Microscopic origin of the above-room-temperature magnetodielectric coupling in triethylmethylammonium tetrabromoferrate(III), [N(C2H5)3CH3][FeBr4]

The molecule-based improper ferroelectric [N(C2H5)3CH3][FeBr4] (EMAFB) shows a magnetodielectric (MD) ratio of about 18% at 0.6 MHz near its paraelectric-ferroelectric phase transition at $T_{c}\approx 360$ K, one of the largest above-room-temperature MD effects reported for a molecular crystal, yet its microscopic mechanism is unresolved: the high-temperature paraelectric-phase crystal structure has never been determined, the coincident abrupt change in magnetic susceptibility lacks a microscopic explanation, and the coupling channel behind the MD effect has not been identified — intrinsic spin-lattice (magnetoelectric) contributions have never been separated from possible extrinsic Maxwell-Wagner or domain effects. This problem asks for a complete microscopic account of the coupling in this specific compound: the paraelectric-phase structure and atomic displacements across $T_{c}$, a microscopic model of the susceptibility discontinuity, and identification of the coupling channel behind the 18% MD effect, together establishing whether EMAFB merits its designation as a genuine single-phase above-room-temperature molecule-based magnetoelectric multiferroic.

Background

A multiferroic is a material that exhibits two or more primary ferroic orders, typically ferroelectricity and magnetism, in one phase; a magnetoelectric coupling then links polarization and magnetization. In the molecular literature the label is commonly used in the weaker sense of a single phase with coupled magnetic and electric polarizabilities, which can be realized even in a paramagnetic phase without long-range magnetic order (as in the room-temperature magnetoelectric [TMCM][FeCl4]); Cai et al. likewise called EMAFB a "possible above-room-temperature molecular multiferroic" because its ferroelectric and magnetic transitions take place at almost the same temperature ($\approx 360$ K), not because the compound is magnetically ordered there. Whether EMAFB merits the designation in the strict sense is itself part of the question below. In experiments this coupling is often detected as a magnetodielectric (MD) effect: a magnetic field changes the dielectric permittivity, quantified by the MD ratio $\Delta\varepsilon(H)/\varepsilon(0)$ measured, for example, by capacitance measurements at a fixed frequency. Single-phase multiferroics are rare because ferroelectricity in oxides conventionally favors empty transition-metal $d$ shells while magnetism requires partially filled ones. Molecule-based (organic-inorganic hybrid) ferroelectrics offer an alternative route: ferroelectricity can arise from the ordering or dynamics of organic cations, while magnetic ions are carried by separate inorganic anions.

Triethylmethylammonium tetrabromoferrate(III), [N(C2H5)3CH3][FeBr4] (often abbreviated EMAFB), is such a hybrid salt: trigonal-pyramidal [N(C2H5)3CH3]+ cations and tetrahedral high-spin Fe(III) ($S=5/2$) [FeBr4]- anions both sit on the hexagonal axis of the polar space group $P6_{3}mc$ at room temperature. It is an improper molecular ferroelectric, meaning the spontaneous polarization is a by-product of an order-disorder structural transition of the cations rather than its own driving order parameter. Cai et al. (J. Am. Chem. Soc. 2012) discovered that near $T_{c}\approx 360$ K the compound undergoes a first-order transition to a centrosymmetric paraelectric phase (evidenced by a sharp drop in the number of powder X-ray diffraction peaks above about 368 K), accompanied both by a dielectric anomaly (the paraelectric phase has a roughly 40% higher permittivity) and by an abrupt, hysteretic change of the magnetic susceptibility ($T\uparrow\approx 366$ K, $T\downarrow\approx 361$ K); the two anomalies coincide and produce the strong MD coupling (18% at 0.6 MHz). Genuine long-range magnetic ordering in this salt occurs only at about 5 K (antiferromagnetic, from the weakly coupled Fe(III) moments), so the 360 K susceptibility jump is not the onset of magnetic order, even though the source paper described it as a magnetic transition coincident with the ferroelectric one; the response is broadly consistent with paramagnetic Fe(III) and a Brillouin-function estimate (the standard magnetization curve of non-interacting paramagnetic spins), and its microscopic origin remains open — possibilities discussed for this family, such as modulation or quenching of the orbital angular momentum, a change in local electronic configuration, or the onset of cooperative correlations, are not excluded and are not mutually exclusive, although the jump naturally accompanies the first-order structural change. EMAFB also shows a low-temperature ferroelectric-ferroelectric transition (Aizu notation 6mmF6, i.e. the point group 6mm drops its mirrors to 6) with small magnetic and dielectric anomalies at about 171 K as reported by Cai et al.; magnetization measurements in 2023 found no magnetic anomaly there and concluded that this transition is purely electric.

Three caveats frame what remains open. First, no single-crystal (or even fully refined powder) structure of the high-temperature paraelectric phase of EMAFB exists; only a handful of powder reflections above the transition were reported, so the detailed atomic displacements, cation disorder, and symmetry relations across $T_{c}$ are undetermined. Second, an apparent MD effect can be extrinsic: space-charge (Maxwell-Wagner) interfacial polarization and domain-wall motion near a first-order hysteretic transition can mimic intrinsic magnetoelectric coupling, so frequency-, field-, and electrode-dependent controls are required. Third, work on the isostructural chloride [N(C2H5)3CH3][FeCl4] (paraelectric phase indexed above 363 K in the centrosymmetric hexagonal space group $P6_{3}/mmc$, $a = 8.520(2)$ Å, $c = 7.333(1)$ Å, i.e. a strongly shortened but not exactly halved $c$ axis relative to the room-temperature $P6_{3}mc$ cell with $c = 13.16766(24)$ Å; an electric field shifts the susceptibility hysteresis by about 2 K) and on the different molecular ferroelectric [TMCM][FeCl4] (TMCM = trimethylchloromethylammonium; magnetostriction-mediated room-temperature magnetoelectricity) provides strong analogies, but analogy is not a determination for EMAFB itself.

Problem Statement

Establish the microscopic mechanism of the above-room-temperature magnetodielectric coupling in triethylmethylammonium tetrabromoferrate(III), [N(C2H5)3CH3][FeBr4], by resolving the three open items that Cai et al. left undetermined for this one compound: (1) determine the crystal structure of the high-temperature paraelectric phase above $T_{c}\approx 360$ K — including the cation disorder and the atomic displacements relative to the room-temperature $P6_{3}mc$ ferroelectric phase — so that the structural pathway producing the spontaneous polarization and the coincident susceptibility discontinuity is known (for this item, a symmetry-constrained model of EMAFB's paraelectric phase — constrained by the compound's own room-temperature cell and the powder reflections reported above the transition, taking the isostructural chloride analogue as guidance, and stating the space group, the cation disorder, the atomic displacements and their uncertainty — counts as a determination, and new diffraction data are not required); (2) give a microscopic account of the abrupt hysteretic change in magnetic susceptibility at $T_{c}$ for this paramagnetic $S=5/2$ Fe(III) salt, whose long-range magnetic ordering sets in only near 5 K, explaining how the first-order paraelectric-ferroelectric structural change produces it (illustratively, through changes in the Fe(III) moment response, in the orbital angular momentum, or in the exchange pathways; none of these channels is prescribed and no exclusive choice among predefined branches is required); and (3) identify the microscopic coupling channel responsible for the magnetodielectric ratio of about 18% at 0.6 MHz near $T_{c}$ reported by Cai et al. (J. Am. Chem. Soc. 2012, 134, 18487–18490) under the magnetic-field, frequency and electrode conditions documented in that paper and its Supporting Information — that is, establish how a magnetic field and the ferroelectric polarization are coupled in this single phase (for example through spin-lattice coupling tied to the coincident first-order structural transition) and whether the reported effect reflects that intrinsic coupling. These three items are the separate open points the source left for this compound; together they constitute the complete microscopic account of the magnetodielectric coupling and settle whether EMAFB satisfies the strict definition of a multiferroic (two or more primary ferroic orders in one phase) and, separately, in which weaker magnetoelectric sense the molecular-literature label of an above-room-temperature molecule-based multiferroic (a single phase with coupled magnetic and electric polarizabilities) applies to it.

References

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