84 Fig. 4 (a) Magnetization as a function of the magnetic ﬁeld of the b-MnO2 nanorods at 5, 55 and 110 K. (b) Expanded portions of the M(H) curves, showing hysteresis at 5 K (below 1000 Oe), the zfc–fc splitting increases with the ﬁeld (at the lowest measuring temperature of 2 K, the splitting in 1000 Oe is three times larger than in 50 Oe), whereas at higher ﬁelds, the splitting becomes smaller again, showing tendency to vanish. The zfc–fc curves also show features typical of magnetically unstable systems: (i) the shapes of the zfc and fc curves are strongly affected by the applied ﬁeld and (ii) in the highest ﬁeld 5 T, the zfc curve even crosses the fc curve and becomes higher above 30 K. This demonstrates that, within the regime of the zfc–fc splitting, magnetic ordering in the b-MnO2 nanorods is soft with internal ﬁelds of comparable magnitude to the externally applied ﬁeld. In order to check whether the zfc–fc magnetization splitting is related to a magnetic phase transition, we performed ac magnetization measure- ments at frequencies 1, 10, 100 and 1000 Hz (Fig. 5f). We observe a frequency-independent peak at 40.5 K, Nanoscale Res Lett (2007) 2:81–86 indicating a thermodynamic FM-type phase transition with a critical slowing-down of the spin ﬂuctuations. Discussion The rich structure of the M(T) curves can be analyzed by considering magnetic properties of the b-MnO2 and a-Mn2O3 bulk phases. Bulk b-MnO2 undergoes a transition to an incommensurately-modulated helical AFM state at TN 92.5 K that exhibits both long- and short-range magnetic orders [11, 12]. Its magnetic susceptibility exhibits well-developed peak at TN [12]. Since b-MnO2 is also the dominant phase of our investigated nanorods, it is straightforward to attribute the peak in the magnetization at 93 K in Fig. 5 to the same magnetic phase transition. The nanodimensions of the material obviously do not destroy the AFM state of the bulk phase. Regarding magnetic ordering of the a-Mn2O3 bulk phase, a neutron study has shown [13] that majority of the magnetic peaks disappear above TN ~ 80 K (a similar transition temperature TN ~ 79 – 80 K was reported also from heat capacity measure- ments [14] and magnetic susceptibility and Mo¨ ssbauer effect [15] on Mn2–xFexO3). According to the neutron results [13], magnetic order in the bulk a-Mn2O3 can be described by a set of six collinear AFM spin arrange- ments on a cubic lattice. The peak at 80 K in the M(T) of the investigated b-MnO2 nanorods can be thus associated with the magnetic ordering within the a-Mn2O3 surface layer. Therefore, the two maxima in the M(T) of the nanorods at 93 and 80 K can be given a simple explanation by invoking magnetic properties of the bulk b-MnO2 and a-Mn2O3 phases (in Fig. 5a, the temperatures of the magnetization maxima expected for these two bulk phases are indicated by dashed lines). A surprising effect is the low-temperature FM magnetization component that cannot be attributed to any of these two phases. The ac magnetization peak at 40.5 K suggests that additional manganese-oxide phases could be present in the investigated b-MnO2 nanorods. The Mn2O3 material has two structural isomers: a-Mn2O3 is the thermally stable mineral bixbyte, whereas c-Mn2O3 is thermally less stable and does not occur naturally. On heating up to 600–800 C in air, c-Mn2O3 transforms into the stable a-Mn2O3. Recent magnetic measurements on c-Mn2O3 nanopar- ticles [16] have shown that the nanoparticle-material exhibits ferrimagnetism below TC = 39 K with high coercivity (~8 kOe at 5 K). Similarly, the Mn3O4 bulk material (that is isostructural with c-Mn2O3) was reported [17] to undergo a transition to a ferrimagnetic state at TC = 42 K. In another study [18], Mn3O4