Spin glass or ferromagnets?

Spin glass and ferromagnets are very different state of matter from theoretical point of view. Ferromagnets have global alignment of atomic moments which generates macroscopic magnetization. Spin glass can be characterized by quenched disorder and frustration. They look very different conceptually. However, in terms of experimental observation, they actually share some common feature and can be confused.

Figure 1, Ferromagnet

Figure 2, spin glass.

Let’s think about a field cool (FC) and zero field cool (ZFC) experiment with small DC magnetic field.  

1) Ferromagnets

Due to the anisotropy and the domain energy, all ferromagnets have a finite coercive force which decreases with temperature. This makes the magnetization as a function of temperature different for FC and ZFC conditions. In FC, the magnetic moment can be aligned gradually starting from Tc where corecive force is very small. As the temperature goes down, the coercive force increases, bu the magnetic moment is already partly aligned. Therefore, in this case, the magnetization can be close to the saturation magnetization if not the same as the saturation magnetization. On the other hand, in ZFC,  the magnetization is actually measured when the temperature is raised. Since at low temperature, the coercivity is high, the magnetization measured is actually a small value. It increases when the temperature is raise due to the decrease of coercivity.

2) Spin glass.

For FC, the magnetization rises according to the paramagnetic behavior about T_F (freezing temperature). Below that, the magnetization is frozen at a certain value M_F. For ZFC, the magnetization measured is also very small due to the frozen individual moments. The magnetization increased with temperature to the values of M_F at the freezing temperature.

As shown in Fig. 1 and Fig. 2, the two M v T curve does share some similarities. On the other hand, there are important differences to distinguish them:

1) M v T is very different around  phase transition temperature.

For FM, it has a sudden sharp increase at T_C. For Spin glass, it stays flat after T_F.

2) The peak of the ZFC curve.

For spin glass, the peak always occurs at T_F. For FM, it is a function of the applied magnetic field. The higher field, the smaller value of the peak temperature.

In the end, the ultimate way to distinguish the two is to look at the frequency dependence of the magnetization. For FM, it should not change between 1Hz to 1kHz range. For spin glass, there should be a peak for the susceptibility, both real and imaginary parts. The peak position is supposed to move with the frequency.