Field-induced spin density wave and spiral phases in a layered antiferromagnet

We determine the low-field ordered magnetic phases of the $S=1$ dimerized antiferromagnet ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ using single-crystal neutron diffraction. We find that for magnetic fields between ${\mu }_{0}H=8.80\mathrm{T}$ and $10.56\mathrm{T}$ applied along the $\left[1\overline{1}0\right]$ direction the system exhibits spin density wave order with incommensurate wave vectors of type $(\eta ,\eta ,\epsilon )$. For ${\mu }_{0}H>10.56\mathrm{T}$, the magnetic order changes to a spiral phase with incommensurate wave vectors only along the $\left[hh0\right]$ direction. For both field-induced ordered phases, the magnetic moments are lying in the plane perpendicular to the field direction. The nature of these two transitions is fundamentally different: the low-field transition is a second-order transition to a spin density wave ground state, while the one at higher field, toward the spiral phase, is of first order.

Figure 1

(a) Magnetic field versus temperature phase diagram for ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ with ${\mu }_{0}H\perp c$. Open and closed black points for $T>0.3$ K are from the low magnetic field range of Ref. [11], and were determined from magnetocaloric effect (MCE) and heat capacity ($C_p$) measurements. Points for $T<0.2$ K correspond to the critical fields observed in neutron scattering measurements (e.g., Fig. 2). Phase boundary lines are guides to the eye. Phase I and phase II are described in the text. Phase QP is a quantum paramagnetic disordered phase. Inset shows the nuclear crystal structure only illustrating the ${\mathrm{Mn}}^{5+}S=1$ sites. Intradimer (interdimer) exchange is depicted with solid (dashed) lines with labeling of exchange paths as in Ref. [10]. (b) Rocking curves of magnetic Bragg peaks at ${\mu }_{0}H=10$ T. (c) Rocking curves of magnetic Bragg peaks at ${\mu }_{0}H=12$ T. Rocking curves have been offset by their peak location in $\omega$, the sample rotation angle, such that they are centered at $\omega =0$. Rocking curves have been offset vertically by their fitted background value. Solid lines through rocking curves are Gaussian fits. The scattering vectors of the individual rocking curves are listed in the figure caption.

Figure 2

Intensity as a function of magnetic field for two magnetic Bragg peaks corresponding to the two low-temperature ($T\approx 0.05$ K) magnetic phases in ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$. Vertical triangle symbols correspond to increasing the magnetic field; inverted triangle symbols correspond to decreasing the applied magnetic field during the measurement. Solid lines are fits to a power law for a range of 1 T above the critical field for each measurement. Extracted order parameter values are discussed in the text.

Figure 3

(a) Ordered magnetic structure as determined for ${\mu }_{0}H=10$ T, phase II. Structure corresponds to domain ${\mathbf{k}}_1^{II}$. (b) 2-$\mathbf{k}$ magnetic structure scenario for phase II with different colored spin vectors representing the alternating canting angle along the $c$ axis. (c) Ordered magnetic structure, ${\mathbf{k}}_3^I$, as determined for ${\mu }_{0}H=12$ T. Only the ${\mathrm{Mn}}^{5+}$ sites with the ordered spin vector are shown in the figures for clarity. The vertical axis of the figures corresponds to the crystallographic $c$ axis. The spins lie in the plane perpendicular to the direction of the applied magnetic field ($H\parallel \left[1\overline{1}0\right]$). Gray lines are the boundaries of unit cells. Red lines between ${\mathrm{Mn}}^{5+}$ sites are shown to illustrate the dimers. Blue and black vectors are the directions of the $S=1$ moments. Blue shaded disks in (c) illustrate the cycloid structure. Measurements were performed in the $\left[hh\ell \right]$ scattering plane with the magnetic field perpendicular to this plane. The direction of the magnetic field is approximately normal to the page.