Figure 1

A schematic drawing of the positions of Mn${}^{2+}$ ions ($3d^5$) having localized spin 5/2 in SrMn${}_3$P${}_4$O${}_{14}$.[18] Two crystallographically independent Mn${}^{2+}$ sites (Mn1 and Mn2) exist. Two kinds of short Mn-Mn bonds exist and have Mn-O-Mn paths. The Mn-Mn distances are 3.27 and 3.34 Å at room temperature. The exchange interaction parameters are respectively defined as $J_1$ and $J_2$. The dominant AF $J_1$ interactions form the spin trimers indicated by the ellipses. The Hamiltonian is expressed as $\mathcal{H}=J_1(S_1{S}_2+S_2{S}_3).$ The spin trimer can account for the magnetic field and temperature dependences of the magnetization when $J_1=4.0$ K. Mn-Mn distances in the other bonds are more than 4.89 Å. These bonds have no Mn-O-Mn paths.Reuse & Permissions

Figure 2

The inelastic neutron-scattering intensity vs energy transfer $\omega$ [constant-$Q$ (magnitude of the scattering vector) scan spectra] of SrMn${}_3$P${}_4$O${}_{14}$ around 5 K (circles). The solid line represents the sum of two Gaussians and one Lorentzian (plus constant backgrounds). The dashed lines indicate each Gaussian or Lorentzian. The values of the parameters are given in Table .Reuse & Permissions

Figure 3

Constant-$Q$ scan spectra of SrMn${}_3$P${}_4$O${}_{14}$ at $Q=1.0$ Å${}^{-1}$ (circles). The solid line represents the sum of three Gaussians and one Lorentzian (plus constant backgrounds). The dashed lines indicate each Gaussian or Lorentzian. The values of the parameters are given in Table .Reuse & Permissions

Figure 4

(a) A schematic drawing of low-lying energy levels in the spin-5/2 AF linear trimer [ground state (GS) and excited states (ESs)].[19] The parameters $\epsilon \equiv E/J_1$ and $S$ indicate the eigenenergy and the total spin, respectively. $S_{13}$ is defined in the text. To distinguish two degenerate eigenstates with $\epsilon =-10$, we name the two states 3ES and 4ES. To distinguish two degenerate eigenstates with $\epsilon =-7$, we name the two states 6ES and 7ES. The arrows indicate allowed transitions from GS, 1ES, or 2ES with an energy difference $\Delta \epsilon$ up to 8. We observed the three black arrow transitions. The gray arrow transitions may exist. We could not detect the white arrow transition. (b) The temperature dependence of the calculated occupation ratio of the five low-lying energy levels when $J_1=4.0$ K.Reuse & Permissions

Figure 5

The temperature dependence of the integrated intensity of the 0.46-, 0.68-, and 1.02-meV excitations in SrMn${}_3$P${}_4$O${}_{14}$ at $Q=1.0$ Å${}^{-1}$.Reuse & Permissions

Figure 6

(a) The $Q$ dependence of the calculated INS intensity in the spin-5/2 AF linear trimer. (b)–(d) The inelastic neutron-scattering intensity vs $Q$ (constant-$\omega$ scan spectra) of SrMn${}_3$P${}_4$O${}_{14}$ (circles). The line indicates the first term in Eq. (3).Reuse & Permissions

Figure 7

Constant-$Q$ scan spectra of SrMn${}_3$P${}_4$O${}_{14}$ at $Q=1.0$ Å${}^{-1}$.Reuse & Permissions