Quasistatic remanence in Dzyaloshinskii-Moriya interaction driven weak ferromagnets and piezomagnets

We explore remanent magnetization $\left(\mu \right)$ as a function of time and temperature, in a variety of rhombohedral antiferromagnets (AFMs) which are also weak ferromagnets (WFMs) and piezomagnets (PzMs). These measurements, across samples with length scales ranging from nano to bulk, firmly establish the presence of a remanence that is quasistatic in nature and exhibits a counterintuitive magnetic field dependence. These observations unravel an ultraslow magnetization relaxation phenomenon related to this quasistatic remanence. This feature is also observed in a defect-free single crystal of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$, which is a canonical WFM and PzM. Notably, $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ is not a typical geometrically frustrated AFM, and in single crystal form it is also devoid of any size or interface effects, which are the usual suspects for a slow magnetization relaxation phenomenon. The underlying pinning mechanism appears exclusive to those AFMs which either are symmetry allowed WFMs, driven by Dzyaloshinskii-Moriya interaction, or can generate this trait by tuning of size and interface. The qualitative features of the quasistatic remanence indicate that such WFMs are potential piezomagnets, in which magnetization can be tuned by stress alone.

Figure 1

SEM images of (a) microcubes of ${\mathrm{MnCO}}_3$, (b) nanocubes of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$, and (c) ${\mathrm{FeCO}}_3$ spheres with diameter $\sim 20$ $\mu \mathrm{m}$. Each sphere consists of triangular ${\mathrm{FeCO}}_3$ nanoparticles $\sim 5$–10 nm. (e, f) Synchrotron XRD data of ${\mathrm{MnCO}}_3\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ and ${\mathrm{FeCO}}_3$ along with Rietveld fitting. Inset: Best-fit lattice parameters derived from Rietveld profile refinement of $I$ vs $2\theta$ data recorded at different temperatures. (g–i) The magnetization as a function of temperature from 300 to 5 K in presence of $H=1$ kOe for all three samples. For ${\mathrm{MnCO}}_3$ and ${\mathrm{FeCO}}_3$, the Neel transition temperature is 30 and 50 K, respectively, as evident from (g) and (i), respectively. For $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$, the Morin transition $T_M$ signifying spin reorientation transition from the WFM to the pure AFM state is around 260 K. The actual Neel transition is around 950 K, shown schematically in (h).

Figure 2

Black dots in (a) show magnetization measured while cooling $(H=100$ Oe) and blue dots are corresponding remanence $(H=0)$ measured while warming for the ${\mathrm{MnCO}}_3$ sample. (b) The same for $H$=30 kOe. (c) $M_{\text{FC}}$ vs $T$ at various $H$ depicting regular AFM behavior with $M_{\text{FC}}$ rising with rise in $H$. (d) Corresponding ${\mu }_{\text{FC}}$ vs $T$ exhibits strikingly different cooling $H$ dependence. (e) Comparison of the magnitude of $M_{\text{FC}}$ (black dots, right axis) and ${\mu }_{\text{FC}}$ (blue dots, left axis) at 5 K as a function of (cooling) $H$ for ${\mathrm{MnCO}}_3$.

Figure 3

Remanence as a function of time for three different cooling fields at a fixed temperature of 5 K for ${\mathrm{MnCO}}_3$. These data show that the remanence is almost constant over a time period of 2 h, thus depicting its quasistatic nature.

Figure 4

(a, b) ${\mu }_{\text{FC}}$ as a function of (cooling) $H$ for $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ and ${\mathrm{FeCO}}_3$, respectively. The corresponding $M$ vs $H$ is shown for each sample in the same graph, indicating the unusual (cooling) field dependence of remanence for both the samples. (c) Comparison of ${\mu }_{\text{FC}}$ as a function of $time$ in all three samples. The observation of the quasistatic nature of remanence is unambiguous in case of ${\mathrm{MnCO}}_3$ as well as $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$. (d) $c/a$ ratio using refined lattice parameters obtained at various temperature from Rietveld fitting of synchrotron XRD data. The $c/a$ ratio has been normalized with its value at 300 K.

Figure 5

(a) Schematic of typical spin configurations in the pure AFM (i) and WFM (ii) phase along with the phenomenon of canting (iii). The red star in (i) is the inversion center and the spins point along the $c$ axis in the pure AFM phase. In the WFM phase, spin tilt in the basal plane is shown in (ii). The spin configuration shown in (ii) is necessary for the observation of DMI driven spin canting that results in the WFM phase. (b) $M_{\text{FC}}$ vs $T$ for a single crystal of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$, with $H$ (1 kOe) parallel to the $a$ axis, exhibiting $T_M$, the Morin transition, marked as a blue arrow in the figure. Inset: The picture of the $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ single crystal. (c) ${\mu }_{\text{FC}}$ vs $T$ run corresponding to the $M_{\text{FC}}$ vs $T$ run shown in (b). Here the remanence is vanishingly small in the pure AFM region and finite in the WFM region. Inset: ${\mu }_{\text{FC}}$ at 300 K along the $a$ axis as a function of various (cooling) $H$. These data points are extracted from various ${\mu }_{\text{FC}}$ vs $T$ runs.

Figure 6

(a) ${\mu }_{\text{ZFC}}$ vs $T$ at 300 K (WFM region) measured along the $c$ axis for the single crystal of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$. Inset: ${\mu }_{\text{FC}}\mathrm{vs}$ $T$ along the $c$ axis at 5 K (pure AFM region). While ${\mu }_{\text{FC}}$ is negligibly small in the pure AFM region, it is substantially large (at least by a few orders of magnitude) in the WFM region. (b) ${\mu }_{\text{ZFC}}$ vs $T$ measurements parallel to the $c$ axis for a waiting time of 100 min (red stars) and 1 min (red dots). Inset: ${\mu }_{\text{ZFC}}$ vs $T$ parallel to the $a$ axis showing a discrete jump.

Figure 7

$M$ vs $T$ recorded while cooling in presence of $H=+100$ Oe (blue dots). At 5 K, $H=+100$ Oe is removed and $H=-100$ Oe is applied while the temperature is held constant at 5 K. Subsequently $M$ vs $T$ in presence of $H=-100$ Oe is again recorded in the warming cycle (black dots). The measured magnetization is basically the remanence prepared during the previous cooling cycle. Since the sample is already in the WFM state, the presence of $H=-100$ Oe is not sufficient to rotate the magnetization. The robustness of the pinned moment, which leads to quasistatic remanence, for ${\mathrm{MnCO}}_3$ is evident from these data.