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The motion of a single hole in an arbitrary magnetic background isinvestigated for the 2D t-J model. The wavefunction of the hole is describedwithin a generalized string picture which leads to a modified concept of spinpolarons. We calculate the one-hole spectral function using a large stringbasis for the limits of a Neel ordered and a completely disordered background.In addition we use a simple approximation to interpolate between these cases.For the antiferromagnetic background we reproduce the well-known quasiparticleband. In the disordered case the shape of the spectral function is found to bestrongly momentum-dependent, the quasiparticle weight vanishes for all holemomenta. Finally, we discuss the relevance of results for the lowest energyeigenvalue and its dispersion obtained from calculations using a polaron ofminimal size as found in the literature.Comment: 13 pages, 8 figures, to appear in Phys. Rev.

Hole motion in an arbitrary spin background: Beyond the minimal spin-polaron approximation