other two are found at only slightly higher fields than for the other two directions, i.e., at 19.4 and 22.2 T. This is not surprising when considering the strong magnetic anisotropy highlighted in preceding studies. 20,22,23,26,27…”

Coexisting spinons and magnons in the frustrated zigzag spin- 12 chain compound β−TeVO4

“…The acquired data provide detailed information about the interactions that constitute the exchange network in β-TeVO 4 . Previous experimental studies offered a good estimate of the main exchange interactions, J 1 and J 2 , 19 an approximate estimation of their anisotropies, 22 and a rough assessment of the interchain interactions. 19 On the other hand, density-functional-theory calculations, 26,27 investigating the exchange interactions up to the eightshortest vanadium-vanadium distances, offered a quantitative estimate for all interactions included in calculations.…”

“…At T N 1 = 4.65 K the paramagnetic phase is replaced by an SDW phase with the incommensurate amplitude-modulated (ICAM) arXiv:1808.10174v1 [cond-mat.str-el] 30 Aug 2018 magnetic order defined by the magnetic wave vector k ≈ (−0.20, 0, 0.41). 19,22 The SDW phase is succeeded by an unconventional spin-stripe phase, which develops at T N 2 = 3.28 K. In this phase an additional weak ICAM magnetic component with k' = (k+∆k) and ∆k ≈ (−0.03, 0, 0.02) introduces a nanometer-sized stripe modulation of the spin structure. Finally, at T N 3 = 2.28 K, ∆k becomes zero and an elliptical-spiral magnetic order is established reflecting the dominance of the VC correlations at low temperatures.…”