Erratum: Magnetic excitations and orbital physics in the ferrimagnetic spinels MnB2O4(B=Mn

Abstract

In this paper, we calculated the linear spin wave energies using incorrectly normalized exchange constants such thatJ ij = S i S j J ij andD i = S 2 i D i . In this Erratum we provide the results of our revised analysis, but also argue that the main conclusion of the original paper is still intact. First, the correct way for normalization should have beenJ ij = S i S j J ij andD i = S i D, respectively, since the spin wave frequency is proportional to S. The best-fit values of the exchange constants given in Table I of the original paper thus correspond toJ ij = S i S j J ij orD i = S i D, respectively.The above treatment in fact still ignores the cross terms that occur between different spin moments. To clarify this issue, we performed new calculations without using normalization. The spin moments were explicitly fixed to be S A = 5 2 and S B = 2 (for Mn 3 O 4 ) or 1 (for MnV 2 O 4 ). The new parameters are summarized in Table I, which replaces Table I of the original paper. The dispersions and intensities calculated using the new parameters for MnV 2 O 4 are summarized in the revised Fig. 3, which replaces Fig. 3 of the original paper. The new results for Mn 3 O 4 are essentially identical to what was shown in Fig. 2 of the original paper. We note that the new parameters provided in this Erratum are comparable to those shown in the original paper when converted by the corrected normalization. Most importantly, the ratio indicating the spatial anisotropy of the B-B exchange, J BB /J BB = 0.3 ± 0.1, is equal to the value reported in the original paper. It is thus confirmed that the conclusions of the original paper still stand without any reservations.TABLE I. The best-fit parameters used to calculate spin wave energies and intensities of Mn 3 O 4 and MnV 2 O 4 (J and D are in meV).

Exchange constants and spin waves of the orbital-ordered noncollinear spinel MnV2O4

“…A possible resolution of this puzzle is that trigonal distortion has been ignored in these simple proposals. With trigonal distortion, we expect a more complex orbital ordering which has the requisite symmetry I4 1 /a and would give the observed (or fitted) J c V−V along the c-axis 13 . This is exactly what has been found in the abinitio work of Ref.…”

“…In Ref. 13, the authors start with a nearest-neighbor Heisenberg Hamiltonian including the anisotropy term and calculate spin-wave spectra and corresponding eigenmodes using linear spin-wave theory (LSWT) for the non-collinear, tetragonal phase. By fitting the spectrum to inelastic neutron scattering data, they were able to determine the exchange couplings between Mn-V, V-V in ab-plane, and V-V between abplanes along the c-axis.…”

“…The low-T magnetic excitations of the compound have been mapped along high-symmetry directions using inelastic neutron scattering 3,13 . At the Γ point, these excitations are gapped for the acoustic modes, indicating the presence of single-ion anisotropy, which essentially occurs due to the interplay between SOC and crystal-fields 14 .…”

Variety of elastic anomalies in an orbital-active nearly itinerant cobalt vanadate spinel

“…Upon cooling, AV 2 O 4 , with nonmagnetic A = Zn, Mg, and Cd, undergoes a structural phase transition followed by an antiferromagnetic phase transition [2][3][4][5][6][7][8][9][10]. With magnetic A = Mn and Fe, owing to the presence of additional A 2+ -V 3+ exchange interactions, AV 2 O 4 exhibits a more complex structural and magnetic behavior, with successive structural and ferrimagnetic phase transitions [11][12][13][14][15][16][17][18][19][20][21][22][23][24] ]. For AV 2 O 4 (A = Zn, Mg, Cd, Mn, and Fe), the structural phase transition is considered to arise from a longrange ordering of the V t 2g orbitals, where the lowering of the lattice symmetry should result in the release of frustration (magnetic ordering).…”

The nature of itineracy in CoV2O4: a first-principles study

“…Things become more interesting when the A-site is also occupied by one of the transition metal (TM) ions which is magnetic. Competing exchange interactions among the spins at A and B sites often result in more than one magnetic transitions with change in temperature and at times in a complicated non-collinear magnetic ordering at low temperatures [4,6]. Spinel vanadates such as MnV 2 O 4 , FeV 2 O 4 and CoV 2 O 4 with magnetic transition metal ions at A and B sites show a ferrimagnetic order of A and B spins at low temperatures where all the vanadium spins are parallel to one another but are antiparallel to those at A sites [7,8].…”