Unraveling the complex magnetic structure of multiferroic pyroxene NaFeGe2O6 : A combined experimental and theoretical study

Abstract

Magnetic order and the underlying magnetic model of the multiferroic pyroxene NaFeGe 2 O 6 are systematically investigated by neutron powder diffraction, thermodynamic measurements, density-functional bandstructure calculations, and Monte-Carlo simulations. Upon cooling, NaFeGe 2 O 6 first reveals one-dimensional spin-spin correlations in the paramagnetic state below about 50 K, uncovered by magnetic diffuse scattering. The sinusoidal spin-density wave with spins along the a-direction sets in at 13 K, followed by the cycloidal configuration with spins lying in the (ac) plane below 11.6 K. Microscopically, the strongest magnetic coupling runs along the structural chains, J 1 ≃ 12 K, which is likely related to the one-dimensional spin-spin correlations. The interchain couplings J 2 ≃ 3.8 K and J 3 ≃ 2.1 K are energetically well balanced and compete, thus giving rise to the incommensurate order in sharp contrast to other transition-metal pyroxenes, where one type of the interchain couplings prevails. The magnetic model of NaFeGe 2 O 6 is further completed by the weak single-ion anisotropy along the a-direction. Our results resolve the earlier controversies regarding the magnetic order in NaFeGe 2 O 6 and establish relevant symmetries of the magnetic structures. These results, combined with symmetry analysis, enable us to identify the possible mechanisms of the magnetoelectric coupling in this compound. We also elucidate microscopic conditions for the formation of incommensurate magnetic order in pyroxenes.

Chiral Order and Multiferroic Domain Relaxation in NaFeGe$_2$O$_6$

“…In this material multiferroic order does not result from the spin-current or inverse Dzyaloshinski-Moriya mechanism [14][15][16]32] but from the combina-tion of the chiral order and the monoclinic distortion. In contrast, multiferroic order in SrMnGe 2 O 6 [30] and in NaFeGe 2 O 6 [33] seems to follow the most common inverse Dzyaloshinski-Moriya mechanism [14][15][16]32] but with differently oriented cycloidal and ferroelectric order.…”

“…Below T ≈ 35 K, short-range ordering was observed and two different magnetic phases with incommensurate longrange order were reported for NaFeGe 2 O 6 with transition temperatures at T N ≈ 13 K and T MF ≈ 11.6 K [33][34][35][36]. First at T N an incommensurate spin-density wave (SDW) evolves with moments pointing roughly along a-direction [33] and below T MF , spins form a chiral spin structure with moments lying within the ac plane [34,35]. A small b component of the chiral structure was controversially discussed [34,35], and in [35] only a single transition is observed.…”

“…NaFeGe 2 O 6 exhibits a simple phase diagram with the typical sequence of two incommensurate ordered phases and with just one magnetic site [29,[33][34][35][36]. The system crystallizes in the monoclinic spacegroup C2/c with a = 10.0073(8) A, b = 8.9382(7) A, c = 5.5184(4) A and β = 107.524(1)° [35,37].…”

Domain switching and exchange bias control by electric field in the multiferroic conical magnet Mn2GeO4

“…These so-called type-II multiferroics are improper ferroelectrics; their polarization is rather weak but can be strongly influenced by external magnetic fields. Studies on multiple spin-driven multiferroic materials, e.g., TbMnO 3 [7], Ni 3 V 2 O 8 [8], MnWO 4 [9,10], and NaFeX 2 O 6 (X = Si, Ge) [11][12][13][14], determined the underlying coupling mechanisms. Most members show two magnetic ordering transitions with a paraelectric intermediate phase with incommensurate and collinear order and a low-temperature ferroelectric phase arising from an inversion-symmetry breaking magnetic structure.…”

Forming a ferrimagnetic-like structure in the PbMn1−xFexBO4 (x ≈ 0.1) single crystal upon partial substitution

“…Of even greater interest are the families of isomorphic crystals in which the replacement of one paramagnetic ion by another changes the magnetic order type. Examples of this fairly rare family are pyroxenes, including the NaCrGe 2 O 6 chain ferromagnet [16] and NaFeGe 2 O 6 multiferroic compound with a complex magnetic phase diagram containing incommensurately modulated antiferromagnetic structure of cycloidal type and sinusoidal spin-density wave configuration [17][18][19][20]. A great variety of magnetic structures is typical of the perovskite family, which involves the BiMnO 3 and BiCrO 3 solid solutions [21] with the well-studied magnetic properties; the former has a ferromagnetic structure and the latter is an antiferromagnet.…”