### What are Temperature Coefficients (α and β) of Permanent Magnets?

A permanent magnet’s magnetic properties change as a variation of temperature. For a permanent magnet, remanence (B_{r}) and intrinsic coercivity (H_{cj} or H_{ci}) are two major parameters, it is important to consider their changes with corresponding temperature variation at work. In order to describe the relative changes, they are calculated according to the following two formulas:

α = [B_{r}(T_{1})-B_{r}(T_{2})]/B_{r}(T_{1})/[ T_{1}-T_{2}]×100 (1)

β = [H_{cj}(T_{1})-H_{cj}(T_{2})]/H_{cj}(T_{1})/[T_{1}-T_{2}]×100 (2)

where α is temperature coefficient of remanence from T_{1} to T_{2}, its unit is %/°C or %/K,

β is temperature coefficient of intrinsic coercivity from T_{1} to T_{2}, its unit is %/°C or %/K,

T_{1} is starting temperature of corresponding temperature range,

T_{2} is terminal temperature of corresponding temperature range,

B_{r}(T_{1}) and B_{r}(T_{2}) are corresponding remanence at T_{1} and T_{2}, respectively,

H_{cj}(T_{1}) and H_{cj}(T_{2}) are corresponding intrinsic coercivity at T_{1} and T_{2}, respectively.

Take an N48SH grade NdFeB magnet for example, the following figure shows its demagnetization curves at 20, 100 and 150 °C, respectively. Its remanence at 20 and 150 °C are 13.82 and 11.69 kGs, respectively. Its intrinsic coercivity at 20 and 150 °C are 21.06 and 6.29 kOe, respectively. According to formulas (1) and (2), its temperature coefficients of remanence and intrinsic coercivity from 20 to 150 °C are calculated to be α: -0.119 %/°C and β: -0.539 %/°C.

The typical temperature coefficients of sintered NdFeB (neodymium iron boron) magnets are α: -0.09 to -0.12 %/°C and β: -0.4 to -0.6 %/°C, respectively. The typical temperature coefficients of sintered SmCo (samarium cobalt) magnets are α: -0.03 to -0.05 %/°C and β: -0.2 to -0.3 %/°C, respectively. It is obvious that the flux loss rate of sintered NdFeB magnets is much higher than that of sintered SmCo magnets. Although sintered NdFeB magnets have the highest maximum energy product ((BH)_{max}) at room temperature, they loss most of their magnetic properties when the working temperature is higher than 200 °C. Sintered SmCo magnets still work well with high performance at 200 to 300 °C, even they are able to work at as high as 350 °C. For more information about temperature coefficients of other permanent magnets, please refer to the table of typical physical and chemical properties of some magnetic materials.