4U 0142+61 is one of the Anomalous X-ray Pulsars exhibiting hard X-ray emission above 10 keV discovered with INTEGRAL. In this paper we present detailed spectral and temporal characteristics both in the hard X-ray (>10 keV) and soft X-ray (<10 keV) domains obtained using data from INTEGRAL, XMM-Newton, ASCA and RXTE. Accumulating data collected over four years with the imager IBIS-ISGRI aboard INTEGRAL, the time-averaged total spectrum shows a power-law like shape with photon index Γ = 0.93 ± 0.06. 4U 0142+61 is detected up to 229 keV and the flux between 20 keV and 229 keV is (15.01 ± 0.82) × 10-11 erg cm-2 s-1, which exceeds the energy flux in the 2-10 keV band by a factor of ~2.3. Using simultaneously collected data with the spectrometer SPI of INTEGRAL the combined total spectrum yields the first evidence for a spectral break above 100 keV. Assuming a logparabolic function for the spectral shape above 20 keV the peak energy of 4U 0142+61 is 228+65-41 keV. There is no evidence for significant long-term time variability of the total emission from 4U 0142+61. Both the total flux and the spectral index are stable within the 17% level (1σ). Pulsed emission is measured with ISGRI up to 160 keV. The 20-160 keV profile shows a broad double-peaked pulse with a 6.2σ detection significance. The total pulsed spectrum can be described with a very hard power-law shape with a photon index Γ = 0.40 ± 0.15 and a 20-150 keV flux of (2.68 ± 1.34) × 10-11 erg cm-2 s-1. To perform accurate phase-resolved spectroscopy over the total X-ray window, we produced pulse profiles in absolute phase for INTEGRAL-ISGRI, RXTE-PCA, XMM-Newton-PN and ASCA-GIS. The two known pulses in all soft X-ray profiles below 10 keV are located in the same phases. Three XMM-Newton observations in 2003-2004 show statistically identical profiles. However, we find a significant profile morphology change between an ASCA-GIS observation in 1999 following a possible glitch of 4U 0142+61. This change can be accounted for by differences in relative strengths and spectral shapes (0.8-10 keV) of the two pulses. The principle peak in the INTEGRAL pulse profile above 20 keV is located at the same phase as one of the pulses detected below 10 keV. The second pulse detected with INTEGRAL is slightly shifted with respect to the second peak observed in the soft X-ray band. We performed consistent phase-resolved spectroscopy over the total high-energy band and identify at least three genuinely different pulse components with different spectra. The high level of consistency between the detailed results from the four missions is indicative of a remarkably stable geometry underlying the emission scenario. Finally, we discuss the derived detailed characteristics of the high-energy emission of 4U 0142+61 in relation to three models for the non-thermal hard X-ray emission.
