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Register a new userStrong magnetoelastic coupling at the transition from harmonic to anharmonic order in NaFe(WO$_4$)$_2$ with 3d$^5$ configuration
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The crystal structure of the double tungstate NaFe(WO$_4$)$_2$ arises from that of the spin-driven multiferroic MnWO$_4$ by inserting non-magnetic Na layers. NaFe(WO$_4$)$_2$ exhibits a three-dimensional incommensurate spin-spiral structure at low temperature and zero magnetic field, which, however, competes with commensurate order induced by magnetic field. The incommensurate zero-field phase corresponds to the condensation of a single irreducible representation but it does not imply ferroelectric polarization because spirals with opposite chirality coexist. Sizable anharmonic modulations emerge in this incommensurate structure, which are accompanied by large magneto-elastic anomalies, while the onset of the harmonic order is invisible in the thermal expansion coefficient. In magnetic fields applied along the monoclinic axis, we observe a first-order transition to a commensurate structure that again is accompanied by large magneto-elastic effects. The large magnetoelastic coupling, a reduction of the $b$ lattice parameter, is thus associated only with the commensurate order. Upon releasing the field at low temperature, the magnetic order transforms to another commensurate structure that considerably differs from the incommensurate low-temperature phase emerging upon zero-field cooling. The latter phase, which exhibits a reduced ordered moment, seems to be metastable.
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The structural distortion and magnetoelastic coupling induced through commensurate magnetism has been investigated by neutron diffraction in structurally related MnWO$_4$ and NaFe(WO$_4$)$_2$. Both systems exhibit a competition of incommensurate spiral and commensurate spin up-up-down-down ordering along the magnetic chains. In the latter commensurate phases, the alternatingly parallel and antiparallel arrangement of Fe$^{3+}$ respectively Mn$^{2+}$ moments leads to sizeable bond-angle modulation and thus to magnetic dimerization. For NaFe(WO$_4$)$_2$ this structural distortion has been determined to be strongest for the low-field up-up-down-down arrangement, and the structural refinement yields a bond-angle modulation of $pm 1.15(16)$ degrees. In the commensurate phase of MnWO$_4$, superstructure reflections signal a comparable structural dimerization and thus strong magneto-elastic coupling different to that driving the multiferroic order. Pronounced anharmonic second- and third-order reflections in the incommensurate and multiferroic phase of MnWO$_4$ result from tiny commensurate fractions that can depin multiferroic domains.
We report high-resolution capacitance dilatometry studies on the uniaxial length changes in a NdB$_4$ single crystal. The evolution of magnetically ordered phases below $T_{rm N}$= 17.2~K (commensurate antiferromagnetic phase, cAFM), $T_{rm IT}$= 6.8~K (intermediate incommensurate phase, IT), and $T_{rm LT}$= 4.8~K (low-temperature phase, LT) is associated with pronounced anomalies in the thermal expansion coefficients. The data imply significant magneto-elastic coupling and evidence of a structural phase transition at $T_{rm LT}$ . While both cAFM and LT favor structural anisotropy $delta$ between in-plane and out-of-plane length changes, it competes with the IT-type of order, i.e., $delta$ is suppressed in that phase. Notably, finite anisotropy well above $T_{rm N}$ indicates short-range correlations which are, however, of neither cAFM, IT, nor LT-type. Gruneisen analysis of the ratio of thermal expansion coefficient and specific heat enables the derivation of uniaxial as well as hydrostatic pressure dependencies. While $alpha$/$c_{rm p}$ evidences a single dominant energy scale in LT, our data imply precursory fluctuations of a competing phase in IT and cAFM, respectively. Our results suggest the presence of orbital degrees of freedom competing with cAFM and successive evolution of a magnetically and orbitally ordered ground state.
We describe a new mechanism leading to the formation of rational magnetization plateau phases, which is mainly due to the anharmonic spin-phonon coupling. This anharmonicity produces plateaux in the magnetization curve at unexpected values of the magnetization without explicit magnetic frustration in the Hamiltonian and without an explicit breaking of the translational symmetry. These plateau phases are accompanied by magneto-elastic deformations which are not present in the harmonic case.
The crystal and magnetic structure of multiferroic LiFe(WO$_4$)$_2$ were investigated by temperature and magnetic-field dependent specific heat, susceptibility and neutron diffraction experiments on single crystals. Considering only the two nearest-neighbour magnetic interactions, the system forms a $J_1$, $J_2$ magnetic chain but more extended interactions are sizeable. Two different magnetic phases exhibiting long-range incommensurate order evolve at $T_{text{N}1}approx 22.2 text{ K}$ and $T_{text{N}2}approx 19 text{ K}$. First, a spin-density wave develops with moments lying in the $ac$ plane. In its multiferroic phase below $T_{text{N}2}$, LiFe(WO$_4$)$_2$ exhibits a spiral arrangement with an additional spin-component along $b$. Therefore, the inverse Dzyaloshinskii-Moriya mechanism fully explains the multiferroic behavior in this material. A partially unbalanced multiferroic domain distribution was observed even in the absence of an applied electric field. For both phases only a slight temperature dependence of the incommensurability was observed and there is no commensurate phase emerging at low temperature or at finite magnetic fields up to $6text{ T}$. LiFe(WO$_4$)$_2$ thus exhibits a simple phase diagram with the typical sequence of transitions for a type-II multiferroic material.
The magnetoelastic coupling in Ca$_{1.8}$Sr$_{0.2}$RuO$_4$ and in Ca$_{1.5}$Sr$_{0.5}$RuO$_4$ has been studied combining high-resolution dilatometer and diffraction techniques. Both compounds exhibit strong anomalies in the thermal-expansion coefficient at zero and at high magnetic field as well as an exceptionally large magnetostriction. All these structural effects, which are strongest in Ca$_{1.8}$Sr$_{0.2}$RuO$_4$, point to a redistribution of electrons between the different $t_{2g}$ orbitals tuned by temperature and magnetic field. The temperature and the field dependence of the thermal-expansion anomalies in Ca$_{1.8}$Sr$_{0.2}$RuO$_4$ yield evidence for a critical end-point lying close to the low-temperature metamagnetic transition; however, the expected scaling relations are not well fulfilled.
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