Interplay among spin, orbital, and lattice degrees of freedom in a frustrated spinel Mn${}_3$O${}_4$

We have investigated magnetic-field ($H$∥[100]) effect on a spin-frustrated tetragonally distorted spinel Mn${}_3$O${}_4$ by measurements of magnetization, dielectric constant, and strain as well as synchrotron x-ray and neutron diffraction. In two low-temperature phases below 40 K, long-wavelength lattice modulations coupled with magnetic order have been confirmed, revealing spin-lattice coupling caused by the exchange striction in the geometrically frustrated Mn${}^{3+}$ spin moments on the distorted pyrochlore lattice. A magnetic-field-induced phase transition has been found at low temperatures, which involves an abrupt change in both structural and magnetic configurations. The magnetostructural phase transition by the application of a magnetic field $H$∥[100] is discussed in terms of interplay among spin, orbital, and lattice degrees of freedom.

Figure 1

(a) Energy levels of tetrahedral A-site Mn${}^{2+}$ and octahedral B-site Mn${}^{3+}$ in Mn${}_3$O${}_4$. The orbital degree of freedom at B-site Mn${}^{3+}$ is lifted by a gigantic elongation along the $c$ axis below a cubic-tetragonal phase transition temperature. (b) Schematic view of spin arrangements in YK and CD phases. The A-site Mn${}^{2+}$ and B-site Mn${}^{3+}$ forms YK-type triangular spin configuration on $\left(1\overline{1}0\right)$ plane. (c) Formation of 1D-AF chains of B-site Mn${}^{3+}$ ions along [110] and $\left[1\overline{1}0\right]$ due to the dominant exchange $J_{\mathrm{BB}}$. There still remains magnetic frustration about how to stack the antiferromagnetic chains via an interchain interaction ($J^{\prime }$${}_{\mathrm{BB}}$).

Figure 2

Temperature dependence of (a) magnetization, (b) dielectric constant, and (c) strain under various magnetic field strengths. The measurements were performed upon cooling in a magnetic field along [100]. The relative changes in the dielectric constant and the strain are defined as $\Delta \varepsilon /\varepsilon =\left\{\varepsilon \right(T)-\varepsilon (60\mathrm{K}\left)\right\}/\varepsilon \left(60\mathrm{K}\right)$ and $\Delta L/L=\left\{L\right(T)-L(60\mathrm{K}\left)\right\}/L\left(60\mathrm{K}\right)$. (d) Magnetic-field dependence of strain along [100], [010], and [001] at 5 K in a magnetic field along [100].

Figure 3

(a) Phase diagram in $H$∥[100]. Symbols indicate transition points obtained from the anomalies in Fig. 2. Tetragonal and body-centered-orthorhombic, and face-centered-orthorhombic structures are represented by T, O${}_{\mathrm{I}}$ and O${}_{\mathrm{II}}$, respectively. (b)–(d) Schematic drawing of (b) T, (c) O${}_{\mathrm{I}}$, and (d) O${}_{\mathrm{II}}$ structures, respectively. The principal axes in the $ab$ plane are different by 45° between O${}_{\mathrm{I}}$ and O${}_{\mathrm{II}}$ structures.

Figure 4

(a) and (b) Temperature dependence of (0 8 0) profiles in a magnetic field of (a) 1 T and (b) 3 T, respectively. The magnetic field is applied ($H$∥[100]) perpendicular to both the scattering vector $q$∥(080) and the tetragonal $c$ axis. (d) Two orthorhombic domains corresponding to a tetragonal domain shown in (c). The subscript $o$ indicates the index in orthorhombic setting.

Figure 5

(a) Magnetic-field dependence of neutron magnetic reflections at 11 K. (b) Magnetic-field dependence of ($-$0.5 8.5 0) superlattice reflection of synchrotron x-ray at 10 K. The magnetic field is applied along [100] in both neutron and synchrotron x-ray diffraction measurements. (c) and (d) The integrated intensities of the magnetic scattering shown in (a) and the ($-$0.5 8.5 0) superlattice reflection shown in (b) as a function of magnetic field. Open circles, triangles, and rectangles in (c) indicate the calculated intensities of (2 0 0), (0 2 0), and (1.5 0.5 0) reflections for CD-O${}_{\mathrm{I}}$ (0 T) and YK-O${}_{\mathrm{II}}$ phases (0.8 T), respectively (see text).

Figure 6

Arrangements of 1D-AF B-site Mn${}^{3+}$ chains projected on the (001) plane for (a) the CD-O${}_{\mathrm{I}}$ phase and (b) the YK-O${}_{\mathrm{II}}$ phase, respectively. Black and white circles represent up and down spin components along the tetragonal $c$ axis. (c) A Mn${}_4$ tetrahedron of B sites at the crossing point of two neighboring chains stacked along the $c$ axis. Due to exchange striction between these two chains, AF (F) bonds would become short (long). (d), (e) Orthorhombic distortions of Mn${}_4$ tetrahedra $Q_2=({\varepsilon }_{xx}-{\varepsilon }_{yy})$. The sign of $Q_2$ depends on the phases of two relevant 1D-AF chains. The exchange striction mechanism can explain the elongation along $H$ and contraction perpendicular to $H$ when the phase transition from the CD-O${}_{\mathrm{I}}$ to the YK-O${}_{\mathrm{II}}$ takes places.

Figure 7

(a) Temperature dependence of profiles of a ($-q$ $8+q$ 0) ($q$ ∼ 0.5) superlattice reflection of synchrotron x-ray. The measurement was undertaken upon warming without a magnetic field. (b) and (c) Temperature dependence of the integrated intensities and the propagation vector $q$ of the superlattice reflections shown in (a), in comparison with those of ($2+q$ $-q$ 0) ($q$ ∼ 0.5) magnetic superlattice reflection obtained by neutron scattering at 0 T. The correspondence indicates a presence of spin-lattice coupling.

Figure 8

Arrangements of 1D-AF chains with two types of orthorhombic distortions of Mn${}_4$ tetrahedra projected on the $c$ plane for (a) the CD-O${}_{\mathrm{I}}$ and (b) the YK-O${}_{\mathrm{II}}$ phases, respectively. The local distortion of each Mn${}_4$ tetrahedron is characterized by small arrows. Black and white circles indicate up and down spin components of Mn${}^{3+}$ ions along the $c$ axis. (c) and (d) Orthorhombically distorted Mn${}_4$ tetrahedra in (c) the CD-O${}_{\mathrm{I}}$ and (d) the YK-O${}_{\mathrm{II}}$ phases, respectively. (e) and (f) Relationship between spin, orbital, and distortion of surrounding octahedron of Mn${}^{3+}$ sites in (e) the CD-O${}_{\mathrm{I}}$ and (f) the YK-O${}_{\mathrm{II}}$ phases. Arrows (green) on the Mn${}^{3+}$ hole-orbitals represent the in-plane component of the spin. Small arrows (black) beside oxygen atoms show their displacement.