Because my question includes images I link the question from Physics Stack Exchange http://physics.stackexchange.com/questions/139460/outcome-from-this-experiment-with-solid-hydrogen
If you cool down the hydrogen to get the solid state you will produce so-called para-hydrogen with antiparallel proton spins only (anti-symmetric combination of both anti-parallel states). When you try now to polarize the solid hydrogen block in different ways you will transfer energy to the hydrogen during the transition from para- to ortho-hydrogen (with parallel proton spins). The solid hydrogen will be melted in this process. Therefore, solid ortho-hydrogen with parallel nuclear spins is not posible to my knowledge.
You might try the experiment with deuterium. Here the S=2 state with parallel deuteron spins is the ground state and can be populated at very low temperatures.
After reading second time your answer I realize that I haven't presented my experiment clear enough. I don't mind para-hydrogen state, it's just fine. My goal is to have two lattices where those protons can contact (when lattices are put together) in transverse spin-spin fashion. I was hoping that those para-hydrogen diatomic molecules could be polarized to meet the requirement presented in those pictures.
I am wondering.. the triplet ortho to singlet para transition is a very slow process, right? As one cools down n-H2 with 75% o-H2, would there be sufficient number of o-H2 in the solid hydrogen for long enough to study its structure or thermal properties?
In solid Hydrogen you will not find o-H2 in first order. Yes, it is a slow process, but the energy difference is enough to heat up the H2 at very low temperatures. And when you get a lower temperature of the hydrogen the o- to para-H2 transitions speed up. In cryo-physics it is well known that the production of solid hydrogen is quiet difficult, because you have to overcome the so-called "slush-ice" phase of the hydrogen at about 30 K.
One exception might be possible: If you add a very(!) strong magnetic field then you will split the o-H2 states into the substates and the S=1, m_S=-1 state (Both proton spins antiparallel to the external field) will cross the binding energy of the para-H2 (similar to the Breit-Rabi-Diagram). In this case a population of this state might be possible.
Thank you very much for the explanation. To be honest, while I have experimentally studied phenomenon at cryogenic temperatures, solid hydrogen is not my expertise. I will continue to develop an understanding of the topic.
After thinking about my setup (while keeping in mind received feedback) it might be better to use ortho-hydrogen instead of para-hydrogen. Gaining the wanted spin orientation is much easier with ortho-hydrogen.