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So if we consider an ideal type II superconductor the magnetization should look like this magnetization of type II superconductor

The Meissner state is to be found between $0$ and $H_{c1}$ and the superconductor works as an ideal diamagnet in this region. Between $H_{c1}$ and $H_{c2}$ is the mixed state where the vortices dominate the superconducting behaviour.

Now if we look at magnetization loops of real Type II superconductors then we see something like this magnetization loop of a real type II superconductor
(source: scielo.br)

[Braz. J. Phys. vol.32 no.3 São Paulo Sept. 2002]

After the first loop we dont see here any ideal diamagnetic curve anymore (like the one represented as a straight line in the first picture).

But is the Meissner state still located in the region between $0$ and $H_{c1}$ or is it even existing in real Type II superconductors (how they are found in reality)?

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The brief answer: In the real magnetization curve only the straight section of the curve emerging from the axes' origin corresponds to the Meissner state. Everything else is a Shubnikov state containing vortices (magnetic flux).

Let me elaborate: The Meissner state describes the superconductor without magnetic flux (vortices). This state is achieved by cooling the sample in zero magnetic field and then increasing the field (remaining below Hc1). Above Hc1, vortices penetrate the sample. However due to the pinning of vortices on material defects, the magnetization curve usually differs from the ideal one in your first figure and becomes more rounded (second figure). This is well described by the Bean model Bean1962, Bean1964 of vortex pinning, see also Wikipedia entry. Once a real superconductor (with non-zero pinning) is placed in a field above Hc2, vortices are stuck in the material and the true Meissner state can not be recovered. This irreversibility is obviously manifested By the fact that the initial part of the magnetization curve can not be reached again by sweeping the magnetic field. To get back to a Meissner state the system has to be reinitialized, i.e., the system is heated to the normal state and cooled back to the superconducting state in zero field (or fields below Hc1).

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