Real-space visualization of thermomagnetic irreversibility within supercooling and superheating spinodals in ${\text{Mn}}_{1.85}{\text{Co}}_{0.15}\text{Sb}$ using scanning Hall probe microscopy

Phase coexistence across disorder-broadened and magnetic-field-induced first-order antiferromagnetic to ferrimagnetic transition in polycrystalline ${\text{Mn}}_{1.85}{\text{Co}}_{0.15}\text{Sb}$ has been studied mesoscopically by scanning Hall probe microscope at 120 K and up to 5 T magnetic fields. We have observed hysteresis with varying magnetic fields and evolution of coexisting antiferromagnetic and ferrimagnetic states on mesoscopic length scale. These studies show that the magnetic state of the system at low field depends on the path followed to reach 120 K. The low-field magnetic states are mesoscopically different for virgin and second field increasing cycle when 120 K is reached by warming from 5 K but are the same within measurement accuracy when the measuring temperature of 120 K is reached from 300 K by cooling.

Figure 1

(Color online) (a) Resistivity in zero field and (b) magnetization in 0.1 T magnetic field as a function of temperature measured during cooling and subsequent warming for ${\text{Mn}}_{1.85}{\text{Co}}_{0.15}\text{Sb}$. Inset shows the schematic of supercooling $\left(H^{\ast },T^{\ast }\right)$ and superheating $\left(H^{\ast \ast },T^{\ast \ast }\right)$ spinodals in $H\text{−}T$ space. Isothermal measurements presented in Fig. 2 (Fig. 3) were carried out along path $QS$ when point $Q$ is reached by cooling (warming) following path $PQ$ $\left(RQ\right)$.

Figure 2

(Color online) (a)–(g) SHPM Images of ${\text{Mn}}_{1.85}{\text{Co}}_{0.15}\text{Sb}$ as a function of magnetic field at 120 K (reached by cooling from 300 K) along with corresponding resistivity and magnetization curve. Scan area is $27\times 27\mu {\text{m}}^2$, and image label corresponds to respective point in resistivity and magnetization curves. Dark (light) color corresponds to FRI (AFM) state. Bottom row shows the histograms of magnetic images at labeled field values for increasing and decreasing field cycles. Inhomogeneous magnetic state and similar magnetic state after field cycling at low field are highlighted along with characteristic hysteresis associated with magnetic field-induced first-order transition.

Figure 3

(Color online) (a)–(f) SHPM images of ${\text{Mn}}_{1.85}{\text{Co}}_{0.15}\text{Sb}$ at 0.1 and 1.0 T taken at 120 K (reached from 5 K) along with corresponding resistivity and magnetization curve. Scan area is $27\times 27\mu {\text{m}}^2$ and magnetic scale is same for each row separately. Dark (light) color corresponds to FRI (AFM) state.

Figure 4

(Color online) Histograms of SHPM images of ${\text{Mn}}_{1.85}{\text{Co}}_{0.15}\text{Sb}$ at 0.1 and 1.0 T for virgin curve, field decreasing cycle, and second field increasing cycle at 120 K (reached by warming from 5 K). These curves highlight that the histogram corresponding to second field increasing cycle is distinctly different from first cycle.