Magnetism and the phase diagram of ${\mathrm{MnSb}}_2{\mathrm{O}}_6$

Static and dynamic magnetic properties of P$\overline{3}$1$m$-phase ${\mathrm{MnSb}}_2{\mathrm{O}}_6$ have been studied by means of muon-spin relaxation ($\mu \mathrm{SR}$), high-frequency electron-spin resonance (HF-ESR), specific heat, and magnetization studies in magnetic fields up to 25 T. The data imply onset of long-range antiferromagnetic order at $T_{\mathrm{N}}$ = 8 K and a spin-flop-like transition at $B_{\mathrm{SF}}$ $\approx$ 0.7–1 T. Below $T_{\mathrm{N}}$, muon asymmetry exhibits well-defined oscillations indicating a narrow distribution of the local fields. A competing antiferromagnetic phase appearing below $T_{\mathrm{N}2}$ = 5.3 K is evidenced by a step in the magnetization and a slight kink of the relaxation rate. Above $T_{\mathrm{N}}$, both $\mu \mathrm{SR}$ and HF-ESR data suggest short-range spin order. HF-ESR data show that local magnetic fields persist up to at least $12T_{\mathrm{N}}\approx 100$ K. Analysis of the antiferromagnetic resonance modes and the thermodynamic spin-flop field suggest zero-field splitting of $\mathrm{\Delta }\approx 18$ GHz which implies small but finite magnetic anisotropy.

Figure 1

Static magnetic susceptibility $\chi =M/B$ of ${\mathrm{MnSb}}_2{\mathrm{O}}_6$ at low temperatures and at various magnetic fields $B\le 1$ T. The inset displays $\chi$ and its derivative $\partial \chi /\partial T$, at $B=0.5$ T, in order to highlight the anomaly at $T_{\mathrm{N}2}$. The dashed lines and the double arrow indicate the jump size of the associated anomaly.

Figure 2

Magnetization $M$ and magnetic susceptibility $\partial M/\partial B$ vs magnetic field at (a) $T=2$ K and (b) various temperatures up to 9 K. The inset in (a) enlarges the field range where the spin-flop occurs. The vertical dashed line indicates $B_{\mathrm{SF}}$ and the straight line in the inset linearly extrapolates $M$ to $B=0$ T.

Figure 3

Pulsed field magnetization obtained at $T=2.4$ K and $T=4.2$ K. Arrows indicate the saturation fields.

Figure 4

Specific heat of ${\mathrm{MnSb}}_2{\mathrm{O}}_6$ at low temperatures and at various magnetic fields and of ${\mathrm{ZnSb}}_2{\mathrm{O}}_6$. Arrows indicate $T_{\mathrm{N}}$($B$). Inset: Magnetic entropy changes (see text).

Figure 5

ZF-$\mu \mathrm{SR}$ spectra of ${\mathrm{MnSb}}_2{\mathrm{O}}_6$ at (a) representative temperatures $\ge T_{\mathrm{N}}$ and (b) early decay times below the magnetic ordering temperature $T_{\mathrm{N}}$. The symbols and the lines represent the experimental data and the corresponding model description (for details see the main text), respectively. For clarity, the spectrum at $T=7.5$ K in (b) is vertically shifted by 0.25, while no offset is applied to the spectra in (a).

Figure 6

Temperature dependence of (a) muon-spin relaxation time, (b) the order parameter, i.e., the oscillation frequency f, and (c) relaxation time of the oscillation divided by the frequency, ${\lambda }_{\mathrm{T}}/\mathit{f}$. (d) Temperature dependence of the order parameter on a double-logarithmic scale. The vertical (dashed) lines show $T_{\mathrm{N}2}$ ($T_{\mathrm{N}}$) derived from Fig. 1. The dashed lines in (b) and (d) represent a phenomenological fit to the experimental data at $T_{\mathrm{N}2}$ $\le T\le$ $T_{\mathrm{N}}$ (see text). The dotted line in (d) is an extrapolated guide line for the data at $T<$ $T_{\mathrm{N}2}$.

Figure 7

HF-ESR absorption frequencies vs magnetic field at $T=4$ K, together with representative spectra obtained at 50, 141, 230, and 259 GHz. The inset shows how the resonance features ${\omega }_1$ (black circles) and ${\omega }_2$ (red squares) were obtained by fitting the resonance by means of a powder spectrum. The diamond represents the resonance field observed in previous X-band ESR measurements in Ref. [8].

Figure 8

(a) HF-ESR spectra at $f=320.2$ GHz at different temperatures between 2 and 175 K. The vertical dashed line represents $g=2$. The data are vertically shifted for clarity. (b) Temperature dependence of the effective $g$ factors associated with ${\omega }_1$ and ${\omega }_2$. The inset enlarges the low-temperature region with $T\le$ $T_{\mathrm{N}}$ (11 T) highlighted in grey.

Figure 9

Magnetic phase diagram of ${\mathrm{MnSb}}_2{\mathrm{O}}_6$ as derived from $c_{\mathrm{p}}$ (open squares), $M$ vs $B$ and $T$ (filled circles). $T_{\mathrm{N}}$, $T_{\mathrm{N}2}$, and $B_{\mathrm{SF}}$ indicate the onset of long-range antiferromagnetic order, the transition AFM I to AFM II, and the spin-flop transition. The inset shows the phase diagram up to high magnetic fields. All lines are guides to the eye.