Indeed, magnetic "rotational hysteresis" is not a frequent object of investigations and remains mostly unknown to many researchers. Yet qualitatively it is rather easy to understand, no matter that it may be quite complicated underneath.  When the sample is magnetically anisotropic, due to the magnetocrystalline anisotropy as well as to shape anisotropy, the effect (hysteretic torque) is rather obvious.  The explanation for hysteretic behavior of resistance seems more complicated and should probably be related to possible anisotropy of conductance tensor and (I think) to the Hall effect.  In case of multiferroic materials things become even more complex and non-linear.  Even photostriction may appear non-negligible ...

Largely unexplored field, so a good chance for a nice article.

Sir Marek Wojciecch, Thank you for your addition. I am searching some physics behind such kind of behaviour.

Here is some relevant literature on origin, modeling and other aspects of rotational magnetic hysteresis:

Journal of Magnetism and Magnetic Materials: 254-255 (2003) p. 97, 160 (1996) p. 115, 215-216 (2000) p. 33, 320 (2008) p. 2682, 215-216 (2000) p. 626, 384 (2015) p. 70, 223 (2001) p. 88,

Physica B: 406 (2011) p. 906, 486 (2016) p. 29,

IEEE Transactions on Magnetics: 51(3) (2015) 7300604, 33(5) (1997) p. 4155, 50(2) (2014) 7008704, 2(2) (1966) p. 68, 50(1) (2014) 4001604,

IEEE Magetic Letters 6 (2015) 3800204

Phys. Rev. Lett. 78(25) (1997) p. 4865, 99 (2007) 057201,

Journal of Applied Physics: 85(8) (1999) p. 4382, 115 (2014) 17D117, 117 (2015) 215301, suppl. to vol. 33(3) (1962) p. 1308,

J. Phys. D 29 (1996) p. 2304,

Phys. Rev. B 88 (2013) 214427,

Scientific Reports 5 (2015) 9183