Magnetic Barkhausen Noise (MBN), which contains microstructure information of materials, is widely used in Non-Destructive Testing (NDT) of magnetic materials. The magnetic Barkhausen noise energy (<i>MBN</i><sub>energy</sub>) is one of the time-independent indicators for NDT, but the initial <i>MBN</i><sub>energy</sub> has no clear physical meaning and cannot be used to explain the relationship with the hysteresis loop. In this paper, based on the physical mechanism of MBN, the proportional relation is built between MBN voltage signal <i>V</i><sub>B</sub> and energy loss, and then relate it with the energy loss through wall pinning of J-A hysteresis model. We define a novel magnetic Barkhausen noise energy eigenvalue (<i>MBNE)</i> as the time integral of the product of the absolute value of <i>V</i><sub>B</sub> and the sign function sign(d<i>H</i>/d<i>t</i>). We have proved that the <i>MBNE</i> is proportional to the irreversible magnetization <i>M</i><sub>irr</sub>. Since <i>M</i><sub>irr</sub> is equal to the saturation magnetization <i>M</i><sub>s</sub> when the magnetization of ferromagnetic material reaches saturation, we scale the <i>MBNE</i> to make its maximum value equal to <i>M</i><sub>s</sub>, and find that the relationship curve <i>MBNE</i>(<i>H</i>) of <i>MBNE</i> with respect to the magnetic field <i>H</i> coincides with the irreversible hysteresis loop <i>M</i><sub>irr</sub>(<i>H</i>). We call the <i>MBNE</i>(<i>H</i>) as the magnetic Barkhausen noise energy loop. Then, the <i>MBNE</i>(<i>H</i>) and <i>M</i><sub>irr</sub>(<i>H</i>) of two kinds of electrical steel sheets are compared by experimental results, which validates the adaptability of the <i>MBNE</i>(<i>H</i>) construction method. The method to obtain <i>M</i><sub>irr</sub>(H) from the MBN raw signal revels the physical mechanism of MBN and the irreversible magnetization process of magnetic material.