Diffuse scattering due to Geometrical Frustration in Mn3O4

Abstract

The tetrahedral geometry in the spinel B site forms the pyrochlore network, which consists of corner-linked arrays of tetrahedral plaquettes. If the B–B exchange coupling is antiferromagetic and the spin direction is collinear, the pyrochlore lattice leads to intense frustration of the magnetic bonds. Among the transition metal spinel, Mn3O4 has a tetragonal (I41=amd; Z 1⁄4 4) structure due to the Jahn–Teller instability of Mn3þ (d) at the B site (octahedral site). Such a lattice distortion is advantageous for a collinear spin arrangement of the spinel B lattice. This compound shows a magnetic transition into the spin ordered phase at Tc 1⁄4 41K. Jensen and Nielsen have performed magnetic structural analysis on single crystalline Mn3O4 and reported a rather complicated spin structure with the two-fold periodicity along b. The A-spins (Mn2þ) are ferromagnetically ordered along b. On the other hands, the B-spins (Mn3þ) align nearly along c reflecting the Jahn–Teller distortion of the MnO6 octahedra. The B-spin chains along a and b are antiferromagnetically ordered. The B–B antiferromagnetic exchange coupling is considered to be stronger than the A–B exchange coupling, since the Mn2þ (d) at the A-site is electronically stable. Then, the B-site pyrocholre lattice is amenable to the geometrical frustration in the paramagnetic phase ( Tc) where the long-range spin order disappears. Neutron powder diffraction measurements were performed using the Kinken powder diffractometer for high efficiency and high resolution measurements (HERMES) of Institute for Materials Research, Tohoku University, installed at the JRR-3M reactor at the Japan Atomic Energy Research Institute, Tokai, Japan. Experimental details were described elsewhere. Powders of Mn3O4 were sealed in a vanadium capsule (10mm ) with helium gas, and mounted at the cold head of a closed-cycle He-gas refrigerator. The powder patterns are measured in the temperature range of 7K T 300K. We performed the Rietveld analysis (RIETAN2000 program) on the powder pattern at 300K (see Table I). Figure 1 shows temperature variation of neutron powder patterns in the small-2 region. At the lowest temperature (7K Tc), intense (101) magnetic Bragg reflection (indicated by a downward arrow) is observed at 21 . [The (101) reflection in the tetragonal setting corresponds to the (111) reflection in the cubic spinel.] With increase of temperature, a broad diffuse scattering (hatched region) appears at 20 . Trace of the scattering is detectable even at 300K ( Tc 1⁄4 41:9K). This diffuse scattering can be ascribed to the short-range spin correlation on the B-site pyrochlore lattice, because the scattering extends around the (101) magnetic Bragg reflection. Existence of the short-range correlation of the B-spins is also supported by the specific heat measurements. We measured specific heat of a meltgrown Mn3O4 crystal with use of Quantum Design PPMS machine. We observed -type anomaly at Tc (not shown), and estimated the spin entropy change S ( 2:2kB/ Mn3O4) at Tc. Magnitude of S is roughly consistent with the previous report [2:6ð1ÞkB/Mn3O4]. Here, S is much smaller than the ideal value [2 ln 5þ ln 6 ð 5:0ÞkB/Mn3O4], and is rather close to the A-spin contribution to the entropy change [ln 6 ð 1:8ÞkB/Mn3O4]. Table I. Refined structural parameters of Mn3O4 at 300K, determined by Rietveld analysis of neutron powder patterns. The crystal symmetry is tetragonal (I41=amd; Z 1⁄4 4). The lattice constants are a 1⁄4 5:7602ð2Þ A and c 1⁄4 9:4602ð4Þ A. g and B are the occupancy and isotropic atomic thermal parameter, respectively. Rwp ( 1⁄2 iwiðyi yi;calcÞ 2 iwiy 2 i ) and RI ( K jIK;calc IK j K IK;calc ) are 9.48% and 3.86%, respectively.